Thomas Aquinas
In libros Aristotelis De caelo et mundo expositio
THE HEAVENStranslated by Fabian R.Larcher and Pierre H. Conway
CONTENTS
[The numbers in brackets refer to the passages in the text of Aristotle.]
Prooemium
INTRODUCTION BY SAINT THOMAS
Subject matter of this book
and its relation to the subject matter of natural science in generalSicut philosophus dicit in I Physic., tunc opinamur cognoscere unumquodque, cum causas cognoscimus primas, et principia prima, et usque ad elementa. Ex quo manifeste philosophus ostendit in scientiis esse processum ordinatum, prout proceditur a primis causis et principiis usque ad proximas causas, quae sunt elementa constituentia essentiam rei. Et hoc est rationabile: nam processus scientiarum est opus rationis, cuius proprium est ordinare; unde in omni opere rationis ordo aliquis invenitur, secundum quem proceditur ab uno in aliud. Et hoc patet tam in ratione practica, cuius consideratio est circa ea quae nos facimus, quam in ratione speculativa, cuius consideratio est circa ea quae sunt aliunde facta. 1. As the Philosopher says in Physics I, "We judge that we know a thing when we know the first causes and the first. principles down to the elements." Plainly from this the Philosopher shows that in sciences there is an orderly process, a procedure from first causes and principles to the proximate causes, which are the elements constituting the essence of a thing. And this is reasonable: For the method pursued in sciences is a work of reason, whose prerogative it is to establish order; wherefore, in every work of reason is found some order according to which one goes from one thing to another. And this shows up not only in the practical reason, which considers things that we make, but in the speculative reason as well, which considers things made by some other source. Invenitur autem processus de priori ad posterius in consideratione practicae rationis secundum quadruplicem ordinem: primo quidem secundum ordinem apprehensionis, prout artifex primo apprehendit formam domus absolute, et postea inducit eam in materiam; secundo secundum ordinem intentionis, secundum quod artifex intendit totam domum perficere, et propter hoc facit quidquid operatur circa partes domus; tertio secundum ordinem compositionis, prout scilicet prius dolat lapides, et postea compingit eos in unum parietem; quarto secundum ordinem sustentationis artificii, prout artifex primo iacit fundamentum, super quod ceterae partes domus sustentantur. Similiter etiam invenitur quadruplex ordo in consideratione rationis speculativae. Primus quidem secundum quod proceditur a communibus ad minus communia. Et hic ordo respondet proportionaliter primo ordini, quem diximus apprehensionis: universalia enim considerantur secundum formam absolutam, particularia vero secundum applicationem formae ad materiam; sicut philosophus in I de caelo dicit quod qui dicit caelum, dicit formam, qui autem dicit hoc caelum, dicit formam in materia. Secundus ordo est secundum quod proceditur a toto ad partes. Et hic ordo proportionaliter respondet ordini quem diximus intentionis, prout scilicet totum est prius in consideratione quam partes, non qualescumque, sed partes quae sunt secundum materiam et quae sunt individui; sicut semicirculus, in cuius definitione ponitur circulus (est enim semicirculus media pars circuli), et acutus angulus, in cuius definitione ponitur rectus (est enim acutus angulus minor recto). Accidit autem circulo et recto angulo sic dividi: unde huiusmodi non sunt partes speciei. Huiusmodi enim partes sunt priores in consideratione quam totum, et ponuntur in definitione totius, sicut carnes et ossa in definitione hominis, ut dicitur in VII Metaphys. 2. The process from prior to subsequent is found in the act of the practical reason with respect to a fourfold order: first, according to the order of apprehension, inasmuch as an artisan first apprehends the form of a house absolutely and then realizes it in matter; secondly, according to the order of intention, inasmuch as an artisan intends to complete the house and for that purpose does whatever he does to the parts of the house; thirdly, according to the order of combining, inasmuch as he first trims the stones and then joins them into one wall; fourthly, according to the order of supporting the edifice, inasmuch as the artisan first lays the foundation, upon which the other parts of the house are supported.
In like manner, a fourfold order is found in the consideration of speculative reason. First, because there is a process from the general to the less general.. And this order corresponds to the first order which we have called "the order of apprehension," for universals are considered according to an absolute form, but particulars by applying form to matter, as the Philosopher in On the Heavens says, that the word "heaven" signifies a form, and "this heaven" signifies a form in matter.
The second order is that according to which one goes from the whole to the parts. And this corresponds to "the order of intention," inasmuch as, namely, the whole is considered prior to the parts, not just any parts but parts which are according to matter and which are of the individual — as in the case of a semi-circle, in the definition of which "circle" is used (for it is "half a circle") and of an acute angle, in the definition of which "right angle" is used (for an acute angle is an angle "less than a right angle"). To be divided in that manner is incidental to a circle and to a right angle; hence, neither is a part of the species of a circle or right angle. For parts of this sort [i.e. parts of the species] are prior in consideration to the whole and are used in the definition of the whole, as are flesh and bones in the definition of man, as is said in Metaphysics VII.Tertius autem ordo est secundum quod proceditur a simplicibus ad composita, inquantum composita cognoscuntur per simplicia, sicut per sua principia. Et hic ordo comparatur tertio ordini, quem diximus compositionis. Quartus autem ordo est secundum quod principales partes necesse est prius considerare, sicut cor et hepar quam arterias et sanguinem. Et hic proportionatur practico ordini, secundum quod fundamentum prius iacitur. The third order is that according to which one goes from the simple to the combined, inasmuch as composites are known in terms of the simple, as through their principles. And this order is compared to the third order, which is the "order of combining." But the fourth order is the one that calls for the principal parts to be considered first, as are the heart and liver before the arteries and blood. And this corresponds in the practical order to that order according to which the foundation is laid first. Et hic quadruplex ordo consideratur etiam in processu scientiae naturalis. Nam primo determinantur communia naturae in libro physicorum, in quo agitur de mobili inquantum est mobile. Unde restat in aliis libris scientiae naturalis huiusmodi communia applicare ad propria subiecta. Subiectum autem motus est magnitudo et corpus: quia nihil movetur nisi quantum. This fourfold order is also considered in the procedure of natural science. For, first of all, things common to nature are determined in the book of the Physics, in which mobile being is treated insofar as it is mobile. Hence what remains in the other books of natural science is to apply these common things to their proper subjects. The subject of motion, however, is a magnitude and body, because nothing is moved except what is quantified. In corporibus autem est attendere tres alios ordines: uno quidem modo secundum quod totum universum corporeum est prius in consideratione quam partes eius; alio modo secundum quod simplicia corpora prius considerantur quam mixta; tertio secundum quod inter simplicia corpora prius necesse est de priori considerare, scilicet de caelesti corpore, per quod omnia alia firmantur. Et haec tria in hoc libro aguntur, qui apud Graecos intitulatur de caelo. Traduntur enim in hoc libro quaedam pertinentia ad totum universum, sicut patet in primo libro; quaedam pertinentia ad corpus caeleste, sicut patet in secundo; quaedam pertinentia ad alia simplicia corpora, sicut patet in tertio et quarto. Et ideo rationabiliter hic liber ordinatur primus post librum physicorum. Et propter hoc statim in principio huius libri agitur de corpore, cui necesse est applicari omnia quae tradita sunt de motu in libro physicorum. Now it is in bodies that the three other orders are considered: in one way, insofar as the entire corporeal universe is prior in consideration to its parts; in another way, insofar as simple bodies are considered before the mixed; thirdly, insofar as, among the simple bodies, the first must be considered first, i.e., the heavenly body, through which all the others are sustained. And these three are treated in this book, which the Greeks entitle On the Heavens. For in this book are treated certain things that pertain to the entire universe, as is plain in Book I; and things that pertain to the heavenly body, as is plain in Book II; and things that pertain to the simple bodies, as is plain in Books III-IV. Consequently, it is with good reason that this book is first in order after the book of the Physics. For this reason the first topic of discussion in the very beginning of this book is body, to which must be applied all that was set forth about motion in the Physics. Quia igitur diversa in hoc libro traduntur, dubium fuit apud antiquos expositores Aristotelis de subiecto huius libri. Alexander enim opinatus est quod subiectum de quo principaliter in hoc libro agitur, sit ipsum universum. Unde, cum caelum tripliciter dicatur, quandoque ipsa ultima sphaera, quandoque totum corpus quod circulariter movetur, quandoque autem ipsum universum, asserit hunc librum intitulari de caelo, quasi de universo vel de mundo: in cuius assertionem assumit quod philosophus in hoc libro determinat quaedam ad totum universum pertinentia, puta quod sit finitum, quod sit unum tantum, et alia huiusmodi. Because diverse things are treated in this book, there was among the early expositors of Aristotle a question about the subject of this book. For Alexander believed that the subject principally treated herein is the universe. Hence, since "the heavens" is subject to a threefold meaning — for sometimes it refers to the outermost sphere, sometimes to the whole body moved circularly, and sometimes to the entire universe — he asserts that this book is entitled On the Heavens as though meaning On the Universe or On the World. In asserting this he assumes that the Philosopher is here determining certain matters pertaining to the entire universe, for example, that it is finite, that it is unique, and things of this sort. E contrario autem aliis videtur quod subiectum de quo principaliter in hoc libro intenditur, est corpus caeleste quod circulariter movetur; et propter hoc intitulatur de caelo. De aliis autem corporibus determinatur in hoc libro vel ex consequenti, inquantum continentur a caelo et eius influentiam recipiunt, sicut Iamblichus dixit; vel per accidens, inquantum aliorum corporum notitia assumitur ad manifestandum ea quae dicuntur de caelo, ut dixit Syrianus. Sed hoc non videtur probabile: quia postquam philosophus in secundo libro determinavit de caelo, in tertio et quarto subiungit considerationem de aliis simplicibus corporibus, quasi principaliter de eis intendens. Non enim consuevit philosophus principalem partem alicuius scientiae assignare his quae per accidens assumuntur. On the other hand, it seems to some that the main subject handled in this book is the heavenly body which is moved circularly, for which reason it is entitled On the Heavens. Other bodies, however, are discussed therein consequentially, insofar as they are contained by the heavens and influenced by them, as Iamblichus said; or only incidentally, insofar as a knowledge of other bodies is assumed in order to explain what is being said of the heavens, as Syrianus says. But this does not seem probable, for after the Philosopher has finished his discussion of the heavens in Book II, he treats in Books III and IV of the other simple bodies as though they were his main subject. Now the Philosopher is not wont to assign a principal part in some science to things that are brought up only incidentally. Et ideo aliis visum est, sicut Simplicius dixit, quod intentio philosophi in hoc libro est determinare de simplicibus corporibus, inquantum conveniunt in communi intentione simplicis corporis: et quia inter simplicia corpora principalius est caelum, a quo alia dependent, ideo denominatur totus liber a caelo. Et, sicut dicit, non obstat quod in hoc libro determinantur quaedam quae pertinent ad totum universum: quia huiusmodi conditiones conveniunt universo inquantum conveniunt caelesti corpori, scilicet esse finitum et sempiternum, et alia huiusmodi. Si autem intentio principalis philosophi esset determinare de universo, sive de mundo, oporteret quod Aristoteles considerationem suam extenderet ad omnes partes mundi, etiam usque ad plantas et animalia, sicut Plato in Timaeo. Therefore it seemed to others, as Simplicius said, that the intention of Aristotle in this book is to determine about simple bodies inasmuch as they share in the common notion of simple body; and because among simple bodies. The chief is the heavens, on which the others depend, the entire book gets its name from the heavens. And, so he says, it makes no difference that in this book things pertaining to the whole universe are considered, for the conditions in question belong to the universe insofar as they belong to the heavenly body, i.e., to be finite and eternal, and so on. But if the principal intention of the Philosopher were to determine about the universe or the world, then he would have had to extend his consideration to all the parts of the world, even down to plants and animals, as Plato does in the Timaeus. Sed eadem ratione possumus arguere contra Simplicium: quia si in hoc libro principaliter intenderet de corporibus simplicibus, oporteret quod omnia quae pertinent ad corpora simplicia in hoc libro traderentur; nunc autem in hoc libro traduntur solum ea quae pertinent ad levitatem et gravitatem ipsorum, alia vero traduntur in libro de generatione. But the same argument could be used against Simplicius, because if Aristotle in this book intended to treat principally of the simple bodies, then in this book he would have had to mention everything that pertains to the simple bodies, whereas he discusses only what pertains to their lightness and heaviness, while he treats the other aspects in the book, On Generation. Et ideo rationabilior videtur sententia Alexandri, quod subiectum huius libri sit ipsum universum, quod dicitur caelum vel mundus; et quod de simplicibus corporibus determinatur in hoc libro, secundum quod sunt partes universi. Constituitur autem universum corporeum ex suis partibus secundum ordinem situs: et ideo de illis solum partibus universi determinatur in hoc libro, quae primo et per se habent situm in universo, scilicet de corporibus simplicibus. Unde et de quatuor elementis non determinatur in hoc libro secundum quod sunt calida vel frigida, vel aliquid huiusmodi; sed solum secundum gravitatem et levitatem, ex quibus determinatur eis situs in universo. Aliis autem partibus universi, puta lapidibus, plantis et animalibus, non determinatur situs secundum se, sed secundum simplicia corpora: et ideo de his non erat in hoc libro agendum. Et hoc consonat ei quod consuevit apud Latinos dici, quod in hoc libro agitur de corpore mobili ad situm, sive secundum locum: qui quidem motus communis est omnibus partibus universi. 5. Accordingly, the opinion of Alexander appears more reasonable, i.e., that the subject of this book is the universe itself, which is called "the heavens" or "the world," and that determination is made concerning simple bodies in this book accordingly as they are parts of the universe. Now, the corporeal universe is composed of its parts according to an order of position [situs]; consequently this book determines only concerning those parts of the universe that primarily and per se have position in the universe, namely, the simple bodies. That is why the four elements are not dealt with in this book from the aspect of their being hot or cold or something of that sort, but only with respect to their heaviness and lightness, from which their position in the universe is determined. Other parts of the universe, such as stones, plants and animals, have a determined place [situs] in the universe not according to what they are in themselves but according to the simple bodies; consequently, they are not treated in this book. And this agrees with what is usually said among the Latins, that this book discusses body that is mobile with respect to position or place, such motion being common to all the parts of the universe.
Α
DE COELO, BOOK ILecture 1
The things it pertains to natural science to consider.Chapter 1 (268a.) Ἡ περὶ φύσεως ἐπιστήμη σχεδὸν ἡ πλείστη φαίνεται περί τε σώματα καὶ μεγέθη καὶ τὰ τούτων οὖσα πάθη καὶ τὰς κινήσεις, ἔτι δὲ περὶ τὰς ἀρχάς, ὅσαι τῆς τοιαύτης οὐσίας εἰσίν τῶν γὰρ φύσει συνεστώτων τὰ μέν ἐστι σώματα καὶ μεγέθη, τὰ δ' ἔχει σῶμα καὶ μέγεθος, τὰ δ' ἀρχαὶ τῶν ἐχόντων εἰσίν. 1 THE science which has to do with nature clearly concerns itself for the most part with bodies and magnitudes and their properties and movements, but also with the principles of this sort of substance, as many as they may be. For of things constituted by nature some are bodies and magnitudes, some possess body and magnitude, and some are principles of things which possess these.
Quia igitur in hoc libro primo incipit applicare Aristoteles ad corpora, ea quae communiter dicta sunt de motu in libro physicorum, ideo primo prooemialiter ostendit quod ad scientiam naturalem pertinet determinare de corporibus et magnitudinibus; secundo incipit prosequi suum propositum, ibi: continuum quidem et cetera. 6. In this first book Aristotle begins for the first time to apply to bodies the things that were said about motion in a general way in the book of the Physics. For that reason he first shows by way of introduction that it pertains to natural science to determine about bodies and magnitudes; Secondly, he begins to carry out his proposal (Lecture 2). Circa primum ponit talem rationem. Res naturales sunt corpora et magnitudines, et quae ad haec pertinent: sed scientia naturalis est de rebus naturalibus: ergo scientia naturalis consistit circa corpora et magnitudines. With respect to the first he presents this argument: Natural things are bodies and magnitudes and whatever pertains to these. But natural science is about natural things. Therefore, natural science consists in treating of bodies and magnitudes. Primo ergo ponit conclusionem, dicens quod scientia quae est de natura, fere plurima, idest in maiori parte, videtur esse existens circa corpora et magnitudines, idest lineas et superficies. De quibus tamen aliter considerat naturalis quam geometra. Naturalis quidem considerat de corporibus inquantum sunt mobilia, de superficiebus autem et lineis inquantum sunt termini corporum mobilium: geometra autem considerat de eis prout sunt quaedam quanta mensurabilia. Et quia ad scientiam pertinet non solum considerare subiecta, sed etiam passiones, ut dicitur in I Poster., ideo subiungit quod naturalis scientia existit circa praedictorum passiones et motus: ut per passiones intelligantur alterationes et alii motus consequentes, secundum quos alteratur aliquid in substantia rei: subdit autem et motus, quasi procedens a speciali ad commune. Vel per motus intelligit specialiter motus locales, qui sunt perfectiores in genere motuum. Vel per passiones intelligit proprietates, per motus autem operationes rerum naturalium, quae non sunt sine motu. Et quia in qualibet scientia oportet considerare principia, subiungit quod naturalis scientia est circa quaecumque principia praedictae substantiae; scilicet corporeae mobilis. Per quod datur intelligi quod ad naturalem pertinet praecipue considerare de corpore inquantum est in genere substantiae, sic enim est subiectum motus: ad geometram autem inquantum est in genere quantitatis, sic enim mensuratur. 7. First [1] therefore, he posits the conclusion, saying that the science which treats of nature seems to be "for the most part" concerned with bodies, and "magnitudes," i.e., lines and surfaces. However, the natural philosopher considers these in a different way from the geometer. For the former treats of bodies insofar as they are mobile, and of surfaces and lines insofar as they are the boundaries of mobile bodies; the geometer, on the other hand, considers them insofar as they are measurable quantities. And because a science should consider not only subjects but also their passions, as is said in Post. Anal. I, he therefore adds that natural science is concerned with the passions and motions of the aforesaid — by "passions" meaning alterations and other consequent motions, with respect to which something is altered in the substance of a thing; and he adds, "and motions," as though going from the particular to the general. Or perhaps by "motions" he specifically understands local motions, which are the more perfect in the genera of motions. Or by "passions" is meant the properties, and by "motions" the operations of natural things, which do not occur without motion. And because, in every science, principles must be considered, he adds that natural science is concerned with any and all the principles of the afore-mentioned substance, namely, mobile corporeal substance. By this we are given to understand that it pertains to natural science primarily to consider body insofar as it is in the genus of substance, for it is in this respect that it is the subject of motion; whereas it pertains to the geometer to consider it insofar as it is in the genus of quantity, for thus it is measured. Et quia minor est manifesta, scilicet quod scientia naturalis sit de rebus naturalibus, subiungit maiorem, dicens quod ideo scientia naturalis existit circa praedicta, quia eorum quae sunt secundum naturam, quaedam sunt corpora et magnitudines, sicut lapides et alia inanimata; quaedam habent corpus et magnitudinem, sicut plantae et animalia, quorum principalior pars est anima (unde magis sunt id quod sunt secundum animam quam secundum corpus); quaedam vero sunt principia habentium corpus et magnitudinem, sicut anima, et universaliter forma, et materia. Since the minor premise is plain, namely, that natural science is concerned with natural things, he adds the major, saying that the reason why natural science is concerned with the aforementioned is that among things which are according to nature, some are bodies and magnitudes, e.g. stones and other inanimate things; and some have body and magnitude, as do plants and animals, whose principal part is the soul (hence they are what they are more with respect to soul than with respect to body); finally, some things are principles of things having body and magnitude — for example, the soul, and universally form, and matter. Et ex hoc apparet quare dixit quod scientia de natura fere plurima existit circa corpora et magnitudines: quaedam enim pars eius est circa habentia corpus et magnitudines; est etiam circa principia horum; est etiam circa quaedam quae non sunt in natura, quae aliqui attribuerunt corporibus et magnitudinibus, scilicet circa vacuum et infinitum. From this is clear why he said that the science of nature is "for the most part" concerned with bodies and magnitudes: for one part of this science is concerned with things having body and magnitude; it is also concerned with the principles of these; it is further concerned with some things which do not exist in nature but which some have attributed to bodies and magnitudes, namely, the void and the infinite.
Lecture 2
The perfection of the universe both as body and as containing all.Chapter 1 cont. Συνεχὲς μὲν οὖν ἐστι τὸ διαιρετὸν εἰς ἀεὶ διαιρετά, 2 Now a continuum is that which is divisible into parts always capable of subdivision, σῶμα δὲ τὸ πάντῃ διαιρετόν. 3 and a body is that which is every way divisible. Μεγέθους δὲ τὸ μὲν ἐφ' ἓν γραμμή, τὸ δ' ἐπὶ δύο ἐπίπεδον, τὸ δ' ἐπὶ τρία σῶμα 4 A magnitude if divisible one way is a line, if two ways a surface, and if three a body. καὶ παρὰ ταῦτα οὐκ ἔστιν ἄλλο μέγεθος διὰ τὸ τὰ τρία πάντα εἶναι καὶ τὸ τρὶς πάντῃ. 5 Beyond these there is no other magnitude, because the three dimensions are all that there are, and that which is divisible in three directions is divisible in all. Καθάπερ γάρ φασι καὶ οἱ Πυθαγόρειοι, τὸ πᾶν καὶ τὰ πάντα τοῖς τρισὶν ὥρισται τελευτὴ γὰρ καὶ μέσον καὶ ἀρχὴ τὸν ἀριθμὸν ἔχει τὸν τοῦ παντός, ταῦτα δὲ τὸν τῆς τριάδος. 6 For, as the Pythagoreans say, the world and all that is in it is determined by the number three, since beginning and middle and end give the number of an 'all', and the number they give is the triad. Διὸ παρὰ τῆς φύσεως εἰληφότες ὥσπερ νόμους ἐκείνης, καὶ πρὸς τὰς ἁγιστείας χρώμεθα τῶν θεῶν τῷ ἀριθμῷ τούτῳ. 7 And so, having taken these three from nature as (so to speak) laws of it, we make further use of the number three in the worship of the Gods. Ἀποδίδομεν δὲ καὶ τὰς προσηγορίας τὸν τρόπον τοῦτον τὰ γὰρ δύο ἄμφω μὲν λέγομεν καὶ τοὺς δύο ἀμφοτέρους, πάντας δ' οὐ λέγομεν, ἀλλὰ κατὰ τῶν τριῶν ταύτην τὴν κατηγορίαν κατάφαμεν πρῶτον. Ταῦτα δ', ὥσπερ εἴρηται, διὰ τὸ τὴν φύσιν αὐτὴν οὕτως ἐπάγειν ἀκολουθοῦμεν. 8 Further, we use the terms in practice in this way. Of two things, or men, we say 'both', but not 'all': three is the first number to which the term 'all' has been appropriated. And in this, as we have said, we do but follow the lead which nature gives. Ὥστ' ἐπεὶ τὰ πάντα καὶ τὸ πᾶνκαὶ τὸ τέλειον οὐ κατὰ τὴν ἰδέαν διαφέρουσιν ἀλλήλων, ἀλλ' εἴπερ, ἐν τῇ ὕλῃ καὶ ἐφ' ὧν λέγονται, τὸ σῶμα μόνον ἂν εἴη τῶν μεγεθῶν τέλειον μόνον γὰρ ὥρισται τοῖς τρισίν, τοῦτο δ' ἐστὶ πᾶν. Τριχῇ δὲ ὂν διαιρετὸν πάντῃ διαιρετόν ἐστιν τῶν δ' ἄλλων τὸ μὲν ἐφ' ἓν τὸ δ' ἐπὶ δύο ὡς γὰρ τοῦ ἀριθμοῦ τετυχήκασιν, οὕτω καὶ τῆς διαιρέσεωςκαὶ τοῦ συνεχοῦς τὸ μὲν γὰρ ἐφ' ἓν συνεχές, τὸ δ' ἐπὶ δύο, τὸ δὲ πάντῃ τοιοῦτον. 9 Therefore, since 'every' and 'all' and 'complete' do not differ from one another in respect of form, but only, if at all, in their matter and in that to which they are applied, body alone among magnitudes can be complete. For it alone is determined by the three dimensions, that is, is an 'all'. But if it is divisible in three dimensions it is every way divisible, while the other magnitudes are divisible in one dimension or in two alone: for the divisibility and continuity of magnitudes depend upon the number of the dimensions, one sort being continuous in one direction, another in two, another in all. Ὅσα μὲν οὖν διαιρετὰ τῶν μεγεθῶν, καὶ συνεχῆ ταῦτα εἰ δὲ καὶ τὰ συνεχῆ πάντα διαιρετά, οὔπω δῆλον ἐκ τῶν νῦν. Ἀλλ' ἐκεῖνο μὲν δῆλον, ὡς οὐκ (268b.) ἔστιν εἰς ἄλλο γένος μετάβασις, ὥσπερ ἐκ μήκους εἰς ἐπιφάνειαν, εἰς δὲ σῶμα ἐξ ἐπιφανείας οὐ γὰρ ἂν ἔτι τὸ τοιοῦτον τέλειον εἴη μέγεθος ἀνάγκη γὰρ γίγνεσθαι τὴν ἔκβασιν κατὰ τὴν ἔλλειψιν, οὐχ οἷόν τε δὲ τὸ τέλειον ἐλλείπειν πάντῃ γάρ ἐστιν. 10 All magnitudes, then, which are divisible are also continuous. Whether we can also say that whatever is continuous is divisible does not yet, on our present grounds, appear. One thing, however, is clear. We cannot pass beyond body to a further kind, as we passed from length to surface, and from surface to body. For if we could, it would cease to be true that body is complete magnitude. We could pass beyond it only in virtue of a defect in it; and that which is complete cannot be defective, since it has being in every respect. Τῶν μὲν οὖν ἐν μορίου εἴδει σωμάτων κατὰ τὸν λόγον ἕκαστον τοιοῦτόν ἐστιν πάσας γὰρ ἔχει τὰς διαστάσεις ἀλλ' ὥρισται πρὸς τὸ πλησίον ἁφῇ διὸ τρόπον τινὰ πολλὰ τῶν σωμάτων ἕκαστόν ἐστιν. 11 Now bodies which are classed as parts of the whole are each complete according to our formula, since each possesses every dimension. But each is determined relatively to that part which is next to it by contact, for which reason each of them is in a sense many bodies. Τὸ δὲ πᾶν οὗ ταῦτα μόρια, τέλειον ἀναγκαῖον εἶναι καὶ καθάπερ τοὔνομα ημαίνει πάντῃ, καὶ μὴ τῇ μὲν τῇ δὲ μή. 12 But the whole of which they are parts must necessarily be complete, and thus, in accordance with the meaning of the word, have being, not in some respect only, but in every respect.
Postquam philosophus ostendit prooemialiter quod determinandum est de corporibus et magnitudinibus in scientia naturali, hic incipit prosequi principale propositum. Et quia, ut supra dictum est, in hoc libro principaliter intendit Aristoteles determinare de universo corporeo et principalibus partibus eius, quae sunt corpora simplicia, inter quae potissimum est corpus caeleste, ideo dividitur liber iste in partes tres: After showing by way of introduction that bodies and magnitudes are to be studied in natural science, the Philosopher here begins to carry out his main resolve. And because, as was said above, Aristotle in this book is mainly concerned with determining about the corporeal universe and its principal parts which are the simple bodies, among which the most important is the heavenly body, the book therefore is divided into three parts: in prima determinat de universo corporeo;
in secunda determinat de corpore caelesti, et hoc in secundo libro, ibi: quod quidem igitur neque factum est etc.;
in tertia parte determinat de aliis simplicibus corporibus, scilicet de gravi et levi, in tertio libro, ibi: de primo quidem igitur caelo et cetera.
In the first he determines concerning the corporeal universe;
In the second concerning the heavenly body, in Book II;
In the third about other simple bodies, i.e., heavy and light, in Book III.
Circa primum duo facit: With respect to the first he does two things: primo ostendit perfectionem universi;
secundo determinat quasdam conditiones seu proprietates ipsius, ibi: sed quoniam manifestum de his et cetera.
First he shows the perfection of the universe;
Secondly, he determines certain of its conditions or properties (L. 13. 9).
Circa primum duo facit: About the first he does two things: primo ostendit perfectionem universi;
secundo ostendit ex quibus partibus eius perfectio integretur, ibi: de totius quidem igitur natura et cetera.
First he shows the perfection of the universe;
Secondly, he explains of what parts it is composed (L. 13).
Circa primum duo facit: As to the first he does two things: primo ostendit perfectionem universi quam habet secundum communem rationem sui generis, inquantum scilicet est corpus;
secundo probat perfectionem propriam ipsius, ibi: partialium quidem igitur corporum et cetera.
First he shows the perfection which the universe has in virtue of the common notion of its genus, i.e., inasmuch as it is a body, at 9.
Secondly, he proves the perfection proper to it, at 18.
Circa primum tria facit: About the first he does three things: primo manifestat definitionem corporis, qua utitur ad propositum ostendendum;
secundo probat propositum, ibi: itaque quoniam omne et totum etc.;
tertio ostendit quid ex praemissis possit esse manifestum, ibi: quaecumque quidem igitur et cetera.
First he explains the definition of body, to be used in proving his proposition, at 10.
Secondly, he proves the proposition, at 15;
Thirdly, he shows what could be clear from the foregoing, at 16.
Circa primum duo facit: As to the first he does two things: primo definit continuum, quod est genus corporis;
secundo manifestat corporis definitionem, ibi: corpus autem et cetera.
First he defines "continuum," which is the genus of body;
Secondly, he clarifies the definition of body, at 10.
Circa primum considerandum est quod continuum invenitur a philosopho dupliciter definitum. Uno modo definitione formali, prout dicitur in praedicamentis quod continuum est cuius partes copulantur ad unum communem terminum: unitas enim continui est quasi forma ipsius. Alio modo definitione materiali, quae sumitur ex partibus, quae habent rationem materiae, ut dicitur in II Physic.: et sic definitur hic, quod continuum est quod est divisibile in semper divisibilia. Nulla enim pars continui potest esse indivisibilis: quia ex indivisibilibus non componitur aliquod continuum, ut probatur in VI Physic. Et satis convenienter haec definitio ponitur hic, alia autem in praedicamentis: quia consideratio naturalis versatur circa materiam, consideratio autem logici circa rationem et speciem. With regard to the first [2], we must consider that the continuum is found defined in two ways by the Philosopher. In one way with a formal definition, where it is said in the Predicaments (c.4) that the continuum is "that whose parts are joined at one common term"; for the unity of a continuum is, as it were, its form. In another way, with a material definition taken from the parts, which have the aspect of matter, as is said in Physics II — and it is thus that the continuum is defined here, namely, as "what is divisible into parts always divisible." For no part of a continuum can be indivisible, because no continuum is composed of indivisibles, as is proved in Physics VI. And it is fitting that this latter definition be used here, and the other one in the Predicaments, because the consideration of natural science is concerned with matter, while that of logic is concerned with notions and species. Deinde cum dicit: corpus autem etc., definit corpus. 10. Then at [3] he defines "body." Et primo proponit definitionem, dicens quod corpus est continuum quod est divisibile omniquaque, idest ad omnem partem, vel secundum omnem dimensionem.
Secundo ibi: magnitudinis autem etc., probat propositam definitionem tali ratione.
First he proposes the definition, saying that body is "a continuum which is divisible in every way," i.e., at every part or according to every dimension.
Secondly, at [4] he proves the proposed definition with this argument:
Corpus dividitur secundum tres dimensiones: quod autem dividitur secundum tres dimensiones, dividitur secundum omnes: ergo corpus est divisibile secundum omnes dimensiones. Body is divided according to three dimensions. But what is divided according to three dimensions is divided according to all. Therefore, body is divisible according to all the dimensions. Primo ergo manifestat minorem, quasi per divisionem. Nam magnitudinum quaedam est quae dividitur ad unam partem, et haec dicitur linea: quaedam autem est quae dividitur ad duas partes, et haec dicitur planum, idest superficies: quaedam autem est quae dividitur secundum tres dimensiones; et cum talis magnitudo non sit linea neque superficies, sequitur quod sit corpus. First, therefore, he explains the minor proposition as though by division. For among magnitudes there is one which is divided with respect to one dimension, and this is called "line"; another is divided with respect to two dimensions, and this is called "plane," i.e., a surface; still another is divided according to three dimensions, and since such a magnitude is neither line nor surface, it follows that it is body. Maiorem propositionem ponit ibi: et praeter has et cetera. Et primo ponit eam: et dicit quod praeter has magnitudines seu dimensiones non est alia magnitudo seu dimensio, propter hoc quod tria habent rationem ut sint omnia, quia habent rationem cuiusdam totalitatis; et quod est ter, videtur esse omniquaque, vel omnino, idest secundum omnem modum. The major proposition he gives at [5]. First he mentions it and says that, besides these magnitudes or dimensions, there is no other magnitude or dimension, on the ground that "three" has the property of being all, because it implies a certain totality, and because whatever is thrice seems to be "in all ways" and "entirely," i.e., according to every mode. Secundo ibi: quemadmodum enim etc., probat quod dixerat tripliciter. 11. Secondly, at [6] he proves what he had said in three ways. Primo quidem secundum rationem Pythagoricorum, qui dixerunt quod id quod dicitur totum et omne, determinatur ternario numero. Principium enim et medium et consummatio, idest finis, habent numerum qui convenit toti et omni: in rebus enim divisibilibus prima pars non sufficit ad integritatem totius, quod constituitur per ultimum, ad quod a principio pervenitur per medium. Haec autem, scilicet principium, medium et finis, habent numerum ternarium: et sic patet quod numerus ternarius convenit omni et toti. First, according to the teaching of Pythagoras who said that what is called "whole" and "all" is determined by the number 3. For the beginning and the middle and the "consummation," i.e., the end, have a number which befits what is "whole" and "all" — for in things divisible, the first part is not enough to complete the whole, which is completed by the ultimate that is reached by passing from the beginning through the middle. But these three, namely, beginning, middle and end, have 3 as their number. Consequently, it is clear that the number 3 belongs to the "all" and "whole." Secundo ibi: propter quod a natura etc., probat idem per ea quae in cultu divino observantur. Utimur enim numero hoc, scilicet ternario, ad sanctificationes deorum (quos scilicet gentiles colebant), idest in sacrificiis et laudibus ipsorum, ac si acceperimus a natura leges et regulas ipsius: ut scilicet, sicut natura perficit omnia ternario numero, ita illi qui instituerunt cultum divinum, volentes Deo attribuere omne quod perfectum est, attribuunt ei ternarium numerum. 12. Secondly, at [7] he proves the same by means of what is observed in divine worship. For we use this number 3 "in the worship of the gods" (whom, namely, the gentiles worshipped), i.e., in sacrifices and praises for them, as though we should receive from nature its laws and rules: just as nature completes all things with the number 3, so those who established the divine worship have, in their desire to attribute to God everything perfect, attributed to Him the number 3. Tertio ibi: assignamus autem etc., probat idem per communem usum loquendi. Et dicit quod etiam assignamus vocabula rebus secundum modum praedictum, quo scilicet perfectio competit ternario. Si enim aliqua sunt duo, dicimus quod sint ambo, et duos homines dicimus ambos: non autem de his dicimus omnes, sed primo hoc vocabulo utimur circa tres. Et istum modum loquendi sequimur communiter omnes, propter hoc quod natura ad hoc nos inclinat. Ea enim quae sunt propria singulis in modo loquendi, videntur provenire ex propriis conceptionibus uniuscuiusque: sed id quod observatur communiter apud omnes, videtur ex naturali inclinatione provenire. 13. Thirdly, he proves at [8] the same by appealing to the general way we speak. And he says that we even assign names to things according to the aforementioned method, in which perfection agrees with the number 3. For when there are two things, we say "both," — thus we speak of two men as "both" — but we do not say "all," which we use for the first time in the case of three. And we all in general use this way of speaking, because nature so inclines us. For whatever is peculiar to individuals in their way of speaking seems to arise from the particular conceptions of each, but what is generally observed among all would seem to arise from natural inclination. Est autem attendendum quod nusquam alibi Aristoteles invenitur Pythagoricis rationibus utens ad propositum ostendendum; neque invenitur alibi per numerorum proprietates aliquid de rebus concludere: et forte hoc hic facit propter affinitatem numerorum ad magnitudines, de quibus hic agitur. 14. Now, it should be noted that nowhere else does Aristotle either use the arguments of Pythagoras to explain a proposition, or from the properties of numbers conclude anything about things. And perhaps he does so here on account of the affinity of numbers to magnitudes, which he is now considering. Videtur tamen quod haec probatio non sit efficax: non enim magis videtur sequi quod dimensiones sint tres, propter hoc quod ternarius est numerus totius et omnis: alioquin sequeretur per eandem rationem quod essent solum tria elementa, vel tres digiti manus. Be that as it may, the proof here given does not seem valid, for it does not seem, if 3 is the number corresponding to "whole" and "all" that it follows there are three dimensions. Otherwise, it would follow according to the same reasoning that there would be only three elements or only three fingers on the hand. Sed sciendum est quod, sicut dicit Simplicius in commento, Aristoteles non procedit hic demonstrative, sed secundum probabilitatem: et hic modus sufficiens est post demonstrationes praemissas, vel praesuppositas ab alia scientia. Manifestum est autem quod determinare de dimensionibus corporum inquantum huiusmodi, per se pertinet ad mathematicum: naturalis autem assumit a mathematico ea quae circa dimensiones considerat. Et ideo probare demonstrative esse solum tres dimensiones, pertinet ad mathematicum: sicut Ptolomaeus probat per hoc quod impossibile est coniungi simul lineas perpendiculares plures quam tres super idem punctum; omnis autem dimensio mensuratur secundum aliquam lineam perpendicularem. Huius igitur demonstrationem Aristoteles supponens a mathematico, utitur testimonio et signis, sicut consuevit facere post demonstrationes a se inductas. But it should be known that, as Simplicius says in his Commentary 13, Aristotle is not here proceeding demonstratively but according to probability, and this is sufficient after previous demonstrations or ones supposed from another science. Now, it is plain that the task of deciding about the dimensions of bodies as such pertains to mathematics; and whatever the natural philosopher considers with dimensions, he takes from mathematics. Therefore, to prove demonstratively that there are just three dimensions pertains to mathematics — thus Ptolemy proves it by showing that it is impossible for more than three perpendicular lines to meet at the same point, while each dimension is measured according to a perpendicular line. Supposing such a demonstration from mathematics, Aristotle here uses testimony and signs, just as he customarily does after his own demonstrations. Deinde cum dicit: itaque quoniam omne etc., ex eo quod ostensum est, procedit ad principale propositum ostendendum. Et dicit quod haec tria, omne et totum et perfectum, non differunt ab invicem secundum speciem, idest secundum formalem rationem, quia omnia important integritatem quandam: sed si in aliquo differant, differunt in materia et subiecto, inquantum de diversis dicuntur. Nam hoc quod dicitur omne, utimur in discretis, sicut dicimus omnem hominem: utimur etiam eo in continuis quae sunt propinqua divisioni, sicut dicimus omnem aquam et omnem aerem. Totum autem dicitur et in his et in continuis: dicimus enim totum populum et totum lignum. Perfectum autem dicimus et in his et in formis: dicimus enim perfectam albedinem et perfectam virtutem. Quia igitur omne et perfectum est idem, consequens est quod corpus sit perfectum inter magnitudines: quia solum corpus est determinatum tribus dimensionibus, et hoc habet rationem omnis, ut supra ostensum est: cum enim sit tribus modis divisibile, sequitur quod sit divisibile omniquaque, idest secundum omnem dimensionem. Sed inter alias magnitudines aliquid est divisibile secundum duas dimensiones, scilicet superficies; aliud autem secundum unam, scilicet linea. Ut enim numerum adepta sunt, idest sicut magnitudines habent numerum dimensionum, ita habent divisionem et continuitatem: ita scilicet quod aliqua magnitudo est continua secundum unum modum, scilicet linea; alia est continua duobus modis, scilicet superficies; corpus autem est continuum secundum omnem modum. Unde patet quod corpus est magnitudo perfecta, quasi habens omnem modum continuitatis. 15. Then at [9] he goes on to manifest the main proposition from what has been shown. And he says that these three, namely, "all," "whole," and "perfect," do not differ from one another according to species, i.e., according to their formal notion, because all imply a certain completeness; but if they do differ in any way, it is in matter and subject, insofar as they are said of diverse things. For we use "all" in discrete things, as we say "all men"; we use it also with respect to continua which are easily divided, as we say "all water" and "all air." "Whole," however, is used both with these and with all continua, as we say "the whole people" and "the whole world." But "perfect" is used with respect to these and forms: for we say "perfect whiteness" and "perfect virtue." Therefore, because "all" and "perfect" are the same, the consequence is that among magnitudes the perfect one is body, because only a body is determined by three dimensions, and this carries with it the notion of "all," as has been shown above, for since it is divisible in three ways, it follows that it is divisible in every way, i.e., according to every dimension. But among other magnitudes, there is one divisible according to two dimensions, namely, a surface; and another according to one, namely, a line. "Now according to the number that it has," i.e., the number of dimensions that a magnitude has, so is it divisible and continuous. Thus one magnitude is continuous in one way, namely, a line; another in two ways, namely, a surface; but a body is continuous in every way. Hence it is plain that body is a perfect magnitude, as possessing all ways of being continuous. Deinde cum dicit: quaecumque quidem igitur etc., ostendit quid ex praemissis manifestum sit vel non: et ponit tria. Quorum primum secundum se manifestum est, scilicet quod quaecumque magnitudo est divisibilis, sit continua: si enim non esset continua, non haberet rationem magnitudinis, sed potius numeri. Secundum autem est conversum huius, scilicet quod omne continuum sit divisibile, sicut in definitione fuit positum. Et hoc quidem manifestum est ex his quae probata sunt in VI Physic., ut supra dictum est. Non est autem manifestum ex his quae nunc dicta sunt: quia quod continuum sit divisibile, hic supposuit, non probavit. Tertium est manifestum ex praemissis, scilicet quod non fit transitus a corpore in aliud genus magnitudinis, sicut fit transitus ex longitudine in superficiem, et ex superficie in corpus. Et utitur modo loquendi quo utuntur geometrae, imaginantes quod punctus motus facit lineam, linea vero mota facit superficiem, superficies autem corpus. A corpore autem non fit transitus ad aliam magnitudinem: quia talis exitus, sive processus, ad aliud genus magnitudinis, est secundum defectum eius a quo transitur (unde etiam motus naturalis est actus imperfecti). Non est autem possibile quod corpus, quod est perfecta magnitudo, deficiat secundum hanc rationem, quia est continuum secundum omnem modum: et ideo non potest fieri transitus a corpore in aliud genus magnitudinis. 16. Then at [10] he shows what is or is not plain from the foregoing. And he mentions three things. The first of these is plain in itself, namely, that any magnitude that is divisible is continuous; for if it were not continuous, it would not be a magnitude but a number. The second is the converse of this, namely, that every continuum is divisible, as was indicated in the definition. And this is plain from what was proved in Physics VI, as was said above. But it is not plain from what was just said, however, because here he supposes, but does not prove, that a continuum is divisible. The third thing is plain from the foregoing, namely, that unlike the passing from length to surface and from surface to body, there is no passing from body to another kind of magnitude. And he uses a way of speaking employed by geometers imagining that a point in motion makes a line, and a line in motion a surface, and a surface a body. But from body there is no transition to another magnitude, because such a passing, i.e., to another kind of magnitude is due to a defect in that from which the process beings — that is why natural motion is the act of an imperfect thing. But it is not possible that body, which is perfect magnitude, should be defective in this way, because it is continuous in every way. Consequently, no transition from body to another kind of magnitude is possible. Deinde cum dicit: partialium quidem etc., manifestat propriam perfectionem universi, per differentiam ad corpora particularia. Et primo ponit qualiter particularia corpora se habeant ad perfectionem. Et dicit quod unumquodque particularium corporum, secundum rationem communem corporis, est tale, idest perfectum, inquantum habet omnes dimensiones: sed tamen terminatur ad proximum corpus, inquantum contingit ipsum. Et ita unumquodque talium corporum quodammodo est multa, idest perfectum, inquantum habet omnes dimensiones, et imperfectum, inquantum habet aliud corpus extra se ad quod terminatur. Vel est multa secundum contactum ad diversa corpora: vel est multa, quia sunt plura unius speciei propter imperfectionem; quod non contingit de universo. 17. Then at [113 he manifests the proper perfection of the universe based on its difference from particular bodies. First he mentions how particular bodies are related to perfection. And he says that each particular body, according to the common notion of body, is such, i.e., perfect, inasmuch as it has three dimensions; nevertheless, it is terminated at an adjacent body, inasmuch as it touches it. And thus every such body is in a certain way "many," i.e., perfect, in having three dimensions, but imperfect in having another body outside it at which it is terminated. Or it is "many" according to contact with diverse bodies; or it is "many" because there are more than one in one species due to imperfection, whereas such is not the case with the universe. Secundo ibi: totum autem etc., ostendit quomodo universum se habeat ad perfectionem. Et dicit quod totum, idest universum, cuius partes sunt particularia corpora, necesse est quod sit perfectum omnibus modis; et sicut ipsum nomen universi significat, omniquaque, idest omnibus modis, perfectum, et non secundum unum modum ita quod non secundum alium: quia et habet omnes dimensiones, et comprehendit in se omnia corpora. 18. Secondly at [12] he shows how the universe is related to perfection. And he says that "the whole," i.e., the universe, which has particular bodies as its parts, must be perfect in all ways, for the word "universe" signifies perfect "in all ways," and not in one way to the exclusion of some other way, and it both has all the dimensions, and includes in itself all bodies.
Lecture 3:
Preliminary notions for showing the parts perfecting the universe.Chapter 2 Περὶ μὲν οὖν τῆς τοῦ παντὸς φύσεως, εἴτ' ἄπειρός ἐστι κατὰ τὸ μέγεθος εἴτε πεπέρανται τὸν σύνολον ὄγκον, ὕστερον ἐπισκεπτέον περὶ δὲ τῶν κατ' εἶδος αὐτοῦ μορίων νῦν λέγωμεν ἀρχὴν ποιησάμενοι τήνδε. 13 The question as to the nature of the whole, whether it is infinite in size or limited in its total mass, is a matter for subsequent inquiry. We will now speak of those parts of the whole which are specifically distinct. Let us take this as our starting-point. Πάντα γὰρ τὰ φυσικὰ σώματα καὶ μεγέθη καθ' αὑτὰ κινητὰ λέγομεν εἶναι κατὰ τόπον τὴν γὰρ φύσιν κινήσεως ἀρχὴν εἶναί φαμεν αὐτοῖς. 14 All natural bodies and magnitudes we hold to be, as such, capable of locomotion; for nature, we say, is their principle of movement. Πᾶσα δὲ κίνησις ὅση κατὰ τόπον, ἣν καλοῦμεν φοράν, ἢ εὐθεῖα ἢ κύκλῳ ἢ ἐκ τούτων μικτή 15 But all movement that is in place, all locomotion, as we term it, is either straight or circular or a combination of these two, ἁπλαῖ γὰρ αὗται δύο μόναι. Αἴτιον δ' ὅτι καὶ τὰ μεγέθη ταῦτα ἁπλᾶ μόνον, ἥ τ' εὐθεῖα καὶ ἡ περιφερής. 16 which are the only simple movements. And the reason of this is that these two, the straight and the circular line, are the only simple magnitudes. Κύκλῳ μὲν οὖν ἐστιν ἡ περὶ τὸ μέσον, 17 Now revolution about the centre is circular motion, εὐθεῖα δ' ἡ ἄνω καὶ κάτω. Λέγω δ' ἄνω μὲν τὴν ἀπὸ τοῦ μέσου, κάτω δὲ τὴν ἐπὶ τὸ μέσον. 18 while the upward and downward movements are in a straight line, 'upward' meaning motion away from the centre, and 'downward' motion towards it. Ὥστ' ἀνάγκη πᾶσαν εἶναι τὴν ἁπλῆν φορὰν τὴν μὲν ἀπὸ τοῦ μέσου, τὴν δ' ἐπὶ τὸ μέσον, τὴν δὲ περὶ τὸ μέσον. 19 All simple motion, then, must be motion either away from or towards or about the centre. Καὶ ἔοικεν ἠκολουθηκέναι κατὰ λόγον τοῦτο τοῖς ἐξ ἀρχῆς τό τε γὰρ σῶμα ἀπετελέσθη ἐν τρισὶ καὶ ἡ κίνησις αὐτοῦ. 20 This seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms. Ἐπεὶ δὲ τῶν σωμάτων τὰ μέν ἐστιν ἁπλᾶ τὰ δὲ σύνθετα ἐκ τούτων (λέγω δ' ἁπλᾶ μὲν ὅσα κινήσεως ἀρχὴν ἔχει κατὰ φύσιν, οἷον πῦρ καὶ γῆν καὶ τὰ τούτων εἴδη καὶ τὰ συγγενῆ τούτοις), ἀνάγκη καὶ τὰς κινήσεις εἶναι τὰς μὲν ἁπλᾶς τὰς δὲ μικτάς πως, (269a.) καὶ τῶν μὲν ἁπλῶν ἁπλᾶς, μικτὰς δὲ τῶν συνθέτων, κινεῖσθαι δὲ κατὰ τὸ ἐπικρατοῦν. 21 Bodies are either simple or compounded of such; and by simple bodies I mean those which possess a principle of movement in their own nature, such as fire and earth with their kinds, and whatever is akin to them. Necessarily, then, movements also will be either simple or in some sort compoundᾰsimple in the case of the simple bodies, compound in that of the compositeᾰand in the latter case the motion will be that of the simple body which prevails in the composition.
Postquam philosophus ostendit universum esse perfectum et ratione suae corporeitatis et ratione suae universitatis, hic ostendit ex quibus partibus eius perfectio integratur. After showing that the universe is perfect by reason both of its corporeity and its universalness, the Philosopher here shows from which parts its perfection is made up. Et primo dicit de quo est intentio;
secundo ostendit propositum, ibi: omnia enim physica corpora et cetera.
First he expresses his intention;
Secondly, he proves his proposition, at 20.
Circa primum considerandum est quod, sicut dicitur in III Physic., antiqui dixerunt infinitum esse extra quod nihil est. Quia igitur probavit universum esse perfectum ex hoc quod nihil est extra ipsum, sed omnia complectitur, posset aliquis suspicari ipsum esse infinitum. Et ideo huic opinioni occurrens, concludit subdens quod posterius intendendum est quantum ad naturam totius universi, si est infinitum secundum magnitudinem, sive finitum secundum totam suam molem. Interim tamen, antequam hoc tractetur, dicendum est de partibus eius quae sunt secundum speciem, in quibus scilicet integritas speciei ipsius consistit, cuiusmodi sunt simplicia corpora. Nam animalia et plantae et alia huiusmodi sunt secundariae partes eius, quae magis pertinent ad bene esse ipsius quam ad primam eius integritatem. Et hanc considerationem inchoabimus a principio infra posito. With respect to the first [13] it should be considered that, as is said in Physics III, the ancients described the infinite as "that outside of which there is nothing." Now, since he has proved that the universe is perfect on the ground that nothing is outside it, but that it embraces all things, one might think it to be infinite. Accordingly, meeting this opinion, he concludes by adding that later on, in discussing the nature of the whole universe, there will be treated the question of whether it is infinite in magnitude, or finite with respect to its total mass. But meanwhile, before treating of this, something must be said about those parts of it that are "according to the species," namely, those parts in which the integrity of its species consists, and which are the simple bodies. For animals and plants and other such are its secondary parts, and pertain more to the well-being of the universe than to its basic integrity. And we shall begin this consideration from a principle given below. Deinde cum dicit: omnia enim physica etc., ostendit propositum, scilicet ex quibus partibus principalibus perfecta species universi integretur. 20. Then at [14] he starts to manifest the proposition stating of which principal parts the perfect species of the universe is made. Et primo ostendit quod praeter quatuor elementa, necesse est esse aliud corpus simplex;
secundo ostendit quod praeter quinque corpora simplicia non est aliud corpus, ibi: manifestum autem ex dictis et cetera.
First he shows that in addition to the four elements, another simple body must exist;
Secondly, that there is no simple body other than these five (L. 8).
Circa primum duo facit: About the first he does two things: primo ostendit esse quintum corpus praeter quatuor elementa;
secundo ostendit differentiam eius ad quatuor elementa, ibi: quoniam autem haec quidem supponuntur et cetera.
First he shows that there is a fifth body besides the four elements;
Secondly, how it differs from the four elements (L. 5).
Circa primum duo facit: With respect to the first he does two things: primo praemittit quaedam quae sunt necessaria ad propositum ostendendum;
secundo argumentatur ad propositum, ibi: si quidem igitur est simplex motus et cetera.
First he mentions some preliminary facts needed in proving his proposition;
Secondly, he argues to the proposition (L. 4).
Circa primum duo facit: About the first he does two things: primo praemittit quaedam quae pertinent ad motus;
secundo ponit quaedam quae pertinent ad corpora mobilia, ibi: quoniam autem corporum haec quidem et cetera.
First he premises facts regarding motion;
Secondly, facts pertaining to mobile bodies, at 32.
Circa primum duo facit: About the first he does two things: primo praemittit continuitatem motus localis ad corpora naturalia;
secundo ponit distinctionem motuum localium, ibi: omnis autem et cetera.
First he mentions the connection between local motion and mobile bodies;
Secondly, he distinguishes the kinds of local motion, at 23.
Dicit ergo primo quod omnia corpora physica, idest naturalia, dicimus esse mobilia secundum locum secundum seipsa, idest secundum sui naturam; et similiter alias magnitudines naturales, puta superficies et lineas, prout sunt termini naturalium corporum; ita tamen quod corpora per se moventur, aliae tamen magnitudines per accidens, motis corporibus. Et ad huius probationem inducit definitionem naturae, quae est principium motus in eis in quibus est, ut dicitur in II Physic. Ex hoc autem sic argumentatur. Corpora naturalia sunt quae habent naturam: sed natura est principium motus in eis in quibus est: ergo corpora naturalia habent principium motus in seipsis. Sed quaecumque moventur quocumque motu, moventur localiter, non autem e converso, ut patet in VIII Physic., eo quod motus localis est primus motuum. Omnia ergo corpora naturalia moventur naturaliter motu locali, non autem omnia aliquo aliorum motuum. 21. He says therefore first [14] that all physical, i.e., natural, bodies are said to be mobile with respect to place according to themselves, i.e., according to their very natures, and the same is true for other natural magnitudes, e.g. planes and lines, insofar as they are the boundaries of natural bodies. And this is true in the sense that bodies are moved per se, but the other magnitudes per accidens, when the bodies are moved. In proof of this he adduces the definition of nature, which is "the principle of motion in those things in which it exists," as is said in Physics II. From this he argues thus: Natural bodies are ones that have a nature, but nature is a principle of motion in things in which it is; therefore, natural bodies have a principle of motion in them. But whatever is moved with any sort of motion is moved locally, but not conversely, as is plain in Physics VII, because local motion is the first of motions. Therefore all natural bodies are naturally moved with a local motion, but not all of them with all of the other motions. Sed videtur hoc esse falsum: caelum enim est corpus naturale, nec tamen eius motus videtur esse a natura, sed magis ab aliquo intellectu, sicut ex his quae determinantur in VIII Physic. et XII Metaphysic. patet. This, however, seems to be false: for the heavens are a natural body, but their motion seems to be due, not to nature but to intellect, as is plain from what has been determined in Physics VIII and Metaphysics XII. Sed dicendum est quod duplex est principium motus: unum quidem activum, quod est ipse motor, et tale principium motus animalium est anima: aliud autem est principium motus passivum, scilicet secundum quod corpus habet aptitudinem ut sic moveatur, et huiusmodi principium motus est in gravibus et levibus. Non enim componuntur ex movente et moto, ut philosophus dicit in VIII Physic.: quod quidem, inquit, nihil horum, scilicet gravium et levium, ipsum movet seipsum, manifestum est: sed motus habent principium, non movendi neque faciendi, sed patiendi. Sic igitur dicendum est quod principium activum motus caelestium corporum est intellectualis substantia: principium autem passivum est natura illius corporis, secundum quam natum est tali motu moveri. Et esset simile in nobis si anima non moveret corpus nostrum nisi secundum naturalem inclinationem eius, scilicet deorsum. But it must be said that there are two kinds of principles of motion: one is active, i.e., the mover, as the soul is the active principle of the motion of animals; the other is a passive principle of motion, i.e., a principle according to which a body has an aptitude to be thus moved, and such a principle of motion exists in the heavy and the light. For these are not composed of a mover and a moved, because, as the Philosopher says in Physics VIII, "it is plain that none of these — i.e., the heavy and the light — moves itself, but each has, with respect to its motion, a principle not of causing motion or of acting, but of being acted upon." Consequently, it must be said that the active principle of the motion of heavenly bodies is an intellectual stance, but the passive principle is that body's nature according to which it is apt to be moved with such a motion. And the same situation would prevail in us, if the soul did not move our body in any way other than according to its natural inclination, namely, down. Deinde cum dicit: omnis autem motus etc., ponit distinctionem localium motuum. 23. Then at [15] he distinguishes local motions. Et primo distinguit communiter motus locales tam compositos quam simplices;
secundo distinguit motus simplices, ibi: circulatio quidem igitur et cetera.
First he distinguishes in a general way both composite and simple local motions;
Secondly, he distinguishes simple motions, at 27.
Circa primum duo facit. With respect to the first he does two things: Primo proponit quod intendit, scilicet quod omnis motus localis (qui vocatur latio) aut est circularis, aut rectus, aut mixtus ex his, sicut motus obliquus eorum quae hac illacque feruntur. First at [15] he proposes what he intends, namely, that every local motion — which is called latio — is either circular, or straight, or composed of these, as is the oblique motion of things that are borne this way and that. Secundo ibi: simplices enim etc., probat quod dixerat, per hoc quod motus simplices non sunt nisi duo, scilicet rectus et circularis. Et huius causam assignat ex hoc quod solae sunt duae magnitudines simplices, scilicet recta et circularis: motus autem localis secundum loca specificatur, sicut et quilibet alius motus secundum suos terminos. Secondly, at [16] he proves what he had said, on the ground that there are just two simple motions, the straight and the circular. And the reason for this, he says, is that there exist just two simple magnitudes, namely, the straight and the circular: but local motion is specified according to places, just as every other motion is specified according to its termini. Sed videtur quod probatio Aristotelis non sit conveniens: quia, ut dicitur in I Poster., transcendentem in aliud genus non contingit demonstrare. Inconvenienter igitur per divisionem magnitudinum, quae pertinet ad mathematicum, concluditur aliquid circa motus, qui pertinent ad naturalem. 24. But it seems that Aristotle's proof is not suitable, because, as is said in Post. Anal. I, one does not demonstrate who crosses into another genus. Consequently, it seems unfitting to use the division of magnitudes, which pertain to mathematics, in order to reach a conclusion about motion, which pertains to natural science. Sed dicendum quod scientia quae se habet ex additione ad aliam, utitur principiis eius in demonstrando, sicut geometria utitur principiis arithmeticae: magnitudo enim addit positionem supra numerum, unde punctus dicitur esse unitas posita. Similiter autem corpus naturale addit materiam sensibilem supra magnitudinem mathematicam: et ideo non est inconveniens si naturalis in suis demonstrationibus utatur principiis mathematicis: non enim est omnino aliud genus, sed quodammodo sub illo continetur. But it must be said that a science which is by addition to some other science uses the latter's principles in demonstrating, as geometry uses the principles of arithmetic — for magnitude adds position to number, and thus a point is said to be "a positioned unit." In like manner, natural body adds sensible matter to mathematical magnitude. Consequently, it is not unfitting for the natural philosopher in his demonstrations to use the principles of mathematics — for the latter is not of a completely different genus but is in a certain way contained under the former. Item videtur esse falsum quod solae duae magnitudines sint simplices, scilicet recta et circularis. Elix enim videtur esse una linea simplex, quia omnis pars eius est uniformis; et tamen linea elica nec est recta nec est circularis. Likewise, it seems to be false that only two magnitudes are simple, namely, the straight and the circular. For a helix [spiral] seems to be one simple line, because every one of its parts is uniform, and yet a helical line [such as a screw thread] is neither straight nor circular. Sed dicendum quod elix, si quis eius originem consideret, non est linea simplex, sed mixta ex recta et circulari. Causatur enim elix ex duobus motibus imaginatis, quorum unus est lineae circumeuntis columnam, alius autem est puncti moti per lineam: si enim uterque motus simul et regulariter perficiatur, constituetur elica linea per motum puncti in linea mota. But it must be said that a helix, if one considers its origin, is not a simple line, but a combination of straight and circular. For a helix is produced by two imaginary motions, one of which is the motion of a line moving round a cylinder, and the other of a point moving through the line: if two such motions take place in a regular manner at the same time, a helix will be formed by the motion of the point in the moving line. Item videtur quod motus circularis non sit simplex. Partes enim sphaerae circulariter motae non uniformiter moventur, sed pars quae est circa polos vel circa centrum, movetur tardius, quia peragit minorem circulum in eodem tempore: et ita motus sphaerae videtur compositus ex tardo et veloci. Likewise, it seems that circular motion is not simple. For the parts of a sphere that is in circular motion are not in uniform motion but the parts near the poles or near the center are moved more slowly, because they traverse a smaller circle in a given time; consequently, the motion of a sphere seems to be composed of fast and slow motions. Sed dicendum quod continuum non habet partes in actu, sed solum in potentia: quod autem non est actu, non movetur actu: unde partes sphaerae, cum sint corpus continuum, non moventur actu. Unde non sequitur quod in motu sphaerico vel circulari sit diversitas actualis, sed solum potentialis; quae non repugnat simplicitati de qua nunc loquimur; omnis enim magnitudo habet pluralitatem potentialem. But it must be said that a continuum does not have parts in act but only in potency. Now, what is not in act is not in actual motion. Hence the parts of a sphere, since they are a continuous body, are not actually being moved. Hence it does not follow that, in a spherical or circular motion, there is actual diversity, but this is only potentially. This does not conflict with the simplicity about which we are now speaking, for every magnitude possesses potential plurality. Deinde cum dicit: circulatio quidem igitur etc., distinguit motus simplices. 27. Then at [17] he distinguishes simple motions. Et primo ponit unum, scilicet circularem;
secundo ponit duos rectos, ibi: rectus autem etc.;
tertio concludit numerum ternarium simplicium motuum, ibi: itaque necesse et cetera.
First he mentions one, namely, the circular;
Secondly, he mentions two that are straight, at 29;
Thirdly, he concludes that the number of simple motions is three, at 30.
Dicit ergo primo quod circulatio, idest motus circularis, dicitur qui est circa medium. Et est intelligendum circa mundi medium: rota enim, quae movetur circa medium sui, non movetur proprie circulariter; sed motus eius est compositus ex elevatione et depressione. He says therefore first [17] that circulation, i.e., circular motion is around the middle. And this is to be understood as around the middle of the world: for a wheel which is in motion around its own middle is not in circular motion in the proper sense of the word, but its motion is composed of ups and downs. Sed videtur secundum hoc quod non omnia corpora caelestia circulariter moveantur: nam, secundum Ptolomaeum, motus planetarum est in excentricis et epicyclis; qui quidem motus non sunt circa medium mundi, quod est centrum terrae, sed circa quaedam alia centra. But it seems according to this that not all heavenly bodies are in circular motion: for according to Ptolemy, the motion of the planets is in eccentrics and epicycles, which are motions, not around the middle of the world, which is the earth's center, but around certain other centers. Dicendum est autem quod Aristoteles non fuit huius opinionis, sed existimavit quod omnes motus caelestium corporum sunt circa centrum terrae, ut ponebant astrologi sui temporis. Postmodum autem Hipparchus et Ptolomaeus adinvenerunt motus excentricorum et epicyclorum, ad salvandum ea quae apparent sensibus in corporibus caelestibus. Unde hoc non est demonstratum, sed suppositio quaedam. Si tamen hoc verum sit, nihilominus omnia corpora caelestia moventur circa centrum mundi secundum motum diurnum, qui est motus supremae sphaerae revolventis totum caelum. But it must be said that Aristotle was not of this opinion, but thought that all motions of the heavenly bodies are about the center of the earth, as did all the astronomers of his time. But later, Hipparchus and Ptolemy hit upon eccentric and epicyclic motions to save what appears to the senses in heavenly bodies. Hence this is not a demonstration, but a certain assumption. Yet if it be true, all the heavenly bodies are still in motion about the center of the world with respect to the diurnal motion, which is the motion of the supreme sphere that revolves the entire heaven. Deinde cum dicit: rectus autem etc., distinguit motum rectum in duos, scilicet in eum qui est sursum, et in eum qui est deorsum: et describit utrumque per habitudinem ad medium mundi, sicut descripserat motum circularem, ut sit uniformis descriptio. Et dicit quod motus sursum est qui est a medio mundi; motus autem deorsum qui est ad medium mundi. Quorum primus est motus levium, secundum motus gravium. 29. Then at [18] he distinguishes straight motion into two: namely, one which is up, and one that is down, and describes each in relation to the middle of the world, as he had described circular motion, in order to keep the description uniform. And he says that an upward motion is one from the middle of the world, but a downward motion is one to the middle of the world. The first of these is the motion of light things, the second of heavy things. Deinde cum dicit: itaque necesse etc., concludit numerum simplicium motuum. Et primo inducit conclusionem intentam: et dicit quod necesse est simplicem lationem, idest motum localem, quendam esse a medio, et hic est motus sursum corporum levium; quendam vero esse ad medium, et hic est motus deorsum corporum gravium; alium vero esse circa medium, et huiusmodi est motus circularis corporum caelestium. 30. Then at [19] he concludes to the number of simple motions. First he expresses the conclusion he intended, and says that as to simple latio, i.e., simple local motion, one must be from the middle, and this is the upward motion of light bodies; another must be to the middle, and this is the downward motion of heavy bodies; still another must be about the middle, and such is the circular motion of heavenly bodies. Secundo ibi: et videtur sequi etc., ostendit hanc conclusionem supra dictis congruere. Et dicit quod hoc quod dictum est de numero simplicium motuum, videtur consequenter se habere ad id quod supra dictum est de perfectione corporis: sicut enim perfectio corporis consistit in tribus dimensionibus, ita et motus simplices corporis in tres distinguuntur. Hoc autem dicit esse secundum rationem, idest secundum probabilitatem quandam: non enim proprie tres motus coaptantur tribus dimensionibus. 31. Secondly, at [20] he shows that this conclusion agrees with what has been said above. And he says that what has just been said about the number of simple motions seems to be a consequence of what was said above about the perfection of body, for just as the perfection of body consists in three dimensions, so the simple motions of body are distinguished into three kinds. But he says that this is "according to reason," i.e., according to a certain probability: for three motions are not properly equated to three dimensions. Deinde cum dicit: quoniam autem corporum etc., ponit quaedam ex parte corporum mobilium. Circa quod sciendum est quod, sicut habitum est in III Physic., motus est actus mobilis; actus autem proportionatur perfectibili; unde oportet motus proportionari corporibus mobilibus. Sunt autem corporum quaedam simplicia, quaedam composita. Simplex autem corpus est quod habet principium alicuius naturalis motus in seipso; sicut patet de igne, qui est simpliciter levis, et de terra, quae est simpliciter gravis, et de speciebus horum (sicut flamma dicitur esse quaedam species ignis, et bitumen quaedam species terrae). Addit autem et cognata his, propter media elementa; quorum aer habet maiorem affinitatem cum igne, aqua vero cum terra. Et per consequens necesse est corpus mixtum esse quod non habet in se secundum propriam naturam principium alicuius motus simplicis. 32. Then at [21] he gives some reflections about mobile bodies. In regard to this it must be known that, as was stated in Physics III, motion is an act of a mobile. Now an act is proportionate to the thing to be perfected. Hence motions ought to be proportionate to mobile bodies. But some bodies are simple, some composite. A simple body is one that has a principle of some natural motion in it, as is plain in the case of fire, which is light simply, and in that of earth, which is heavy simply, and in their species — as a flame is said to be a species of fire, and bitumen a species of earth. He adds the phrase, "and those related to them," on account of the intermediate elements, of which air has a greater affinity to fire, and water to earth. As a consequence, a mixed body must be one that, according to its proper nature, does not have in itself the principle of some simple motion. Et ex hoc concludit quod necesse est motuum quosdam esse simplices, quosdam autem aliqualiter mixtos: sive ita quod motus mixtus non sit unus, sed habens diversas partes, sicut ille qui componitur ex elevatione et depressione, aut ex pulsu et tractu; sive ita quod motus mixtus sit unus, sicut patet de motu qui in obliquum tendit, et de motu qui est super lineam elicam. Unde simplicium corporum necesse est esse simplices motus: mixtorum autem, mixtos, ut patet de motu pluviae aut alicuius huiusmodi corporis, in quo non totaliter gravitas aut levitas dominatur. Et si aliquando contingat quod corpus mixtum moveatur motu simplici, hoc erit secundum elementum in eo praedominans; sicut ferrum movetur deorsum secundum motum terrae, quae in eius mixtione dominatur. And from this he concludes that some motions must be simple and some mixed: whether the mixed motion is not one but has diverse parts, as one composed of elevation and depression, or of a push and a pull, or whether the mixed motion is one, as is plain in oblique motion and motion upon a helical line. Accordingly, the motions of simple bodies must be simple and those of mixed bodies mixed, as seen in the motion of rain, or any body of this kind in which neither heaviness nor lightness totally predominates. And if it sometimes happens that a mixed body is moved with a simple motion, that will be due to the element predominant in it, as iron is moved downwards according to the motion of earth which is predominant in its composition.
Lecture 4:
Five reasons why, besides the elements, there must be another simple bodyChapter 2 cont. Εἴπερ οὖν ἐστιν ἁπλῆ κίνησις, ἁπλῆ δ' ἡ κύκλῳ κίνησις, καὶ τοῦ τε ἁπλοῦ σώματος ἁπλῆ ἡ κίνησις καὶ ἡ ἁπλῆ κίνησις ἁπλοῦ σώματος (καὶ γὰρ ἂν συνθέτου ᾖ, κατὰ τὸ ἐπικρατοῦν ἔσται), ἀναγκαῖον εἶναί τι σῶμα ἁπλοῦν ὃ πέφυκε φέρεσθαι τὴν κύκλῳ κίνησιν κατὰ τὴν ἑαυτοῦ φύσιν βίᾳ μὲν γὰρ ἐνδέχεται τὴν ἄλλου καὶ ἑτέρου, κατὰ φύσιν δὲ ἀδύνατον, εἴπερ μία ἑκάστου κίνησις ἡ κατὰ φύσιν τῶν ἁπλῶν. 22 Supposing, then, that there is such a thing as simple movement, and that circular movement is an instance of it, and that both movement of a simple body is simple and simple movement is of a simple body (for if it is movement of a compound it will be in virtue of a prevailing simple element), then there must necessarily be some simple body which revolves naturally and in virtue of its own nature with a circular movement. By constraint, of course, it may be brought to move with the motion of something else different from itself, but it cannot so move naturally, since there is one sort of movement natural to each of the simple bodies. Ἔτι εἰ ἡ παρὰ φύσιν ἐναντία τῇ κατὰ φύσιν καὶ ἓν ἑνὶ ἐναντίον, ἀνάγκη, ἐπεὶ ἁπλῆ ἡ κύκλῳ, εἰ μὴ ἔσται κατὰ φύσιν τοῦ φερομένου σώματος, παρὰ φύσιν αὐτοῦ εἶναι. Εἰ οὖν πῦρ ἢ ἄλλο τι τῶν τοιούτων ἐστὶ τὸ κύκλῳ φερόμενον, ἐναντία ἡ κατὰ φύσιν αὐτοῦ φορὰ ἔσται τῇ κύκλῳ. Ἀλλ' ἓν ἑνὶ ἐναντίον ἡ δ' ἄνω καὶ κάτω ἀλλήλαις ἐναντίαι. Εἰ δ' ἕτερόν τί ἐστι σῶμα τὸ φερόμενον κύκλῳ παρὰ φύσιν, ἔσται τις αὐτοῦ ἄλλη κίνησις κατὰ φύσιν. Ἀλλὰ τοῦτ' ἀδύνατον εἰ μὲν γὰρ ἡ ἄνω, πῦρ ἔσται ἢ ἀήρ, εἰ δ' ἡ κάτω, ὕδωρ ἢ γῆ. 23 Again, if the unnatural movement is the contrary of the natural and a thing can have no more than one contrary, it will follow that circular movement, being a simple motion, must be unnatural, if it is not natural, to the body moved. If then (1) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. But a single thing has a single contrary; and upward and downward motion are the contraries of one another. If, on the other hand, (2) the body moving with this circular motion which is unnatural to it is something different from the elements, there will be some other motion which is natural to it. But this cannot be. For if the natural motion is upward, it will be fire or air, and if downward, water or earth. Ἀλλὰ μὴν καὶ πρώτην γε ἀναγκαῖον εἶναι τὴν τοιαύτην φοράν. Τὸ γὰρ τέλειον πρότερον τῇ φύσει τοῦ ἀτελοῦς, ὁ δὲ κύκλος τῶν τελείων, εὐθεῖα δὲ γραμμὴ οὐδεμία οὔτε γὰρ ἡ ἄπειρος (ἔχοι γὰρ ἂν πέρας καὶ τέλος) οὔτε τῶν πεπερασμένων οὐδεμία (πασῶν γάρ ἐστί τι ἐκτός αὐξῆσαι γὰρ ἐνδέχεται ὁποιανοῦν). Ὥστ' εἴπερ ἡ μὲν προτέρα κίνησις προτέρου τῇ φύσει σώματος, ἡ δὲ κύκλῳ προτέρα τῆς εὐθείας, ἡ δ' ἐπ' εὐθείας τῶν ἁπλῶν σωμάτων ἐστί (τό τε γὰρ πῦρ ἐπ' εὐθείας ἄνω φέρεται καὶ τὰ γεηρὰ κάτω πρὸς τὸ μέσον), ἀνάγκη καὶ τὴν κύκλῳ κίνησιν τῶν ἁπλῶν τινος εἶναι σωμάτων τῶν γὰρ μικτῶν τὴν φορὰν ἔφαμεν εἶναι κατὰ τὸ ἐπικρατοῦν ἐν τῇ μίξει τῶν ἁπλῶν. 24 Further, this circular motion is necessarily primary. For the perfect is naturally prior to the imperfect, and the circle is a perfect thing. This cannot be said of any straight line:—not of an infinite line; for, if it were perfect, it would have a limit and an end: nor of any finite line; for in every case there is something beyond it, since any finite line can be extended. And so, since the prior movement belongs to the body which naturally prior, and circular movement is prior to straight, and movement in a straight line belongs to simple bodies—fire moving straight upward and earthy bodies straight downward towards the centre—since this is so, it follows that circular movement also must be the movement of some simple body. For the movement of composite bodies is, as we said, determined by that simple body which preponderates in the composition. These premises clearly give the conclusion that there is in nature some bodily substance other than the formations we know, prior to them all and more divine than they. Ἔκ τε δὴ τούτων φανερὸν ὅτι πέφυκέ τις οὐσία σώματος ἄλλη παρὰ τὰς ἐνταῦθα συστάσεις, θειοτέρα καὶ προτέρα τούτων ἁπάντων, κἂν εἴ τις ἔτι λάβοι πᾶσαν εἶναι κίνησιν ἢ κατὰ φύσιν ἢ παρὰ φύσιν, καὶ τὴν ἄλλῳ παρὰ φύσιν ἑτέρῳ κατὰ φύσιν, οἷον ἡ ἄνω καὶ ἡ κάτω πέπονθεν ἡ μὲν γὰρ τῷ πυρί, ἡ δὲ τῇ γῇ παρὰ φύσιν καὶ κατὰ φύσιν (269b.) ὥστ' ἀναγκαῖον καὶ τὴν κύκλῳ κίνησιν, ἐπειδὴ τούτοις παρὰ φύσιν, ἑτέρου τινὸς εἶναι κατὰ φύσιν. 25 But it may also be proved as follows. We may take it that all movement is either natural or unnatural, and that the movement which is unnatural to one body is natural to another—as, for instance, is the case with the upward and downward movements, which are natural and unnatural to fire and earth respectively. It necessarily follows that circular movement, being unnatural to these bodies, is the natural movement of some other. Πρὸς δὲ τούτοις εἰ μέν ἐστιν ἡ κύκλῳ τινὶ φορὰ κατὰ φύσιν, δῆλον ὡς εἴη ἄν τι σῶμα τῶν ἁπλῶν καὶ πρώτων, ὃ πέφυκεν, ὥσπερ τὸ πῦρ ἄνω καὶ ἡ γῆ κάτω, ἐκεῖνο κύκλῳ φέρεσθαι κατὰ φύσιν. Εἰ δὲ παρὰ φύσιν φέρεται τὰ φερόμενα κύκλῳ τὴν πέριξ φοράν, θαυμαστὸν καὶ παντελῶς ἄλογον τὸ μόνην εἶναι συνεχῆ ταύτην τὴν κίνησιν καὶ ἀΐδιον, οὖσαν παρὰ φύσιν φαίνεται γὰρ ἔν γε τοῖς ἄλλοις τάχιστα φθειρόμενα τὰ παρὰ φύσιν. Ὥστ' εἴπερ ἐστὶ πῦρ τὸ φερόμενον, καθάπερ φασί τινες, οὐδὲν ἧττον αὐτῷ παρὰ φύσιν ἡ κίνησίς ἐστιν αὕτη ἢ ἡ κάτω πυρὸς γὰρ κίνησιν ὁρῶμεν τὴν ἀπὸ τοῦ μέσου κατ' εὐθεῖαν. Διόπερ ἐξ ἁπάντων ἄν τις τούτων συλλογιζόμενος πιστεύσειεν ὡς ἔστι τι παρὰ τὰ σώματα τὰ δεῦρο καὶ περὶ ἡμᾶς ἕτερον κεχωρισμένον, τοσούτῳ τιμιωτέραν ἔχον τὴν φύσιν ὅσῳπερ ἀφέστηκε τῶν ἐνταῦθα πλεῖον. 26 Further, if, on the one hand, circular movement is natural to something, it must surely be some simple and primary body which is ordained to move with a natural circular motion, as fire is ordained to fly up and earth down. If, on the other hand, the movement of the rotating bodies about the centre is unnatural, it would be remarkable and indeed quite inconceivable that this movement alone should be continuous and eternal, being nevertheless contrary to nature. At any rate the evidence of all other cases goes to show that it is the unnatural which quickest passes away. And so, if, as some say, the body so moved is fire, this movement is just as unnatural to it as downward movement; for any one can see that fire moves in a straight line away from the centre. On all these grounds, therefore, we may infer with confidence that there is something beyond the bodies that are about us on this earth, different and separate from them; and that the superior glory of its nature is proportionate to its distance from this world of ours.
Postquam philosophus praemisit quaedam necessaria ad propositum ostendendum, hic incipit arguere ad propositum; et hoc quinque rationibus. Quarum prima talis est. Motus circularis est motus simplex: motus autem simplex est primo et per se simplicis corporis (quia etsi contingat quod aliquis motus simplex sit alicuius corporis compositi, hoc erit secundum corpus simplex quod in eo praedominatur; sicut in lapide praedominatur terra, secundum cuius naturam movetur deorsum): ergo necesse est esse aliquod corpus simplex, quod moveatur naturaliter secundum motum circularem. 33. After stating in advance certain things necessary for showing the proposition, the Philosopher here begins to reason toward the proposition, and this with five arguments. The first [22] is this: Circular motion is a simple motion. But a simple motion belongs primarily and per se to a simple body — because even though a simple motion might occur in a composite body, this will be with respect to the simple body that is predominant in it; for example, in a stone, earth predominates, according to whose nature it is moved down. Therefore, there must be a simple body which is naturally moved according to a circular motion. Posset autem aliquis huic rationi obviare, dicendo quod, licet simplex motus sit simplicis corporis, non tamen oportet quod illud simplex corpus quod movetur circulariter, sit aliud a corpore simplici quod movetur motu simplici recto. Et ideo hoc excludit, subdens quod nihil prohibet quin diversa corpora moveantur uno motu non naturaliter, ita scilicet quod unum corpus moveatur per violentiam motu alterius; sed quod unum corpus moveatur secundum naturam motu naturali alterius corporis, est impossibile. Necesse enim est esse unum motum simplicem naturalem unius simplicis corporis, et diversos diversorum. Unde, si motus circularis est simplex, et alius a motibus rectis, necesse est quod sit naturalis corpori simplici, quod sit aliud a corporibus simplicibus quae moventur motu recto. Now, someone could object to this argument and say that, although a simple motion belongs to a simple body, yet that simple body which is circularly moved would not necessarily be different from the simple body that is moved with a simple straight motion. Accordingly, he rejects this by adding that nothing prevents diverse bodies from being moved unnaturally with some one motion, as when one body might be moved violently with the motion of another; but that one body be moved according to nature with the natural motion of some other body is impossible. For one simple natural motion must belong to one simple body, and diverse to diverse. Hence, if circular motion is simple and distinct from straight motions, then it must belong to a natural simple body that is different from the simple bodies that are moved with a straight motion. Sed videtur hoc esse falsum, quod unus motus simplex sit solum unius corporis simplicis: motus enim deorsum est naturalis aquae et terrae, et motus sursum est naturalis igni et aeri. 34. But this seems to be false, namely, that one simple motion belongs to just one simple body, for downward motion is natural to both water and earth, and upward motion to fire and air. Sed dicendum quod motus localis attribuitur elementis, non secundum calidum et frigidum, humidum et siccum, secundum quae distinguuntur quatuor elementa, ut patet in II de Generat.: haec enim sunt principia alterationum. Motus autem localis attribuitur elementis secundum gravitatem et levitatem. Unde duo corpora gravia comparantur ad motum localem sicut unum corpus; et similiter duo corpora levia. Humidum enim et siccum, secundum quae differunt terra et aqua vel ignis et aer, accidentalem habitudinem habent ad motum localem. Et tamen in gravi et levi differentia quaedam est: nam ignis est levis simpliciter et absolute, terra autem gravis; aer autem est levis per comparationem ad duo elementa, et similiter aqua est gravis. Unde non omnino est idem secundum speciem motus aquae et terrae, vel ignis et aeris: quia non sunt idem termini, secundum quos specificantur eorum motus: aer enim natus est moveri ad locum qui subsidet igni, aqua autem ad locum qui supereminet terrae. But it must be said that local motion is attributed to the elements, not according to hot and cold, moist and dry, with respect to which the four elements are distinguished — as is plain in On Generation II — for these four properties are principles of alterations. But local motion is attributed to the elements with respect to heaviness and lightness. Hence the two heavy bodies are compared to local motion as one body; and the same for the two light bodies. For moist and dry, according to which earth and water, or fire and air, differ, have an incidental relationship to local motion. Yet in the realm of heavy and light there is a difference, for fire is light simply and absolutely, and earth heavy; while air is light compared to two elements and likewise water is heavy. Hence the motions of water and earth, or fire and air, are not completely the same according to species, because the termini according to which their motions are specified are not the same: for air is apt to be moved to a place below fire, and water to a place above earth. Item videtur quod non sit necessarium, si corporis simplicis est unus motus simplex, quod propter hoc aliquis motus simplex sit alicuius corporis simplicis: sicut etiam non est necessarium quod tot sint corpora composita quot sunt motus compositi, qui diversificantur in infinitum. 35. Likewise it seems not necessary, if of one simple body there is one simple motion, that on this account any simple motion should belong to some [different?] simple body, any more than it is necessary that there be as many composite bodies as there are composite motions, which are infinitely diverse. Sed dicendum est quod, sicut motus simplex localis non respondet corpori simplici quantum ad calidum et frigidum, humidum et siccum, ita etiam neque motus compositus respondet corpori mixto secundum gradus mixtionis praedictarum qualitatum, sed secundum compositionem gravis et levis; secundum cuius diversitatem diversificatur obliquatio corporis mixti a simplici motu gravis vel levis. Utraque autem diversitas non tendit in infinitum secundum speciem, sed solum secundum numerum. But it must be said that just as simple local motion does not correspond to a simple body with respect to hot and cold, and moist and dry, so neither does composite motion correspond to mixed body according to the degrees of mixture of those qualities, but rather according to a composition of heavy and light, according to the diversity of which is diversified the obliquity of a mixed body from the simple motion of the heavy or light. Neither of these diversities tends to infinity with respect to species, but only with respect to number. Item videtur quod secundum hoc sint multa corpora simplicia: quia sicut motus sursum et deorsum videntur esse motus simplices, ita motus qui est dextrorsum vel sinistrorsum, et qui est ante et retro. 36. Likewise it seems that according to this there are many simple bodies. For just as motions upward and downward seem to be simple motions, so too motions to the right and to the left, and those ahead and to the rear. Et dicendum est quod, cum corpora simplicia sint essentiales et primae partes universi, oportet quod motus simplices, qui sunt naturales corporibus simplicibus, attendantur secundum conditionem universi. Quod cum sit sphaericum, ut infra probabitur, oportet quod motus eius attendatur per comparationem ad medium, quod est immobile: quia omnis motus fundatur supra aliquod immobile, ut dicitur in libro de causa motus animalium. Et ideo oportet esse solum tres motus simplices, secundum diversas habitudines ad medium: scilicet eum qui est a medio, et eum qui est ad medium, et eum qui est circa medium. Dextrum autem et sinistrum, ante et retro, considerantur in animalibus, et non in toto universo, nisi secundum quod ponuntur in caelo, ut in secundo dicetur: et secundum hoc motus circularis caeli est secundum dextrum et sinistrum, ante et retro. It must be stated therefore that, since simple bodies are the essential and first parts of the universe, the simple motions which are natural to simple bodies must be considered in relation to the condition of the universe. Since this latter is spherical, as will be proved later, its motion must be considered in relation to the middle, which is immobile, because every motion is founded upon something immobile, as is stated in the book, On the Cause of the Motion of Animals. Consequently, there must be but three simple motions, according to their diverse relations to the middle [center]: i.e., one which is from the center, one which is to the center, and one which is around the center. To the right and left, ahead and to the rear, are considered in animals but not in the whole universe, except in the sense that" they are placed in the heavens, as will be said in Book II. And according to this the circular motion of the heavens is with respect to right and left, ahead and to the rear. Item videtur quod motus rectus et circularis non sint eiusdem rationis. Est enim motus rectus corporis nondum habentis complementum suae speciei, ut in quarto dicetur, et existentis extra proprium locum: motus autem circularis est corporis habentis complementum suae speciei, et in loco proprio existentis. Unde non videtur quod secundum eandem rationem motus simplices corporales sint simplicium corporum; sed quod alii motus sint corporum prout sunt in fieri, circularis autem prout sunt in facto esse. 37. In like manner it seems that straight motion and circular are not of the same kind. For a straight motion belongs to a body not yet having its completeness of species, as will be said in Book IV, and existing outside its proper place, while a circular motion belongs to a body that has completeness of species and is existing in its proper place. Hence simple bodily motions do not seem to belong to simple bodies according to a same notion, but some motions seem to belong to bodies inasmuch as they are coming into being, while circular motion insofar as they have complete existence. Sed dicendum quod, quia motus proportionatur mobili tanquam actus eius, conveniens est quod corpori quod est separatum a generatione et a corruptione, et non potest per violentiam expelli a proprio loco, debeatur motus circularis, qui est corporis in suo loco existentis: corporibus autem aliis generabilibus et corruptibilibus debetur motus extra proprium locum, qui est absque complemento speciei. Non tamen ita quod corpus quod movetur naturaliter motu recto, non habeat primum complementum suae speciei, quod est forma; hanc enim sequitur talis motus: sed quia non habet ultimum complementum, quod est in consecutione finis, qui est locus conveniens et conservans. But it must be said that, since a motion is proportionate to the mobile as being its act, it is fitting that a body which is separated from generation and corruption and cannot be expelled from its proper place by violence should have a circular motion, which is proper to a body existing in its own place; but to other bodies that can be generated and corrupted there belongs a motion outside their proper place and which is incomplete in species. But this is not in the sense that a body which is naturally moved with a straight motion lacks the first complement of its species, namely, form, for it is the form that such a motion is consequent upon; but in the sense that it does not have its final complement which consists in attaining the end, which is a place that agrees with it and conserves it. Secundam rationem ponit ibi: adhuc si qui praeter naturam etc.: in qua praesupponit duo principia. Quorum unum est quod motus qui est praeter naturam, idest violentus, contrarietur motui naturali; sicut terra movetur deorsum secundum naturam, sursum autem contra naturam. Secundum principium est quod unum uni est contrarium, ut probatum est in X Metaphys. Oportet autem et tertium supponere, quod sensu videtur, scilicet esse aliquod corpus circulariter motum. Et si quidem ille motus sit illi corpori naturalis, habemus propositum secundum praemissam rationem, quod scilicet illud corpus naturaliter motum circulo, sit aliud a quatuor corporibus simplicibus. Si vero motus huiusmodi non sit ei naturalis, oportet quod sit ei contra naturam. 38. The second argument he gives at [23] and in it he presupposes two principles: one of which is that a motion which is outside nature, i.e., violent, is contrary to a natural motion, as earth is according to nature moved downward but upward against its nature. The second principle is that one thing is contrary to one thing, as is proved in Metaphysics X. A third also must be presupposed from sense experience, namely, that there exists a body which is moved circularly. Now, if that motion is natural to that body, we have the proposition, in keeping with the previously given reason, namely, that that body which is moved in a circle naturally is distinct from the four simple elements. But if such a motion is not natural to it, it must be against its nature. Ponatur ergo primo quod illud corpus circulariter motum sit ignis, ut quidam dicunt, vel quodcumque aliud quatuor elementorum. Oportebit ergo quod motus naturalis ignis, qui est moveri sursum, sit contrarius motui circulari. Sed hoc non potest esse: quia uni unum est contrarium, motui autem sursum contrariatur motus deorsum, et sic non potest ei contrariari motus circularis. Et eadem ratio est de aliis tribus elementis. Et similiter, si detur quod illud corpus quod contra naturam movetur circulariter, sit quodcumque aliud corpus praeter quatuor elementa, oportebit quod habeat aliquem alium motum naturalem. Sed hoc est impossibile: quia si sit ei naturalis motus qui est sursum, erit ignis aut aer; si autem motus qui est deorsum, erit aqua aut terra; positum est autem quod sit extra quatuor elementa. Sic ergo necesse est corpus quod movetur circulariter, naturaliter hoc motu moveri. Let us therefore first assume that that body in circular motion is fire, as some claim, or any of the other four elements. Then the natural motion of fire, which is to be moved upward, will have to be contrary to the circular motion. But this cannot be, for to one thing, one thing is contrary, and the motion contrary to an upward motion is a downward one; consequently, circular motion cannot be contrary to it. And the same holds for the other three elements. Likewise, if it be assumed that the body which is being moved circularly against its nature is a body other than the four elements, it would have to have some other natural motion. But this is impossible, because if its natural motion is up, it will be fire or air; if its motion is down, it will be water or earth. But we supposed that it is not one of the four elements. Accordingly it must be that the body moved in circular motion is being moved naturally with this motion. Videtur autem Aristoteles, secundum ea quae hic dicit, contrarius esse Platoni, qui posuit corpus quod circulariter fertur, esse ignem. Sed secundum veritatem eadem est circa hoc utriusque philosophi opinio. Plato enim corpus quod circulariter fertur, ignem vocat propter lucem, quae species ignis ponitur; non quod sit de natura ignis elementaris. Unde et posuit quinque corpora in universo, quibus adaptavit quinque figuras corporales quas geometrae tradunt, quintum corpus aetherem nominans. Now according to what he says here Aristotle seems to be contrary to Plato who assumed that the body which is circularly moved is fire. But with respect to the truth, the opinion of both philosophers is the same on this point. For Plato calls the body which is being circularly moved "fire" on account of light, which is posited as a form of fire, but not as being of the nature of elemental fire. Hence he posited five bodies in the universe, and to these he adapted five bodily figures which geometers teach, calling the fifth body "aether." Sed ulterius, quod hic dicitur, ignem moveri circulariter esse praeter naturam, videtur contrarium ei quod dicitur in I Meteor., ubi ipse Aristoteles ponit quod hypeccauma, idest ignis, et superior pars aeris feruntur circulariter motu firmamenti, sicut patet per motum stellae comatae. 39. But further, what is said here, namely, that for fire to be moved circularly is outside nature seems to be contrary to what is said in Meteorology I, where Aristotle himself sets forth that hypeccauma, i.e., fire, and the upper portion of the air, are carried along circularly by the motion of the firmament, as is plain in the motion of a comet. Sed dicendum est quod illa circulatio ignis vel aeris non est eis naturalis, quia non causatur ex principio intrinseco; neque iterum est per violentiam, sive contra naturam; sed est quodammodo supra naturam, quia talis motus inest eis ex impressione superioris corporis, cuius motum ignis et aer sequuntur secundum completam circulationem, quia haec corpora sunt caelo propinquiora; aqua vero secundum circulationem incompletam, scilicet secundum fluxum et refluxum maris; terra autem, velut remotissima a caelo, nihil de tali permutatione participat, nisi secundum solam alterationem partium ipsius. Quod autem inest inferioribus corporibus ex impressione superiorum, non est eis violentum nec contra naturam: quia naturaliter apta sunt moveri a superiori corpore. But it must be said that that circulation of fire or air is not natural to them, because it is not caused from an intrinsic principle. Neither is it through violence or against nature, because such a motion is in them from the influence of a higher body, whose motion fire and air follow according to a complete circulation because these bodies are closer to the heavens, but water according to an incomplete circulation, i.e., according to the ebb and flow of the sea. Earth, however, as being most remote from the heavens, suffers no such change except with respect to the sole alteration of its parts. Now whatever is present in lower bodies from the impression of the higher is not violent for them or against nature, for they are naturally apt to be moved by the higher body. Item videtur falsum esse quod hic dicitur, unum uni esse contrarium: uni enim vitio contrariatur et virtus et vitium oppositum, sicut illiberalitati prodigalitas et liberalitas. 40. Likewise it seems to be false, as here stated, that to one thing one thing is contrary, for to one vice both a virtue and the opposite vice are contrary, as to illiberality both prodigality and liberality are opposed. Dicendum est autem quod eidem secundum idem est unum tantum contrarium; nihil tamen prohibet quin uni secundum diversa sint plura contraria, sicut si sit idem subiectum dulce et album, contrariabitur ei nigrum et amarum. Sic igitur illiberalitati contrariatur virtus liberalitatis sicut ordinatum inordinato; prodigalitas autem sicut superabundantia defectui. Non potest autem dici quod uterque motus, scilicet qui est sursum et qui est deorsum, contrarietur motui circulari secundum communem rationem recti. Rectum enim et circulare non sunt contraria: pertinent enim ad figuram, cui nihil est contrarium. But it must be said that there is only one contrary to one thing according to the same aspect, although from different aspects nothing forbids one thing from having several contraries: thus, if the same subject is sweet and white, black and bitter will be contrary to it. Accordingly, the virtue of liberality is contrary to illiberality as what is well ordered to what is disordered, but prodigality is contrary to it as superabundance is to defect. Now, it cannot be said that both motions, namely, the one that is upward and the one that is downward, are contrary to circular motion according to the common aspect of straightness. For straight and circular are not contrary, for they pertain to figure, to which nothing is contrary. Tertiam rationem ponit ibi: sed adhuc et primam et cetera. Circa quam primo ostendit quod motus circularis sit primus inter motus locales. Est enim comparatio motus circularis ad motum rectum, qui est sursum vel deorsum, sicut comparatio circuli ad lineam rectam. Probatur autem quod circulus, idest linea circularis, sit prior linea recta, quia perfectum naturaliter est prius imperfecto; circulus autem sive linea circularis est perfecta, quia quidquid in ea accipitur, est principium et finis et medium; unde non recipit alicuius exterioris additionem. Linea autem recta nulla est perfecta. Quod patet et quantum ad lineam infinitam, quae imperfecta est quia fine caret, ex quo denominatur aliquid perfectum in Graeco: et idem patet in linea finita, quia quamlibet lineam finitam contingit augeri, idest accipere maiorem quantitatem, et sic est aliquid extra eam. Et sic linea circularis naturaliter est prior quam recta. Ergo et motus circularis est prior naturaliter motu recto. 41. He gives the third argument at [24]. With regard to this he first shows that circular motion is the first of local motions. For circular motion is related to straight motion, such as up or down, as circle is compared to straight line. A circle, i.e., a circular line, is proved to be prior to a straight line because the perfect is naturally prior to the imperfect. But a circle, or circular line, is perfect, because whatever is taken in it is a beginning and middle and end. Hence it does not suffer the addition of anything from without. But no straight line is perfect, whether it be an infinite line, which is imperfect because it lacks an end, from which things are called perfect in Greek, or a finite line, because every finite line can be increased, i.e., receive more quantity and so there is something outside it. Consequently a circular line is naturally prior to the straight. Therefore circular motion, too, is naturally prior to straight motion. Sed prior motus est naturaliter prioris corporis. Motus autem rectus est naturaliter alicuius simplicium corporum, sicut ignis movetur sursum, et terra deorsum et ad medium: et si contingat quod motus rectus sit corporum mixtorum, hoc erit secundum naturam simplicis corporis dominantis in mixtione. Cum igitur corpus simplex sit naturaliter prius mixto, consequens est quod motus circularis est proprius et naturalis alicuius corporis simplicis, quod est prius corporibus elementaribus quae sunt hic apud nos. Et ita ex his patet quod, praeter substantias corporales quae hic sunt apud nos, nata est esse quaedam substantia corporalis, quae est dignior et prior omnibus corporibus quae sunt apud nos. But a prior motion naturally belongs to a prior body. Now straight motion naturally belongs to some one or other of the simple bodies, as fire is moved upward and earth downward and toward the middle. And if it happens that a straight motion is found in mixed bodies, that will be due to the nature of the simple body predominant in it. Since, therefore, a simple body is naturally prior to the mixed, the consequence is that circular motion is proper and natural to some simple body which is prior to the elementary bodies that exist here among us. Thus it is clear from these facts that besides the bodily substances that exist here among us, there must be some bodily substance which is nobler and prior to all the bodies that exist among us. Videtur autem esse falsum quod nulla linea recta sit perfecta. Si enim perfectum est quod habet principium, medium et finem, ut supra habitum est, videtur quod linea recta finita, quae habet principium et medium et finem, sit perfecta. 42. But the assertion that no straight line is perfect seems to be false. For if the perfect is what has a beginning, middle and end, as we held above, it seems that a straight finite line, which has beginning, middle and end, is perfect. Sed dicendum est quod ad hoc quod aliquid sit perfectum partialiter, oportet quod habeat principium, medium et finem in seipso: sed ad rationem perfecti simpliciter, requiritur quod non sit aliquid extra ipsum. Et hic modus perfectionis competit primo et supremo corpori, quod est omnium corporum contentivum: et secundum hunc modum linea recta dicitur esse imperfecta, circularis vero perfecta. But it should be stated that in order for something to be partially perfect it must have the beginning, middle and end in itself; but to be completely perfect it is required that there be nothing outside it. And this mode of perfection belongs to the first and supreme body which contains all bodies; and with respect to this mode a straight line is said to be imperfect and a circular line perfect. Item videtur quod etiam secundum hunc modum aliqua linea recta sit perfecta: quia diameter caeli non potest additionem accipere. Yet it seems that even according to this mode some straight lines are perfect, because the diameter of a circle cannot suffer addition. Sed dicendum est quod hoc ei accidit inquantum est in tali materia, non autem hoc habet ex hoc quod est linea recta: secundum hoc enim non impediretur ne ei possit additio fieri. Sed circulus ex propria ratione circuli habet quod non sit additionis susceptivus. But it must be said that this happens to it insofar as it is in such and such a matter, and not insofar as it is a straight line, from which aspect there is nothing to prevent additions being made. But a circle, precisely as circle, cannot suffer such addition. Videtur quod secundum hoc concludi non possit quod motus circularis sit perfectus: additionem enim recipit, cum sit continuus et sempiternus, secundum Aristotelem. 43. But it seems that, if this is so, one cannot conclude that circular motion is perfect, because it does receive addition, since it is continuous and eternal, according to Aristotle. Ad quod dicendum est quod una circulatio habet complementum suae speciei, cum redierit ad principium a quo incoepit. Unde non fit additio ad eandem circulationem: sed quod sequitur, ad aliam circulationem pertinet. To this it should be said that one revolution is complete in species when it returns to the beginning from which it started. Hence no addition is being made to the same revolution, but whatever follows pertains to another revolution. Item, si hoc solum perfectum dicitur, cui non potest fieri additio, sequitur quod neque homo neque aliquid aliud finitum in corporibus sit perfectum, cum eis possit additio fieri. Yet if only a thing to which no addition can be made is to be called perfect, it follows that neither man nor any finite thing in bodies is perfect, since additions can be made to them. Et dicendum quod huiusmodi dicuntur esse perfecta secundum speciem, inquantum non potest eis fieri additio alicuius quod pertineat ad rationem speciei ipsorum: lineae autem rectae fit additio eius quod pertinet ad speciem suam, et pro tanto dicitur imperfecta inquantum est linea. And it should be answered that things of this kind are said to be perfect with respect to their species, inasmuch as they can suffer no addition of anything pertaining to the notion of their species; but to a straight line can be added something that pertains to its species, and to that extent it is said to be imperfect insofar as it is a line. Praeterea videtur quod circulus non sit perfectus. Perfectum enim est in magnitudinibus quod habet tres dimensiones: hoc autem lineae circulari non competit. But still it seems that a circle is not perfect. For a perfect thing among magnitudes is something having three dimensions; which our circular line certainly lacks. Et dicendum est quod linea circularis non est simpliciter magnitudo perfecta, quia non habet quidquid pertinet ad rationem magnitudinis: est tamen quoddam perfectum in linea, quia linealiter aliquid ei addi non potest. To this it should be responded that a circular line is not an absolutely perfect magnitude, because it does not have everything that pertains to the notion of a magnitude, Yet it is perfect in the realm of lines, because linearly something cannot be added to it. Videtur etiam falsum esse quod perfectum sit prius imperfecto. Simplex enim est prius composito, cum tamen compositum se habeat ad simplicia ut perfectum ad imperfecta. Ad quod dicendum quod perfectum ad imperfectum se habet sicut actus ad potentiam: qui quidem simpliciter est prior potentia in diversis; in uno autem et eodem, quod movetur de potentia ad actum, potentia est prior actu tempore, sed actus est prior secundum naturam; quia scilicet hoc est quod primo et principaliter natura intendit. Non autem philosophus hic intendit quod perfectum sit prius imperfecto in uno et eodem, sed in diversis: nec etiam quod sit prius tempore, sed natura, sicut expresse dicit. 44. It also seems false that the perfect is prior to the imperfect. For the simple is prior to the composite and yet the latter is to the former as perfect to imperfect. To this it must be said that perfect is to imperfect as act to potency, and simply speaking, act is prior to potency in things that are diverse, although in one and the same thing that is moved from potency to act, potency is prior to act in time, but act is prior to potency according to nature, for this is what nature intends first and principally. Now the Philosopher does not mean here that the perfect is prior to the imperfect in one and the same thing, but in diverse things, nor does he intend to say that it is prior in time but in nature, as he expressly states. Item, videtur quod philosophus inconvenienter argumentetur. Procedit enim ex perfectione lineae circularis ad probandum perfectionem circularis motus; ex cuius perfectione procedit ad probandum perfectionem circularis corporis; et sic videtur eius probatio esse circularis, quia linea circularis non videtur esse alia quam quae est ipsius corporis quod circulariter movetur. Et dicendum est quod motus circularis probatur esse perfectus ex perfectione lineae circularis absolute; ex perfectione autem motus circularis in communi, probatur hoc corpus quod circulariter movetur, esse perfectum; et sic non proceditur ab eodem in idem, sed ex communi ad proprium. 45. Moreover it seems that the Philosopher is arguing in an unsuitable manner. For he proceeds from the perfection of a circular line to prove the perfection of a circular motion, and from the latter perfection he goes on to prove the perfection of a circular body. And so his proof seems to be circular, because a circular line does not seem to be anything other than that of the very body that is being moved circularly. And it should be said that a circular motion is proved to be perfect on account of the perfection of the circular line absolutely; then from the perfection of circular motion in common one proves that this body which is moved circularly is perfect. Thus one does not go from the same to the same, but from common to proper. Quartam rationem ponit ibi: et utique si quis etc.: quae quidem procedit ex duabus propositionibus suppositis. Quarum prima est, quod omnis motus simplex aut est secundum naturam, aut praeter naturam. Secunda est, quod motus qui est praeter naturam uni corpori, est alii corpori secundum naturam; sicut patet in motu qui est sursum, qui est secundum naturam igni et praeter naturam terrae; et in motu qui est deorsum, qui est naturalis terrae et praeter naturam igni. Manifestum est autem quod motus circularis inest alicui corpori, quod ad sensum circulariter movetur. Et si quidem talis motus sit ei naturalis, habebimus propositum, scilicet quod praeter quatuor elementa sit quoddam aliud corpus, quod circulariter movetur. Si autem motus circularis sit praeter naturam corpori quod circulariter fertur, sequitur ex praemissa suppositione quod sit alicuius alterius corporis secundum naturam: quod consequenter erit aliud in natura a quatuor elementis. 46. The fourth argument is given at [25], and it proceeds from two assumptions. The first is that every simple motion is either according to nature or outside nature. The second is that a motion which is outside nature for one body is according to nature for another, as is clear in the upward motion which, for fire, is according to nature, and for earth is outside nature; and in the downward motion which is natural to earth, but outside nature for fire. Now it is manifest that a circular motion is present in some body, which the senses observe is moved circularly. And if such a motion is natural to it, we will have the conclusion, namely, that, besides the four elements, there is an additional body which is moved circularly. But if the circular motion is outside the nature of the body that is moved circularly, it follows from the foregoing assumption that for some other body it is according to nature, which body, consequently, will be of a different nature from the four elements. Videtur autem Aristoteles sibi ipsi esse contrarius: nam supra probavit quod motus circularis non est praeter naturam corpori quod circulariter fertur, hic autem supponit contrarium. 47. Aristotle here seems to be at odds with himself, for above he proved that circular motion is not outside the nature of the body in circular motion, but here he supposes the contrary. Dicunt igitur quidam quod philosophus supra accepit praeter naturam pro eo quod est contra naturam: sic enim oportet quod motus contra naturam alicuius corporis, sit contrarius motui etiam naturali eiusdem, ut supra procedebat. Hic autem accipit praeter naturam communius, secundum quod praeter naturam idem est quod non secundum naturam. Sic autem in se comprehendit tam id quod est contra naturam, quam id quod est supra naturam: et hoc modo supponit hic quod aliquod corpus potest circulariter praeter naturam moveri; sicut dictum est supra quod ignis in sua sphaera circulariter movetur praeter naturam, delatus a motu caeli. Accordingly some say that above the Philosopher was taking "outside nature" in the sense of "against nature" — for then a motion against the nature of some body would also be contrary to its natural motion, as he proceeded above. But here he takes "outside nature" in the more general sense of "not according to nature." Thus it includes both what is against nature and what is above nature, and it is in this sense that he assumes here that a body can be moved circularly outside its nature, just as it was said above that fire in its sphere is moved circularly outside its nature under the influence of the motion of the heavens. Sed hoc videtur esse contra intentionem Aristotelis. Eodem enim modo videtur utrobique accipere praeter naturam: quia tam hic quam supra exemplificat de motu qui est sursum et deorsum, qui est uni corpori contra naturam et alteri secundum naturam. Et ideo dicendum est, et melius, quod Aristoteles in prima ratione probavit quod aliquod corpus secundum naturam circulariter movetur. Et quia posset aliquis dicere quod corpus quod videtur circulariter moveri, movetur hoc motu contra naturam, dupliciter contra hoc argumentatur: uno modo ostendendo quod iste motus non est contra naturam, ut patet in secunda ratione et etiam in tertia; alio modo ostendendo quod etiam si moveatur contra naturam, adhuc sequitur esse aliud corpus, quod secundum naturam movetur circulariter. Sic ergo quod supra negavit secundum veritatem propriae opinionis loquens, hic negat quasi utens suppositione adversariorum. But this seems to be against the intention of Aristotle. For he seems to take "outside nature" in the same sense in both cases, because both here and above he uses the example of motion which is upward and downward, which is against nature for one body, and according to nature for another. Therefore it is better to say that Aristotle in the first argument proved that some body is being moved circularly according to nature. And because someone could say that that body which is seen to be moved circularly is being moved against nature by this movement, he argues against this in two ways: in one way, by showing that that motion is not against nature, as is clear in the second argument and also in the third; in another way, by showing that, even if it is being moved against nature, it still follows that there is some other body which is moved circularly according to nature. Consequently what he denied above when speaking according to the truth of his own opinion, he here denies by using, so to speak, the assumptions of his adversaries. Item, non videtur sequi quod, si aliquis motus sit praeter naturam alicui corpori, quod sit alteri corpori naturalis. Potest enim ignis, vel quodcumque aliud corpus, multiformiter moveri: nec tamen propter hoc oportet quod huiusmodi motus omnes sint naturales aliquibus corporibus. 48. Likewise it does not seem to follow that, if some motion is outside nature for one body, it is natural to some other body. For fire or any other body can be moved in a number of ways — yet this does not prove that such motions are natural to certain bodies. Est autem advertendum quod philosophus hic loquitur de simplici motu, ad quem natura corporis simplicis inclinat sicut ad aliquid unum: motus autem diversimode variati magis videntur ex arte dispositi, quae potest esse principium diversorum. Est etiam considerandum quod, licet motus qui est alicui corpori praeter naturam, sit alteri corpori secundum naturam, non tamen oportet quod omne corpus cui est aliquis motus secundum naturam, habeat aliquem motum praeter naturam: quia omne corpus quod est susceptivum alienae impressionis, habet aliquid sibi proprium et connaturale; non autem omne corpus potest extraneam impressionem recipere, ut sic possit naturalem motum habere. But it should be noted that the Philosopher is here speaking of simple motion, to which the nature of a simple body is inclined as to one definite thing, whereas motions diversely various seem to be rather brought about by art, which can be a principle of diverse things. It should also be considered that, although a motion which for one body is beside nature is according to nature for another, yet it is not necessary that every body for which some motion is natural should have a motion that is beside nature: for every body which can suffer an impression from without has something proper and connatural to it, yet not every body can receive an impression from without so as to be able to have a natural motion. Quintam rationem ponit ibi: adhuc autem etc., quae talis est. Conclusum est ex praemissa ratione quod si corpus quod ad sensum circulariter movetur, moveatur praeter naturam, oportet quod talis motus sit alteri corpori secundum naturam. Quod quidem si concedatur, scilicet quod circularis motus sit alicui corpori secundum naturam, manifestum est quod erit aliquod corpus simplex et primum quod circulariter movetur, propter simplicitatem et prioritatem circularis motus, ut ex praemissis rationibus patet, sicut ignis movetur sursum et terra deorsum. Si autem non concedatur processus praecedentis rationis, sed dicatur quod omnia quae moventur circulariter secundum peripheriam, idest secundum circumferentiam, moventur praeter naturam, ita quod hic motus nulli corpori sit secundum naturam: hoc videtur esse mirabile, immo omnino irrationabile. Ostensum est enim in VIII Physic. quod solum motum circularem contingit esse continuum et sempiternum: irrationabile autem est quod id quod est sempiternum, sit praeter naturam, et motus non sempiternus sit secundum naturam. Videmus enim quod ea quae sunt praeter naturam, citissime transeunt et corrumpuntur, sicut calefactio aquae et proiectio lapidis in altum: ea vero quae sunt secundum naturam, videntur diutius permanere. Sic ergo oportet omnino motum circularem esse alicui corpori naturalem. 49. The fifth argument is at [26], and it is this. The conclusion of the foregoing argument was that if a body observed to be in circular motion is being moved outside its nature, then such a motion must be according to nature for some other body. And if this is granted, namely, that circular motion is according to nature for some body, then it is clear that there will be some first and simple body which is being moved circularly, on account of the simplicity and priority of circular motion, as is plain from the foregoing arguments, just as fire is moved upward and earth downward. But if the procedure of the foregoing argument is not admitted, and it is stated rather that all things in circular motion with respect to a periphery, i.e., a circumference, are being moved outside their nature, in such a way that this motion is not natural to any body, then such a thing seems to be marvelous and, indeed, wholly unreasonable. For it was proved in Physics VIII that only circular motion can be continuous and eternal. Now it is unreasonable that what is eternal should be outside nature, and that a non-eternal motion should be according to nature. For we see that things which are outside nature quickly pass and cease to be, as in the case of the heat of water and the projecting of a stone into the air, while things that are according to nature are seen to last a longer time. Thus it is wholly necessary that circular motion be natural to some body. Si ergo istud corpus quod videmus circulariter ferri, est de natura ignis, ut quidam dicunt, motus iste erit ei praeter naturam, sicut et motus qui est deorsum: videmus enim quod motus naturalis ignis est sursum secundum rectam lineam. Et sic, sicut motus qui est deorsum est alteri corpori naturalis, scilicet terrae, ita erit motus circularis alicui alii corpori naturalis. If therefore the body which is observed to be carried along circularly is of the nature of fire, as some say, that motion will be beside its nature, just as a downward motion is. For we see that the natural motion of fire is upward according to a straight line. Accordingly, just as a downward motion is natural for another body, namely, earth, so a circular motion will be natural to some other body. Ultimo autem epilogando concludit, quod si aliquis ex omnibus praemissis syllogizaverit per modum praedictum, credet, idest firmiter assentiet, quod sit aliquod corpus praeter corpora quae sunt hic circa nos (idest quatuor elementa et ex his composita), separatum ab eis, et in natura tanto habens nobiliorem naturam, quanto est magis elongatum secundum loci distantiam ab his quae sunt hic: corpora enim continentia in universo se habent ad corpora contenta sicut forma ad materiam et actus ad potentiam, ut dictum est in IV Physic. 50. Finally, in summary, he concludes that if someone should reason from all the foregoing in the aforesaid manner, he will believe, i.e., firmly assent, that there is a body over and above the bodies which exist among us (i.e., the four elements and composites of them), a body that is separated from them and of a nature that is more noble than they to the extent that it is farther separated from them in space. For in the universe the bodies that contain are to contained bodies as form to matter, and act to potency, as was said in Physics IV.
Lecture 5: Difference of the body moved circularly as to light and heavy
Chapter 3 Ἐπεὶ δὲ τὰ μὲν ὑπόκειται τὰ δ' ἀποδέδεικται τῶν εἰρημένων, φανερὸν ὅτι οὔτε κουφότητα οὔτε βάρος ἔχει σῶμα ἅπαν, 28 In consequence of what has been said, in part by way of assumption and in part by way of proof, it is clear that not every body either possesses lightness or heaviness. δεῖ δὲ ὑποθέσθαι τί λέγομεν τὸ βαρὺ καὶ τὸ κοῦφον, νῦν μὲν ἱκανῶς ὡς πρὸς τὴν παροῦσαν χρείαν, ἀκριβέστερον δὲ πάλιν, ὅταν ἐπισκοπῶμεν περὶ τῆς οὐσίας αὐτῶν. Βαρὺ μὲν οὖν ἔστω τὸ φέρεσθαι πεφυκὸς ἐπὶ τὸ μέσον, κοῦφον δὲ τὸ ἀπὸ τοῦ μέσου, 29 As a preliminary we must explain in what sense we are using the words 'heavy' and 'light', sufficiently, at least, for our present purpose: we can examine the terms more closely later, when we come to consider their essential nature. Let us then apply the term 'heavy' to that which naturally moves towards the centre, and 'light' to that which moves naturally away from the centre. βαρύτατον δὲ τὸ πᾶσιν ὑφιστάμενον τοῖς κάτω φερομένοις, κουφότατον δὲ τὸ πᾶσιν ἐπιπολάζον τοῖς ἄνω φερομένοις. 30 The heaviest thing will be that which sinks to the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward. Ἀνάγκη δὴ πᾶν τὸ φερόμενον ἢ κάτω ἢ ἄνω ἢ κουφότητ' ἔχειν ἢ βάρος ἢ ἄμφω, μὴ πρὸς τὸ αὐτὸ δέ πρὸς ἄλληλα γάρ ἐστι βαρέα καὶ κοῦφα, οἷον ἀὴρ πρὸς ὕδωρ, καὶ πρὸς γῆν ὕδωρ. Τὸ δὲ κύκλῳ σῶμα φερόμενον ἀδύνατον ἔχειν βάρος ἢ κουφότητα οὔτε γὰρ κατὰ φύσιν οὔτε παρὰ φύσιν ἐνδέχεται αὐτῷ κινηθῆναι ἐπὶ τὸ μέσον ἢ ἀπὸ τοῦ μέσου. Κατὰ φύσιν μὲν γὰρ οὐκ ἔστιν αὐτῷ ἡ ἐπ' εὐθείας φορά μία γὰρ ἦν ἑκάστου τῶν ἁπλῶν, ὥστ' ἔσται τὸ αὐτὸ τῶν οὕτω τινὶ φερομένων. Παρὰ φύσιν δ' ἐνεχθέντος, εἰ μὲν ἡ κάτω (270a.) παρὰ φύσιν, ἡ ἄνω ἔσται κατὰ φύσιν, εἰ δ' ἡ ἄνω παρὰ φύσιν, ἡ κάτω κατὰ φύσιν ἔθεμεν γὰρ τῶν ἐναντίων ᾧ ἡ ἑτέρα παρὰ φύσιν, τὴν ἑτέραν εἶναι κατὰ φύσιν. Now, necessarily, everything which moves either up or down possesses lightness or heaviness or both—but not both relatively to the same thing: for things are heavy and light relatively to one another; air, for instance, is light relatively to water, and water light relatively to earth. The body, then, which moves in a circle cannot possibly possess either heaviness or lightness. For neither naturally nor unnaturally can it move either towards or away from the centre. Movement in a straight line certainly does not belong to it naturally, since one sort of movement is, as we saw, appropriate to each simple body, and so we should be compelled to identify it with one of the bodies which move in this way. Suppose, then, that the movement is unnatural. In that case, if it is the downward movement which is unnatural, the upward movement will be natural; and if it is the upward which is unnatural, the downward will be natural. For we decided that of contrary movements, if the one is unnatural to anything, the other will be natural to it. Ἐπεὶ δ' εἰς τὸ αὐτὸ φέρεται τὸ ὅλον καὶ τὸ μόριον κατὰ φύσιν, οἷον πᾶσα γῆ καὶ μικρὰ βῶλος, συμβαίνει πρῶτον μὲν μήτε κουφότητ' ἔχειν αὐτὸ μηδεμίαν μήτε βάρος (ἢ γὰρ ἂν πρὸς τὸ μέσον ἢ ἀπὸ τοῦ μέσου ἠδύνατο φέρεσθαι κατὰ τὴν ἑαυτοῦ φύσιν), ἔπειθ' ὅτι ἀδύνατον κινηθῆναι τὴν κατὰ τόπον κίνησιν ἢ ἄνω ἢ κάτω κατασπώμενον οὔτε γὰρ κατὰ φύσιν ἐνδέχεται κινηθῆναι κίνησιν αὐτῷ ἄλλην οὔτε παρὰ φύσιν, οὔτ' αὐτῷ οὔτε τῶν μορίων οὐδενί ὁ γὰρ αὐτὸς λόγος περὶ ὅλου καὶ μέρους. But since the natural movement of the whole and of its part of earth, for instance, as a whole and of a small clod—have one and the same direction, it results, in the first place, that this body can possess no lightness or heaviness at all (for that would mean that it could move by its own nature either from or towards the centre, which, as we know, is impossible); and, secondly, that it cannot possibly move in the way of locomotion by being forced violently aside in an upward or downward direction. For neither naturally nor unnaturally can it move with any other motion but its own, either itself or any part of it, since the reasoning which applies to the whole applies also to the part.
Postquam philosophus ostendit quod est corpus quoddam aliud a corporibus quae sunt hic, scilicet a quatuor elementis et his quae componuntur ex eis, hic ostendit differentiam huius corporis ad corpora quae sunt hic. 51. After showing that there is a body distinct from those that are here, namely, from the four elements, and from things composed of them, the Philosopher here shows the difference of this body from those which exist here. Et primo per comparationem ad motum localem; secundo secundum alios motus, ibi: similiter autem rationabile et cetera. First by comparing them with respect to local motion; Secondly, with respect to other motions (L. 6);
Circa primum tria facit: About the first he does three things: primo proponit quod intendit;
secundo ostendit propositum, ibi: oportet autem supponere etc.;
tertio excludit quandam obviationem, ibi: quoniam autem in idem feruntur et cetera.
First he proposes what he intends;
Secondly, he proves the proposition, at 52;
Thirdly, he dismisses an objection, at 56.
Dicit ergo primo quod, quia eorum quae dicta sunt quaedam sunt supposita (scilicet quod unum uni sit contrarium, et quod sint solae duae simplices magnitudines, scilicet recta et circularis, et si qua alia sunt huiusmodi), quaedam autem sunt demonstrata ex quibusdam praemissis (puta quod sint tres motus simplices, et quod motus circularis sit naturalis alicui corpori quod est aliud in natura a corporibus quae sunt hic), manifestum potest esse ex praedictis quod totum corpus illud quod circulariter movetur, non habet gravitatem neque levitatem, quae sunt principia quorundam motuum localium. He says therefore first [28] that, since some of the foregoing statements were supposed (namely, that one thing has one contrary, and that there are but two simple magnitudes, the straight line and the circle, and any other such suppositions) and others were demonstrated from certain premises (for example, that there are three simple motions, and that circular motion is natural to some body which is different in nature from the bodies that exist here), it can be plain from the foregoing that that entire body which is being moved circularly has neither heaviness nor lightness, which are principles of certain local motions. Deinde cum dicit: oportet autem supponere etc., ostendit propositum. Et quia principium demonstrationis est quod quid est, ut dicitur in libro Poster., 52. Then at [29] he manifests his proposition. And because the principle of demonstration is "that which something is," as is said in Post. Anal. II, primo supponit definitiones gravis et levis;
secundo ex his argumentatur ad propositum, ibi: necesse autem et cetera.
he first supposes the definitions of heavy and light, at 52;
Secondly, from these he argues to his proposition, at 54.
Circa primum duo facit: primo describit quid est grave et quid est leve; secundo describit quid est gravissimum et quid levissimum, ibi: gravissimum autem et cetera. Dicit ergo primo quod ad propositum ostendendum, oportet supponere quid dicamus grave et quid leve. Ideo autem dicit supponere, quia non perfecte investigat hic eorum definitiones; sed utitur eis ut suppositionibus, quantum sufficit ad necessitatem praesentis demonstrationis. Diligentius autem considerabitur de eis in quarto huius, ubi exponetur substantia, sive natura, ipsorum. Definit ergo grave, quod natum est moveri ad medium: leve autem, quod natum est moveri a medio. He says therefore first [29] that in order to prove the proposition we ought to suppose what it is that we call "heavy" and what "light." And he says "suppose" because he is not perfectly investigating their definitions here, but he uses them as suppositions to the extent that the present demonstration requires. But they will be considered more carefully in Book IV, where their "substance," or nature, will be explained. Accordingly, he defines heavy as "That which is apt to be moved to the middle," and the light as "that which is apt to be moved from the middle." Utitur autem tali modo definiendi, ut observet se a contrarietate Platonis, qui dicebat quod in mundo secundum se non est sursum et deorsum, propter rotunditatem mundi: corpus enim rotundum est undique uniforme. Dicebat autem quod sursum et deorsum est in mundo solum quoad nos, qui nominamus sursum id quod est supra caput nostrum, deorsum autem id quod est sub pedibus nostris: si autem essemus e contrario situati, e contrario nominaremus sursum et deorsum. Sic ergo Plato non accipit id quod est sursum et deorsum, secundum rei naturam, sed quoad nos. 53. He uses this mode of defining in order to keep himself from the contrary position of Plato, who said that in the world according to itself there is no "up" and "down," on account of the rotundity of the world: for a rotund body is everywhere uniform. He said that there is "up" and "down" in the world only with respect to us, who call "up" that which is above our head, and "down" that which is below our feet, so that if we were contrarily situated, we would call "up" and "down" in a contrary manner. Consequently, Plato does not admit an "up" and "down" in the very nature of things but only with respect to us. Aristoteles autem utitur his nominibus secundum communem modum loquendi, prout dicit in II Topic. quod nominibus utendum est ut plures: unde sursum et deorsum appellat in mundo id quod communiter ab hominibus appellatur sursum et deorsum. Nec tamen est distinctum solum quoad nos, sed etiam secundum naturam. Sicut enim in nobis distinguitur dextrum et sinistrum secundum diversam habitudinem ad motum animalem qui est secundum locum, ita sursum et deorsum determinatur in mundo secundum habitudinem ad motus simplicium corporum, quae sunt principales partes mundi. Et propter hoc ipse dicit quod sursum est locus in quem feruntur levia, deorsum autem locus in quem feruntur gravia. Et hoc rationabiliter: nam sicut in nobis nobilior pars est quae est sursum, ita in mundo corpora levia sunt nobiliora, quasi formaliora. Hic tamen, ut sine calumnia procedat ad propositum ostendendum, definit grave et leve per habitudinem ad medium. Aristotle, however, uses these names according to the common way of speaking, in keeping with his statement in Topics II, that names are to be used as they are used for the most part; hence he calls "up" and "down" in the world what are generally called "up" and "down" by men. Yet they are distinct not only with respect to us, but also according to nature. For just as we distinguish "right" and "left" in ourselves according to the diverse relationship to animal motion which is with respect to place, so too "up" and "down" in the world are distinguished with relation to the motions of the simple bodies which are the principal parts of the world. On this account he says that "up" is the place where light things are carried, and "down" the place where heavy things are carried. And this is reasonable: for just as in us the nobler part is that which is above, so in the world, light bodies are more noble, as if more formal. But here in order to proceed without calumny to the proof of the proposition, he defines "heavy" and "light" by their relation to the middle. Deinde cum dicit: gravissimum autem etc., definit gravissimum et levissimum. Et dicit quod gravissimum est quod substat omnibus quae deorsum feruntur: levissimum autem est quod supereminet omnibus quae sursum feruntur. Et est intelligendum inter ea quae sursum et deorsum feruntur: nam caelum non est levissimum, quamvis omnibus superemineat, quia non sursum fertur. Est autem attendendum quod hic iam utitur eo quod est sursum et deorsum, tanquam sursum et deorsum esse accipiat ad quae terminatur motus qui est a medio, vel ad medium. 54. Then at [30] he defines "heaviest" and "lightest." And he says that the heaviest is "that which stands under all things that are carried downward," while the lightest is "that which is at the top of all things that are carried up." And this must be understood as concerning those things that are carried upward and downward — for the heaven is not the lightest, even though it is above all, because it is not carried upward. Now it should be recognized that here he is already using "up" and "down" as though "up" and "down" arise as being where a motion from the middle, or to the middle, is terminated. Deinde cum dicit: necesse autem etc., ostendit propositum ex praemissis, dicens necessarium esse quod omne corpus quod fertur deorsum aut sursum, habeat absolute gravitatem, tanquam gravissimum, sicut terra, quae substat omnibus; aut quod habeat levitatem absolute, sicut ignis, qui superstat omnibus; aut habeat ambo, non quidem respectu eiusdem, sed respectu diversorum. Media enim elementa, scilicet aer et aqua, sunt ad invicem gravia et levia: sicut aer est levis per respectum ad aquam, quia superfertur ei, et eadem ratione aqua ad terram; aer vero ad ignem quidem est gravis, quia substat ei, et similiter aqua ad aerem. Corpus autem quod circulariter movetur, impossibile est quod habeat gravitatem aut levitatem. Neque enim potest moveri ad medium vel a medio secundum naturam, neque praeter naturam. 55. Then at [31] he proves his proposition from the foregoing, and says that every body carried up or down must have heaviness absolutely, as does the heaviest, namely, earth, which stands under all, or must have lightness absolutely, as does fire, which is above all, or must have both, not in respect to the same, but in respect to diverse things. For the intermediate elements, namely, air and water, are mutually heavy and light, as air is light with respect to water, because it is carried above it, and the same is true of water with respect to earth; meanwhile, air with respect to fire is heavy, because it exists under it, and similarly water with respect to air. But the body that is moved circularly can have neither heaviness nor lightness. For it cannot be moved to the middle or from the middle, either according to nature, or outside nature. Et quod non possit secundum naturam hoc modo moveri, manifestat per hoc quod motus rectus, qui est ad medium vel a medio, est naturalis quatuor elementis: dictum est autem supra quod unus motus est naturalis uni simplicium corporum: ergo sequeretur quod corpus quod circulariter fertur, sit eiusdem naturae cum aliquo corporum quod movetur motu recto; cuius contrarium est supra ostensum. Similiter non potest dici quod motus rectus praeter naturam conveniat corpori quod circulariter fertur. Quia si unus contrariorum motuum inest alicui corpori praeter naturam, alius motus erit ei secundum naturam, ut ex supra dictis patet. Si ergo motus deorsum sit quinto corpori praeter naturam, motus sursum erit ei secundum naturam, et e converso. Utrumque autem eorum est falsum, ut patet per praecedentem rationem. Sequitur ergo quod corpus quintum, quod circulariter fertur, non moveatur a medio vel ad medium, neque secundum naturam neque praeter naturam. Omne autem corpus habens gravitatem aut levitatem, movetur uno horum motuum secundum naturam, et altero praeter naturam. Ergo corpus quintum neque habet gravitatem neque levitatem. And, that it cannot be so moved according to nature, is clear from the fact that a straight motion, which is to the middle, or from the middle, is natural to the four elements. But it was said above that one motion is natural to one of the simple bodies. Therefore it would follow that the body which is moved circularly would be of the same nature as one of the bodies that is moved in a straight line, the contrary of which was proved above. Similarly it cannot be said that a straight motion outside nature belongs to the body that is moved circularly. For if one of a pair of contrary motions is present in a body outside its nature, the other will be for it according to nature, as is plain from what has been said above. Therefore, if downward motion is outside nature for the fifth body, upward motion will be for it according to nature, and conversely. But both are false, as is plain from the preceding argument. It follows therefore that the fifth body, which is carried circularly, is not carried from the middle or to the middle, either according to nature or outside its nature. But every body having lightness or heaviness is moved according to nature by one of these motions, and outside its nature by the other. Therefore, the fifth body has neither heaviness nor lightness. Deinde cum dicit: quoniam autem in idem etc., excludit quandam obviationem. Dicebant enim quidam quod partes elementorum sunt corruptibiles, ita quod extra proprium locum existentes, moventur naturaliter motu recto: ipsa autem elementa secundum suam totalitatem sunt incorruptibilia, et nunquam extra proprium locum esse possunt: unde in locis suis moventur circulariter. Et sic corpus quod circulariter movetur in suo loco secundum suam totalitatem, non oportet quod careat gravitate et levitate. 56. Then at [32] he excludes a certain objection. For some said that the parts of the elements are perishable, so that when existing outside their proper place they are naturally moved with a straight motion, while the elements themselves according to their totality are imperishable and cannot ever be outside their proper place — whence they are being moved circularly in their places. Consequently a body that is being moved circularly in its place according to its totality need not lack heaviness and lightness. Ad hoc igitur excludendum, philosophus proponit quod in eundem locum feruntur naturaliter pars et totum, sicut tota terra et unus bolus eius. Et hoc patet ex quiete: quia unumquodque movetur naturaliter ad locum in quo quiescit naturaliter, in eodem autem loco quiescit naturaliter tota terra et pars eius. Unde manifestum est quod tota terra habet inclinationem naturalem quod moveatur ad medium, si esset extra suum locum. To exclude this the Philosopher proposes that part and whole are naturally carried to the same place, as, for example, in the case of the whole earth and one clod. And this is clear from the state of rest: for each thing is naturally moved to the place in which it is naturally at rest, and it is in the same place that the whole earth and part of it naturally rest. Hence it is clear that the whole earth has a natural inclination to be moved to the center, should it be outside its own place. Sic ergo ex praemissis duo sequuntur. Quorum primum est quod totum corpus quintum nullam levitatem neque gravitatem habet: quia, ut patet ex ratione praedicta, moveretur naturaliter ad medium vel a medio. Secundo sequitur ex suppositione nunc inducta, quod si aliqua pars detraheretur a corpore caelesti, non moveretur neque sursum neque deorsum: quia cum sit eadem ratio de toto et partibus, non convenit neque toti quinto corpori neque alicui parti eius quod moveatur vel secundum naturam vel praeter naturam alio motu quam circulari. Therefore from the foregoing two things follow: The first of these is that the whole fifth body has no lightness or heaviness — for, as is clear from the aforesaid reason, it would be moved naturally to or from the middle. Secondly, it follows from the supposition now introduced that, if any part were detached from a heavenly body it would be moved neither up nor down, for, since the whole and part are of the same nature, it does not befit either the entire fifth body, or any part of it, to be moved either according to its nature or outside it with any motion other than the circular.
Lecture 6:
The fifth body not subject to other motionsChapter 3 cont. Ὁμοίως δ' εὔλογον ὑπολαβεῖν περὶ αὐτοῦ καὶ ὅτι ἀγένητον καὶ ἄφθαρτον καὶ ἀναυξὲς καὶ ἀναλλοίωτον, 33 It is equally reasonable to assume that this body will be ungenerated and indestructible and exempt from increase and alteration, διὰ τὸ γίγνεσθαι μὲν ἅπαν τὸ γιγνόμενον ἐξ ἐναντίου τε καὶ ὑποκειμένου τινός, καὶ φθείρεσθαι ὡσαύτως ὑποκειμένου τέ τινος καὶ ὑπ' ἐναντίου καὶ εἰς ἐναντίον, καθάπερ ἐν τοῖς πρώτοις εἴρηται λόγοις τῶν δ' ἐναντίων καὶ αἱ φοραὶ ἐναντίαι. Εἰ δὴ τούτῳ μηδὲν ἐναντίον ἐνδέχεται εἶναι διὰ τὸ καὶ τῇ φορᾷ τῇ κύκλῳ μὴ εἶναι ἄν τιν' ἐναντίαν κίνησιν, ὀρθῶς ἔοικεν ἡ φύσις τὸ μέλλον ἔσεσθαι ἀγένητον καὶ ἄφθαρτον ἐξελέσθαι ἐκ τῶν ἐναντίων ἐν τοῖς ἐναντίοις γὰρ ἡ γένεσις καὶ ἡ φθορά. 34 since everything that comes to be comes into being from its contrary and in some substrate, and passes away likewise in a substrate by the action of the contrary into the contrary, as we explained in our opening discussions. Now the motions of contraries are contrary. If then this body can have no contrary, because there can be no contrary motion to the circular, nature seems justly to have exempted from contraries the body which was to be ungenerated and indestructible. For it is in contraries that generation and decay subsist.
Postquam philosophus ostendit differentiam quinti corporis ad alia corpora quae sunt hic, ex parte levitatis et gravitatis, secundum quod corpora habent inclinationem ad motum localem; hic ostendit differentiam quinti corporis ad corpora quae sunt hic, secundum alios motus; ostendens scilicet quod illud corpus non subiicitur aliis motibus, quibus haec corpora subiiciuntur. 58. After having shown the difference between the fifth body and the other bodies that exist here from the standpoint of lightness and heaviness, according to which bodies have an inclination to local motion, the Philosopher here shows how the fifth body differs from bodies that exist here from the standpoint of other motions, and shows that the former is not subject to the other motions to which these bodies are subject. Et primo ostendit hoc per rationem;
secundo per signa, ibi: videtur autem et ratio et cetera.
First he shows this by an argument;
Secondly, by signs (L. 7);
Circa primum duo facit. With respect to the first he does two things: Primo proponit quod intendit: et dicit quod sicut dictum est de quinto corpore quod caret gravitate et levitate, similiter rationabile est aestimare de ipso quod sit ingenitum et incorruptibile et inaugmentabile et inalterabile, idest non subiectum generationi et corruptioni, neque augmento neque alterationi. Secundo ibi: propter fieri quidem etc., probat propositum:
First he proposes what he intends [33] and says that just as it has been pointed out above that the fifth body lacks heaviness and lightness, in like manner it is reasonable to believe that it is unproduced and imperishable, and incapable of increase and alteration, i.e., that it is not subject to generation and ceasing-to-be, or to growth or alteration. Secondly [34], he proves the proposition: et primo ostendit corpus caeleste esse ingenerabile et incorruptibile;
secundo quod est inaugmentabile, ibi: at vero et augmentabile etc.;
tertio quod non est alterabile, ibi: si autem est et inaugmentabile et cetera.
First he shows that the heavenly body is incapable of being generated or corrupted;
Secondly, that it cannot be increased (L. 7);
Thirdly, that it cannot be altered (also in L. 7).
Circa primum ponit talem rationem. Omne generabile fit ex contrario et subiecto quodam, sive materia: nam ex contrario fit aliquid sicut ex non permanente, ex subiecto autem sicut ex permanente, ut patet in I Physic. Et similiter etiam omne corruptibile corrumpitur existente aliquo subiecto. Est etiam omnis corruptio a contrario activo: omnis etiam corruptio terminatur in contrarium, sicut dictum est in primis sermonibus, idest in I Physic. Sed corpori quinto non est aliquid contrarium: ergo nec est generabile nec corruptibile. Mediam probat per hoc quod contrariorum contrarii sunt motus, sicut leve movetur sursum et grave deorsum: sed motui naturali quinti corporis, qui est motus circularis, nullus motus est contrarius, ut infra probabitur: ergo huic corpori nihil est contrarium. Et ita recte videtur natura fecisse, eximens hoc corpus a contrarietate, tanquam futurum, idest debens esse, ingenitum et incorruptibile. 59. With regard to the first he presents the following argument: Whatever can be generated comes to be from a contrary and a certain subject or matter — for something comes to be from a contrary as from something non-permanent, but from a subject as from something permanent, as is plain in Physics I. Likewise, every body that is perishable ceases to be while some subject [continues to] exist Also every case of ceasing-to-be is from a contrary active principle, for every ceasing-to-be is terminated at a contrary, as was said in the first discussions, i.e., in Physics I. But nothing is contrary to the fifth body. Therefore, it can be neither generated nor destroyed. He proves the middle [minor] proposition through the fact that the motions of contraries are contrary, as the light is moved upward and the heavy downward; but the fifth body's natural motion, which is circular motion, has no contrary motion, as will be proved later. Therefore nothing is contrary to this body. Thus nature seems to have acted rightly, exempting this body from contrariety as destined to be, i.e., having to be, unproduced and imperishable. Sed circa ea quae hic Aristoteles dicit, duplex consideratio occurrit: una quidem circa positionem eius, qua ponit corpus caeli esse ingenerabile et incorruptibile; alia autem est circa rationem ipsius. 60. But two thoughts come to mind regarding what Aristotle says here: one is about his assumption that the body of the heaven is incapable of being generated and destroyed; the other is about the reason for it. Sciendum est autem circa primum, quod quidam posuerunt corpus caeli esse generabile et corruptibile secundum suam naturam, sicut Ioannes grammaticus, qui dictus est Philoponus. Et ad suam intentionem adstruendam, primo utitur auctoritate Platonis, qui posuit caelum esse genitum et totum mundum. Secundo inducit talem rationem. Omnis virtus corporis finiti est finita, ut probatur in VIII Physic.: sed virtus finita non potest se extendere ad durationem infinitam (unde per virtutem finitam non potest aliquid moveri tempore infinito, ut ibidem probatur): ergo corpus caeleste non habet virtutem ut sit infinitum tempore. Tertio obiicit sic. In omni corpore naturali est materia et privatio, ut patet ex I Physic.: sed ubicumque est materia cum privatione, est potentia ad corruptionem: ergo corpus caeleste est corruptibile. Si quis autem dicat quod non est eadem materia caelestium corporum et inferiorum, obiicit in contrarium: quia secundum hoc oporteret quod materia esset composita, ex eo scilicet quod est commune utrique materiae, et ex eo quod facit diversitatem inter materias. Now it should be known, with regard to the first, that some supposed the body of the heaven to be generable and perishable according to its very nature, as did John the Grammarian, called Philoponus. And in support of his contention he uses first the authority of Plato who supposed that the heavens and the entire world were generated. Secondly, he presents this argument: Every power of a finite body is finite, as was proved in Physics VIII; but a finite power cannot extend itself unto infinite duration (that is why something cannot be moved for an infinite time through a finite power, as was proved in the same book); therefore, a heavenly body does not have the power to be infinite in time. Thirdly, he forms the following objection: In every natural body there is matter and privation, as is plain from Physics I; but wherever there is matter with privation, there is potency to cease to be; therefore, the heavenly body is perishable. And if anyone says that the matter of heavenly bodies is not the same as that of inferior bodies, he objects to the contrary — for, according to this, matter would have to be composite, made out of what is common to both matters, and out of what produces diversity between matters. Sed haec necessitatem non habent. Quod enim Plato posuit caelum genitum, non intellexit ex hoc quod est generationi subiectum, quod Aristoteles hic negare intendit: sed quod necesse est ipsum habere esse ab aliqua superiori causa, utpote multitudinem et distensionem in suis partibus habens; per quod significatur esse eius a primo uno causari, a quo oportet omnem multitudinem causari. 61. But these statements lack necessity. For the fact that Plato posited the heavens as generated was not drawn from an understanding that they were subject to generation, which Aristotle intends here to deny, but because it was necessary for them to have their existence from a higher cause, as composed of parts multiple and extended — which meant that their existence was caused by some one first thing, from which all multiplicity must be caused. Quod autem obiicit virtutem corporis caelestis esse finitam, solvit Averroes dicendo quod in corpore caelesti est virtus sive potentia ad motum secundum locum, non est autem virtus sive potentia ad esse, neque finita neque infinita. 62. The objection that the power of a heavenly body is finite Averroes solved by saying that in a heavenly body there is a power for local motion, but no power, either finite or infinite, respecting existence. Sed in hoc manifeste dixit contra Aristotelem, qui infra in hoc eodem libro ponit in sempiternis virtutem ad hoc quod sint semper. Fuit autem deceptus per hoc quod existimavit virtutem essendi pertinere solum ad potentiam passivam, quae est potentia materiae; cum magis pertineat ad potentiam formae, quia unumquodque est per suam formam. Unde tantum et tamdiu habet unaquaeque res de esse, quanta est virtus formae eius. Et sic non solum in corporibus caelestibus, sed etiam in substantiis separatis est virtus essendi semper. But in this he is clearly going against Aristotle who later on in the same book supposes in sempiternal things a power to exist forever. But Averroes was deceived by supposing that the power respecting existence pertains solely to the passive power, which is the potency of matter; but the truth is that it pertains more to the power of the form, because everything exists through its form. Hence a thing has as much and as long an existence as the power of its form. Thus there is a power to exist forever, not only in heavenly bodies, but also in separated substances. Dicendum est ergo quod id quod requirit virtutem infinitam, oportet esse infinitum. Infinitum autem, secundum philosophum in I Physic., pertinet ad quantitatem; ita quod id quod quantitate caret, neque finitum neque infinitum est. Motus autem quantitatem habet, quae mensuratur tempore et magnitudine, ut patet in VI Physic.: et ideo virtus quae potest in motum sempiternum, potest in effectum infinitum: et propter hoc talem virtutem oportet esse infinitam. Ipsum autem esse alicuius rei secundum se consideratum non est quantum: non enim habet partes, sed totum est simul. Accidit autem ei quod sit quantum, uno quidem modo secundum durationem, inquantum est subiectum motui et per consequens tempori, sicut esse rerum variabilium: unde virtus cuiuslibet rei corporalis cuius esse subiectum est variationi, non potest nisi in durationem finitam. Alio autem modo esse alicuius rei potest per accidens dici quantum, ex parte subiecti, quod habet determinatam quantitatem. Dicendum est ergo quod esse caeli non est subiectum variationi nec tempori: unde non est quantum quantitate durationis, et per consequens neque finitum neque infinitum. Est autem quantum secundum quantitatem corporis extensi; et secundum hoc est finitum. Sic igitur dicendum est quod virtus essendi corporis caelestis est finita: nec tamen sequitur quod sit ad essendum tempore finito; quia finitum et infinitum temporis accidit ipsi esse rei, quod non est subiectum varietati temporis. Non tamen posset huiusmodi virtus causare esse in infinita magnitudine, vel etiam in maiori quam sit magnitudo caelestis corporis. Therefore it should be said that whatever requires infinite power must be infinite. But the infinite, according to the Philosopher in Physics I, pertains to quantity, so that what lacks quantity is neither finite nor infinite. Now motion does have a quantity that is measured by time and magnitude, as is plain in Physics VI, and therefore the power which is capable of eternal motion is capable of an infinite effect — and consequently such a power must be infinite. But a thing's existence considered in itself is not a quantity, for it has no parts, but is entire and all at once. Rather it is accidental to it that it is quantified in one sense according to duration, insofar as it is subject to motion, and consequently to time, just as is the existence of changeable things. That is why the power of any bodily thing whose existence is subject to change cannot go beyond a finite duration. In another way the existence of a thing can be called quantified per accidens on the part of the subject, which has a definite quantity. Therefore it must be said that the existence of the heavens is not subject either to variation or time; hence it is not quantified by a quantity of duration, and consequently is neither finite nor infinite in this respect. But it is quantified according to the quantity of an extended body, and in this respect it is finite. Consequently. it must be said that the power of existing of a heavenly body is finite, but that does not mean that it is limited to existing in a finite time, because temporal finiteness or infinity are accidental to a thing's existence, which is not subject to the variation of time. Nevertheless a power of this kind could not cause existence in an infinite magnitude nor even in a magnitude greater than the magnitude of the heavenly body. Similiter tertium quod obiicit, Averroes solvit per interemptionem. Negat enim corpus caeleste habere materiam: sed dicit corpus caeleste esse subiectum actu ens, ad quod comparatur anima eius sicut forma ad materiam. Et si quidem intelligat quod corpus caeleste non habeat materiam secundum quod dicitur materia in ordine ad motum vel mutationem, verum dicit: sic enim etiam Aristoteles in VIII et XII Metaphys. ponit corpus caeleste habere materiam non ad esse sed ad ubi; quia scilicet non est subiecta transmutationi quae est secundum esse, sed ei quae est secundum ubi. Si vero intelligat quod corpus caeleste nullo modo habet materiam, vel quodcumque subiectum, manifeste dicit falsum. Patet enim quod corpus illud est actu ens: alioquin non ageret in haec inferiora. Omne autem quod est actu ens, vel est actus, vel est habens actum. Non potest autem dici quod corpus caeleste sit actus: quia sic esset forma subsistens, et esset aliquid intellectum in actu, non autem sensu apprehensum. Oportet ergo in corpore caelesti ponere aliquod subiectum suae actualitati. Similarly Averroes solves the third objection by destroying it. For he denies that a heavenly body has matter, but says that a heavenly body is a subject that is actual being, to which its soul is compared as form to matter. Now if in stating that a heavenly body does not have matter he should mean matter in relation to motion or change, then it is true — for thus does Aristotle also say in Physics VIII and Metaphysics XII, namely, that a heavenly body has matter not with respect to existence but to "where," for the simple reason that this matter is not subject to a change according to being but to one according to "where." But if he means that a heavenly body has matter in no way at all or no subject at all, then plainly he is wrong. For it is clear that that body is a being in act; otherwise it would not act on the lower bodies. But whatever is a being in act is either act itself, or has act. Now it cannot be said that a heavenly body is act, for then it would be a subsistent form, and something understood in act but not apprehended by sense. Therefore in a heavenly body there must be something which is the subject of its actuality. Non tamen oportet quod istud subiectum vel materia habeat privationem: quia privatio nihil aliud est quam absentia formae quae est nata inesse, huic autem materiae vel subiecto non est nata inesse alia forma, sed forma sua replet totam potentialitatem materiae, cum sit quaedam totalis et universalis perfectio. Quod patet ex hoc, quod virtus activa eius est universalis, non particularis sicut virtus inferiorum corporum; quorum formae, tanquam particulares existentes, non possunt replere totam potentialitatem materiae; unde simul cum una forma remanet in materia privatio formae alterius, quae est apta nata inesse. Sicut etiam videmus quod corpora inferiora sunt susceptiva diversarum figurarum: sed corpus caeli non est figurabile alia figura. Sic igitur in corpore caelesti non est privatio alicuius formae, sed solum privatio alicuius ubi. Unde non est mutabile secundum formam per generationem et corruptionem; sed solum secundum ubi. Ex quo patet quod materia caelestis corporis est alia et alterius rationis a materia inferiorum corporum, non quidem per aliquam compositionem, sicut Philoponus existimavit; sed per habitudinem ad diversas formas, quarum una est totalis et alia partialis: sic enim potentiae diversificantur secundum diversitatem actuum ad quos sunt. However this subject or matter does not need to have privation, for privation is nothing but the absence of a form which is apt to exist in the matter; but in this matter or subject there is no other form apt to be — rather its form fills out the entire potentiality of the matter, since it is a certain total and universal perfection. And this is clear from the fact that its active power is universal, and not particular like the power of the lower bodies, whose forms as being particular cannot exhaust the entire potentiality of the matter; hence, together with one form there remains in matter the privation of another form which is apt to be in it. Similarly, we see that the lower bodies are subject to diverse shapes, but the heavenly body not. Accordingly, in a heavenly body there is not privation of any form but only privation of some "where." Consequently, it is not changeable with respect to form through generation and ceasing to be, but only with respect to "where." From this it is plain that the matter of the heavenly body is distinct and of a different nature from the matter of lower bodies, not on account of some composition, as Philoponus supposed, but on account of their relationship to diverse forms, of which one is total and the other partial — for thus potencies are diversified, namely, according to the diversity of acts to which they are in potency. Manifestum est igitur ex his quod corpus caeli secundum suam naturam non est subiectum generationi et corruptioni, utpote primum in genere mobilium, et propinquissimum rebus immobilibus. Et inde est quod minimum habet de motu. Movetur enim solum motu locali, qui nihil variat intrinsecum rei. Et inter motus locales habet motum circularem, qui etiam minimum variationis habet: quia in motu sphaerico totum non mutat suum ubi subiecto, sed solum ratione, ut probatur in VI Physic.; sed partes mutant ubi diversum etiam subiecto. 64. Therefore it is manifest from the foregoing that the body of the heavens according to its nature is not subject to generation and ceasing-to-be, as being first in the genus of mobiles, and the closest to immobile things. That is why it has a minimum of motion. For it is moved only with local motion, which varies nothing intrinsic to a thing. And among local motions it has a circular motion, which also has a minimum of variation, because in spherical motion the whole does not vary its "where" as to subject, but only in conception, as was proved in Physics VI; but the parts change their "where" even as to subject. Non tamen dicimus secundum fidem Catholicam, quod caelum semper fuerit, licet dicamus quod semper sit duraturum. Nec hoc est contra demonstrationem Aristotelis hic positam: non enim dicimus quod incoeperit esse per generationem, sed per effluxum a primo principio, a quo perficitur totum esse omnium rerum, sicut etiam philosophi posuerunt. A quibus tamen in hoc differimus, quod illi ponunt Deum produxisse caelum coaeternum sibi; nos autem ponimus caelum esse productum a Deo secundum totam sui substantiam ab aliquo determinato principio temporis. However, we do not say according to the Catholic faith that the heavens always existed, although we say that they will endure forever. Nor is this against Aristotle's demonstration here, for we do not say that they began to be through generation, but through an efflux from the first principle, by whom is perfect the entire existence of all things, as even the philosophers posited. From whom, however, we differ in this, that they suppose God to have produced the heavens co-eternal to Himself, but we posit that the heavens were produced by God according to their whole substance at some definite beginning of time. Contra quod tamen obiicit Simplicius, Aristotelis Commentator, super hunc locum, tripliciter. Primo quidem quia Deus produxit caelum secundum suum esse, non per aliquid aliud additum: unde, cum esse suum sit aeternum et invariabile, semper caelum ab ipso processit. Item, si bonitas Dei est causa rerum, fuisset bonitas Dei otiosa et vacans antequam mundus esset, si ex aliquo determinato principio temporis incoepit. Item, omne quod incipit esse in aliqua determinata parte temporis cum prius non fuerit, hoc contingit ei ex ordine alicuius superioris motus, ex quo contingit quod hoc nunc incoepit et non prius; sicut homo incoepit esse nunc et non prius, secundum ordinem revolutionis caelestis corporis. Non est autem dare aliquam superiorem revolutionem aut motum ultra corpus caeleste. Non ergo potest dici quod corpus caeli ita nunc incoeperit quod prius non fuerit. 65. Against this, however, Simplicius, a commentator on Aristotle, at this passage, objects on three counts. First, since God produced the heavens, therefore, through His essence and not through something added, since His essence is eternal and unchanging, the heavens have always proceeded from Him. Again, if the goodness of God is the cause of things, the goodness of God would have been idle and disengaged before the world existed, if the latter began to exist from some definite beginning of time. Again, whatever begins to exist in some determined part of time after previously not existing, this happens to it from the ordination of some higher motion from which it happens that this being begins now and not before, as a man begins to be now and not previously, according to the order of the revolution of the heavenly body. But there is no higher revolution or motion beyond the heavenly body. Therefore it cannot be said that the body of the heavens began to be now, so as not to have been before. Sed haec necessitatem non habent. Quod enim primo dicitur, quod Deus agit per suum esse et non per aliquid superadditum, verum est: sed esse suum non est distinctum a suo intelligere, sicut in nobis, nec etiam a suo velle: unde producit secundum intelligere et velle suum. In his autem quae producuntur ab aliquo agente inquantum est intelligens et volens, oportet esse illud quod producitur, hoc modo sicut est intellectum a producente; non autem eo modo quo est ipse producens secundum suum esse. Unde, sicut non oportet quod id quod est productum a Deo producente secundum suum esse, sit in aliis conditionibus tale quale est esse divinum, sed quale est determinatum per eius intelligere; ita non est necessarium quod id quod est productum a Deo, sit tam diuturnum quantum Deus, sed quantum determinatum est per intellectum ipsius. But these lack necessity. For the first statement that God acts through His essence and not through something superadded is true, but His essence is not distinct from His understanding, as in us, nor from His willing. Hence He produces according to His understanding and His willing. Now in things produced by an agent acting in virtue of his understanding and will, that which is produced must be as it was understood by the producer, and not as the producer is in his being. Hence, just as what is produced by God acting through His essence does not have to be, in other respects, in the same way as the divine essence, but such as it is determined by His understanding, so too it is not necessary that what is produced by God be as long-lasting as God, but only to the degree determined by His understanding. Et hoc etiam potest dici circa quantitatem dimensivam caeli. Quod enim caelum habeat tantam quantitatem et non maiorem, provenit ex determinatione intellectus divini determinantis sibi talem quantitatem, et coaptantis ei naturam proportionatam tali quantitati: sicut etiam exemit ipsum a contrariis, ut esset ingenitum et incorruptibile, ut dicitur in littera. Quod enim dicit recte fecisse naturam, importat actionem intellectus agentis propter aliquem finem: non enim alia natura superior exemit eum a contrariis nisi divina. And this applies also to the dimensive quantity of the heavens. For the fact that the heavens have such-and-such a quantity, and no greater, is a result of a determination of the divine intellect determining such a quantity for them, and adapting to them a nature proportionate to such quantity, just as He frees them from contraries so that they may be ungenerated and incorruptible, as stated in the text. The phrase in the text that "nature acted rightly" implies the action of an intellect acting for an end, for it is no nature other than the divine that has freed them from contraries. Similiter, quod dicit bonitatem divinam fuisse vacantem et otiosam ante productionem mundi, non habet rationem. Otiosum enim dicitur quod non consequitur finem ad quem est: bonitas autem Dei non est propter creaturas. Unde creaturae essent otiosae si non consequerentur divinam bonitatem: divina autem bonitas non esset otiosa, etiam si nullam unquam creaturam produxisset. Similarly, the statement that the divine goodness would have been idle and disengaged before the production of the world does not have any weight. For a thing is called "idle" that does not attain the end for which it is. But the goodness of God is not for the sake of creatures. Hence creatures would be idle if they did not attain to the divine goodness, but the divine goodness would not be idle even if It never produced a creature. Similiter etiam quod tertio obiicit, locum habet in agente particulari, quod praesupponit tempus et in parte temporis aliquid facit: et ita oportet quod id quod fit, proportionetur ab agente et ad aliam partem temporis et ad totum tempus, vel etiam ad causam totius temporis. Sed nunc agimus de agente universali, quod producit ipsum totum tempus simul cum his quae sunt in tempore. Et ideo non habet hic locum ut quaeratur quare nunc et non prius: quasi praesupponatur alia pars temporis praecedens, vel aliqua alia causa universalior causans totum tempus. Sed habet hic locum quaestio, quare agens universale, scilicet Deus, voluit tempus non esse semper et ea quae sunt in tempore. Et hoc dependet ex determinatione intellectus ipsius: sicut et in domo artifex quantitatem alicuius partis domus accipit secundum proportionem ad aliam partem vel ad totam domum; sed quantitatem totius domus determinat secundum suum intellectum et voluntatem. Again, the third objection applies to a particular agent, which supposes time and works in time. In this way what comes to be must be proportioned by the agent both to some part of time, and to the whole of time, or even to the cause of the whole of time. But we are dealing now with a universal agent who produces the whole time together with the things in time. So there is no place here for the question of why now and not before, as though there were presupposed some other preceding part of time, or some more general cause producing all of time. But the pertinent question here is why the universal agent, namely, God, willed time and the things in time not always to exist. And this depends on a determination of His intellect, just as in a house the artisan determines the size of one part of the house in relation to another part or to the whole house, but the size of the entire house he himself determines according to his understanding and will. Restat autem alia consideratio circa demonstrationem Aristotelis, contra quam obiicit Ioannes grammaticus: quia si nihil generatur et corrumpitur nisi quod habet contrarium, cum substantiae non sit aliquid contrarium, quod maxime manifestum est in animalibus et plantis (similiter etiam nec figuris et relationibus est aliquid contrarium), nihil horum generabitur aut corrumpetur. 67. Another point remains to be considered about Aristotle's demonstration against which John the Grammarian objects: if nothing but what has a contrary can be generated and cease to be, then since there is no contrary of a substance, as is plain in animals and plants (similarly, nothing is contrary to a figure or a relation), none of these will be generated and cease to be. Respondet autem ad hoc Simplicius quod hoc est intelligendum de contrario communiter dicto, prout includit etiam contrarietatem privationis et speciei: sic enim Aristoteles loquitur de contrario in I Physic., quo nos remittit. Et hoc modo contrarium invenitur in omnibus praedictis, sicut informe est contrarium formato, et infiguratum figurato: privatio autem non habet locum in corporibus caelestibus, ut dictum est. To this Simplicius responds that this is to be understood about a contrary in the general sense as including even contrariety of privation and species, for that is Aristotle's meaning when he speaks of contraries in Physics I. And that is the way in which contrariety is found in all the foregoing, as the unformed is contrary to the formed, and the unfigured to the figured; but privation has no place in heavenly bodies, as has been said. Haec autem responsio, etsi sit vera, non tamen habet locum in proposito. Aristoteles enim dicit contrarietatem motuum localium respondere contrarietati corporum; cum tamen certum sit quod privationi non respondet aliquis motus localis. Unde dicendum est quod, sicut ipse etiam post dicet, substantiae nihil est contrarium secundum compositum, vel secundum materiam, vel secundum formam substantialem: est tamen aliquid sibi contrarium secundum propriam dispositionem ad talem formam, sicut ignis dicitur esse contrarius aquae contrarietate calidi et frigidi. Et talis contrarietas requiritur in omnibus quae generantur et corrumpuntur. Huiusmodi autem contrarietatem consequitur contrarietas motuum secundum grave et leve: per quorum subtractionem intelligitur corpus caeleste esse exemptum ab omnibus aliis contrariis quae comitantur grave et leve. But this response, although true, is not ad rem, For Aristotle says that contrariety of local motions corresponds to contrariety of bodies; and it is certain that no local motion corresponds to a privation. Consequently, it must be said that, as he himself will say later, nothing is contrary to substance with respect to its being a composite, or according to matter or substantial form; but there is something contrary to it according to its proper disposition to such a form, as fire is said to be contrary to water by reason of the contrariety of hot and cold. And such contrariety is required in all things that are generated and cease to be. But it is upon such contrariety that contrariety of motions according to heavy and light follow: through the absence of which, a heavenly body is understood to be free of all the contraries that accompany the heavy and the light. Item videtur, secundum hoc quod contrarietati corporum dicit respondere contrarietatem motuum, quod ignis magis sit contrarius terrae quam aquae, cum qua convenit in una qualitate, scilicet in siccitate. 68. Likewise, since he says that contrariety of motions corresponds to contrariety of bodies, it seems that fire is contrary more to earth than to water, because fire agrees with the former in respect of one quality, namely, dryness. Et dicendum est quod philosophus in hoc libro agit de corporibus simplicibus secundum situm: sic enim constituunt universum ut partes. Et secundum hoc maior est contrarietas ignis ad terram quam ad aquam: licet ad aquam sit maior contrarietas ignis secundum qualitates activas et passivas, quod pertinet ad considerationem libri de generatione. And it must be said that in this book the Philosopher is discussing simple bodies with respect to their position; for it is under this aspect that they are parts making up the universe. And according to this, the contrariety of fire to earth is greater than its contrariety to water. Yet it is true that fire has a greater contrariety to water from the viewpoint of active and passive qualities, which consideration belongs to the book On Generation. Videtur etiam non ex necessitate sequi quod corpori caelesti nihil sit contrarium, ex eo quod motui circulari, quo movetur, nihil sit contrarium: quia etiam ignis in propria sphaera, et suprema pars aeris circulariter moventur, ut in I Meteor. dicitur; aeri tamen et igni est aliquid contrarium. 69. Again, it does not seem to follow of necessity that nothing is contrary to a heavenly body just because nothing is contrary to the circular motion with which it is moved, because fire also in its own sphere, and the upper region of air, are moved circularly, as is said in Meteorology I, and yet there is a contrary to fire and air. Sed dicendum est quod ignis et aer non moventur circulariter quasi proprio motu, sed deferuntur per motum caeli: corpora autem caelestia moventur circulariter proprio motu: unde non est similis ratio. But it should be said that fire and air are not moved circularly as though by their own motion; rather they are carried along by the motion of the heavens. The heavenly bodies, however, are moved circularly by their own motion; consequently, the case is not the same. Item videtur quod contrarietas motuum non attestetur contrarietati mobilium. Eadem enim substantia numero, quae sibi non contrariatur, est susceptiva contrariorum, ut dicitur in praedicamentis; et ita movetur motibus contrariis, qui sunt ad contraria, puta dealbatione et denigratione et similibus motibus. Praeterea aer movetur sursum in loco aquae existens, deorsum autem existens in loco ignis: idem ergo contrariis motibus movetur, et sic contrarietas motuum non consequitur contrarietatem mobilium. Adhuc etiam videmus quod eadem anima movetur motu virtutis et vitii, qui sunt contrarii motus. 70. Again, it seems that contrariety of motions does not attest to contrariety of mobiles. For the same numerical substance, which is not contrary to itself, is subject to contraries, as is said in the Predicaments; thus it is moved by contrary motions which are terminated at contraries: for example, a substance is moved by whitening and blackening and similar motions. Moreover, air existing in the place of water is moved upward, but in the place of fire downwards. Therefore the same thing is moved by contrary motions, and, consequently, contrariety of motions does not follow upon contrariety of mobiles. Furthermore, we see that the same soul is moved by the motions of vice and virtue, which are contrary motions. Est autem circa hoc considerandum quod philosophus utitur hac propositione: quod si motus non sint contrarii, quod etiam mobilia non sunt contraria. Non autem ponit e converso quod si mobilia non sunt contraria, quod motus non sint contrarii (quia posset aliquis dicere quod omnium corporum contrarietatem habentium sint contrarii motus, non autem omnes contrarii motus sunt contrariorum): contra quod praedictae obiectiones procedunt. Tamen, secundum rei veritatem, contrarietas motuum naturalium consequitur proprietatem principiorum activorum sive formalium, ad quae consequitur motus; non autem contrarietatem principiorum passivorum sive materialium, quia eadem materia susceptiva est contrariorum. Et ideo alterationes quae fiunt ex principiis extrinsecis, nihil prohibet esse circa idem subiectum, quamvis sint contrariae. Si qua vero est alteratio ex intrinseco principio proveniens, sicut sanatio quando fit per naturam, oportet quod contrarietas talium alterationum consequatur contrarietatem mobilium. Et eadem ratio est de motibus localibus, de quibus nunc intendit: huiusmodi enim motus consequuntur principia formalia intrinseca. With regard to this it must be considered that the Philosopher uses this proposition, namely, that if motions are not contrary, the mobiles also are not contrary. But he does not state the converse, that if the mobiles are not contrary the motions are not contrary (because someone could say that the motions of all bodies having contrariety are contrary, but not that all contrary motions involve contrary things): against which the foregoing objection is directed. Yet in truth contrariety of natural motions follows upon what is proper to the active or formal principles (which the motion follows upon), and not upon the contrariety of the passive or material principles, because the same matter is subject to contraries. And therefore nothing prevents the same subject from being affected by alterations caused by extrinsic principles, even though such alterations be contrary. But if an alteration arises from an intrinsic principle, as when health is restored by the nature, then the contrariety of such alterations follows upon the contrariety of the mobiles. And the same holds for local motions, which we are now discussing: for such motions follow upon intrinsic formal principles Ad id vero quod obiicitur de aere, dicendum quod contradictio quae includitur in omnibus oppositis, habet in sui ratione quod sit secundum idem et respectu eiusdem. Motus autem aeris naturalis non est sursum et deorsum respectu eiusdem; sed sursum quidem respectu aquae et terrae, deorsum vero respectu ignis. Unde huiusmodi motus non sunt contrarii: non enim sunt ad contraria loca, sed ad eundem locum, qui scilicet supereminet aquae et subsidet igni. Now, regarding the objection about air, it must be said that the contradiction which is included in all opposites requires in its very notion that it be with respect to the same thing and according to the same aspect. But the natural motion of air is not up and down with respect to the same thing; rather it is upward with respect to water and earth, and downward with respect to fire. Consequently such motions are not contrary, for they are not tending to contrary places but to the same place, i.e., the place which is above water and below fire. Quod autem dicitur de motu animae secundum virtutem et vitium, non est ad propositum: quia huiusmodi motus non sunt naturales, sed voluntarii. What is said about the motion of the soul according to virtue and vice is not ad rem — for such motions are not natural but voluntary.
Lecture 7: The heavenly body is not subject to growth and decrease, or to alteration.
Chapter 3 cont. Ἀλλὰ μὴν καὶ τὸ αὐξανόμενον ἅπαν αὐξάνεται [καὶ τὸ φθῖνον φθίνει] ὑπὸ συγγενοῦς προσιόντος καὶ ἀναλυομένου εἰς τὴν ὕλην τούτῳ δ' οὐκ ἔστιν ἐξ οὗ γέγονεν. 35 Again, that which is subject to increase increases upon contact with a kindred body, which is resolved into its matter. But there is nothing out of which this body can have been generated. Εἰ δ' ἐστὶ καὶ ἀναύξητον καὶ ἄφθαρτον, τῆς αὐτῆς διανοίας ἐστὶν ὑπολαβεῖν καὶ ἀναλλοίωτον εἶναι. Ἔστι μὲν γὰρ ἡ ἀλλοίωσις κίνησις κατὰ τὸ ποιόν, τοῦ δὲ ποιοῦ αἱ μὲν ἕξεις καὶ διαθέσεις οὐκ ἄνευ τῶν κατὰ τὰ πάθη γίγνονται μεταβολῶν, οἷον ὑγίεια καὶ νόσος. Κατὰ δὲ πάθος ὅσα μεταβάλλει τῶν φυσικῶν σωμάτων, ἔχονθ' ὁρῶμεν πάντα καὶ αὔξησιν καὶ φθίσιν, οἷον τά τε τῶν ζῴων σώματα καὶ τὰ μόρια αὐτῶν καὶ τὰ τῶν φυτῶν, ὁμοίως δὲ καὶ τὰ τῶν στοιχείων ὥστ' εἴπερ τὸ κύκλῳ σῶμα μήτ' αὔξησιν ἔχειν ἐνδέχεται μήτε φθίσιν, εὔλογον καὶ ἀναλλοίωτον εἶναι. (270b.) Διότι μὲν οὖν ἀΐδιον καὶ οὔτ' αὔξησιν ἔχον οὔτε φθίσιν, ἀλλ' ἀγήρατον καὶ ἀναλλοίωτον καὶ ἀπαθές ἐστι τὸ πρῶτον τῶν σωμάτων, εἴ τις τοῖς ὑποκειμένοις πιστεύει, φανερὸν ἐκ τῶν εἰρημένων ἐστίν. 36 And if it is exempt from increase and diminution, the same reasoning leads us to suppose that it is also unalterable. For alteration is movement in respect of quality; and qualitative states and dispositions, such as health and disease, do not come into being without changes of properties. But all natural bodies which change their properties we see to be subject without exception to increase and diminution. This is the case, for instance, with the bodies of animals and their parts and with vegetable bodies, and similarly also with those of the elements. And so, if the body which moves with a circular motion cannot admit of increase or diminution, it is reasonable to suppose that it is also unalterable. The reasons why the primary body is eternal and not subject to increase or diminution, but unaging and unalterable and unmodified, will be clear from what has been said to any one who believes in our assumptions. Ἔοικε δ' ὅ τε λόγος τοῖς φαινομένοις μαρτυρεῖν καὶ τὰ φαινόμενα τῷ λόγῳ πάντες γὰρ ἄνθρωποι περὶ θεῶν ἔχουσιν ὑπόληψιν, καὶ πάντες τὸν ἀνωτάτω τῷ θείῳ τόπον ἀποδιδόασι, καὶ βάρβαροι καὶ Ἕλληνες, ὅσοι περ εἶναι νομίζουσι θεούς, δῆλον ὅτι ὡς τῷ ἀθανάτῳ τὸ ἀθάνατον συνηρτημένον ἀδύνατον γὰρ ἄλλως. Εἴπερ οὖν ἔστι τι θεῖον, ὥσπερ ἔστι, καὶ τὰ νῦν εἰρημένα περὶ τῆς πρώτης οὐσίας τῶν σωμάτων εἴρηται καλῶς. 37 Our theory seems to confirm experience and to be confirmed by it. For all men have some conception of the nature of the gods, and all who believe in the existence of gods at all, whether barbarian or Greek, agree in allotting the highest place to the deity, surely because they suppose that immortal is linked with immortal and regard any other supposition as inconceivable. If then there is, as there certainly is, anything divine, what we have just said about the primary bodily substance was well said. Συμβαίνει δὲ τοῦτο καὶ διὰ τῆς αἰσθήσεως ἱκανῶς, ὥς γε πρὸς ἀνθρωπίνην εἰπεῖν πίστιν ἐν ἅπαντι γὰρ τῷ παρεληλυθότι χρόνῳ κατὰ τὴν παραδεδομένην ἀλλήλοις μνήμην οὐθὲν φαίνεται μεταβεβληκὸς οὔτε καθ' ὅλον τὸν ἔσχατον οὐρανὸν οὔτε κατὰ μόριον αὐτοῦ τῶν οἰκείων οὐθέν. 38 The mere evidence of the senses is enough to convince us of this, at least with human certainty. For in the whole range of time past, so far as our inherited records reach, no change appears to have taken place either in the whole scheme of the outermost heaven or in any of its proper parts. Ἔοικε δὲ καὶ τοὔνομα παρὰ τῶν ἀρχαίων παραδεδόσθαι μέχρι καὶ τοῦ νῦν χρόνου, τοῦτον τὸν τρόπον ὑπολαμβανόντων ὅνπερ καὶ ἡμεῖς λέγομεν οὐ γὰρ ἅπαξ οὐδὲ δὶς ἀλλ' ἀπειράκις δεῖ νομίζειν τὰς αὐτὰς ἀφικνεῖσθαι δόξας εἰς ἡμᾶς. Διόπερ ὡς ἑτέρου τινὸς ὄντος τοῦ πρώτου σώματος παρὰ γῆν καὶ πῦρ καὶ ἀέρα καὶ ὕδωρ, αἰθέρα προσωνόμασαν τὸν ἀνωτάτω τόπον, ἀπὸ τοῦ θεῖν ἀεὶ τὸν ἀΐδιον χρόνον θέμενοι τὴν ἐπωνυμίαν αὐτῷ. Ἀναξαγόρας δὲ καταχρῆται τῷ ὀνόματι τούτῳ οὐ καλῶς ὀνομάζει γὰρ αἰθέρα ἀντὶ πυρός. 39 The common name, too, which has been handed down from our distant ancestors even to our own day, seems to show that they conceived of it in the fashion which we have been expressing. The same ideas, one must believe, recur in men's minds not once or twice but again and again. And so, implying that the primary body is something else beyond earth, fire, air, and water, they gave the highest place a name of its own, aither, derived from the fact that it 'runs always' for an eternity of time. Anaxagoras, however, scandalously misuses this name, taking aither as equivalent to fire.
Postquam philosophus ostendit quod corpus quintum non est subiectum generationi et corruptioni, hic ostendit quod non est subiectum augmento et deminutioni. Et utitur tali ratione. Omne corpus augmentabile est quantum ad aliquid subiectum generationi et corruptioni. Ad cuius manifestationem proponit quod omne corpus augmentabile augetur per appositionem alicuius connaturalis advenientis; quod quidem, cum prius esset dissimile, factum est simile per resolutionem in propriam materiam, quae, deposita forma priori, formam corporis augmentandi assumpsit; sicut panis, resolutus in materiam, accipit formam carnis, et ita per additionem ad carnem praeexistentem facit augmentum. Unde ubicumque est augmentum, ibi oportet quod sit generatio et corruptio in aliquid. Corpori autem caelesti non est dare aliquid ex quo sit generatum, ut ostensum est. Ergo non potest esse augmentabile vel deminuibile. After showing that the fifth body is not subject to generation and corruption, the Philosopher here shows that it is not subject to increase and diminution [35] and uses this argument: Every augmentable body is, with respect to something, subject to generation and corruption. To explain this, he proposes that every augmentable body is increased by the addition of something connatural that comes to it. This, indeed, while being first unlike, has become like by being resolved into its proper matter which, doffing its previous form, has assumed the form of the body to be increased — as bread, after being resolved into matter, receives the form of flesh, and thus, through being added to pre-existing flesh, produces increase. Hence wherever there is growth there must be generation and corruption into something. But there is nothing from which a heavenly body can be generated, as has been shown. Therefore it cannot be augmentable or decreasable. Deinde cum dicit: si autem est etc., ostendit quod non sit subiectum alterationi. Posset autem videri alicui quod brevis via removendi alterationem a corpore caelesti, esset per remotionem contrarietatis: sicut enim generatio est ex contrariis, ita et alteratio. Sed advertendum quod Aristoteles removit contrarietatem a quinto corpore removendo ab eo contrarietatem motus: alteratio autem videtur fieri non solum secundum contrarietatem cui respondent contrarii motus locales, quae est gravis et levis et eorum quae assequuntur; sed etiam secundum alia contraria quae ad hoc non pertinent, puta secundum album et nigrum: et ideo utitur alia via, quae sumitur ex parte augmenti. 72. Then at [36] he shows that it is not subject to alteration. Now it might seem to someone that an easy way to remove alteration from the heavenly body would be by removing contrariety, for just as generation occurs from contraries, so too, does alteration. But it should be observed that Aristotle removed contrariety from the fifth body by removing from it contrariety of motion. Alteration, however, seems to occur not only according to the contrariety to which contrary local motions correspond, namely, heavy and light and whatever results from them, but also according to other contraries which do not pertain to this, for example, according to black and white. Accordingly, he uses another way, based on increase. Et dicit quod eiusdem rationis est aestimare quod corpus caeleste non sit alterabile, et quod non sit augmentabile seu corruptibile. Quia alteratio est motus secundum qualitatem, ut dictum est in V Physic. Alteratio autem, ut in VII Physic. ostensum est, proprie fit secundum tertiam speciem qualitatis, quae est passio et passibilis qualitas: quamvis enim habitus et dispositio pertineant ad genus qualitatis, non tamen causantur sine transmutatione quae fit secundum passiones; sicut sanitas et languor proveniunt ex transmutatione frigidi et calidi, humidi et sicci. Omnia autem corpora naturalia quae transmutantur secundum passionem vel passibilem qualitatem, per consequens videntur habere augmentum et decrementum; sicut patet de corporibus animalium et de partibus eorum, et etiam de plantis, in quibus proprie est augmentum. Ita etiam est de elementis: quae quidem secundum transmutationem calidi et frigidi rarefiunt et condensantur, et per consequens transmutantur in maiorem vel minorem quantitatem, quod est quodammodo augeri et deminui. Sic igitur patet quod, si corpus quod circulariter movetur, non subiacet augmento vel decremento, quod etiam non subiaceat alterationi. And he says that it is for the same reason that we estimate a heavenly body not to be alterable and not to be augmentable or perishable. For alteration is a motion affecting quality, as has been said in Physics V. But alteration, as was shown in Physics VII, properly takes place according to the third species of quality, which is "passion and passible quality": for although "habit and disposition" pertain to [the first species of] the genus of quality, they are not produced without a change made according to the passions, just as health and languor result from a change of cold and hot, moist and dry. Now all natural bodies that are changed with respect to passion or passible quality seem as a consequence to have growth and decrease, as is clear from the bodies of animals and their parts and even of plants, in which growth properly exists. The same applies also to the elements, which rarefy and condense with respect to a change in hot and cold, from which results a change into larger or smaller quantity which is in a sense the same as being increased and decreased. Thus it is plain that if a body which is moved circularly is not subject to increase or decrease it is not subject to alteration. Ultimo autem epilogando concludit manifestum esse ex dictis, si quis velit assentire prioribus demonstrationibus, non proterve contradicendo, quod corpus primum, quod scilicet movetur motu primo et perfecto, idest circulari, est sempiternum, quasi non subiacens generationi et corruptioni; neque etiam habet augmentum neque decrementum; et non subiacet senectuti, neque alterationi, neque passioni. Finally, in summary he concludes that it is plain from the foregoing — if anyone wants to assent to the previous demonstrations without wantonly contradicting — that the first body, which, namely, is moved with the first and perfect motion, i.e., circular motion, is sempiternal (as not being subject to generation and corruption), that it undergoes neither increase nor decrease, and that it is not subject to aging or alteration or passion. Potest autem obiici contra hanc Aristotelis rationem dupliciter. Primo quidem contra conclusionem. Videtur enim esse falsum quod corpus caeleste non alteretur: manifeste enim apparet lunam a sole illuminari, et per umbram terrae obscurari. 73. Nevertheless objections can be leveled against this argument of Aristotle on two counts. First of all against the conclusion. For it seems to be false that a heavenly body is not altered, for it is plainly evident that the moon is illumined by the sun and obscured by the shadow of the earth. Dicendum est autem quod duplex est alteratio. Una quidem passiva, secundum quam ita aliquid adiicitur, quod etiam aliquid aliud abiicitur; sicut cum aliquid alteratur de calido in frigidum, amittit calorem et recipit frigiditatem: et talem alterationem, quae fit secundum passiones, intendit hic philosophus excludere a corpore caelesti. Est autem alia alteratio perfectiva, quae fit secundum quod aliquid ab alio perficitur absque alterius abiectione, qualem alterationem ponit philosophus in II de anima etiam in potentia sensitiva: et talem alterationem nihil prohibet esse in corporibus caelestibus, quorum quaedam recipiunt virtutes ab aliis secundum coniunctiones et varios aspectus, absque hoc quod aliquod eorum propriam virtutem amittat. But it must be said that alteration is of two kinds. One is passive and according to it things are so added that something else is cast off, as, when something is altered from hot to cold, it loses heat and receives coldness. It is that kind of alteration, which takes place according to passions, that the Philosopher is here excluding from heavenly body. But there is another kind of alteration which is perfecting, which occurs insofar as something is perfected by something else without loss to the former — this is the kind of alteration that the Philosopher in On the Soul II posits even in a sense power. Such an alteration nothing prevents from being in heavenly bodies, some of which receive virtues from others according to conjunctions and various aspects, but without any of them losing their own virtue. Secundo obiicitur contra processum rationis hic inductae: non enim videtur esse verum quod quaecumque alterantur, augmentum et decrementum suscipiant. Augmentum enim et decrementum fit per additionem alicuius quod est conversum in substantiam eius quod augetur, ut dicitur in libro de Generat. et in II de anima; et etiam hoc supra dictum est. Hic autem motus augmenti non est nisi in animalibus et plantis: nam ea quae rarefiunt et condensantur, non augentur ex aliquo addito, ut probatur in IV Physic. Inconvenienter igitur videtur hic Aristoteles attribuere motum augmenti non solum animalibus et plantis et partibus eorum, sed etiam elementis. 74. The second objection is directed against the procedure of his argument: for it does not seem to be true that whatever is altered receives increase and decrease. For these result from the addition of something that is converted into the substance of what is increased, as is said in the book On Generation and in On the Soul II, and as was said above. Now the motion of increase does not exist except in animals and plants, for things that rarefy and condense are not increased by the addition of anything, as was proved in Physics V. Consequently, it seems unsuitable for Aristotle here to attribute the motion of increase not only to animals and plants and their parts, but to the elements as well. Dicendum est autem quod Aristoteles hic loquitur de augmento pro quolibet motu quo aliquid proficit in maiorem quantitatem. Nondum enim perfecte explicaverat naturam motus augmenti: est autem suae consuetudinis ut ante manifestationem veritatis, utatur opinionibus communibus. Nec impedit virtutem probationis eius, quod supra exclusit augmentum a corpore caelesti per exclusionem additionis corporis in ipsum quod augetur transmutati: quia sicut quod augetur per additionem, non est omnino liberum a generatione et corruptione, ita etiam quod augetur per rarefactionem. But it should be said that Aristotle is here speaking of increase in the sense of any motion by which something proceeds to greater quantity. For he has not yet perfectly explained the nature of the motion of increase and it is his custom, before he has shown the true view, to use common opinions. But the force of his proof is not impeded by his having excluded increase from a heavenly body by excluding addition of a body changed into what is increased: for just as anything increased by addition is not utterly free of generation and corruption, so, too, what is increased by rarefaction. Est autem considerandum quod signanter in hac ratione mentionem facit de corporibus physicis: quia in corporibus mathematicis potest esse augmentum sine alteratione, puta cum quadratum crevit apposito gnomone, sed non est alteratum, ut dicitur in praedicamentis; et e converso potest aliquid alterari sine hoc quod augeatur, sicut cum fit triangulus aequalis quadrato. However it is to be noted that in this proof he makes mention of Physica l bodies advisedly, because in mathematical bodies increase can occur without alteration — for example, a square grows by adding to it a gnomon, but it is not altered, as is said in the Predicaments; conversely, a thing can be altered without being increased, as when a triangle is made equal to a square. Deinde cum dicit: videtur autem etc., manifestat propositum per signa. Et dicit quod ratio et ea quae apparent probabiliter videntur in materia ista sibi invicem testificari. Et ponit tria signa. Quorum primum est ex communi hominum opinione, qui ponunt multos deos, vel unum Deum, cui alias substantias separatas deservire dicunt; et omnes sic opinantes attribuunt supremum locum, scilicet caelestem, Deo, sive sint barbari sive Graeci, quicumque scilicet putant esse res divinas. Sic autem attribuunt caelum divinis substantiis, quasi adaptantes immortalem locum immortalibus et divinis rebus; ut sic habitatio Dei in caelo intelligatur esse secundum similitudinis adaptationem, quia scilicet hoc corpus inter cetera corpora magis accedit ad similitudinem spiritualium substantiarum et divinarum. Est enim impossibile quod aliter Deo habitatio caeli attribuatur, quasi indigeat loco corporali a quo comprehendatur. Si igitur ponendae sint res divinae, immo quia pro certo ponendae sunt, consequens est quod bene sint dicta ea quae dicta sunt de prima substantia corporali, scilicet de corpore caelesti, quod scilicet est ingenitum et impassibile. 75. Then at [37] he manifests the proposition through signs. And he says that both reason and things that appear to be probable seem to support one another on this point. And he gives three signs. The first of which is taken from the general opinion of men, who posit many gods or one God, whom the other separated substances serve. All who believe thus, whether Greeks or barbarians, assign the highest place, namely, the heavenly, to God, namely, all those who believe there are divine beings. But they assign the heavens to the divine substances as though adapting an immortal place to immortal and divine beings. In this way God's habitation in the heavens is understood as appropriate according to likeness, that is, that among all other bodies this body more closely approaches to a likeness to spiritual and divine substances. For it is impossible for the habitation of the heavens to be assigned to God for any other reason, as though He should need a bodily place by which He is comprehended. If therefore divine beings are to be posited, and since, indeed, they certainly must, the consequence is that the statements made about the first bodily substance, namely, the heavenly body, were well made, namely, that the heavenly body is ungenerated and unalterable. Quamvis autem existimant homines templa esse locum Dei, hoc tamen non existimant ex parte ipsius Dei, sed ex parte colentium Deum, quos oportet in aliquo loco Deum colere. Unde templa corruptibilia sunt proportionalia hominibus corruptibilibus, caelum autem incorruptioni divinae. Although men suppose that temples are the place of God, they do not suppose this from God's viewpoint but from that of the worshippers, who must worship Him in some place. That is why perishable temples are proportioned to perishable men, but the heavens to the divine imperishability. Secundum signum ponit ibi: accidit autem hoc et per sensum etc.: quod quidem accipitur ab experientia longi temporis. Et dicit quod id quod probatum est per rationem et per communem opinionem, accidit, idest consequitur, sufficienter; non quidem simpliciter, sed sicut potest dici per comparationem ad humanam fidem, idest quantum homines possunt testificari de his quae parvo tempore et a remotis viderunt. Secundum enim memoriam quam sibi invicem tradiderunt astrologi, dispositiones et motus caelestium corporum observantes, in toto praeterito tempore non videtur aliquid transmutatum esse neque secundum totum caelum, neque secundum aliquam propriam partem eius. Quod quidem non esset si caelum generabile et corruptibile esset: quaecumque enim generantur et corrumpuntur, paulatim et successive ad perfectum statum perveniunt, et ex eo paulatim recedunt: quod quidem non posset tanto tempore latere in caelo, si naturaliter generationi et corruptioni subiaceret. 76. The second sign he gives at [38] and it is taken from long experience. And he says that what has been proved by reason and common opinion occurs, i.e., follows, sufficiently — i.e., not absolutely but to the extent of human faith, i.e., so far as men can testify to what they have seen for a short time and from afar. For according to the tradition which astronomers have passed on concerning their observations of the dispositions and motions of heavenly bodies, in the whole time past there does not seem to have been any change affecting either the entire heavens or any of its own parts. Now this would not be, if the heaven were generable or perishable — for things subject to generation and corruption arrive at their perfect state little by little and step by step, and then gradually depart from that state, and this could not have been concealed in the heavens for such a long time, if they were naturally subject to generation and corruption. Nec tamen hoc est necessarium, sed probabile. Quanto enim aliquid est diuturnius, tanto maius tempus requiritur ad hoc quod eius mutatio deprehendatur; sicut transmutatio hominis non deprehenditur in duobus vel tribus annis, in quibus deprehenditur transmutatio canis, vel alicuius alterius animalis breviorem vitam habentis. Posset igitur aliquis dicere quod, etsi caelum sit naturaliter corruptibile, est tamen tam diuturnum, quod totum tempus cuius memoria potest haberi, non sufficit ad deprehendendam eius transmutationem. However, this is not necessary but probable. For the more lasting something. is, the greater the time required for its change to be noted, just as change in a man is not noticed in two or three years, as it is in a dog or other animals having a shorter life-span. Consequently someone could say that, even though the heavens are naturally corruptible, nevertheless they are so lasting that the whole extent of human memory is not sufficient to observe their change. Tertium signum ponit ibi: videtur autem et cetera. Quod quidem sumitur a nomine imposito ab antiquis, quod durat usque ad praesens tempus; per quod datur intelligi quod ipsi etiam hoc modo opinabantur caelum esse incorruptibile, sicut nos opinamur. Et ne aliquis contra hoc obiiceret quod aliqui ante suum tempus, caelum generabile et corruptibile posuerunt, subiungit quod opiniones verae renovatae sunt secundum diversa tempora non semel aut bis, sed infinities, supposita infinitate temporis. Destruuntur enim studia veritatis per diversas mutationes in his inferioribus accidentes: sed quia mentes hominum naturaliter inclinantur ad veritatem, cessantibus impedimentis, renovantur studia, et homines tandem perveniunt ad opiniones veras quae prius fuerant: opiniones autem falsas non necesse est renovari. 77. The third sign is given at [39] and is based on a name given by the ancients, which endures to the present, and which gives us to understand that they thought the heaven to be imperishable just as we do. And lest anyone object that some before their time thought the heavens were subject to generation and corruption, he adds that true opinions are revived according to diverse times not once or twice but infinitely, supposing that time is infinite. For the studies of truth are destroyed by various changes occurring in these lower things, but because the minds of men are naturally inclined to truth, then when obstacles are removed, studies are renewed and men at last arrive at the true opinions which previously flourished, but false opinions need not be revived. Et ideo antiqui, opinantes quod primum corpus, scilicet caeli, esset alterius naturae praeter quatuor elementa, nominaverunt supremum locum mundi aethera, ponentes scilicet ei nomen ab eo quod semper currit sempiterno tempore: thein enim in Graeco idem est quod currere. Sed Anaxagoras male interpretatus est hoc nomen, attribuens ipsum igni, quasi caeleste corpus sit igneum: aethein enim in Graeco idem est quod ardere, quod est proprium ignis. Sed quod caeleste corpus non sit igneum, patet ex supra dictis. Consequently the ancients, supposing that the first body, namely, the heaven, to be of a nature different from the four elements, named the highest place of the world the "aether," thus applying to it a name based on the fact that it always runs for an eternity of time — for thein in Greek is the same as "to run." But Anaxagoras misinterpreted this name, attributing it to fire, as though the heavenly body were fiery — for aether in in Greek is the same as "to burn," which is proper to fire. But that a heavenly body is not of fire is plain from what has been said above [in L. 4].
Lecture 8: Only five simple bodies required. No motion contrary to circular.
Chapter 3 cont. Φανερὸν δ' ἐκ τῶν εἰρημένων καὶ διότι τὸν ἀριθμὸν ἀδύνατον εἶναι πλείω τὸν τῶν λεγομένων σωμάτων ἁπλῶν τοῦ μὲν γὰρ ἁπλοῦ σώματος ἀνάγκη τὴν κίνησιν ἁπλῆν εἶναι, μόνας δὲ ταύτας εἶναί φαμεν ἁπλᾶς, τήν τε κύκλῳ καὶ τὴν ἐπ' εὐθείας, καὶ ταύτης τὰ δύο μόρια, τὴν μὲν ἀπὸ τοῦ μέσου, τὴν δ' ἐπὶ τὸ μέσον. 41 It is also clear from what has been said why the number of what we call simple bodies cannot be greater than it is. The motion of a simple body must itself be simple, and we assert that there are only these two simple motions, the circular and the straight, the latter being subdivided into motion away from and motion towards the centre. Chapter 4 Ὅτι δ' οὐκ ἔστι τῇ κύκλῳ φορᾷ ἐναντία ἄλλη φορά, πλεοναχόθεν ἄν τις λάβοι τὴν πίστιν πρῶτον μὲν ὅτι τῇ περιφερεῖ τὴν εὐθεῖαν ἀντικεῖσθαι μάλιστα τίθεμεν τὸ γὰρ κοῖλον καὶ τὸ κυρτὸν οὐ μόνον ἀλλήλοις ἀντικεῖσθαι δοκεῖ (271a.) ἀλλὰ καὶ τῷ εὐθεῖ, συνδυαζόμενα καὶ λαβόντα σύνθεσιν ὥστ' εἴπερ ἐναντία τίς ἐστι, τὴν ἐπὶ τῆς εὐθείας μάλιστα ἀναγκαῖον ἐναντίαν εἶναι πρὸς τὴν κύκλῳ κίνησιν. Αἱ δ' ἐπὶ τῆς εὐθείας ἀλλήλαις ἀντίκεινται διὰ τοὺς τόπους τὸ γὰρ ἄνω κάτω τόπου τέ ἐστι διαφορὰ καὶ ἐναντίωσις. 42 That there is no other form of motion opposed as contrary to the circular may be proved in various ways. In the first place, there is an obvious tendency to oppose the straight line to the circular. For concave and convex are a not only regarded as opposed to one another, but they are also coupled together and treated as a unity in opposition to the straight. And so, if there is a contrary to circular motion, motion in a straight line must be recognized as having the best claim to that name. But the two forms of rectilinear motion are opposed to one another by reason of their places; for up and down is a difference and a contrary opposition in place. Ἔπειτ' εἴ τις ὑπολαμβάνει τὸν αὐτὸν εἶναι λόγον ὅνπερ ἐπὶ τῆς εὐθείας καὶ ἐπὶ τῆς περιφεροῦς (τὴν γὰρ ἀπὸ τοῦ Α πρὸς τὸ Β φορὰν ἐναντίαν εἶναι τῇ ἀπὸ τοῦ Β πρὸς τὸ Α), τὴν ἐπὶ τῆς εὐθείας λέγει αὕτη γὰρ πεπέρανται, περιφερεῖς δ' ἄπειροι ἂν εἶεν περὶ τὰ αὐτὰ σημεῖα. 43 Secondly, it may be thought that the same reasoning which holds good of the rectilinear path applies also the circular, movement from A to B being opposed as contrary to movement from B to A. But what is meant is still rectilinear motion. For that is limited to a single path, while the circular paths which pass through the same two points are infinite in number. Ὁμοίως δὲ καὶ ἐπὶ τοῦ ἡμικυκλίου τοῦ ἑνός, οἷον ἀπὸ τοῦ Γ ἐπὶ τὸ Δ καὶ ἀπὸ τοῦ Δ ἐπὶ τὸ Γ ἡ γὰρ αὐτὴ τῇ ἐπὶ τῆς διαμέτρου ἐστίν ἀεὶ γὰρ ἕκαστον ἀπέχειν τὴν εὐθεῖαν τίθεμεν. 44 Even if we are confined to the single semicircle and the opposition is between movement from C to D and from D to C along that semicircle, the case is no better. For the motion is the same as that along the diameter, since we invariably regard the distance between two points as the length of the straight line which joins them. Ὁμοίως δὲ κἂν εἴ τις κύκλον ποιήσας τὴν ἐπὶ θατέρου ἡμικυκλίου φορὰν ἐναντίαν θείη τῇ ἐπὶ θατέρου, οἷον ἐν τῷ ὅλῳ κύκλῳ τὴν ἀπὸ τοῦ Ε πρὸς τὸ Ζ τοῦ Η ἡμικυκλίου τῇ ἀπὸ τοῦ Ζ πρὸς τὸ Ε ἐν τῷ Θ ἡμικυκλίῳ. 45 It is no more satisfactory to construct a circle and treat motion 'along one semicircle as contrary to motion along the other. For example, taking a complete circle, motion from E to F on the semicircle G may be opposed to motion from F to E on the semicircle H. Εἰ δὲ καὶ αὗται ἐναντίαι, ἀλλ' οὔτι γε αἱ ἐπὶ τοῦ ὅλου κύκλου φοραὶ ἀλλήλαις διὰ τοῦτο ἐναντίαι. *—* 46 But even supposing these are contraries, it in no way follows that the reverse motions on the complete circumference contraries. Ἀλλὰ μὴν οὐδ' ἡ ἀπὸ τοῦ Α ἐπὶ τὸ Β κύκλῳ φορὰ ἐναντία τῇ ἀπὸ τοῦ Α ἐπὶ τὸ Γ ἐκ ταὐτοῦ γὰρ εἰς ταὐτὸ ἡ κίνησις, ἡ δ' ἐναντία διωρίσθη φορὰ ἐκ τοῦ ἐναντίου εἰς τὸ ἐναντίον. 46bis Nor again can motion along the circle from A to B be regarded as the contrary of motion from A to C: for the motion goes from the same point towards the same point, and contrary motion was distinguished as motion from a contrary to its contrary. Εἰ δὲ καὶ ἦν ἡ κύκλῳ τῇ κύκλῳ ἐναντία, μάτην ἂν ἦν ἡ ἑτέρα *ἐπὶ τὸ αὐτὸ γάρ, ὅτι ἀνάγκη τὸ κύκλῳ φερόμενον ὁποθενοῦν ἀρξάμενον εἰς πάντας ὁμοίως ἀφικνεῖσθαι τοὺς ἐναντίους τόπους (εἰσὶ δὲ τόπου ἐναντιότητες τὸ ἄνω καὶ κάτω καὶ τὸ πρόσθιον καὶ ὀπίσθιον καὶ τὸ δεξιὸν καὶ ἀριστερόν), αἱ δὲ τῆς φορᾶς ἐναντιώσεις κατὰ τὰς τῶν τόπων εἰσὶν ἐναντιώσεις* εἰ μὲν γὰρ ἴσαι ἦσαν, οὐκ ἂν ἦν κίνησις αὐτῶν, εἰ δ' ἡ ἑτέρα κίνησις ἐκράτει, ἡ ἑτέρα οὐκ ἂν ἦν. Ὥστ' εἰ ἀμφότερα ἦν, μάτην ἂν θάτερον ἦν σῶμα μὴ κινούμενον τὴν αὑτοῦ κίνησιν μάτην γὰρ ὑπόδημα τοῦτο λέγομεν, οὗ μή ἐστιν ὑπόδεσις. Ὁ δὲ θεὸς καὶ ἡ φύσις οὐδὲν μάτην ποιοῦσιν. 47 And even if the motion round a circle is the contrary of the reverse motion, one of the two would be ineffective: for both move to the same point, because that which moves in a circle, at whatever point it begins, must necessarily pass through all the contrary places alike. (By contrarieties of place I mean up and down, back and front, and right and left; and the contrary oppositions of movements are determined by those of places.) One of the motions, then, would be ineffective, for if the two motions were of equal strength, there would be no movement either way, and if one of the two were preponderant, the other would be inoperative. So that if both bodies were there, one of them, inasmuch as it would not be moving with its own movement, would be useless, in the sense in which a shoe is useless when it is not worn. But God and nature create nothing that has not its use.
Postquam philosophus ostendit necesse esse aliquod corpus praeter quatuor elementa, hic ostendit quod praeter ista corpora non requirit integritas universi aliquod aliud corpus. 78. After showing the necessity of some body besides the four elements, the Philosopher here shows that the integrity of the universe requires no other body besides these five. Et primo ostendit propositum;
secundo probat quoddam quod supposuerat, ibi: quod autem non est circulationi et cetera.
First he shows his proposition;
Secondly, he proves something he had assumed, at 79.
Dicit ergo primo quod ex dictis, quibus probatum est esse quintum corpus praeter corpora gravia et levia, potest etiam manifestari quod impossibile est esse maiorem numerum simplicium corporum. Quia, sicut supra dictum est, necesse est quod cuiuslibet simplicis corporis sit aliquis motus simplex. He says therefore first [40] that from what was said in proving that there exists a fifth body in addition to heavy and light bodies, it can be shown that it is impossible for a greater number of simple bodies to exist. For as was said above, for each simple body there must be some simple motion. Sed non est alius motus simplex praeter praedictos, quorum unus est circularis et alius est rectus, qui in duas partes dividitur: nam motuum rectorum unus quidem est a medio, qui dicitur motus sursum; alius autem est ad medium, qui dicitur motus deorsum. Horum autem motuum ille qui est ad medium, est corporis gravis, scilicet terrae et aquae; ille autem qui est a medio, est corporis levis, scilicet ignis et aeris; ille autem qui est circularis, est primi et supremi corporis. Unde relinquitur quod praeter praedicta corpora simplicia non sit aliquod aliud corpus simplex: et ita integritas universi ex istis quinque corporibus consistit. But there is no simple motion other than the ones previously mentioned: one of which is circular and the other straight, the latter being divided into two kinds, one of which is from the middle and is called "upward motion" and the other toward the middle and is called "downward motion." Of the latter two, the one which is toward the middle belongs to a heavy body, namely, to earth and water, while the one from the middle belongs to a light body, namely, to fire and air. Finally, the circular motion is assigned to the first and supreme body. Hence what remains is that there is no other simple body besides the ones mentioned. Consequently, the wholeness of the universe consists of these five bodies. Deinde cum dicit: quod autem non est circulationi etc., probat quoddam quod supposuerat, scilicet quod motui circulari non sit aliquis motus contrarius. Et hoc quidem supposuerat in demonstratione qua probavit corpus caeli non esse subiectum generationi et corruptioni: sed ideo non statim ibi probavit, sed distulit probationem usque huc, quia hoc etiam valet ad ostendendum quod non sit maior numerus simplicium corporum. Si enim motui circulari esset aliquis motus contrarius, posset dici quod sicut est duplex corpus quod movetur motu recto, propter contrarietatem huius motus, ita etiam est duplex corpus quod movetur motu circulari. Hoc autem non continget, si constet quod corpori circulari non sit aliquis motus contrarius. 79. Then at [41] he proves something he had assumed, namely, that there is not a motion contrary to circular motion. This he had assumed in the discussion in which he proved that the body of the heavens is not subject to generation and corruption. But the reason why he did not prove it right away, but waited until now, is that it is also useful in proving that there is not a greater number of simple bodies. For if there were a motion contrary to circular motion, it could be held that just as there are two bodies moved with straight motion on account of the contrariety of this motion, so there are also two bodies moved with circular motion. But this will not occur if it is plain that there is no motion contrary to circular motion. Therefore, on this point, Circa hoc ergo primo proponit quod intendit. Et dicit quod per multas rationes potest aliquis accipere fidem quod motui circulari non sit aliquis motus localis contrarius. First he proposes what he intends, and says that there are many reasons to induce one to believe that there is not a circular motion contrary to circular motion. Secundo ibi: primum quidem etc., ostendit propositum. Circa quod considerandum est quod, si in motu circulari sit contrarietas, oportet hoc esse altero trium modorum: quorum unus est ut motui circulari rectus sit contrarius, alius modus est ut sit aliqua contrarietas in ipsis partibus motus circularis, tertius est ut uni motui circulari alius motus circularis contrarietur. 80. Secondly, he establishes the proposition. In regard to this it must be noted that if there exists contrariety in circular motion, it must be in one of three ways: one is that a straight motion be contrary to circular motion; the second is that there be some sort of contrariety in the parts themselves of circular motion; the third is that one circular motion have some other circular motion contrary to it. Primo ergo ostendit quod motui circulari non contrariatur motus rectus;
secundo ostendit quod non sit contrarietas in partibus motus circularis, ibi: deinde si quis existimat etc.;
tertio quod non sit contrarietas in toto motu circulari, unius scilicet motus circularis ad alium, ibi: at vero neque quae ab a et cetera.
First therefore he shows that a straight motion is not contrary to circular motion;
Secondly, he shows that there is no contrariety in the parts of circular motion, at 10.83;
Thirdly, that there is no contrariety between complete circular motions, i.e., of one to another, at 89.
Dicit ergo primo quod maxime circulari videtur opponi rectum. Linea enim recta nullam fractionem habet; figura autem angularis habet quandam fractionem, non per totum, sed in angulis; sed figura circularis videtur per totum habere fractionem, ac si totum esset angulus. Et secundum hoc rectum et circulare videntur esse contraria quasi maxime distantia. 81. He says therefore first [42] that what seems most opposite to something circular is something straight. For a straight line has no break, while an angular line does have a break, not through the whole, but in the angles; meanwhile a circular figure seems to have breaks throughout, as if the whole were an angle. According to this the straight and the circular seem to be contraries, as though at the farthest extremes. Et quia posset aliquis dicere quod circulari non opponitur rectum, sed concavo opponitur convexum sive gibbosum, ad hanc obviationem excludendam, subiungit quod concavum et gibbosum, idest convexum, non solum videntur habere oppositionem ad invicem, sed etiam ad rectum. Ad se invicem autem videntur habere oppositionem sicut combinata et iuxta se posita, idest secundum relationem: nam concavum dicitur respectu eorum quae intra sunt, gibbosum autem respectu eorum quae sunt extra. Et sic omni modo rectum contrariatur circulari, sive accipiatur sub ratione concavi, sive sub ratione convexi. And because someone could say that it is not the straight that is opposed to the circular, but rather the convex or "gibbous" which is opposed to the concave, to reject this objection, he adds that concave and "gibbous," i.e., convex, are seen to be opposed not only to one another, but to the straight as well. They seem to be mutually opposed after the manner of the combined and the juxtaposed, i.e., in terms of relation: for "concave" is said in relation to things that are inside [a circle or sphere], but "gibbous" with respect to things outside. Consequently, from every aspect, the straight is contrary to the circular, whether taken as concave or as convex. Et quia contrarietas motuum videtur esse secundum contrarietatem eorum in quibus est motus, videtur esse consequens quod si aliquis motus sit contrarius motui circulari, maxime sit ei contrarius motus rectus, qui scilicet est super lineam rectam. Sed motus recti contrariantur ad invicem, propter loca contraria (motus enim qui est sursum, contrariatur ei qui deorsum est, quia sursum et deorsum important differentiam et contrarietatem loci): et sic uni motui recto contrariabitur alius motus rectus, et circularis. Hoc autem est impossibile: quia uni unum est contrarium. Ergo impossibile est quod motui circulari sit aliquis motus contrarius. And because the contrariety of motions is seen to follow the contrariety of the things in which the motion is, the consequence seems to be that if there is a motion contrary to circular motion, it should be most of all straight motion which, namely, is over a straight line. But straight motions are contrary to one another because of contrary places — for upward motion is contrary to downward because "up" and "down" imply a difference and contrariety of place. Consequently, one straight motion will have as its contrary some other straight motion, and a circular one. This, however, is impossible, for to one thing there is one contrary. Therefore, it is impossible for any motion to be contrary to circular. Potest autem aliquis obiicere contra hoc quod dicitur, quod circulari maxime contrariatur rectum. Dictum est enim in praedicamentis quod figurae nihil est contrarium: rectum autem et circulare sunt differentiae figurarum. 82. But someone could object to the statement that the straight is most contrary to the circular. For it is stated in the Predicaments that nothing is contrary to figure, whereas "straight" and "circular" are differences in figure. Potest autem dici quod philosophus hic ex hypothesi loquitur, et non simpliciter. Si enim aliquid esset contrarium circulari, maxime contrariaretur sibi rectum, ratione supra dicta. But it can be said that the Philosopher is here speaking hypothetically and not categorically. For if anything were contrary to the circular, it would be the straight most of all, for the reason given above. Potest etiam dici quod in quolibet genere invenitur contrarietas differentiarum, ut patet X Metaphys., licet non sit in omni genere contrarietas specierum: etsi enim rationale et irrationale sint contrariae differentiae, non tamen homo et asinus sunt contrariae species. Sic igitur ponitur contrarietas inter rectum et circulare, non sicut inter species, sed sicut inter differentias eiusdem generis. Huiusmodi autem contrarietas, quae posset attendi in motibus secundum differentiam recti et circularis, non est contrarietas corruptiva, qualem intendit hic philosophus excludere a corpore caelesti, sicut est contrarietas calidi et frigidi: contrarietatem autem secundum differentias aliquorum generum nihil prohibet in corpore caelesti esse, puta sicut par vel impar, vel secundum aliquid huiusmodi. It can also be said that in every genus there is found a contrariety of differences, as is plain from Metaphysics X, although there is not a contrariety of species in every genus: for although "rational" and "irrational" are contrary differences, "man" and "ass" are not contrary species. Consequently, there is a contrariety between straight and circular not as between species, but as between differences of the same genus. Such contrariety, which can be discerned in motions on the basis of the difference between straight and circular, is not a corruptive contrariety, of the sort, namely, which the Philosopher here intends to exclude from the heavenly body, such as is the contrariety of hot to cold. But nothing forbids contrariety according to the differences of certain genera from being in a heavenly body, for example, that of equal and unequal, or something of that kind. Obiicit autem Ioannes grammaticus contra id quod philosophus videtur ponere concavum et gibbosum opponi secundum relationem: quia relativa videntur simul esse, concavum autem et gibbosum non sunt simul ex necessitate: potest enim esse aliquod corpus sphaericum exterius convexum absque hoc quod sit interius concavum. Sed in hoc deceptus fuit: quia philosophus hic loquitur de concavo et convexo secundum quod inveniuntur in linea circulari, non autem secundum quod inveniuntur in corpore sphaerico, in quo unum potest esse sine altero, non autem in linea. John the Grammarian, however, objects against the Philosopher's seeming to state that concave and gibbous are opposed according to a relation: because relative things seem to be co-existent, but concave and gibbous are not necessarily together, for a spherical body can be exteriorly convex without being interiorly concave. But in this he has been deceived, for the Philosopher is here speaking of concave and convex as found in a circular line, and not as found in a spherical body, in which latter one can indeed exist without the other, but not in a line. Deinde cum dicit: deinde si quis existimat etc., ostendit non esse contrarietatem in partibus motus circularis. 83. Then at [43] he shows that there is no contrariety in the parts of circular motion. Et primo excludit contrarietatem a partibus huius motus;
secundo ostendit quod contrarietas partium non sufficeret ad contrarietatem totius, ibi: si autem et istae contrariae et cetera.
First he excludes contrariety from the parts of this motion;
Secondly, he shows that contrariety of parts would not be enough for contrariety of the whole, at 88.
Circa primum tria facit: Regarding the first he does three things: primo ostendit quod non est contrarietas in partibus motus circularis quae accipiuntur secundum diversas portiones circuli, quae designantur inter duo puncta;
secundo ostendit quod non est contrarietas in partibus motus circularis quae accipiuntur secundum eundem semicirculum, ibi: similiter autem et quae in semicirculo etc.;
tertio ostendit quod non est contrarietas in partibus motus circularis quae accipiuntur secundum duos semicirculos, ibi: similiter autem et utique et cetera.
First he shows that there is not contrariety in the parts of circular motion if the parts are taken according to diverse portions of the circle which are designated between two points;
Secondly, he shows that there is not contrariety in the parts of circular motion, if the parts are taken according to the same semicircle, at 85;
Thirdly, if the parts are taken according to two semicircles, at 87.
Dicit ergo primo quod posset aliquis existimare quod eadem sit ratio contrarietatis in motu qui est per lineam circularem, et in motu qui est per lineam rectam. Si enim designetur una linea recta inter duo puncta quae sunt a et b, manifestum est quod motus localis qui fiet super lineam rectam ab a in b, contrarius erit motui locali qui fiet e converso a b in a. Sed non est similis ratio si describatur una linea circularis super duo puncta quae sunt a et b: quia inter duo puncta non potest esse nisi una linea recta, sed inter duo puncta possunt describi infinitae lineae curvae, quae sunt diversae portiones circulorum. Sequeretur igitur, si motui qui est ab a in b per lineam circularem, esset contrarius motus qui est a b in a secundum lineam circularem, quod infiniti motus essent contrarii uni. He says therefore first [43] that someone could think that the aspect of contrariety in motion upon a circular line, and that in motion upon a straight line, are the same. For if one straight line between two points, A and B, be designated, it is evident that the local motion occurring on the straight line from A to B will be contrary to the local motion from B to A. But the notion is not the same if a circular line be described through the two points, A and B, because between two points there can be but one straight line, but an infinity of curved lines, which are diverse portions of circles. Therefore it would follow that, if the motion from A to B over a circular line were contrary to the one which is from B to A over a circular line, an infinitude of motions would be contrary to one. Est autem attendendum quod, loco huius quod debuit dicere, quod linea recta est una inter duo puncta, dixit quod lineae rectae sunt finitae: quia si accipiamus in diversis locis duo puncta, erunt inter ea lineae rectae finitae; sed inter quaelibet duo puncta poterunt describi lineae curvae infinitae. But it should be observed that, in place of what he ought to have said, namely, that the straight line between two points is one, he said that straight lines are "finite" — because if we take two points in diverse places, there will be between them finite straight lines [i.e., in finite number], but between any two points there could be described an infinitude of curved lines. Obiicit autem contra hanc rationem Ioannes grammaticus, quia non videtur sequi quod uni motui sint infiniti motus contrarii, sed infiniti infinitis: quia secundum unamquamque portionem circuli qui describitur super duo puncta, erunt duo motus sibi invicem contrarii. Item videtur quod sit idem inconveniens quod sequitur ex contrarietate motuum rectorum. Manifestum est enim quod sicut inter duo puncta possunt describi infinitae lineae curvae, ita a centro mundi ad circumferentiam possunt describi infinitae lineae rectae. 84. Against this argument John the Grammarian objects, since it does not seem to follow that to one motion there is an infinitude of contrary motions, but that to an infinite number there is. For with respect to each portion of the circle described between two points there will be two motions contrary one to the other. Likewise, the same difficulty seems to follow from the contrariety of straight motions. For it is manifest that just as an infinitude of curved lines can be described between two points, so from the center of the world to the circumference there can be described an infinitude of straight lines. Sed dicendum est ad primum quod, si contrarietas sit motuum qui fiunt per lineas curvas secundum contrarietatem terminorum, sicut accidit in motibus rectis, sequitur ex hac suppositione quod quilibet motus qui fit a b in a per quamcumque linearum curvarum, sit contrarius motui qui est ab a in b: et sic sequetur quod non solum uni motui sint infiniti motus contrarii, sed quod cuilibet infinitorum motuum ex una parte incipientium, contrarientur infiniti motus qui incipiunt ex parte contraria. But in regard to the first it must be said that if the contrariety of motions that occur through curved lines is to be according to the contrariety of the termini as happens in straight motions, then, from this supposition it follows that every motion from B to A through any of the curved lines is contrary to a motion from A to B. Thus it will follow not only that there is an infinitude of motions contrary to one motion, but also that to each of the infinite motions starting from one end there will be contrary the infinitude of motions beginning from the contrary end. Ad secundum dicendum quod omnes infinitae lineae rectae quae sunt a centro ad circumferentiam, sunt aequales, et ideo designant eandem distantiam inter contrarios terminos; et ideo in omnibus est eadem ratio contrarietatis, quae importat maximam distantiam. Sed omnes lineae curvae infinitae quae describuntur super eadem puncta, sunt inaequales: unde non est in eis eadem ratio contrarietatis, quia non est una et eadem distantia accepta secundum quantitatem lineae curvae. In regard to the second it must be said that all the infinitude of straight lines from the center to the circumference are equal, and therefore designate the same distance between contrary termini — therefore in all of them is present the same aspect of contrariety, which implies maximum distance. But all the infinitude of curved lines described between the same points are unequal; hence the same aspect of contrariety is not present in them, for the distance taken with regard to the quantity of the curved line is not the same in every case. Deinde cum dicit: similiter autem et quae in semicirculo etc., ostendit quod non sit contrarietas in motu circulari secundum unum et eundem semicirculum. Posset enim aliquis dicere quod motui qui est super unam lineam curvam ab a in b, non contrariatur quilibet motus qui est a b in a per quamcumque lineam curvam, sed per unam et eandem, puta per unum semicirculum. Sit autem semicirculus gd, et sit ita quod motus qui est per semicirculum a g ad d, contrarietur motui qui est super eundem semicirculum a d ad g. 85. Then at [44] he shows that there is not contrariety in circular motion according to one and the same semicircle. For someone could say that the motion upon one curved line from A to B has as its contrary not a motion from R to A through just any curved line but through one and the same — for example, through one semicircle. Let GD be that semicircle, such that the motion through it from G to D is contrary to the one through it from D to G. Sed contra hoc procedit Aristoteles ex hoc quod eadem distantia reputatur quae est inter g et d per semicirculum, illi distantiae quae accipitur per diametrum: non quod semicirculus sit aequalis diametro, sed quia omnem distantiam mensuramus per lineam rectam. Cuius ratio est, quia omnis mensura debet esse certa et determinata et minima: inter duo autem puncta mensura lineae rectae est certa et determinata, quia non potest esse nisi una; et est minima omnium linearum quae sunt inter duo puncta. Lineae vero curvae inter duo puncta describi possunt infinitae, quae omnes sunt maiores linea recta inter eadem puncta descripta. Unde distantia quae est inter duo puncta, mensuratur per lineam rectam, et non per lineam curvam semicirculi, seu cuiuslibet alterius portionis circuli, aut maioris aut minoris circuli. Cum igitur de ratione contrarietatis sit quod habeat maximam distantiam, ut dicitur in X Metaphys., cum distantia quae est inter duo puncta non mensuretur secundum lineam curvam sed secundum rectam, consequens est quod contrarietas terminorum non faciat contrarietatem in motibus qui sunt super semicirculum, sed solum in motibus qui sunt super diametrum. But Aristotle proceeds against this on the ground that the semicircular distance from G to D is computed in terms of the diametric distance, not in the sense that the semicircle is equal to the diameter, but because we measure every distance by a straight line. The reason for this is that every measure ought to be certain and determinate and the smallest. Now between two points the length of a straight line is certain and determinate, because it can be but one, and it is the smallest of all the lines between the two points. But an infinitude of curved lines can be drawn between two points, and all are greater than the straight line drawn between the two given points. Hence the distance between two points is measured by a straight line, and not by the curved line of a semicircle or any other portion of the circle, either of a larger or a smaller circle. Therefore, since it belongs to the very notion of contrariety that it have maximum distance, as is said in Metaphysics X, then, since the distance between two points is not measured according to a curved line but according to a straight, the consequence is that a contrariety of termini does not bring about a contrariety in motions upon a semi-circle, but only in motions upon the diameter. Obiicit autem contra hoc Ioannes grammaticus, quia non solum geometrae et astrologi accipiunt quantitatem lineae curvae per lineam rectam, sed etiam e converso: probant enim quantitatem chordae per arcum, et quantitatem arcus per chordam. 86. But John the Grammarian objects against this, because not only do geometers and astronomers reckon the quantity of a curved line by a straight line, but they also do the converse: for they prove the quantity of a chord by means of the arc and that of the arc by the chord. Sed in hoc deficit ab intellectu Aristotelis. Non enim hoc intendit Aristoteles, quod linea curva mensuretur per rectam; sed quod distantia quae est inter quaelibet duo puncta, mensuretur per lineam rectam, ratione iam dicta. But in this he departs from the intent of Aristotle. For Aristotle does not intend to maintain that a curved line is measured by a straight, but the distance between any two given points is measured by a straight line, for the reason just given. Obiicit etiam quod maxima distantia est in caelo, quae est inter duo puncta opposita, puta inter principium arietis et principium librae: et tunc, si contrarietas est maxima distantia, potest secundum hanc distantiam attendi contrarietas in motu circulari. He [John] objects too that in the heavens there is a greatest distance between two opposite points: for example, between the beginning of Aries and the beginning of Libra; consequently, if contrariety is the greatest distance, then according to this distance, contrariety can be found in circular motion. Sed dicendum est quod ista distantia maxima attenditur secundum quantitatem diametri, et non secundum quantitatem semicirculi: alioquin plus distaret principium arietis a principio sagittarii, quod respicit trino aspectu, quam a principio librae, quod respicit aspectu rectae oppositionis. But to this it should be said that that greatest distance is reckoned according to the quantity of the diameter and not according to the quantity of the semicircle — otherwise the beginning of Aries would be farther from the beginning of Sagittarius, to which it has a trinary aspect, than from the beginning of Libra to which it has the aspect of right opposition. Deinde cum dicit: similiter autem et utique etc., ostendit non esse contrarietatem in motu circulari secundum duos semicirculos. Et dicit quod similis est ratio, si quis describens circulum totum, ponat motum qui est in uno semicirculo, contrarium ei qui est in alio semicirculo. Sit enim circulus cuius diameter sit ez, dividens ipsum in duos semicirculos, in uno quorum describatur I, in alio t. Posset ergo aliquis dicere quod motus qui est ab e ad z per semicirculum I, contrariatur motui qui est a z ad e per semicirculum t. Sed hoc improbatur eadem ratione qua et primum: quia scilicet distantia quae est inter e et z, non mensuratur semicirculo, sed diametro. Et adhuc alia ratio est: quia unus motus continuus est, qui incipiens ab e, venit in z per I semicirculum, et iterum per t semicirculum redit a z in e; duo autem motus contrarii non possunt sibi invicem continuari, ut patet in VIII Physic. 87. Then at [45] he shows that there is not contrariety in circular motion according to two semicircles. And he says that the reasoning is similar to describing a whole circle and positing that the motion in one semicircle is contrary to a motion in the other. For let a circle have a diameter EZ dividing it into two semicircles called I and T respectively. Now someone could say that a motion from E to Z through semicircle I is contrary to the motion from Z to E through semicircle T. But this is disproved by the same argument as the first case: namely, because the distance between E and Z is not measured by a semicircle but by the diameter. But there is still another reason: namely, the motion which begins at E and proceeds to Z through I, and then returns from Z to E through semicircle T, is one continuous motion; but two motions that are contrary cannot be continuous with one another, as is plain in Physics VIII. Deinde cum dicit: si autem et istae etc., ostendit quod etiam si istae partes motuum circularium essent contrariae, non tamen propter hoc sequeretur quod contrarietas esset in motibus circularibus secundum totum: non enim sequitur ad contrarietatem partium contrarietas totius. Et sic patet quod id quod iam ostendit philosophus de contrarietate partium motus circularis, ex abundanti prosecutus est, ut totaliter a motu circulari contrarietatem excluderet. 88. Then at [46] he shows that even if those parts of circular motions were contrary, that would be no reason for concluding that there would be contrariety in circular motions as a whole; for contrariety of parts is no proof for the contrariety of the whole. Consequently, it is plain that what the Philosopher has just showed about contrariety of the parts of circular motion has been done for added measure in order to exclude contrariety entirely from circular motion. Deinde cum dicit: at vero etc., ostendit quod toti motui circulari non est alius totus motus circularis contrarius: et hoc duabus rationibus. Quarum prima sumitur ex consideratione ipsius motus circularis in communi. Sit ergo unus circulus, super quem in tribus punctis describantur a et b et g. Super hunc autem circulum intelligantur duo motus circulares, quorum unus incipiat ab a, et per b vadat in g, et sic revertatur ad a; alius autem motus e converso, incipiens ab a, primo vadat ad g, et sic transiens per b revertatur ad a. Dicit ergo hos duos motus non esse contrarios. Uterque enim horum motuum ab eodem incipit, scilicet ab a, et in idem terminatur, scilicet in ipsum a; et sic patet quod isti duo motus non incipiunt a contrario, neque terminantur ad contrarium; contrarius autem motus localis est qui est a contrario in contrarium. Patet ergo praedictos motus circulares non esse contrarios. 89. Then at [46 bis] he shows that to one complete circular motion there is not another circular motion contrary: and this for two reasons. The first of these is based on considering circular motion in general. Therefore, take a circle upon which A, B and G are described at three points. Suppose two circular motions occur upon this circle, one beginning at A through B to G and back to A; conversely, let the other start at A through G to B and back to A. He says then that these two motions are not contrary. For each begins at the same term A and terminates at the same term, namely, A; consequently, they neither begin at terms that are contrary nor end at terms that are contrary. But a contrary local motion is one that goes from contrary to contrary. Therefore, the two circular motions in question are not contrary. Obiicit autem contra hoc iterum Ioannes grammaticus. Primo quidem quia in diversis videtur esse diversa ratio contrarietatis. Moveri enim a contrario in contrarium determinat contrarietatem in motibus rectis: unde non oportet, si talis contrarietas non est in motibus circularibus, quod propter hoc nulla contrarietas in eis esse possit. Item, sicut est de ratione motus contrarii in motibus rectis quod sit de contrario in contrarium, ita est de ratione motus quod sit de uno in aliud. Per hoc autem quod motus circularis est ab eodem in idem, non solum excluditur quod non sit de contrario in contrarium, sed etiam quod non sit de uno in aliud. Ergo non solum excluditur a motibus circularibus quod non sint contrarii, sed etiam quod penitus non sint motus. 90. The objector against this is once more John the Grammarian. First on the ground that the notion of contrariety in diverse things is seen to be diverse. For to be moved from contrary to contrary determines contrariety in straight motions; hence it is not necessary, if such contrariety is not present in circular motions, that on this account no contrariety may exist therein. Likewise, just as it is of the very nature of contrary motion in straight motions to be from contrary to contrary, so it is of the very nature of motion to be from one thing to another. Now, by the very fact that circular motion is from the same to the same, not only is it not from contrary to contrary, but it is not from one thing to another. Therefore there is excluded from circular motions not only that they be contrary, but that they be motions at all. Dicendum est autem ad primum quod esse a contrario in contrarium non est ratio contrarietatis propria in motibus localibus qui sunt secundum lineam rectam; sed est communis ratio contrarietatis in omnibus motibus, ut patet in V Physic. Et huius ratio est, quia contrarietas est differentia secundum formam, ut ostenditur in X Metaphys.; motus autem habet formam seu speciem ex suo termino; et ideo in nullo motu potest esse contrarietas absque contrarietate terminorum. To the first objection it should be replied that to be from contrary to contrary is not a special property of the contrariety found in local motions in a straight line, but it is a common property of contrariety in all motions, as is plain in Physics V. And the reason for this is that contrariety is a difference according to form, as is shown in Metaphysics X. Now a motion possesses form or species from its terminus. Therefore, there can be contrariety in no motion, unless there is contrariety of termini. Ad secundum dicendum quod motus circularis, quia est primus motuum, minimum habet de diversitate et plurimum de uniformitate. Et hoc quidem apparet proportionaliter in mobili et in motu. In mobili quidem, quia non mutat suum ubi secundum totum subiecto, sed solum ratione: pars vero quaelibet mutat suum ubi etiam subiecto, ut ostensum est in VI Physic. Et similiter etiam pars motus circularis est de uno in aliud subiecto differens: totus autem motus circularis est quidem de eodem in idem secundum subiectum, sed est de uno in aliud differens sola ratione. Si enim accipiatur circulatio una quae ab a redit in a, ipsum a, quod est terminus a quo et in quem, est idem subiecto, sed differt ratione, inquantum accipitur ut principium et finis. Et ideo, quia motus circularis plurimum habet de unitate, est natura eius longinqua a contrarietate, quae est maxima distantia. Et ideo talis motus competit primis corporibus, quae sunt propinquissima substantiis simplicibus, quae penitus contrarietate carent. To the second it must be said that circular motion, because it is the first of motions, has a minimum of diversity and a maximum of uniformity. And this even appears proportionally in the mobile and in the motion. In the mobile, indeed, because it does not change its "where" with respect to the whole subject, but only in conception, whereas each part changes its "where" even as to subject, as was shown in Physics VI. And similarly a part of a circular motion is from one to another with a difference as to subject; but the whole circular motion is indeed from the same to the same according to subject, but from one thing to another that differs only in conception. For if we take one circular motion from A to A, the A which is the terminus a quo and the terminus ad quem is the same as to subject, but differs in conception, insofar as it is taken now as beginning and now as end. And therefore, because circular motion has the most unity, its nature is very far from contrariety, which is a maximum distance. That is why such motion belongs to the first bodies which are the nearest to the simple substances which completely lack contrariety. Secundam rationem ponit ibi: si autem et esset et cetera. Et haec quidem ratio sumitur per applicationem circularis motus ad corpora naturalia. Quae quidem ratio talis est. Si unus motus circularis esset contrarius alii, oporteret quod alter eorum esset frustra; sed nihil est frustra in natura; ergo non sunt duo motus circulares contrarii. 91. The second argument is at [47], and this argument is based on applying circular motion to natural bodies. And this is the argument: If one circular motion were contrary to another, then one of them would have to be in vain. But nothing in nature is in vain. Therefore, there are not two contrary circular motions. Conditionalem autem probat sic. Si essent duo motus circulares contrarii, oporteret quod corpora quae moverentur illis duobus motibus, transirent per eadem signa in circulo signata: et hoc ideo, quia contrarietas motus localis exigit contrarietatem locorum, quae attingit utrumque mobilium. Si ergo essent motus circulares contrarii, oporteret quod loca aliqua designarentur contraria in circulo. In recta quidem linea designantur sola duo loca contraria, quae scilicet maxime distant: alia vero loca signata per lineam rectam, quae sunt infra duo loca extrema, cum non maxime distent, non habent contrarietatem ad invicem. Sed in circulo cuiuslibet puncti est accipere maximam distantiam ad aliquod aliud punctum circuli: quia a quolibet puncto signato in circulo contingit ducere aliquam diametrum, quae est maxima linearum rectarum cadentium in circulo; dictum est autem quod omnis distantia mensuratur secundum lineam rectam. Quia igitur ea quae moventur contrariis motibus, necesse est attingere contraria loca, necesse est, si motus circulares sint contrarii, quod utrumque corpus circulariter motum, a quovis puncto circuli moveri incipiat, perveniat ad omnia loca circuli, quae omnia sunt contraria. Nec est inconveniens si in circulo describantur loca contraria secundum omnem partem: quia contrarietates loci accipiuntur non solum secundum sursum et deorsum, sed etiam secundum ante et retro, et dextrum et sinistrum; dictum est autem quod contrarietates motus localis accipiuntur secundum contrarietates locorum; et sic, si motus circulares sunt contrarii, necesse est accipi contrarietates in circulo secundum praedicta. The truth of the conditional proposition he proves in the following manner: If there were two contrary circular motions, then the bodies subject to them ought to pass through the same signs marked on a circle. The reason for this is that contrariety of local motion demands contrariety of the places, which affect both mobiles. Consequently, if there were contrary circular motions, then contrary places should be able to be designated on the circle. Now on a straight line only two contrary places are designated, namely, those the greatest distance apart, while other places designated on that line, since they are within the extreme places, are not contrary to one another. But on a circle any point at random can be at a greatest distance from some other point on the circle: because from any point on the circle a diameter can be drawn, which is the greatest of the straight lines falling in the circle. And it has been said that every distance is measured according to a straight line. Therefore, because things in contrary motions must reach contrary places, then if circular motions are contrary, it is necessary that each body in circular motion, no matter from which point of the circle its motion begins, reach all the places of the circle, all of which are contrary. (Nor is it unfitting that in a circle places be marked as in every way contrary — for contrariety of place is taken not only with respect to up and down, but according to ahead and to the rear, and left and right.) But it has been said that the contraries of local motion are based on contrariety of places. And thus, if circular motions are contrary, the contrarieties in the circle must be taken according to the forementioned. Ex his autem sequitur quod alterum motuum vel corporum esset frustra. Quia si aequales essent magnitudines motae, idest aequalis virtutis, neutra ipsarum moveretur; quia una totaliter impediret alteram, cum oporteret utramque transire per eadem loca. Si vero alter motus dominaretur propter praeeminentiam virtutis in altero mobilium vel moventium, consequens est quod alter motus esse non posset; quia totaliter impediretur per motum fortiorem. Itaque, si ambo corpora essent, quae essent nata moveri contrariis motibus circularibus, frustra esset alterum ipsorum corporum, quod non posset moveri illo motu qui impediretur per fortiorem: unumquodque enim dicimus esse frustra, quod non potest habere suum usum, sicut dicimus calceamentum esse frustra, quo non potest aliquis calceari. Et similiter corpus erit frustra, quod non poterit moveri proprio motu: et etiam motus erit frustra, quo nihil potest moveri. Now from all this it follows that one of the motions or of the bodies would be in vain. For if the magnitudes moved were equal, i.e., of equal power, neither would be moved, because one would totally obstruct the other, since both would have to traverse the same places. But if one motion dominated on account of a greater power in one of the mobiles or movers, then the other motion could not exist, because it would be totally obstructed by the stronger motion. Therefore, if both were bodies apt to be moved with contrary circular motions, one of them would exist in vain, for it could not be moved with that motion which was obstructed by the stronger. For we say that a thing is "in vain" when it does not realize its usefulness, as we say that a shoe is in vain if no one can wear it. In like manner, a body would be in vain, if it could not be moved with its proper motion; and likewise a motion would be in vain if nothing could be moved with it. Sic ergo patet quod, si sint duo motus circulares contrarii, necesse est aliquid esse frustra in natura. Sed quod hoc sit impossibile, probat sic. Omne quod est in natura, vel est a Deo, sicut primae res naturales; vel est a natura sicut a secunda causa, puta inferiores effectus. Sed Deus nihil facit frustra, quia, cum sit agens per intellectum, agit propter finem. Similiter etiam natura nihil facit frustra, quia agit sicut mota a Deo velut a primo movente; sicut sagitta non movetur frustra, inquantum emittitur a sagittante ad aliquid certum. Relinquitur ergo quod nihil in natura sit frustra. Consequently, it is plain that if there are two contrary circular motions, there would have to be something in vain in nature. But that this is impossible he now proves: Whatever exists in nature is either from God, as are the first natural things, or from nature as from a second cause, as, for example, lower effects. But God makes nothing in vain, because, since He is a being that acts through understanding, He acts for a purpose. Likewise nature makes nothing in vain, because it acts as moved by God as by a first mover, just as an arrow is not moved in vain, inasmuch as it is shot by the bowman at some definite thing. What remains, therefore, is that nothing in nature is in vain. Est autem attendendum quod Aristoteles hic ponit Deum esse factorem caelestium corporum, et non solum causam per modum finis, ut quidam dixerunt. It should be noted that Aristotle here posits God to be the maker of the celestial bodies, and not just a cause after the manner of an end, as some have said. Obiicit autem contra hanc rationem Ioannes grammaticus, quia pari ratione posset aliquis concludere quod in motibus rectis non sit contrarietas; quia contraria mobilia impediunt se invicem. 92. John the Grammarian objects against this argument that, for the same reason, someone could conclude that there is no contrariety in straight motions, because contrary mobiles obstruct one another. Sed dicendum quod alia ratio est in motibus rectis et circularibus, propter duo. Primo quidem quia duo corpora moventur contrariis motibus rectis absque eo quod se invicem impediant, eo quod non attenditur contrarietas in motibus rectis nisi secundum extrema linearum rectarum, puta secundum centrum mundi et circumferentiam eius: a centro autem ad circumferentiam possunt infinitae lineae duci, ita quod id quod movetur per unam earum sursum, non impedit id quod movetur per aliam deorsum. Sed in motu circulari eadem ratio contrarietatis est in omnibus partibus circuli: et ideo oportebit quod per eadem loca circuli utrumque transeat; et sic ex necessitate oportet quod motus circulares contrarii se invicem impediant. But it should be said that the case with straight motions is different from that of circular, for two reasons. First, because two bodies are moved with contrary straight motions without mutually obstructing one another, for in straight motions contrariety is not reckoned except with respect to the extremes of straight lines, for example, with respect to the center of the world and its circumference. Now from the center to the circumference an infinitude of lines can be drawn so that what is moved upward through one of them does not obstruct what is being moved downward through another. But in circular motion the same aspect of contrariety is present in all parts of the circle. Therefore it will be necessary that both move through the same places of the circle. And so of necessity contrary circular motions would have to obstruct one another. Secundo est diversa ratio utrobique, quia corpus quod movetur naturaliter motu recto, sicut naturaliter est aptum corrumpi, ita naturaliter est aptum impediri: unde si impediatur, non est hoc frustra, sicut nec quod corrumpatur. Sed corpus circulariter motum est naturaliter incorruptibile; unde non est natum impediri: unde si in natura esset aliquid impeditivum ipsius, esset frustra. Secondly, in the two cases the aspect is different — for in the case of a body that is being naturally moved with a straight motion, just as it is naturally apt to be corrupted, so it is naturally apt to be obstructed. Hence, if it is obstructed, this is no more in vain than if it be corrupted. But a body circularly moved is naturally incorruptible: hence it is not apt to be obstructed. Hence if there were in nature something to impede it, that impediment would be useless. Item potest obiici de motu planetarum, qui moventur propriis motibus ab occidente in orientem; quod videtur esse in contrarium motus firmamenti, quod movetur motu diurno ab oriente in occidentem. 93. Likewise, it can be objected about the motion of the planets which are moved with their own motions from west to east, which seems to be contrary to the motion of the firmament which in its diurnal motion is from east to west. Sed dicendum est quod tales motus habent quidem aliquam diversitatem ad invicem, quae designat aliquo modo diversam naturam mobilium: non tamen est aliqua contrarietas, propter tria. But it must be said that such motions have indeed a certain mutual diversity which somehow designates the diverse natures of the mobiles. But, for three reasons, there is no contrariety: Primo quidem quia huiusmodi diversitas non est secundum contrarios terminos, sed secundum contrarias vias perveniendi ad eundem terminum; puta quia firmamentum a puncto orientis movetur ad punctum occidentis per hemisphaerium superius, et redit ad punctum orientis per hemisphaerium inferius, planeta autem movetur a puncto occidentis ad orientem per aliud hemisphaerium. First, this is so, because diversity of this kind is not based on contrary termini but on contrary ways of reaching the same terminus: for example, because the firmament is moved from the eastern point to the western point through the upper hemisphere, and returns to the eastern point through the lower hemisphere, while a planet is moved from a western point to the east through another hemisphere. Moveri autem diversis viis ad eundem finem, non facit contrarietatem actionum vel motuum, sed pertinet ad diversum ordinem motuum et mobilium: quia quod nobiliori via pertingit ad terminum est nobilius, sicut melior medicus est qui efficaciori via sanitatem inducit. Et inde est quod motus primus firmamenti est nobilior secundo motu, qui est planetarum, sicut et supremus orbis est nobilior. Unde et orbes planetarum moventur motu primi orbis absque hoc quod impediantur a suis propriis motibus. But to be moved to the same end by diverse routes does not make for contrariety of actions or passions, but pertains to the diverse order of the motions and mobiles — for what reaches its terminus by a nobler route is nobler, just as a better doctor is one who induces health by a more efficacious way. Hence the first motion of the firmament is nobler than the second motion, i.e., that of the planets, just as the supreme orb is nobler. Wherefore, the orbs of the planets are moved with the motion of the first orb without their being impeded from their own proper motions. Secunda ratio est, quia quamvis uterque motus sit super idem centrum, est tamen uterque motus super alios et alios polos: unde non sunt contrarii. The second reason is that, although each motion is over the same center, nevertheless they are over other and other poles; hence they are not contrary. Tertia ratio est, quia non sunt in eodem circulo, sed motus planetarum sunt in inferioribus circulis. The third reason is that they are not in the same circle, but the motions of the planets are in the lower circles. Oportet autem contrarietatem attendi circa eandem distantiam, sicut patet in motibus rectis, quorum contrarietas consistit in distantia centri et circumferentiae. But contrariety must be reckoned with respect to the same distance, as is plain in straight motions, the contrariety of which consists in the distance from the center to the circumference.
Lecture 9:
The need for treating of the infinity of the universe.Chapter 5 (271b.) Ἀλλ' ἐπεὶ δῆλον περὶ τούτων, περὶ τῶν λοιπῶν σκεπτέον, καὶ πρῶτον πότερον ἔστι τι σῶμα ἄπειρον, ὥσπερ οἱ πλεῖστοι τῶν ἀρχαίων φιλοσόφων ᾠήθησαν, ἢ τοῦτ' ἔστιν ἕν τι τῶν ἀδυνάτων 48 This being clear, we must go on to consider the questions which remain. First, is there an infinite body, as the majority of the ancient philosophers thought, or is this an impossibility? τὸ γὰρ οὕτως ἢ ἐκείνως ἔχειν οὔ τι μικρὸν ἀλλ' ὅλον διαφέρει καὶ πᾶν πρὸς τὴν περὶ τῆς ἀληθείας θεωρίαν σχεδὸν γὰρ αὕτη πασῶν ἀρχὴ τῶν ἐναντιώσεων τοῖς ἀποφηναμένοις τι περὶ τῆς ὅλης φύσεως καὶ γέγονε καὶ γένοιτ' ἄν, 49 The decision of this question, either way, is not unimportant, but rather all-important, to our search for the truth. It is this problem which has practically always been the source of the differences of those who have written about nature as a whole. So it has been and so it must be; εἴπερ καὶ τὸ μικρὸν παραβῆναι τῆς ἀληθείας ἀφισταμένοις γίνεται πόρρω μυριοπλάσιον. Οἷον εἴ τις ἐλάχιστον εἶναί τι φαίη μέγεθος οὗτος γὰρ τοὐλάχιστον εἰσαγαγὼν τὰ μέγιστ' ἂν κινήσειε τῶν μαθηματικῶν. Τούτου δ' αἴτιον ὅτι ἡ ἀρχὴ δυνάμει μείζων ἢ μεγέθει, διόπερ τὸ ἐν ἀρχῇ μικρὸν ἐν τῇ τελευτῇ γίνεται παμμέγεθες. Τὸ δ' ἄπειρον καὶ ἀρχῆς ἔχει δύναμιν καὶ τοῦ ποσοῦ τὴν μεγίστην, ὥστ' οὐδὲν ἄτοπον οὐδ' ἄλογον τὸ θαυμαστὴν εἶναι τὴν διαφορὰν ἐκ τοῦ λαβεῖν ὡς ἔστι τι σῶμα ἄπειρον. Διὸ περὶ αὐτοῦ λεκτέον ἐξ ἀρχῆς ἀναλαβοῦσιν. 50 since the least initial deviation from the truth is multiplied later a thousandfold. Admit, for instance, the existence of a minimum magnitude, and you will find that the minimum which you have introduced, small as it is, causes the greatest truths of mathematics to totter. The reason is that a principle is great rather in power than in extent; hence that which was small at the start turns out a giant at the end. Now the conception of the infinite possesses this power of principles, and indeed in the sphere of quantity possesses it in a higher degree than any other conception; so that it is in no way absurd or unreasonable that the assumption that an infinite body exists should be of peculiar moment to our inquiry. The infinite, then, we must now discuss, opening the whole matter from the beginning. Ἀνάγκη δὴ πᾶν σῶμα ἤτοι τῶν ἁπλῶν εἶναι ἢ τῶν συνθέτων, ὥστε καὶ τὸ ἄπειρον ἢ ἁπλοῦν ἔσται ἢ σύνθετον. Ἀλλὰ μὴν καὶ ὅτι γε πεπερασμένων τῶν ἁπλῶν ἀνάγκη πεπερασμένον εἶναι τὸ σύνθετον, δῆλον τὸ γὰρ ἐκ πεπερασμένων καὶ πλήθει καὶ μεγέθει συγκείμενον πεπέρανται καὶ πλήθει καὶ μεγέθει τοσοῦτον γάρ ἐστιν ἐξ ὅσων ἐστὶ συγκείμενον. Λοιπὸν τοίνυν ἰδεῖν πότερον ἐνδέχεταί τι τῶν ἁπλῶν ἄπειρον εἶναι τὸ μέγεθος, ἢ τοῦτ' ἀδύνατον. Προχειρισάμενοι δὴ περὶ τοῦ πρώτου τῶν σωμάτων, οὕτω σκοπῶμεν καὶ περὶ τῶν λοιπῶν. 51 Every body is necessarily to be classed either as simple or as composite; the infinite body, therefore, will be either simple or composite. But it is clear, further, that if the simple bodies are finite, the composite must also be finite, since that which is composed of bodies finite both in number and in magnitude is itself finite in respect of number and magnitude: its quantity is in fact the same as that of the bodies which compose it. What remains for us to consider, then, is whether any of the simple bodies can be infinite in magnitude, or whether this is impossible. Let us try the primary body first, and then go on to consider the others. Ὅτι μὲν τοίνυν ἀνάγκη τὸ σῶμα τὸ κύκλῳ φερόμενον πεπεράνθαι πᾶν, ἐκ τῶνδε δῆλον. 52 The body which moves in a circle must necessarily be finite in every respect, for the following reasons. Εἰ γὰρ ἄπειρον τὸ κύκλῳ φερόμενον σῶμα, ἄπειροι ἔσονται αἱ ἀπὸ τοῦ μέσου ἐκβαλλόμεναι. Τῶν δ' ἀπείρων τὸ διάστημα ἄπειρον διάστημα δὲ λέγω τῶν γραμμῶν, οὗ μηδὲν ἔστιν ἔξω λαβεῖν μέγεθος ἁπτόμενον τῶν γραμμῶν. Τοῦτ' οὖν ἀνάγκη ἄπειρον εἶναι τῶν γὰρ πεπερασμένων ἀεὶ ἔσται πεπερασμένον. Ἔτι δ' ἀεὶ ἔστι τοῦ (272a.) δοθέντος μεῖζον λαβεῖν, ὥστε καθάπερ ἀριθμὸν λέγομεν ἄπειρον, ὅτι μέγιστος οὐκ ἔστιν, ὁ αὐτὸς λόγος καὶ περὶ τοῦ διαστήματος εἰ οὖν τὸ μὲν ἄπειρον μὴ ἔστι διελθεῖν, ἀπείρου δ' ὄντος ἀνάγκη τὸ διάστημα ἄπειρον εἶναι, οὐκ ἂν ἐνδέχοιτο κινηθῆναι κύκλῳ 53 (1) If the body so moving is infinite, the radii drawn from the centre will be infinite. But the space between infinite radii is infinite: and by the space between the radii I mean the area outside which no magnitude which is in contact with the two lines can be conceived as falling. This, I say, will be infinite: first, because in the case of finite radii it is always finite; and secondly, because in it one can always go on to a width greater than any given width; thus the reasoning which forces us to believe in infinite number, because there is no maximum, applies also to the space between the radii. Now the infinite cannot be traversed, and if the body is infinite the interval between the radii is necessarily infinite: circular motion therefore is an impossibility. τὸν δ' οὐρανὸν ὁρῶμεν κύκλῳ στρεφόμενον, καὶ τῷ λόγῳ δὲ διωρίσαμεν ὅτι ἐστί τινος ἡ κύκλῳ κίνησις. 54 Yet our eyes tell us that the heavens revolve in a circle, and by argument also we have determined that there is something to which circular movement belongs.
Postquam philosophus ostendit perfectionem universi et ex quibus partibus eius perfectio integretur, hic incipit inquirere de infinitate ipsius; quia, ut dicitur in III Physic., quidam rationem perfecti attribuerunt infinito. 94. After explaining the perfection of the universe and pointing out the parts that make it complete, the Philosopher here begins to inquire into its infinity, because, as is said in Physics III, some have attributed the notion of "perfect" to the infinite. Potest autem aliquid dici infinitum tripliciter: uno modo secundum magnitudinem, alio modo secundum numerum, tertio modo secundum durationem. Now something can be said to be infinite in three ways: in one way with respect to magnitude; in another with respect to number, and in a third way with respect to duration. Primo igitur inquirit utrum universum sit infinitum secundum magnitudinem;
secundo utrum sit infinitum secundum multitudinem, utrum scilicet sit unus mundus tantum, vel infiniti seu plures, ibi: quia autem neque plures etc.;
tertio utrum sit infinitum duratione, quasi semper existens, ibi: his autem determinatis et cetera.
First, then, he asks whether the universe is infinite according to magnitude;
Secondly, whether according to multitude, i.e., whether there is just one world, or an infinitude, or many (L. 16);
Thirdly, whether it is infinite in duration, as though ever existing (L.22).
Circa primum duo facit: About the first he does two things: primo dicit prooemialiter de quo est intentio;
secundo exequitur propositum, ibi: quod quidem igitur necesse et cetera.
First he speaks in a prefatory manner about his intention;
Secondly, he carries out his proposal, at 99.
Circa primum tria facit: About the first he does three things: primo dicit de quo est intentio;
secundo assignat rationem suae intentionis, ibi: sic enim aut illo modo etc.;
tertio determinat modum agendi, ibi: necesse itaque et cetera.
First he states his intention;
Secondly, he assigns the reason for his intention, at 96;
Thirdly, he decides upon a method of treatment, at 98.
Dicit ergo primo quod, quia manifestum est de praedictis, quod motui circulari non est aliquis motus contrarius, et de aliis quae dicta sunt, oportet nunc intendere ad ea quae residua sunt. Et primo inquirendum est utrum sit aliquod corpus infinitum in actu secundum magnitudinem, sicut plurimi antiquorum philosophorum putaverunt (omnes scilicet qui posuerunt unum principium materiale, puta ignem aut aerem aut aquam aut aliquod medium horum); vel potius hoc est impossibile, quod sit aliquod corpus infinitum in actu, sicut probatum est in III Physic., supponendo tamen quod non sit aliud corpus praeter quatuor elementa, secundum opinionem aliorum. Sed quia iam probavit quod est aliquod corpus praeter quatuor elementa, repetit hanc considerationem, ut universalior sit inquisitio veritatis. 95. He says therefore first [48] that because it is now clear with respect to the foregoing, namely, that there is no motion contrary to circular motion, and as to the other things mentioned, we must now direct our attention to what remains. And first we must inquire whether there exists any body infinite in act with respect to magnitude, as very many of the early philosophers thought (i.e., all those who posited one material principle, such as fire, or air, or water, or something intermediate); or whether it is impossible that there be a body infinite in act, as was proved in Physics III, supposing, however, that there is no body other than the four elements, according to the opinion of others. Since, however, he has just now proved that there is another body besides the four elements, he therefore repeats this consideration in order that the search for the truth may be more universal. Deinde cum dicit: sic enim aut illo modo etc., assignat rationem suae intentionis, ex diversitate quae accidit propter praedictam positionem. Et primo proponit hanc diversitatem consequentem. Et dicit quod non modicum differt in comparatione ad speculationem veritatis in naturali philosophia, utrum hoc aut illo modo se habeat, scilicet quod sit aliquod corpus infinitum secundum magnitudinem vel non: sed magis inducit differentiam circa totum, idest circa totum universum, et circa omnem considerationem naturalem. Hoc enim quod dictum est, fere fuit in praeterito, et erit in futuro principium omnium contradictionum inter eos qui aliquid enuntiaverunt de tota natura rerum. Illi enim qui posuerunt unum infinitum principium, posuerunt alia fieri quasi per separationem ab illo principio; et sic, propter infinitatem illius principii, dixerunt generationem rerum non deficere; sicut si aliquis diceret quod ex infinita massa possunt fieri panes in infinitum. Illi vero qui posuerunt principia finita, dixerunt fieri res in infinitum per reciprocam congregationem et separationem elementorum. Then at [49] he gives a reason for his intention, from the diversity that happens on account of the aforesaid position. And first he mentions this con sequent diversity, and says that it makes no slight difference to the speculation of truth in natural philosophy whether things are this way or that, i.e., whether or not there exists a body that is infinite according to magnitude. Rather, it does make a difference with respect to the whole universe and every natural consideration. For what has just been said, was in the past, and will be in the future, the source of almost all the contradictions between those who have put forth anything about the whole nature of things. For those who posited one infinite principle assumed that all things come to be by a kind of separation from that principle: thus, on account of the infinitude of that principle, they said that the generation of things does not fail. It is as though someone said that from an infinite mass of dough, loaves of bread could be made ad infinitum. But those who posited finite principles said that things come to be ad infinitum through a reciprocal commingling and separating of the elements. Deinde cum dicit: siquidem qui modicum etc., assignat causam quare tanta diversitas ex hoc sequatur: quia scilicet qui modicum transgreditur a veritate circa principium, procedens in ulteriora fit magis longe a veritate decies millies. Et hoc ideo, quia omnia subsequentia dependent ex suis principiis. Et hoc maxime apparet in errore viarum: quia qui parum elongatur a recta via, postmodum procedens fit multum longe. Et ponit exemplum de eo quod dictum est, in his qui posuerunt aliquam minimam magnitudinem, sicut Democritus posuit corpora indivisibilia: sic autem introducens aliquid minimum in quantitate, destruit maximas propositiones mathematicorum, puta quod lineam datam contingit secari in duo media. Et huius causa est, quia principium, etsi sit modicum magnitudine, est tamen magnum virtute, sicut ex modico semine producitur magna arbor: et inde est quod illud quod est modicum in principio, in fine multiplicatur, quia pertingit ad totum id ad quod se extendit virtus principii, sive hoc sit verum sive falsum. Infinitum autem habet rationem principii (omnes enim quicumque sunt locuti de infinito, posuerunt infinitum esse principium, ut dictum est in III Physic.); et cum hoc habet maximam virtutem quantum ad quantitatem, quia excedit omnem quantitatem datam. Si igitur principium quod est minimum quantitate, facit magnam differentiam in sequentibus, multo magis infinitum, quod non solum excedit in virtute principii, sed etiam in quantitate. Et ideo neque inconveniens neque irrationabile est, si mirabilis differentia sequatur in scientia naturali ex eo quod sumitur aliquod corpus esse infinitum. Et ideo de hoc dicendum est, resumendo considerationem nostram a principio quod supra accepimus, de differentia simplicium corporum et compositorum. 97. Then at [50] he assigns the cause why such diversity follows from this: it is because one who makes a slight departure from the truth in his principles gets 10,000 times farther from the truth as he goes on. This is so because all things that follow depend on their principles. This is especially clear in an error at the crossroads: for one who at the beginning is only a slight distance from the right road gets very far away from it later on. And he gives, as an example of what he is talking about, the case of those who posited a smallest magnitude, as Democritus posited indivisible bodies. By thus introducing a least quantity, he overthrew the most important propositions of mathematics — for example, that any given line can be cut into two halves. The reason for this effect is that a principle, though small in stature, is nevertheless great in power, just as from a small seed a mammoth tree is produced. Hence it is that what is small in the beginning becomes multiplied in the end, because it reaches unto all that to which the power of the principle extends, whether this be true or false. Now the infinite has the nature of a principle (for all who have spoken about the infinite considered it a principle, as was said in Physics III); besides, the infinite has the greatest force with respect to quantity, because it exceeds every given quantity. If, therefore, a principle which is the least in quantity makes a great difference in what follows from it, then much more is this so of the infinite, which is outstanding not only in virtue of being a principle but also in quantity. Consequently, it is neither inappropriate nor unreasonable that a remarkable difference should follow in natural science from the assumption that some body is infinite. And therefore it must be discussed by resuming our consideration from the principle which we accepted above about the difference between simple and composite bodies. Deinde cum dicit: necesse itaque etc., ostendit quo ordine agendum sit. Et dicit quod necesse est omne corpus aut de numero simplicium esse aut de numero compositorum corporum: unde oportet quod etiam corpus infinitum aut sit simplex aut compositum. Iterum manifestum est quod, si corpora simplicia essent finita multitudine et magnitudine, necesse est quod compositum sit finitum et multitudine et magnitudine: tantam enim quantitatem habet corpus compositum, quanta est quantitas corporum simplicium ex quibus componitur. Ostensum est autem supra quod corpora simplicia sunt finita multitudine, quia non est aliquod corpus praeter praedicta. Restat igitur videre utrum aliquod corpus simplicium sit infinitum magnitudine, vel si hoc sit impossibile. Et hoc quidem ostendemus primo argumentantes de primo corporum, quod scilicet circulariter movetur; et sic intendemus ad reliqua corpora, quae scilicet moventur motu recto. Then he points out what order must be followed, and says that of necessity every body is either a member of the simple group or of the composite group. Consequently an infinite body must be one or the other. Again, it is plain that if simple bodies are finite in multitude and magnitude, so too must composite body be — for a composite body has as much quantity as the quantity of the simple bodies of which it is composed. However, it has been shown above that simple bodies are finite in multitude, because there is no body other than the ones mentioned. It remains, therefore, to see whether any of the simple bodies is infinite in magnitude, or whether this is impossible. And this we shall show by first arguing from the first body, i.e., the one that is moved circularly; then we shall consider the remaining bodies, namely, those moved with a straight motion. Deinde cum dicit: quod quidem igitur etc., ostendit quod non sit corpus infinitum: 99. Then at [52] he shows that there is not an infinite body: et primo propriis rationibus de singulis corporibus;
secundo tribus communibus rationibus de omnibus, ibi: quod quidem igitur non est infinitum corpus et cetera.
First with reasons proper to the individual bodies;
Secondly, with three general reasons applying to all, (L. 13).
Circa primum duo facit: As to the first he does two things: primo ostendit propositum in corpore quod circulariter movetur;
secundo in corporibus quae moventur motu recto, ibi: sed adhuc neque quod ad medium et cetera.
First he proves the proposition as to the body moved circularly;
Secondly, as to the bodies moved with a straight motion, (L. 12).
Circa primum duo facit. About the first he does two things: Primo proponit quod intendit: et dicit quod manifestum est ex his quae dicentur, quod necesse est omne corpus quod circulariter fertur, esse finitum (hoc enim est primum corporum).
Deinde cum dicit: si enim infinitum etc., probat propositum sex rationibus: quarum prima talis est. Si aliquod corpus est infinitum, non potest moveri circulariter; sed corpus primum movetur circulariter; ergo non est infinitum.
First he proposes his intention and says that it is plain from what will be said that every circularly moved body must be finite (for this is the first of bodies).
Then at [53] he proves his proposition with six arguments, the first of which is this: If any body is infinite, it cannot be moved circularly; but the first body is moved circularly. Therefore, it is not infinite.
Primo ergo probat conditionalem sic: quia si corpus quod circulariter fertur est infinitum, necesse est quod lineae rectae quae egrediuntur a centro ipsius, sint infinitae; protenduntur enim quamdiu durat corporis quantitas. Distantia autem quae est inter infinitas lineas, est infinita. First, then, he proves the conditional proposition as follows: If a circularly moved body is infinite, then the straight lines proceeding from its center are infinite, for they are extended as far as the quantity of the body. But the distance between the infinite lines is infinite. Posset autem aliquis dicere quod, etiam si sint lineae infinitae a centro egredientes, tamen inter eas est aliqua distantia finita: quia omnis distantia mensuratur secundum lineam rectam, potest autem aliqua linea finita protrahi infra duas praedictas lineas, puta in propinquitate ad centrum. Sed manifestum est quod extra illam lineam poterit alia linea recta maior protrahi inter illas lineas de quibus primo loquebamur. Et ideo dicit quod non loquitur de distantia quam mensurant tales lineae; sed illam distantiam dicit esse infinitam, quae mensuratur per lineam extra quam non est sumere aliquam aliam lineam maiorem, quae tangat utramque primarum linearum. Now someone might say that even if there are infinite lines from the center, yet the distance between them is finite, because every distance is measured according to a straight line, and a finite line can be drawn between two such radii, for example, very close to the center. But it is clear that beyond that line a greater straight line can be drawn between the lines we first mentioned. And therefore he says that he is not speaking of the distance that such lines measure, but that that distance is infinite which is measured by a line beyond which no greater line can be taken, and which touches each of the first lines. Et talem distantiam probat esse infinitam dupliciter. Primo quidem quia omnis talis distantia finita est inter lineas egredientes a centro finitas: oportet enim quod iidem sint termini linearum egredientium a centro, et lineae finitae mensurantis extremam distantiam inter eas. That this distance is infinite he proves in two ways. First, because every such distance between any finite lines proceeding from the center is finite; for the ends of the lines proceeding from the center and of the finite line measuring the greatest distance between them must coincide. Secundo probat idem per hoc quod qualibet distantia data inter duas lineas mensuratas egredientes a centro, est accipere aliam maiorem, sicut quolibet numero dato est accipere maiorem: unde sicut est infinitum in numeris, ita est infinitum in tali distantia. Secondly, he proves the same point because it is possible, if the distance between two measured lines proceeding from the center is given, to take another distance which is greater, just as it is possible to take a number greater than a given number. Hence, just as the infinite is in numbers, so is it in this distance under discussion. Ex hoc sic argumentatur. Infinitum non est pertransire, ut probatum est in VI Physic.; sed si corpus sit infinitum, necesse est quod distantia sit infinita inter lineas egredientes a centro, ut probatum est; ad hoc autem quod fiat motus circularis, oportet quod una linea egrediens a centro pertingat ad situm alterius; sic igitur nunquam contingeret aliquid circulariter moveri. From this he argues as follows: The infinite cannot be traversed, as was proved in Physics VI. But if a body be infinite, the distance between the lines proceeding from the center must be infinite, as was proved. But in order that circular motion occur, one line proceeding from the center must reach the position of another. Consequently, it could never happen that anything be moved circularly. Secundo ibi: caelum autem videmus etc., probat destructionem consequentis dupliciter: primo quidem quia ad sensum videmus quod caelum circulariter movetur; secundo quia supra per rationem probatum est quod motus circularis est alicuius corporis. Unde relinquitur quod impossibile sit corpus esse infinitum, quod circulariter movetur. 101. Secondly, at [54] he proves in two ways the destruction of the consequent. First, because it is evident to sense that the heavens are moved circularly; secondly, because it was proved above by reason that circular motion belongs to some body. What remains, therefore, is that it is impossible for the circularly moved body to be infinite.
Lecture 10:
The second and third reasons proving the circularly moved body not infiniteChapter 5 cont. Ἔτι ἀπὸ πεπερασμένου χρόνου ἐὰν ἀφέλῃς πεπερασμένον, ἀνάγκη καὶ τὸν λοιπὸν εἶναι πεπερασμένον καὶ ἔχειν ἀρχήν. Εἰ δ' ὁ χρόνος ὁ τῆς βαδίσεως ἔχει ἀρχήν, ἔστιν ἀρχὴ καὶ τῆς κινήσεως, ὥστε καὶ τοῦ μεγέθους ὃ βεβάδικεν. Ὁμοίως δὲ τοῦτο καὶ ἐπὶ τῶν ἄλλων. Ἔστω δὴ γραμμὴ ἄπειρος, ἐφ' ᾗ ΑΓΕ, ἐπὶ θάτερα, ᾗ τὸ Ε ἡ δ' ἐφ' ᾗ τὰ ΒΒ, ἐπ' ἀμφότερα ἄπειρος. Εἰ δὴ γράψει κύκλον ἡ τὸ ΑΓΕ ἀπὸ τοῦ Γ κέντρου, τέμνουσά ποτε οἰσθήσεται κύκλῳ τὴν τὰ ΒΒ ἡ τὸ ΑΓΕ πεπερασμένον χρόνον ὁ γὰρ πᾶς χρόνος, ἐν ὅσῳ κύκλῳ ἠνέχθη ὁ οὐρανός, πεπερασμένος. Καὶ ὁ ἀφῃρημένος ἄρα, ὃν ἡ τέμνουσα ἐφέρετο. Ἔσται ἄρα τις ἀρχὴ ᾗ πρῶτον ἡ τὸ ΑΓΕ τὴν τὰ ΒΒ ἔτεμεν. Ἀλλ' ἀδύνατον. Οὐκ ἄρα ἔστι κύκλῳ στραφῆναι τὸ ἄπειρον. Ὥστ' οὐδὲ τὸν κόσμον, εἰ ἦν ἄπειρος. 55 (2) Again, if from a finite time a finite time be subtracted, what remains must be finite and have a beginning. And if the time of a journey has a beginning, there must be a beginning also of the movement, and consequently also of the distance traversed. This applies universally. Take a line, ACE, infinite in one direction, E, and another line, BB, infinite in both directions. Let ACE describe a circle, revolving upon C as centre. In its movement it will cut BB continuously for a certain time. This will be a finite time, since the total time is finite in which the heavens complete their circular orbit, and consequently the time subtracted from it, during which the one line in its motion cuts the other, is also finite. Therefore there will be a point at which ACE began for the first time to cut BB. This, however, is impossible. The infinite, then, cannot revolve in a circle; nor could the world, if it were infinite. Ἔτι δὲ καὶ ἐκ τῶνδε φανερόν, ὅτι τὸ ἄπειρον ἀδύνατον κινηθῆναι. Ἔστω γὰρ ἡ τὸ Α φερομένη παρὰ τὴν Β, πεπερασμένη παρὰ πεπερασμένην. Ἀνάγκη δὴ ἅμα τήν τε Α τῆς Β ἀπολελύσθαι καὶ τὴν Β τῆς Α ὅσον γὰρ ἡ ἑτέρα ἐπιβάλλει τῆς ἑτέρας, καὶ ἡ ἑτέρα ἐκείνης τοσοῦτον. Εἰ μὲν οὖν ἄμφω κινοῖντο εἰς τοὐναντίον, θᾶττον ἂν ἀπολύοιντο, εἰ δὲ παρὰ μένουσαν φέροιτο, βραδύτερον, τῷ αὐτῷ τάχει κινουμένου τοῦ παραφερομένου. Ἀλλ' ἐκεῖνό γε φανερόν, ὅτι ἀδύνατον τὴν ἄπειρον διελθεῖν ἐν πεπερασμένῳ χρόνῳ. Ἐν ἀπείρῳ ἄρα δέδεικται γὰρ τοῦτο πρότερον ἐν τοῖς περὶ κινήσεως. Διαφέρει δέ γε οὐθὲν ἢ τὴν πεπερασμένην φέρεσθαι παρὰ τὴν ἄπειρον ἢ τὴν ἄπειρον παρ' ἐκείνην ὅταν γὰρ (272b.) ἐκείνη παρ' ἐκείνην, κἀκείνη παραλλάττει ἐκείνην, ὁμοίως κινουμένη καὶ ἀκίνητος πλὴν θᾶττον, ἐὰν κινῶνται ἀμφότεραι, ἀπολυθήσονται. Καίτοι γ' ἐνίοτ' οὐθὲν κωλύει τὴν κινουμένην παρ' ἠρεμοῦσαν θᾶττον παρελθεῖν ἢ τὴν ἀντικινουμένην, ἐάν τις ποιήσῃ τὰς μὲν ἀντικινουμένας ἀμφοτέρας φερομένας βραδέως, τὴν δὲ παρὰ τὴν ἠρεμοῦσαν πολλῷ ἐκείνων θᾶττον φερομένην. Οὐδὲν οὖν πρὸς τὸν λόγον ἐμπόδιον ὅτι παρ' ἠρεμοῦσαν, ἐπείπερ κινουμένην ἐνδέχεται τὴν Α παρὰ κινουμένην τὴν Β βραδύτερον παρελθεῖν. Εἰ οὖν ἄπειρος ὁ χρόνος ὃν ἡ πεπερασμένη ἀπολύεται κινουμένη, καὶ ἐν ᾧ ἡ ἄπειρος τὴν πεπερασμένην ἐκινήθη ἀνάγκη ἄπειρον εἶναι. Ἀδύνατον ἄρα τὸ ἄπειρον κινεῖσθαι ὅλον ἐὰν γὰρ καὶ τοὐλάχιστον κινηθῇ, ἀνάγκη ἄπειρον γίγνεσθαι χρόνον. Ἀλλὰ μὴν ὅ γ' οὐρανὸς περιέρχεται καὶ στρέφεται ὅλος κύκλῳ ἐν πεπερασμένῳ χρόνῳ, ὥστε περίεισιν ἅπασαν τὴν ἐντός, οἷον τὴν ΑΒ πεπερασμένην. Ἀδύνατον ἄρα ἄπειρον εἶναι τὸ κύκλῳ. 56 (3) That the infinite cannot move may also be shown as follows. Let A be a finite line moving past the finite line, B. Of necessity A will pass clear of B and B of A at the same moment; for each overlaps the other to precisely the same extent. Now if the two were both moving, and moving in contrary directions, they would pass clear of one another more rapidly; if one were still and the other moving past it, less rapidly; provided that the speed of the latter were the same in both cases. This, however, is clear: that it is impossible to traverse an infinite line in a finite time. Infinite time, then, would be required. (This we demonstrated above in the discussion of movement.) And it makes no difference whether a finite is passing by an infinite or an infinite by a finite. For when A is passing B, then B overlaps A and it makes no difference whether B is moved or unmoved, except that, if both move, they pass clear of one another more quickly. It is, however, quite possible that a moving line should in certain cases pass one which is stationary quicker than it passes one moving in an opposite direction. One has only to imagine the movement to be slow where both move and much faster where one is stationary. To suppose one line stationary, then, makes no difficulty for our argument, since it is quite possible for A to pass B at a slower rate when both are moving than when only one is. If, therefore, the time which the finite moving line takes to pass the other is infinite, then necessarily the time occupied by the motion of the infinite past the finite is also infinite. For the infinite to move at all is thus absolutely impossible; since the very smallest movement conceivable must take an infinity of time. Moreover the heavens certainly revolve, and they complete their circular orbit in a finite time; so that they pass round the whole extent of any line within their orbit, such as the finite line AB. The revolving body, therefore, cannot be infinite.
Praemissa prima ratione, quae procedebat ad ostendendum corpus non esse infinitum quod circulariter fertur, ex hoc quod distantia quae est inter duas lineas a centro egredientes erit infinita et impertransibilis, hic ponit secundam rationem, ex hoc quod lineae descriptae imaginatae in corpore infinito, sive in eius loco, non possunt se invicem intersecare. 102. After setting forth the first argument showing that the circularly moved body is not infinite, on the ground that the distance between two lines proceeding from the center will be infinite and untraversable, the Philosopher now presents the second argument, based on the fact that imaginary lines described in an infinite body, or in its place, cannot intersect. Et praemittit in hac ratione quoddam principium, scilicet quod si a tempore finito subtrahatur tempus finitum, quod relinquitur necesse est esse finitum: quia pars finiti non potest esse infinita, alioquin totum esset minus sua parte. Et si illud residuum temporis est finitum, consequens est quod habeat principium: hoc enim tempus dicimus esse finitum, quod habet principium et finem. Demonstratum est autem in VI Physic. quod tempus et motus et mobile consequuntur se invicem in hoc quod est esse finitum vel infinitum. Unde si tempus mensurans incessum sive motum, est finitum et habens principium, necesse est quod motus sit finitus et quod habeat principium, et quod etiam magnitudo mota sit finita et habens principium. Et sicut hoc dicimus in motu caeli, similiter oportet se habere in aliis motibus et mobilibus. And in this argument he sets forth the principle that if a finite time is subtracted from a finite time, the remainder will be finite, because part of a finite cannot be infinite; otherwise the whole would be less than the part. And if that remainder of time is finite, it has a beginning, for we say a time is said to be finite, if it has a beginning and end. But it has been demonstrated in Physics VI that time and motion and mobile follow one another in respect to being finite or infinite. Hence if the time which measures a starting out or motion is finite and has a beginning, then the motion must be finite and have a beginning, and so also must be the magnitude moved. And just as this applies to celestial motion, so too to other motions and mobiles. Istis igitur praemissis tanquam principiis, procedit ad demonstrandum propositum. Supponatur ergo quod a centro corporis infiniti quod est a, protrahatur quaedam linea, scilicet age, quae sit infinita ad aliam partem, scilicet ex parte e; et intelligatur ista linea circumvolvi secundum motum totius corporis, et quod secundum punctum g describat quendam circulum suo motu. Imaginemur etiam in spatio imaginato in quo revolvitur corpus infinitum, quandam lineam stantem immobilem, quae non transeat per centrum, sed sit infinita ex utraque parte, et sit linea bb. Si ergo, sicut dictum est, linea quae est age, sua incessione describat circulum a g, idest cuius semidiameter sit ag, continget quod linea age, circumeundo circulum praedictum, secabit totam lineam bb in tempore finito. Manifestum est enim quod semidiameter circuli non potest volvi in circuitu nisi incidat vel secet successive totam lineam immobilem imaginatam in circulo extra centrum. Et quod tempus sit finitum in quo linea quae educitur a centro, secet lineam infinitam quae describitur extra centrum, manifestat per hoc quod totum tempus in quo caelum movetur, est finitum, sicut patet ad sensum: unde consequens est quod pars illius temporis, quod aufertur a toto tempore, sit finita, in quo scilicet linea age incidit lineam bb. Vel potius sequitur illud tempus esse finitum, in quo illa linea incidens fertur usque ad lineam quae inciditur; et hoc oportet auferri a toto tempore finito, ut residui temporis accipiatur quoddam principium, secundum principium supra positum. Sequitur ergo quod sit aliquod principium temporis, in quo linea age incipit incidere lineam bb. Hoc autem est impossibile: quia, cum unam partem incidat ante aliam, si sit dare principium temporis in quo incipit incidere, esset dare principium aliquod in linea infinita, quod est contra rationem infiniti. Having set these things down as principles, he proceeds to demonstrate the proposition. Suppose that, from the center of an infinite body A, there is drawn the line AGE, which is infinite in one direction, namely, toward E; and let that line be revolving with the motion of the whole body, and that, with respect to the point G its motion describes a circle. Let us imagine also, in that imaginary space in which the infinite body is revolved, a certain immobile fixed line BB which does not cross the center but is nevertheless infinite. If then, as has been said, the line AGE by its motion describes a circle from G, i.e., whose radius is AG, it will turn out that the line AGE in making a revolution will cross the entire line BB in finite time. For it is manifest that the radius of a circle cannot be revolved in its circuit without covering or cutting successively the whole fixed immobile line imagined to be in the circle and not passing through the center. And that it is in a finite time that the line drawn from the center cuts the infinite line not passing through the center is manifest from the fact that the whole time in which the heaven is moved is finite, as is evident to our senses. Consequently, a part of that time which is subtracted from the whole time is finite, namely, the time in which AGE falls on line BB. Or rather it follows that that time is finite in which that cutting line is moved to the line which is cut; and this is the time that must be subtracted from all of finite time, so that the remaining time has a beginning, in keeping with the principle enunciated above. It follows, therefore, that the time in which AGE begins to cut BB has a beginning. However, this is impossible, because since it cuts one part before another, then if there is a beginning of the time in which it begins to cut, there would be a beginning in the infinite line, and that is contrary to the notion of infinite. Sic ergo patet quod corpus infinitum non contingit revolvi circulariter. Unde si mundus sit infinitus, sequitur quod non moveatur circulariter. Videmus autem firmamentum moveri circulariter: non ergo est infinitum. In this way, then, it is plain that an infinite body cannot be revolved circularly. Hence if the world is infinite, it follows that it is not moved circularly. However, we do observe that the firmament is moved circularly. Hence it is not infinite. Tertiam rationem ponit ibi: adhuc autem et ex his etc.: et sumitur haec ratio ex infinitate totius corporis quod ponitur circulariter moveri. Dicit ergo quod ex his etiam quae sequuntur, manifestum est quod impossibile est corpus infinitum moveri circulariter. Praemittit autem quod si sint duae lineae finitae, quarum una sit a et alia b, ita quod a feratur iuxta b quiescentem, ex necessitate sequitur quod simul linea mota quae est a, separetur a linea stante quae est b, et e contra linea stans quae est b, separetur a linea mota quae est a. Et huius ratio est, quia quantam partem una earum accipit de alia, tantam e converso alia accipit de ipsa. Sed tamen si ambae moveantur una contra aliam, velocius separabuntur lineae ab invicem; si autem una moveatur iuxta aliam quiescentem, tardius separabuntur lineae ab invicem; dummodo sit aequalis velocitas duarum motarum contra se invicem, et unius motae iuxta aliam stantem. Et hoc ideo praemisit, quia idem est tempus quo una linea pertransit aliam, et quo alia pertransit ipsam. 104. The third argument is given at [56] and is based on the infinity of the whole body which is posited as moving circularly. He says, therefore, that also from what follows it is manifestly impossible for an infinite body to be moved circularly. As a premise he says that if A and B are two finite lines so that A is in motion beside B which is stationary, it follows of necessity that as A moves along it departs from the stationary line B, and conversely that the stationary line B is separated from the moved line A. The reason for this is that each of them overlaps the other to the same extent. But now if both are moved in contrary directions, the lines will separate more quickly. If, however, one is in motion beside the other which is stationary, they will separate more slowly — provided, of course, that they have the same speeds when both are in a separating motion and when one alone is in motion. The reason for presenting this as a premise is that the time in which one line traverses the other is the same as that in which the other traverses it. Et postquam hoc manifestavit per lineas finitas, applicat hoc ad lineas infinitas, de quibus intendit. Et dicit manifestum esse quod impossibile est lineam infinitam pertransiri tempore finito a linea finita; unde relinquitur quod linea finita pertranseat infinitam tempore infinito; quod quidem ostensum est prius in his quae de motu, idest in VI Physic. Sicut autem apparet ex his quae dicta sunt de lineis finitis, nihil differt quod linea finita moveatur per infinitam, et quod infinita moveatur super finitam: cum enim linea infinita moveatur per lineam finitam, similis ratio est si linea finita moveatur vel non moveatur; manifestum est autem quod si moveatur linea finita sicut et infinita, utraque earum pertransibit aliam. After manifesting this point with respect to finite lines, he applies it to the infinite lines he is discussing. And he says that it is manifestly impossible for an infinite line to be traversed by a finite line in finite time. Hence it remains that a finite line traverses an infinite line in infinite time, and this was shown previously in the treatise on motion, i.e., in Physics VI. But as appears from what has been said about finite lines, it makes no difference whether it is a finite line being moved through an infinite or an infinite line being moved over a finite, for when an infinite line is being moved through a finite line, the same reasoning holds, whether the finite line is being moved or not. However, it is manifest that if the finite line is being moved as well as the infinite, each traverses the other. Unde manifestum est quod etiam si non moveatur linea finita, simile erit quod pertransitur a linea infinita, ac si pertransiret illam. Hence it is manifest that even if the finite line is not being moved, being traversed by the infinite line will be similar to traversing it. Sed quia dixerat quod similiter se habet sive moveatur altera sive non, ostendit in quo circa hoc posset esse differentia: quia si utraque linearum moveatur una contra aliam, velocius separabuntur ab invicem. Sed hoc intelligendum est, si sit eadem velocitas, sicut supra dictum est: aliquando tamen nihil prohibet quin linea quae movetur iuxta quiescentem, velocius pertranseat eam, quam si moveretur iuxta lineam in contrarium motam; puta quando duae lineae quae contra se moverentur, haberent motum lentum, illa vero quae moveretur iuxta quiescentem, haberet motum velocem. Sic igitur patet quod nullum impedimentum est quantum ad rationem istam, quod linea infinita moveatur iuxta lineam finitam quietam: quia contingit quod linea mota quae est a, tardius pertransit lineam b motam, quam si non moveretur, dummodo ponatur quod, linea b quiescente, linea a velocius moveretur. But because he had said that the situation is similar whether the other is moved or not, he now shows wherein there could be a difference: if each of the lines is being moved in a contrary direction, they will separate more swiftly. But this must be understood if the speed is the same, as was said above. For sometimes nothing prevents the line which is being moved next to a stationary one from traversing it more quickly than if it were moved next to a line in contrary motion; for example, when the two lines in contrary motion would have a slow motion, while the one in motion next to the stationary one would have a swift motion. Accordingly, it is no obstacle, so far as the argument is concerned, that the infinite line be moved next to a stationary finite line — since it happens that the moving line A more slowly traverses the moving line B than if the latter were not in motion, provided, of course, that in this second case, while B is stationary, line A is being moved more swiftly. Sic igitur ostenso quod nihil differt lineam infinitam moveri iuxta finitam quiescentem, ab eo quod linea finita moveretur supra infinitam, ex hoc argumentatur quod, si tempus quo linea finita pertransit lineam infinitam, est infinitum, consequens est quod tempus quo linea infinita movetur per lineam finitam, sit infinitum. Sic igitur patet quod impossibile est totum corpus infinitum moveri per totum spatium infinitum, in quo imaginamur motum eius, tempore scilicet finito: quia si infinitum moveretur etiam per minimum spatium finitum, sequeretur quod tempus esset infinitum: probatum est enim quod infinitum movetur per finitum tempore infinito, sicut et finitum per infinitum. Videmus autem quod caelum circuit totum spatium suum tempore finito. Unde manifestum est quod pertransit tempore finito aliquam lineam finitam, puta quae continet interius totum circulum descriptum circa centrum eius, scilicet lineam ab: quod non contingeret si esset infinitum. Impossibile est igitur corpus quod circulariter fertur, esse infinitum. 105. Thus, having shown that it makes no difference whether the infinite line is moved next to a stationary finite line, or whether the finite line is moved against the infinite, he argues from this that if the time in which the finite line traverses the infinite line is infinite, the consequence is that the time in which an infinite line is moved through a finite line is also infinite. Accordingly, it is plainly impossible for an entire infinite body to be moved through an entire infinite space — in which we imagine its motion to occur — in finite time: because if the infinite were moved even through the slightest finite space, it would follow that the time would be infinite, for it has been proved that the infinite is moved through the finite in infinite time, just as the finite through the infinite. But we observe that the heaven circles all its space in finite time. Hence it is manifest that it traverses some finite line in finite time, for example, the line containing within itself the whole circle described about its center, namely, the line AB. Now this would not happen if it were infinite. It is impossible, therefore, that the circularly moved body be infinite.
Lecture 11: Three additional reasons why the body moving circularly cannot be infinite.
Chapter 5 cont. Ἔτι ὥσπερ γραμμὴν ᾗ πέρας ἐστὶν ἀδύνατον εἶναι ἄπειρον, ἀλλ' εἴπερ, ἐπὶ μῆκος, καὶ ἐπίπεδον ὡσαύτως ᾗ πέρας οὐκ ἐνδέχεται ὅταν δ' ὁρισθῇ, οὐθαμῇ, οἷον τετράγωνον ἄπειρον ἢ κύκλον ἢ σφαῖραν, ὥσπερ οὐδὲ ποδιαίαν ἄπειρον. Εἰ οὖν μήτε σφαῖρα [μήτε τετράγωνον] μήτε κύκλος ἐστὶν ἄπειρος, μὴ ὄντος δὲ κύκλου οὐδ' ἂν ἡ κύκλῳ εἴη φορά, ὁμοίως δὲ μηδ' ἀπείρου ὄντος οὐκ ἂν εἴη ἄπειρος, εἰ μηδ' ὁ κύκλος ἄπειρός ἐστιν, οὐκ ἂν κινοῖτο κυκλικῶς ἄπειρον σῶμα. 57 (4) Again, as a line which has a limit cannot be infinite, or, if it is infinite, is so only in length, so a surface cannot be infinite in that respect in which it has a limit; or, indeed, if it is completely determinate, in any respect whatever. Whether it be a square or a circle or a sphere, it cannot be infinite, any more than a foot-rule can. There is then no such thing as an infinite sphere or square or circle, and where there is no circle there can be no circular movement, and similarly where there is no infinite at all there can be no infinite movement; and from this it follows that, an infinite circle being itself an impossibility, there can be no circular motion of an infinite body. Ἔτι εἰ τὸ Γ κέντρον, ἡ δὲ τὸ ΑΒ ἄπειρος καὶ ἡ τὸ Ε πρὸς ὀρθὴν ἄπειρος καὶ ἡ τὸ ΓΔ κινουμένη, οὐδέποτ' ἀπολυθήσεται τῆς Ε, ἀλλ' ἀεὶ ἕξει ὥσπερ ἡ ΓΕ τέμνει γὰρ ᾗ τὸ Ζ. Οὐκ ἄρα περίεισι κύκλῳ ἡ ἄπειρος. 58 (5) Again, take a centre C, an infinite line, AB, another infinite line at right angles to it, E, and a moving radius, CD. CD will never cease contact with E, but the position will always be something like CE, CD cutting E at F. The infinite line, therefore, refuses to complete the circle. Ἔτι εἴπερ ἄπειρος ὁ οὐρανός, κινεῖται δὲ κύκλῳ, ἐν πεπερασμένῳ χρόνῳ ἄπειρον ἔσται διεληλυθώς. Ἔστω γὰρ ὁ μὲν μένων οὐρανὸς ἄπειρος,ὁ δ' ἐν τούτῳ κινούμενος ἴσος. Ὥστ' εἴπερ περιελήλυθε κύκλῳ ἄπειρος ὤν, ἄπειρον τὸν ἴσον αὑτῷ διελήλυθεν ἐν πεπερασμέ— (273a.) νῳ χρόνῳ. Ἀλλὰ τοῦτ' ἦν ἀδύνατον. 59 (6) Again, if the heaven is infinite and moves in a circle, we shall have to admit that in a finite time it has traversed the infinite. For suppose the fixed heaven infinite, and that which moves within it equal to it. It results that when the infinite body has completed its revolution, it has traversed an infinite equal to itself in a finite time. But that we know to be impossible. Ἔστι δὲ καὶ ἀντεστραμμένως εἰπεῖν, ὅτι εἰ πεπερασμένος ὁ χρόνος ἐν ᾧ περιεστράφη, καὶ τὸ μέγεθος ὃ διελήλυθεν ἀναγκαῖον εἶναι πεπερασμένον ἴσον δ' αὑτῷ διελήλυθεν πεπέρανται ἄρα καὶ αὐτός. Ὅτι μὲν οὖν τὸ κύκλῳ κινούμενον οὐκ ἔστιν ἀτελεύτητον οὐδ' ἄπειρον, ἀλλ' ἔχει τέλος, φανερόν. 60 (7) It can also be shown, conversely, that if the time of revolution is finite, the area traversed must also be finite; but the area traversed was equal to itself; therefore, it is itself finite. We have now shown that the body which moves in a circle is not endless or infinite, but has its limit.
Praemissis tribus rationibus ad probandum quod corpus quod circulariter movetur, non possit esse infinitum, hic ponit quartam, quae talis est. Impossibile est lineam esse infinitam, cuius est aliquis finis, nisi forte ad alteram partem habeat finem et ad alteram partem sit infinita. Et simile etiam est de superficie, quod si habeat finem ad unam partem, quod non contingit eam esse infinitam ad illam partem. Sed quando ad omnem partem determinatur, nullo modo potest esse infinita; sicut patet quod non contingit esse tetragonum, idest quadratum, infinitum, neque circulum, qui est superficialis figura, neque sphaeram, quae est figura corporea; haec enim sunt nomina figurarum, figura autem est quae termino vel terminis comprehenditur. Et sic patet quod nulla superficies figurata est infinita. Si ergo neque sphaera est infinita neque quadratum neque circulus, manifestum est quod non potest esse motus circularis infinitus. Sicut enim si non est circulus, non potest esse motus circularis, ita si non sit infinitus circulus, non potest esse infinitus motus circularis. Sed si corpus infinitum moveatur circulariter, necesse est motum circularem esse infinitum: non est ergo possibile quod corpus infinitum circulariter moveatur. 106. Having given three arguments to prove that the body in circular motion cannot be infinite, he now gives a fourth [47] which is this. It is impossible for a line having an end to be infinite, unless it have an end at one extremity and be infinite at the other. The same is true of a surface: if it has an end at one part, it is not infinite at that part. But when it is limited from every part, it is in no sense infinite. Thus, it is clear that no tetragon, i.e., square, is infinite, nor is a circle which is a plane figure, nor a sphere which is a solid — for these are names of figures, and a figure is something bounded by a terminus or by termini. Thus it is clear that no figured plane is infinite. If, therefore, neither a sphere nor a square nor a circle is infinite, it is clear that there cannot be circular motion that is infinite. For just as there can be no circular motion unless there is a circle, so, if there is no infinite circle, there cannot be an infinite circular motion. But if an infinite body were moved circularly, there would have to be a circular motion that is infinite. Therefore, it is not possible for an infinite body to be moved circularly. Quintam rationem ponit ibi: adhuc autem si g etc., quae talis est. Supponatur quod corporis infiniti circulariter moti centrum sit g; ducatur autem per hoc centrum linea ad utramque partem infinita, quae sit linea ab; ducatur autem alia linea praeter centrum, cadens ad rectos angulos super lineam ba, in puncto scilicet e, et sit etiam haec linea infinita ex utraque parte; et hae duae lineae sint stantes, quasi imaginatae in spatio in quo corpus infinitum movetur circulariter. Sit etiam tertia linea egrediens a centro, quae sit linea dg, infinita ex parte d (nam ex parte g oportet eam esse finitam): haec autem linea moveatur per motum corporis, utpote in eo descripta. Quia igitur linea e est infinita, nunquam absolvetur, idest separabitur, ab ea: quia non potest eam pertransire, cum sit infinita, sed semper se habebit quemadmodum ge, idest semper continget vel secabit lineam e, sicut secabat eam in principio a quo incoepit moveri, puta quando linea gd superponebatur lineae ba et secabat lineam e perpendiculariter in puncto e. Recedens enim ab hoc situ incidet lineam e in puncto z, et sic semper in alio et alio puncto secabit illam: nunquam tamen totaliter poterit ab ea separari. Impossibile est autem quod motus circularis compleatur, nisi linea gd dimittat lineam e: quia oportebit, antequam compleatur motus circularis, quod linea gd pertranseat partem circuli quae est in opposito lineae e. Sic patet ergo quod linea infinita nullo modo potest circuire circulum, ita scilicet quod totus motus circularis compleatur. Et ita sequitur quod corpus infinitum non possit circulariter moveri. 107. The fifth argument is presented at [58] and it is this. Let G be the center of the infinite body in circular motion. Then through this center let a line AB be drawn which is infinite in both directions; then draw another infinite line not passing through the center but perpendicular to BA at E. Imagine these two lines as stationary in the space in which the infinite body is moved circularly. Draw a third line DG from the center and let it be infinite in the direction of D — for in the direction G it has to be finite. Finally suppose that this third line is in motion by the motion of the body. Because the line E is infinite, it will never be separated from it, because it cannot traverse it, since it is infinite; rather it will always maintain itself as GE, i.e., it will always touch or cut line E just as it cut it in the beginning when it began to be moved — for example, when the line GD was superimposed on the line BA and cut the line E perpendicularly at point E. For leaving this position it will cut the line E at the point Z, and so it will cut point after point in it; yet it will never be able to be entirely separated from it. It is impossible, however, for the circular motion to be completed, unless the line GD departs from the line E: because before the circular motion can be completed, the line GD will have to traverse that part of the whole that is opposite to the line E. And so it is plain that an infinite line can in no way traverse the circle in such a way that the entire circular motion be completed. Consequently, an infinite body cannot be moved circularly. Sextam rationem ponit ibi: adhuc si quidem et cetera. Et hanc quidem rationem format dupliciter: primo ducendo ad impossibile hoc modo. Sit caelum infinitum, sicut tu ponis. Manifestum est autem ad sensum quod movetur circumquaque tempore finito: videmus enim eius revolutionem perfici in viginti quatuor horis. Ex hoc ergo sequetur quod infinitum sit pertransitum tempore finito: et hoc ideo, quia necesse est imaginari aliquod spatium aequale caelo, in quo caelum movetur. Hoc autem spatium imaginamur ut quiescens: sic igitur oportebit quod sit quoddam caelum manens infinitum, idest ipsum spatium in quo caelum movetur; et quod sit corpus caeli quod movetur in hoc spatio, aequale dicto spatio, quia oportet corpus aequari spatio in quo est. Si igitur caelum infinitum existens circulariter motum est tempore finito, consequens est quod pertransiverit infinitum tempore finito. Hoc autem est impossibile, scilicet infinitum pertransire tempore finito, ut probatum est in VI Physic. Impossibile est igitur quod corpus infinitum circulariter moveatur. The sixth argument is presented at [59] and he forms his argument in two ways. The first is by leading to an impossibility as follows: Suppose, as you say, that the heaven is infinite. Now it is manifest to us that it moves around in finite time — for we see that its revolution is completed in 24 hours. Therefore it will follow that the infinite is traversed in a finite time. This is so because it is necessary to imagine a space equal to the heaven in which the heaven is moved. But we imagine this space as stationary: thus there will have to be an infinite space in which the heaven is moved and a heavenly body equal to the space in which it is moved, because the body must be equal to the space in which it is. If, then, the infinite heaven has been circularly moved in finite time, the consequence is that it traversed the infinite in finite time. But this is impossible, i.e., to traverse the infinite in finite time, as was proved in Physics VI. It is, therefore, impossible for an infinite body to be moved circularly. Secundo ibi: est autem et convertibiliter etc., format rationem e converso, ut sit probatio ostensiva. Et dicit quod possumus e converso dicere quod, ex quo tempus est finitum in quo caelum revolutum est, sicut ad sensum patet, consequens est quod magnitudo quae est pertransita, sit finita. Manifestum est autem quod spatium pertransitum est aequale ipsi corpori pertranseunti. Sequitur ergo corpus quod circulariter movetur, esse finitum. 109. Then at [60] he forms his argument conversely in order to make it an ostensive proof. And he says that we can say conversely that, from the fact that the time in which the heaven is revolved is finite (as is plain to the senses), it follows that the magnitude traversed is finite. Now it is plain that the space traversed is equal to the body traversing it. Therefore, the body which is moved circularly is finite. Sic ergo epilogando concludit manifestum esse quod corpus quod circulariter movetur, non est interminatum, idest carens termino quasi infiguratum: et per consequens non est infinitum, sed habet finem. Therefore he concludes in summary that it is plain that the body which is being moved circularly is not unterminated, i.e., it does not lack a terminus as though it were devoid of shape. Consequently, it is not infinite, but has an ending.
Lecture 12:
Various reasons why a body moving in a straight line is not infinite.Chapter 6 Ἀλλὰ μὴν οὐδὲ τὸ ἐπὶ τὸ μέσον οὐδὲ τὸ ἀπὸ τοῦ μέσου φερόμενον ἄπειρον ἔσται 61 Further, neither that which moves towards nor that which moves away from the centre can be infinite. ἐναντίαι γὰρ αἱ φοραὶ ἡ ἄνω καὶ ἡ κάτω, αἱ δ' ἐναντίαι εἰς ἐναντίους τόπους. Τῶν δ' ἐναντίων εἰ θάτερον ὥρισται, καὶ θάτερον ὡρισμένον ἔσται. Τὸ δὲ μέσον ὥρισται εἰ γὰρ ὁποθενοῦν φέροιτο κάτω τὸ ὑφιστάμενον, οὐκ ἐνδέχεται πορρωτέρω διελθεῖν τοῦ μέσου. Ὡρισμένου οὖν τοῦ μέσου, καὶ τὸν ἄνω τόπον ἀνάγκη ὡρίσθαι. Εἰ δ' οἱ τόποι ὡρισμένοι καὶ πεπερασμένοι, καὶ τὰ σώματα ἔσται πεπερασμένα. 62 For the upward and downward motions are contraries and are therefore motions towards contrary places. But if one of a pair of contraries is determinate, the other must be determinate also. Now the centre is determined; for, from whatever point the body which sinks to the bottom starts its downward motion, it cannot go farther than the centre. The centre, therefore, being determinate, the upper place must also be determinate. But if these two places are determined and finite, the corresponding bodies must also be finite. Ἔτι εἰ τὸ ἄνω καὶ τὸ κάτω ὥρισται, καὶ τὸ μεταξὺ ἀνάγκη ὡρίσθαι. Εἰ γὰρ μὴ ὥρισται, ἄπειρος ἂν εἴη ἡ κίνησις τοῦτο δ' ὅτι ἀδύνατον, δέδεικται πρότερον. Ὥρισται ἄρα τὸ μέσον, ὥστε καὶ τὸ ἐν τούτῳ σῶμα ἢ ὂν ἢ γενέσθαι δυνατόν. 63 Further, if up and down are determinate, the intermediate place is also necessarily determinate. For, if it is indeterminate, the movement within it will be infinite; and that we have already shown to be an impossibility. The middle region then is determinate, and consequently any body which either is in it, or might be in it, is determinate. Ἀλλὰ μὴν τὸ ἄνω καὶ κάτω φερόμενον σῶμα δύναται ἐν τούτῳ γενέσθαι πέφυκε γὰρ τὸ μὲν ἀπὸ τοῦ μέσου κινεῖσθαι, τὸ δ' ἐπὶ τὸ μέσον. Ἔκ τε δὴ τούτων φανερὸν ὅτι οὐκ ἐνδέχεται σῶμα εἶναι ἄπειρον, 64 But the bodies which move up and down may be in it, since the one moves naturally away from the centre and the other towards it. From this alone it is clear that an infinite body is an impossibility; καὶ πρὸς τούτοις εἰ βάρος μή ἐστιν ἄπειρον, οὐδ' ἂν τούτων τῶν σωμάτων οὐθὲν εἴη ἄπειρον ἀνάγκη γὰρ τοῦ ἀπείρου σώματος ἄπειρον εἶναι καὶ τὸ βάρος. (Ὁ δ' αὐτὸς λόγος ἔσται καὶ ἐπὶ τοῦ κούφου εἰ γάρ ἐστιν ἄπειρος βαρύτης, ἔστι καὶ κουφότης, ἐὰν ἄπειρον ᾖ τὸ ἐπιπολάζον). 65 but there is a further point. If there is no such thing as infinite weight, then it follows that none of these bodies can be infinite. For the supposed infinite body would have to be infinite in weight. (The same argument applies to lightness: for as the one supposition involves infinite weight, so the infinity of the body which rises to the surface involves infinite lightness.) Δῆλον δ' ἐκ τῶνδε. Ἔστω γὰρ πεπερασμένον, καὶ εἰλήφθω τὸ μὲν ἄπειρον σῶμα ἐφ' ᾧ τὸ ΑΒ, τὸ δὲ βάρος αὐτοῦ ἐφ' ᾧ τὸ Γ. Ἀφῃρήσθω οὖν ἀπὸ τοῦ ἀπείρου πεπερασμένον μέγεθος ἐφ' ᾧ τὸ ΒΔ καὶ τὸ βάρος αὐτοῦ ἔστω ἐφ' ᾧ τὸ Ε. Τὸ δὴ Ε τοῦ Γ ἔλαττον ἔσται τὸ γὰρ τοῦ ἐλάττονος βάρος ἔλαττον. Καταμετρείτω δὴ τὸ ἔλαττον ὁποσακισοῦν, (273b.) καὶ ὡς τὸ βάρος τοὔλαττον πρὸς τὸ μεῖζον, τὸ ΒΔ πρὸς τὸ ΒΖ γεγενήσθω ἐνδέχεται γὰρ ἀφελεῖν τοῦ ἀπείρου ὁποσονοῦν. Εἰ τοίνυν ἀνάλογον τὰ μεγέθη τοῖς βάρεσι, τὸ δ' ἔλαττον βάρος τοῦ ἐλάττονός ἐστι μεγέθους, καὶ τὸ μεῖζον ἂν εἴη τοῦ μείζονος. Ἴσον ἄρα ἔσται τὸ τοῦ πεπερασμένου καὶ τὸ τοῦ ἀπείρου βάρος. 66 This is proved as follows. Assume the weight to be finite, and take an infinite body, AB, of the weight C. Subtract from the infinite body a finite mass, BD, the weight of which shall be E. E then is less than C, since it is the weight of a lesser mass. Suppose then that the smaller goes into the greater a certain number of times, and take BF bearing the same proportion to BD which the greater weight bears to the smaller. For you may subtract as much as you please from an infinite. If now the masses are proportionate to the weights, and the lesser weight is that of the lesser mass, the greater must be that of the greater. The weights, therefore, of the finite and of the infinite body are equal. Ἔτι δ' εἰ τοῦ μείζονος σώματος μεῖζον τὸ βάρος, τὸ τοῦ ΗΒ μεῖζον ἔσται βάρος ἢ τὸ τοῦ ΖΒ, ὥστε τὸ τοῦ πεπερασμένου ἢ τὸ τοῦ ἀπείρου [μεῖζον ἔσται βάρος]. 67 Again, if the weight of a greater body is greater than that of a less, the weight of GB will be greater than that of FB; and thus the weight of the finite body is greater than that of the infinite. Καὶ τὸ τῶν ἀνίσων δὲ μεγεθῶν ταὐτὸν ἔσται βάρος ἄνισον γὰρ τῷ πεπερασμένῳ τὸ ἄπειρον. 68 And, further, the weight of unequal masses will be the same, since the infinite and the finite cannot be equal. Οὐθὲν δὲ διαφέρει τὰ βάρη σύμμετρα εἶναι ἢ ἀσύμμετρα καὶ γὰρ ἀσυμμέτρων ὄντων ὁ αὐτὸς ἔσται λόγος οἷον εἰ [τὸ Ε] τρίτον ὑπερβάλλει μετροῦν τὸ βάρος τῶν γὰρ ΒΔ μεγεθῶν τριῶν ὅλων ληφθέντων μεῖζον ἔσται τὸ βάρος ἢ τὸ ἐφ' ᾧ τὸ Γ. Ὥστε τὸ αὐτὸ ἔσται ἀδύνατον. 69 It does not matter whether the weights are commensurable or not. If (a) they are incommensurable the same reasoning holds. For instance, suppose E multiplied by three is rather more than C: the weight of three masses of the full size of BD will be greater than C. We thus arrive at the same impossibility as before. Ἔτι δὲ καὶ ἐγχωρεῖ σύμμετρα λαβεῖν οὐδὲν γὰρ διαφέρει ἄρχεσθαι ἀπὸ τοῦ βάρους ἢ ἀπὸ τοῦ μεγέθους οἷον ἐὰν ληφθῇ σύμμετρον βάρος τῷ Γ τὸ ἐφ' ᾧ τὸ Ε, καὶ ἀπὸ τοῦ ἀπείρου ἀφαιρεθῇ τὸ ἔχον τὸ ἐφ' ᾧ Ε βάρος, οἷον τὸ ΒΔ, εἶτα ὡς τὸ βάρος πρὸς τὸ βάρος, τὸ ΒΔ πρὸς ἄλλο γένηται μέγεθος, οἷον πρὸς τὸ ΒΖ ἐνδέχεται γὰρ ἀπείρου ὄντος τοῦ μεγέθους ὁποσονοῦν ἀφαιρεθῆναι τούτων γὰρ ληφθέντων σύμμετρα ἔσται καὶ τὰ μεγέθη καὶ τὰ βάρη ἀλλήλοις. 70 Again (b) we may assume weights which are commensurate; for it makes no difference whether we begin with the weight or with the mass. For example, assume the weight E to be commensurate with C, and take from the infinite mass a part BD of weight E. Then let a mass BF be taken having the same proportion to BD which the two weights have to one another. (For the mass being infinite you may subtract from it as much as you please.) These assumed bodies will be commensurate in mass and in weight alike. Οὐδὲ δὴ τὸ μέγεθος ὁμοιοβαρὲς εἶναι ἢ ἀνομοιοβαρὲς οὐδὲν διοίσει πρὸς τὴν ἀπόδειξιν ἀεὶ γὰρ ἔσται λαβεῖν ἰσοβαρῆ σώματα τῷ ΒΔ, ἀπὸ τοῦ ἀπείρου ὁποσαοῦν ἢ ἀφαιροῦντας ἢ προστιθέντας. Ὥστε δῆλον ἐκ τῶν εἰρημένων ὅτι οὐκ ἔσται τοῦ ἀπείρου σώματος πεπερασμένον τὸ βάρος. Ἄπειρον ἄρα. Εἰ τοίνυν τοῦτ' ἀδύνατον, καὶ τὸ ἄπειρόν τι εἶναι σῶμα ἀδύνατον. 71 Nor again does it make any difference to our demonstration whether the total mass has its weight equally or unequally distributed. For it must always be Possible to take from the infinite mass a body of equal weight to BD by diminishing or increasing the size of the section to the necessary extent. From what we have said, then, it is clear that the weight of the infinite body cannot be finite. It must then be infinite. We have therefore only to show this to be impossible in order to prove an infinite body impossible. Ἀλλὰ μὴν ὅτι ἄπειρόν τι εἶναι βάρος ἀδύνατον, ἐκ τῶνδε φανερόν. 72 But the impossibility of infinite weight can be shown in the following way. Εἰ γὰρ τοσόνδε βάρος τὴν τοσήνδε ἐν τῷδε τῷ χρόνῳ κινεῖται, τὸ τοσοῦτον καὶ ἔτι ἐν ἐλάττονι, 73 A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, καὶ τὴν ἀναλογίαν ἣν τὰ βάρη ἔχει, οἱ χρόνοι ἀνάπαλιν (274a.) ἕξουσιν, οἷον εἰ τὸ ἥμισυ βάρος ἐν τῷδε, τὸ διπλάσιον ἐν ἡμίσει τούτου. 74 the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given movement. Ἔτι τὸ πεπερασμένον βάρος ἅπασαν πεπερασμένην δίεισιν ἔν τινι χρόνῳ πεπερασμένῳ. 75 Further, a finite weight traverses any finite distance in a finite time. Ἀνάγκη ἄρα ἐκ τούτων, εἴ τι ἔστιν ἄπειρον βάρος, κινεῖσθαι μὲν ᾗ τοσόνδε ὅσον τὸ πεπερασμένον καὶ ἔτι, μὴ κινεῖσθαι δέ, ᾗ ἀνάλογον μὲν δεῖ κατὰ τὰς ὑπεροχὰς κινεῖσθαι, ἐναντίως δὲ τὸ μεῖζον ἐν τῷ ἐλάττονι. Λόγος δ' οὐθείς ἐστι τοῦ ἀπείρου πρὸς τὸ πεπερασμένον, τοῦ δ' ἐλάττονος χρόνου πρὸς τὸν μείζω πεπερασμένον ἀλλ' ἀεὶ ἐν ἐλάττονι. Ἐλάχιστος δ' οὐκ ἔστιν. 76 It necessarily follows from this that infinite weight, if there is such a thing, being, on the one hand, as great and more than as great as the finite, will move accordingly, but being, on the other hand, compelled to move in a time inversely proportionate to its greatness, cannot move at all. The time should be less in proportion as the weight is greater. But there is no proportion between the infinite and the finite: proportion can only hold between a less and a greater finite time. And though you may say that the time of the movement can be continually diminished, yet there is no minimum. Οὐδ' εἰ ἦν, ὄφελός τι ἂν ἦν ἄλλο γὰρ ἄν τι πεπερασμένον ἐλήφθη ἐν τῷ αὐτῷ λόγῳ, ἐν ᾧ τὸ ἄπειρον πρὸς ἕτερον, μεῖζον, ὥστ' ἐν ἴσῳ χρόνῳ τὴν ἴσην ἂν ἐκινεῖτο τὸ ἄπειρον τῷ πεπερασμένῳ. 77 Nor, if there were, would it help us. For some finite body could have been found greater than the given finite in the same proportion which is supposed to hold between the infinite and the given finite; so that an infinite and a finite weight must have traversed an equal distance in equal time. But that is impossible. Ἀλλ' ἀδύνατον. Ἀλλὰ μὴν ἀνάγκη γε, εἴπερ ἐν ὁπηλικῳοῦν χρόνῳ πεπερασμένῳ δὲ κινεῖται τὸ ἄπειρον, καὶ ἄλλο ἐν τῷ αὐτῷ τούτῳ πεπερασμένον βάρος κινεῖσθαί τινα πεπερασμένην. 78 Again, whatever the time, so long as it is finite, in which the infinite performs the motion, a finite weight must necessarily move a certain finite distance in that same time.
Postquam philosophus ostendit quod corpus circulariter motum non est infinitum, hic ostendit idem de corpore quod movetur motu recto, vel a medio vel ad medium. 110. After showing that the circularly moved body is not infinite, the Philosopher here shows the same for the body moved with a straight motion, whether from the middle [center] or to the middle [center]. Et primo proponit quod intendit: dicens quod sicut corpus quod circulariter fertur non potest esse infinitum, ita corpus quod fertur motu recto, vel a medio vel ad medium, non potest esse infinitum.
Secundo ibi: contrariae enim lationes etc., ostendit propositum:
First he proposes what he intends and says that just as the circularly moved body cannot be infinite, so, too, the body which is moved with a straight motion, whether from the middle or to the middle, cannot be infinite;
Secondly, he shows the proposition, at 111, and this:
et primo ex parte locorum quae sunt huiusmodi corporibus propria;
secundo ex parte gravitatis et levitatis, per quae huiusmodi corpora in propria loca moventur, ibi: et adhuc si gravitas et cetera.
First on the part of the places which are proper to such bodies;
Secondly, on the part of heaviness and lightness, through which such bodies are moved to their proper places, at 114.
Circa primum duo facit: About the first he does two things: primo ostendit propositum quantum ad corpora extrema, quorum unum est simpliciter grave, scilicet terra, et aliud simpliciter leve, scilicet ignis;
secundo quantum ad corpora media, quae sunt aer et aqua, ibi: adhuc si sursum et cetera.
First he shows the proposition as to the extreme bodies, of which one is absolutely heavy, namely, earth, and the other absolutely light, namely, fire, at 111;
Secondly, as to the intermediate bodies, which are air and water, 112.
Proponit ergo primo quod huiusmodi motus qui sunt sursum et deorsum, vel a medio et ad medium, sunt motus contrarii: contrarii autem motus locales sunt, qui sunt ad loca contraria, ut supra dictum est, et est ostensum in V Physic.: relinquitur ergo quod loca propria in quae feruntur huiusmodi corpora, sint contraria. 111. He proposes therefore first [62] that motions of the kind that are up and down, or from the middle and to the middle, are contrary motions. For contrary local motions are ones to contrary places, as has been said, and as was shown in Physics V. It remains, therefore, that the proper places to which such bodies are carried are contrary. Ex hoc autem statim concludere posset huiusmodi loca esse determinata: contraria enim sunt quae maxime distant; maxima autem distantia locorum non potest esse nisi sint loca determinata, quia maxima distantia est qua non est alia maior, in infinitis autem semper est maiorem ac maiorem distantiam accipere; unde si loca essent infinita, cessaret locorum contrarietas. Sed Aristoteles, praetermissa hac probatione tanquam manifesta, procedit per alium modum. Verum est enim quod, si unum contrariorum est determinatum, quod aliud erit determinatum, eo quod contraria sunt unius generis. Medium autem mundi, quod est medius terminus motus deorsum, est determinatum: ex quacumque enim parte caeli aliquid feratur deorsum (quod scilicet substat superiori parti quae est versus caelum), non continget longius pertransire recedendo a caelo quam quod perveniat ad medium: si enim pertransiret medium, iam fieret propinquius caelo, et sic moveretur sursum. Sic igitur patet quod medius locus est determinatus. Patet etiam ex praedictis quod, determinato medio, quod est locus deorsum, necesse est et determinatum esse locum qui est sursum, cum sint contraria. Si autem ambo loca sunt determinata et finita, necesse est quod corpora quae sunt nata esse in his locis, sint finita. Unde patet huiusmodi corpora extrema, quae moventur motu recto, esse finita. Now, we could have at once concluded from this that such places are determinate: for contraries are things which are most distant; but places that are the greatest distance apart are determinate, for the greatest distance is such that none is greater, whereas in infinites a greater and greater distance is always possible. Hence if the places were infinite, contrariety of places would cease. However, Aristotle passes over this argument as manifest and proceeds by another tack. For it is true that if one contrary is determinate, so too the other, because contraries are members of one genus. But the middle of the world which is the midway terminus of a downward motion is determinate — for from whatever part of the heavens something is moved downward (which exists under the upper part facing the heavens) it can travel no farther in its journey from the heavens than the middle: for if it should go beyond the middle, it would now get closer to the heavens and thus would be moved upward. Accordingly, it is clear that the middle place is determinate. It is likewise clear from the aforesaid that the middle having been determined, i.e., the downward place, then the upward place is also necessarily determinate, because they are contraries. And if both are determinate, then the bodies which are apt to be in these places must be finite. Hence it is clear that the extreme bodies subject to straight motion are finite. Deinde cum dicit: adhuc si sursum etc., ostendit idem quantum ad media corpora. 112. Then at 13 [63] he shows the same thing for the intermediate bodies. Et primo proponit quandam conditionalem, scilicet quod, si sursum et deorsum sunt determinata, necesse est quod locus intermedius sit determinatus. Et hoc probat duplici ratione. Quarum prima est: si, primis existentibus determinatis, medium non sit determinatum, sequetur quod motus qui est ab uno extremo in aliud, sit infinitus, utpote medio existente infinito. Quod autem hoc sit impossibile, ostensum est prius in his quae dicta sunt de motu circulari, ubi ostensum est quod motus qui est per infinitum, non potest compleri. Sic ergo patet quod locus medius est determinatus. Et ita, cum locatum commensuretur loco, consequens est quod corpus sit finitum quod actu existit in hoc loco, vel quod potest ibi existere. First he proposes a conditional, namely, that if up and down are determinate, the intermediate place must be determinate. And he proves this with two arguments, the first of which is this: If, when the extremes were determinate, the intermediate should not be determinate, it would follow that a motion from one extreme to the other would be infinite, on account of the infinite intermediate. But that this is impossible has been shown previously in the discussion about circular motion where it was pointed out that motion through the infinite cannot be completed. Consequently, the intermediate place is determinate. Thus, since the thing in place is commensurate with the place, it follows that the body actually existing in this place or that can exist there, is finite. Secundam rationem ponit ibi: sed et adhuc etc.: quae talis est. Corpus quod fertur sursum vel deorsum, potest pervenire ad hoc quod sit factum existens in loco tali. Quod quidem patet per hoc quod tale corpus natum est moveri a medio vel ad medium, idest habet naturalem inclinationem ad hunc vel illum locum; naturalis autem inclinatio non potest esse frustra, quia Deus et natura nihil frustra faciunt, ut supra habitum est. Sic igitur omne quod movetur naturaliter sursum vel deorsum, potest motus eius terminari ad hoc quod sit sursum vel deorsum. Sed hoc non posset esse si locus medius esset infinitus. Est ergo locus medius finitus, et corpus in eo existens finitum. 113. He gives the second argument at [64] and it is this: A body that is moved up or down can reach the state of existing in such a place. This is clear from the fact that such a body is apt to be moved from the middle or to the middle, i.e., it has a natural inclination to this or that place. Now a natural inclination cannot be in vain, because God and nature do nothing in vain, as was had above. Consequently whatever is naturally moved upward or downward can have its own motion terminated so as to be up or down. But this could not be, if the intermediate place were infinite. Consequently, the intermediate place is finite; so, too, is the body existing in it. Ex praemissis igitur epilogando concludit, manifestum esse quod non contingit aliquod corpus esse infinitum. Therefore in summary he concludes from the foregoing that it is clear that no body can be infinite. Deinde cum dicit: et adhuc si gravitas etc., ostendit non esse corpus grave vel leve infinitum, ratione sumpta ex gravitate vel levitate: quae talis est. Si est corpus grave vel leve infinitum, necesse est quod sit gravitas vel levitas infinita: sed hoc est impossibile: ergo et primum. Then at [65] he shows that there is no infinite heavy or light body by an argument based on heaviness or lightness. It is this: If a heavy or a light body be infinite, then heaviness or lightness must be infinite. But this is impossible. Therefore, the first supposition [of non-infinity] must be true. Circa hoc ergo duo facit: With respect to this, then, he does two things: primo probat conditionalem;
secundo probat destructionem consequentis, ibi: sed adhuc quoniam infinitam et cetera.
First he proves the conditional proposition, at 114;
Secondly, he proves the destruction of the consequent, at 119.
Circa primum duo facit. As to the first he does two things: Primo proponit quod intendit, dicens: si non est gravitas infinita, nullum erit corporum horum, scilicet gravium, infinitum: et hoc ideo, quia necesse est infiniti corporis infinitam esse gravitatem. Et eadem ratio est de corpore levi: quia si infinita est gravitas corporis gravis, necesse est quod etiam levitas sit infinita, si supponatur corpus leve, quod sursum fertur, esse infinitum. First he proposes what he intends and says[65]: If there is no infinite heaviness, none of these, i.e., no heavy body, will be infinite, for the heaviness of an infinite body must be infinite. And the same goes for a light body — for if the heaviness of a heavy body is infinite, the lightness, too, must be infinite, if one supposes some light body carried upward to be infinite. Secundo ibi: palam autem etc., probat quod supposuerat: Secondly, at [66] he proves what he had supposed. et primo ponit probationem;
secundo excludit obviationes quasdam, ibi: nihil autem differt gravitates et cetera.
First he presents the proof, at 115;
Secondly, he dismisses some objections, at 116.
Ponit ergo primo rationem ducentem ad impossibile, quae talis est. Si non est verum quod supra dictum est, supponatur quod corporis infiniti sit gravitas finita: et sit corpus infinitum ab, gravitas autem eius finita sit g. A corpore igitur infinito praedicto auferatur aliqua pars eius finita quae est magnitudo bd, quam necesse est esse multo minorem toto corpore infinito. Minoris autem corporis minor est gravitas: sic ergo gravitas corporis bd est minor quam sit gravitas g, quae est gravitas totius corporis infiniti; et sit ista minor gravitas e. Haec autem minor gravitas, scilicet e, mensuret maiorem gravitatem finitam quae est g, quotiescumque, idest secundum quemcumque numerum, puta secundum tria, ut scilicet dicatur quod e est tertia pars totius g. Accipiatur autem a corpore infinito aliqua pars, quae superaddatur corpori finito bd, secundum proportionem qua g excedit e, et hoc corpus excedens sit bz; ita scilicet quod, sicut gravitas minor quae est e se habet ad maiorem quae est g, ita corpus bd se habeat ad bz. Et quod hoc fieri possit, probat quia a corpore infinito potest auferri quantumcumque oportuerit; eo quod, sicut dicitur in III Physic., infinitum est cuius quantitatem accipientibus semper est aliquid extra accipere. First, then, he presents an argument leading to an impossibility [66] and it is this: If what was said above is not true, then suppose that the heaviness of an infinite body is finite, and let AB be the infinite body and G its finite heaviness. From this infinite body take away a finite part which is the magnitude BD, which is necessarily much less than the whole infinite body. Now the heaviness of this smaller body is less; consequently, the heaviness of BD is less than the heaviness G which is the heaviness of the whole infinite body body. Let this lesser heaviness be E. Now let E be a measure of the greater but finite heaviness G —for example, E is a third part of the whole G. Now take from the infinite body a part to be added to the finite body BD, according to the proportion by which G exceeds E, and let this exceeding body be BZ, in such a way that the ratio between the lesser heaviness E to the greater G is the same as that between the body BD and body BZ. That this can be done is proved by the fact that from an infinite body can be taken away as much as is needed, since, as is said in Physics II, the infinite is that whose quantity is such that, as much as is taken away, there always remains something beyond to be taken. His igitur praesuppositis, argumentatur ducendo ad tria inconvenientia: primo quidem sic. Eadem est proportio magnitudinum gravium, quae est ipsarum gravitatum: videmus enim quod minor gravitas est minoris magnitudinis, et maior maioris. Sed quae est proportio e ad g, minoris scilicet gravitatis ad maiorem, eadem est proportio bd ad bz, minoris scilicet corporis ad maius, ut suppositum est: cum igitur e sit gravitas corporis bd, sequetur quod g sit gravitas corporis bz. Supponebatur autem quod esset gravitas totius corporis infiniti: ergo aequalis numero eadem erit gravitas corporis finiti et infiniti. Quod est inconveniens, quia sequetur quod totum residuum corporis infiniti nihil habeat gravitatis. Ergo et primum est impossibile, scilicet quod corporis infiniti sit gravitas finita. Therefore, with these presuppositions, he now argues to three incompatible consequences. First he reasons in this manner. The ratio of heavy magnitudes is the same as the ratio of their heaviness — for we see that a larger body has more heaviness and a smaller body less. But the ratio of E to G, i.e., of the lesser to the more heavy is the same as that of BD to BZ, i.e., of the smaller body to the larger, was was supposed. Therefore, since E is the heaviness of BD, it will follow that G is the heaviness of the body BZ. But G was assumed to be the heaviness of the whole infinite body. Therefore the numerical value of the heaviness of the finite and of the infinite body will be the same. But this is unacceptable, because it will follow that the whole remainder of the infinity body will have no heaviness. Therefore, the first is impossible, namely, that the heaviness of an infinite body be finite. Secundo ibi: adhuc autem si maioris etc., ducit ad aliud inconveniens. Quia enim a corpore infinito potest accipi quantumcumque quis voluerit, ut dictum est, accipiatur adhuc aliqua pars corporis infiniti, quae superaddatur corpori bz, et sit unum corpus bi finitum maius corpore finito quod est bz. Maioris autem corporis maior est gravitas, ut supra dictum est: ergo gravitas corporis bi est maior quam gravitas g, quae concludebatur gravitas esse corporis bz. Sed primo supponebatur quod g erat gravitas totius corporis infiniti. Ergo gravitas corporis finiti erit maior quam gravitas corporis infiniti, quod est impossibile. Ergo et primum, scilicet quod gravitas corporis infiniti sit finita. Secondly, at [67] he leads to another unacceptable consequence. For since it is possible to take from an infinite body as much as one wishes, as has been said, let yet another part be taken from the infinite body and added to the body BZ. And let G be one finite body greater than the finite body BZ. Now the heaviness of larger body is greater, as was said above. Therefore, the heaviness of BI is greater than the heaviness G which was proved to be the heaviness of the body BZ. But it was assumed in the beginning that G was the heaviness of the whole infinite body. Therefore, the heaviness of a finite body will be greater than that of an infinite body. This is impossible. Therefore, the first is impossible, namely, that the heaviness of an infinite body be finite. Tertio ibi: et inaequalium etc., ducit ad tertium inconveniens, scilicet quod inaequalium magnitudinum sit eadem gravitas. Quod manifeste sequitur ex praemissis, quia infinitum est inaequale finito, cum sit maius eo. Unde, cum haec sint impossibilia, impossibile est corporis infiniti esse gravitatem finitam. Thirdly, at [68] he leads to the third incompatibility, namely, that the heaviness of unequal magnitudes would be the same. This clearly follows from the foregoing, because the infinite is not equal to the finite, because it is greater than it. Hence, since these conclusions are impossible, it is impossible for the heaviness of an infinite body to be finite. Deinde cum dicit: nihil autem differt etc., excludit duas obviationes contra praemissam rationem: 116. Then at 14 [69] he dismisses two objections against the foregoing argument: primo primam;
secundo secundam, ibi: nec utique magnitudinem et cetera.
First, the first;
Secondly, the second, at 118.
Prima autem obviatio est, quia supposuerat in praecedenti ratione quod gravitas minor quae est e, mensuret secundum aliquem numerum gravitatem maiorem quae est g: quod quidem aliquis posset negare: non enim omne maius mensuratur a minori, quia linea trium palmarum non mensurat lineam octo palmarum. The first objection is that he had supposed in the preceding argument that the lesser heaviness E is a numerical measure of the greater heaviness G. Now this can be denied, for not every greater is measured by a smaller, because a line of 3 hands' length is not a measure of a line of hands' length. Hanc autem obviationem excludit philosophus dupliciter. Primo quidem quia nihil differt ad propositum utrum duae praedictae gravitates, scilicet maior et minor, sint commensuratae, ita scilicet quod minor mensuret maiorem; vel incommensuratae, scilicet quod minor maiorem non mensuret: eadem enim ratio sequitur utrobique. Necesse est enim quod minus aliquoties sumptum aut mensuret maius aut excedat ipsum; sicut binarius ter sumptus mensurat senarium (ter enim duo sunt sex), quinarium autem non mensurat sed excedit. Sic igitur, si gravitas e non mensuret gravitatem g, sit ita quod ter sumpta mensuret quandam maiorem gravitatem, quae excedit gravitatem g. Et ex hoc sequitur inconveniens sicut prius. Quia si assumpserimus ex corpore infinito tres magnitudines secundum quantitatem bd, magnitudinis ex his tribus compositae erit tripla gravitas gravitatis e, quae ponitur esse gravitas corporis bd. Gravitas autem tripla ad e est maior secundum praedicta quam gravitas g, quae est gravitas corporis infiniti. Quare sequitur idem impossibile quod prius, scilicet quod maior sit gravitas corporis finiti quam infiniti. But the Philosopher excludes this objection in two ways. First, because it makes no difference, so far as the conclusion is concerned, whether the two heavinesses, namely, the greater and the less, in question are commensurate, so that the less measures the greater, or not, for the same reasoning holds in either case. For it is necessary that the lesser, taken a certain number of times, either measure or exceed the greater: for example, the product of 2 taken 3 times measures 6 [for 3 times 2 equals 6], while it does not measure 5, but exceeds it. Accordingly, if the heaviness E does not measure the heaviness G, let E be such that 3 times E measures a heaviness greater than the heaviness G. And so in this case the same impossibility as before results, because, if we had taken from the infinite body three magnitudes of quantity BD, the heaviness of such a magnitude will be 3 times that of heaviness E, which is assumed to be the heaviness of the body BD. But a heaviness that is 3 times E is greater (according to our assumptions) than the heaviness G which is the heaviness of the infinite body. Wherefore, the same impossibility as before follows, namely, that the heaviness of a finite body exceed that of an infinite body. Secundo ibi: adhuc autem etiam contingit etc., excludit eandem obviationem alio modo. Et dicit quod possumus sumere in demonstratione praedicta quod duae gravitates sint commensuratae, ita scilicet quod e commensuret g. Supra enim primo sumpta est magnitudinis pars, scilicet bd, cuius gravitatem diximus esse e: et ideo dici poterat quod e non mensurat g. Nihil autem differt ad propositum utrum incipiamus a gravitate, accipiendo partem eius quamcumque volumus, aut a magnitudine sic sumpta; puta si, incipiendo a gravitate, sumatur quaedam pars eius, scilicet e, quae mensuret totum, scilicet g; et consequenter ab infinito corpore accipiamus aliquam partem, scilicet bd, cuius gravitas sit e; et deinde procedamus ut supra, ut scilicet sicut se habet gravitas e ad gravitatem g, ita se habeat magnitudo bd ad aliam magnitudinem maiorem quae est bz. Et hoc ideo, quia ex quo magnitudo totius corporis est infinita, contingit auferri ex ea quantumcumque placuerit. Hoc igitur modo sumptis partibus gravitatis et magnitudinis, sequetur quod et magnitudines et gravitates erunt invicem commensuratae; ita scilicet quod minor gravitas mensurabit maiorem, et similiter minor magnitudo maiorem. 117. Secondly, at [70] he excludes the same objection in another way. And he says that we can assume in the demonstration under discussion that the two heavinesses are commensurate, in such a way that E is commensurate to G. For above we first took from the magnitude a part BD whose heaviness we called E, and this was grounds for saying that E does not measure G. But it makes no difference, so far as the proposition is concerned, whether we begin with the heaviness (by taking any part we want) or with the magnitude so taken. For example, we might begin with the heaviness and take a part of it, namely, E, which measures the whole, namely, G, and then we can take from the infinite body a part BD whose heaviness is E and proceed as above, so that as the heaviness E is to heaviness G, so the magnitude BD is to a greater magnitude BZ. This we can do, because, since the magnitude of the whole body is infinite, as much can be taken from it as we please. By taking the parts of the heaviness and of the magnitude in this way, it will follow that the magnitudes and the heavinesses will be mutually commensurate, i.e., the lesser heaviness will measure the greater, and the smaller magnitude the larger. Deinde cum dicit: nec utique magnitudinem etc., excludit secundam obviationem. Supposuerat enim esse magnitudines proportionales gravitatibus. Quod quidem necesse est in corpore similium partium; cum enim sit undique per totum similis gravitatis, necesse est quod in maiori parte sit maior gravitas: sed in corpore dissimilium partium hoc non est necesse, quia potest esse quod gravitas minoris partis excedat gravitatem maioris, sicut minor pars terrae est gravior maiori parte aquae. 118. Then at [71] he excludes a second objection. For he had supposed that the magnitudes are proportional to the heavinesses. Now this is true in bodies having similar parts, for where there is like heaviness throughout the whole, there must be more heaviness in the larger part. But in a body of unlike parts this is not necessarily so, because the heaviness of a smaller part could be greater than that of a larger part, just as a smaller part of earth is heavier than a larger part of water. Hanc ergo obviationem excludit, dicens quod nihil differt ad demonstrationem praemissam utrum magnitudo infinita de qua loquimur, quantum ad gravitatem sit homoeomera, idest similium partium, vel anomoeomera, idest dissimilium partium. Quia a corpore infinito possumus sumere quantumcumque voluerimus, vel apponendo vel subtrahendo; ita quod accipiamus aliquas partes habere aequalem gravitatem parti primo sumptae, scilicet bd, sive illae partes posterius assumptae sint maiores in magnitudine sive minores. Si enim primo acceperimus quod bd sit tricubitum, habens gravitatem e; et accipiamus alias multas partes, puta decem cubitorum, habentes aequalem gravitatem; idem erit ac si sumeretur alia pars aequalis habens aequalem gravitatem. Sic igitur sequitur idem inconveniens. This objection he therefore excludes by saying that it makes no difference to the aforesaid demonstration whether the infinite magnitude in question is homogeneous, i.e., of similar parts, or heterogeneous, i.e., of dissimilar parts. For from an infinite body we can take as much as we wish, either adding or subtracting; hence we can assume certain parts to have a heaviness equal to the part taken first, namely BD, whether the parts taken later are larger or smaller in magnitude. For if we should first take BD as having 3 Cubits and having heaviness E, and then take many other parts, for example, of 10 cubits, to make an equal heaviness, it will be the same as if we had taken another equal part having the same heaviness. Consequently, the same impossibility follows. Praemissa igitur demonstratione, et exclusis obviationibus, concludit ex dictis quod infiniti corporis non potest esse finita gravitas. Relinquitur ergo quod sit infinita. Si ergo impossibile est esse gravitatem infinitam, ut statim probabit, consequens est quod impossibile sit esse aliquod corpus infinitum. Therefore, having presented his demonstration and excluded the objections thereto, he concludes from the foregoing that the heaviness of an infinite body cannot be finite. Therefore, it must be infinite. If then, as he will immediately prove, infinite heaviness is impossible, the consequence is that it is impossible for there to be an infinite body. Deinde cum dicit: sed adhuc quoniam infinitam etc., ostendit quod supposuerat, scilicet quod non possit esse gravitas infinita: et in hoc destruit consequens praemissae conditionalis. Circa hoc autem duo facit. 119. Then at [72] he proves what he had supposed, namely, that there cannot be infinite heaviness. And in this he destroys the consequent of the previously posited conditional. Concerning this he does two things: Primo proponit quod intendit: et dicit quod adhuc oportet manifestare ex his quae subsequuntur, quod impossibile sit gravitatem infinitam esse.
Secundo ibi: si enim tanta etc., probat propositum.
First he proposes what he intends, and says that we must still show from what will follow that infinite heaviness is impossible.
Secondly, at [73] he proves the proposition.
Et primo praemittit quasdam suppositiones;
secundo ex his argumentatur ad propositum, ibi: necesse igitur ex his etc.;
tertio excludit quandam obiectionem, ibi: neque si esset et cetera.
First he lays down certain presuppositions;
Secondly, he uses them in his argument, at 121;
Thirdly, he excludes an objection, at 122.
Ponit autem primo tres suppositiones. Quarum prima est quod, si gravitas tanta, idest alicuius determinatae mensurae, movet tantam, idest per determinatam magnitudinem spatii, in hoc tempore, scilicet determinato, necesse est quod tanta et adhuc, idest quod gravitas maior quae habet tantam quantam minor et adhuc amplius, moveat per tantam magnitudinem spatii in minori tempore: quia quanto virtus motiva est fortior, tanto motus eius est velocior, et ita pertransit aequale spatium in minori tempore, ut probatum est in VI Physic. First, then, he presents three suppositions. The first of these [73] is that, if such a heaviness, i.e., of some certain amount, moves so much, i.e., throughout a definite magnitude of space, in this time, i.e., a determined time, then necessarily as much and more, i.e., a greater heaviness that has as much and something more than a lesser, will move through as great a magnitude in less time — for by as much as a moving power is stronger, by that much is its motion swifter. Consequently, it will traverse an equal distance in less time, as is proved in Physics VI. Secundam suppositionem ponit ibi: et analogiam etc.: et haec sequitur ex prima. Si enim maior gravitas movet in minori tempore, consequens est quod eadem sit analogia, idest proportio, gravitatum et temporum, tamen e converso; ita scilicet quod, si media gravitas movet in tanto tempore, duplum gravitatis movet in medietate eius, scilicet temporis. The second supposition is at [74] and follows from the first. For if a greater heaviness moves in less time, then the analogy, i.e., proportion between heavinesses and times is the same, but inversely so, i.e., if half the heaviness moves something in a certain amount of time, then double that amount moves in its half, i.e., in half the time. Tertiam suppositionem ponit ibi: adhuc finita et cetera. Et dicit quod finita gravitas movet per finitam magnitudinem spatii in quodam tempore finito. The third supposition, at [75], states that a finite heaviness moves through a finite magnitude of space in a certain finite time. Deinde cum dicit: necesse igitur ex his etc., argumentatur ex praemissis. Si enim sit gravitas infinita, sequentur duo contradictoria; scilicet quod aliquid moveatur secundum eam, et quod non moveatur. Quod moveatur quidem, sequitur ex prima suppositione; quia, si tanta gravitas movet in tanto tempore, maior movebit velocius, scilicet in minori tempore. Quia ergo infinita gravitas est maior quam finita, si finita movet secundum determinatum tempus per determinatum spatium, ut tertia suppositio dicebat, consequens est quod infinita moveat tantum et adhuc amplius, idest vel per maius spatium in aequali tempore, vel per aequale spatium in minori tempore, quod est velocius moveri. 121. Then at [76] he argues from these premises. If an infinite heaviness should exist, two contradictories will follow: namely, that something would be moved according to it, and not moved. That it would be moved follows, indeed, from the first supposition — for if a certain heaviness moves in a certain amount of time, a greater will move more swiftly, i.e., in less time. Since, therefore, an infinite weight is greater than a finite, then, if a finite moves through a definite distance in a definite time, as the third supposition says, the consequence is that an infinite heaviness will move as much and more, i.e., either through a greater distance in the same time, or through an equal distance in less time, which is to be moved more swiftly. Sed quod aliquid non moveatur secundum infinitam gravitatem, sequitur ex secunda suppositione. Oportet enim proportionaliter aliquid moveri secundum excellentias gravitatis e contrario, scilicet quod maior gravitas moveat in minori tempore. Nulla autem proportio potest esse infinitae gravitatis ad finitam: minoris autem temporis ad maius, dummodo sit finitum, est aliqua proportio. Sic igitur non erit aliquod tempus dare in quo infinita gravitas moveat; sed semper erit accipere aliquid moveri in minori tempore quam sit tempus in quo movet gravitas infinita; non est autem dare minimum tempus in quo gravitas infinita moveat, ita quod possit dici quod non potest aliquid in minori tempore moveri. Ideo autem non est minimum tempus accipere, quia, cum omne tempus sit divisibile, sicut et quodlibet continuum, quolibet tempore est accipere aliquod minus, partem scilicet temporis divisi. Sic igitur non potest esse gravitas infinita. But that something is not moved according to infinite heaviness follows from the second supposition. For a thing must be moved in proportion to the greatness of the weight in inverse proportion, i.e., the greater weight will move in less time. But there can be no proportion between an infinite and a finite weight, although there is a proportion between less time and more time, provided the time is finite. Consequently, there can be no time given in which an infinite weight can move, but something will always be able to be taken as moved in less time than the time in which an infinite weight moves, for there can be taken no least time in which an infinite weight can move in the sense that it would be impossible for something to be moved in a lesser time. Now the reason why no such least time can be assumed is that since all time is divisible, as is any continuum, it is always possible to take a time smaller than any given time, i.e., a part of the divided time. Consequently, an infinite heaviness cannot exist. Deinde cum dicit: neque si esset etc., excludit quandam obviationem. Posset enim aliquis dicere aliquod esse minimum tempus, scilicet indivisibile, in quo movet gravitas infinita; sicut et quidam posuerunt aliquas magnitudines esse minimas et indivisibiles. Sed hanc obviationem excludit: 122. Then at [77] he excludes an objection. For someone could say that there is a least time, namely, an indivisible time, in which the infinite heaviness moves, just as some have posited certain minimum and indivisible magnitudes. But he excludes this objection: et primo ostendit quod inconveniens sequatur si ponatur minimum tempus, et quod in hoc infinita gravitas movet;
secundo ostendit idem inconveniens sequi si in quocumque tempore, etiam non minimo, infinita gravitas moveat, ibi: sed adhuc necesse et cetera.
First he shows that an impossibility follows upon assuming a minimum time and that an infinite heaviness moves in that time;
Secondly, he shows that the same impossibility follows if an infinite heaviness should move in any amount of time, even not the minimum, at 123.
Dicit ergo primo quod, etiam si esset tempus minimum, nulla utilitas ex hoc esset ponenti gravitatem infinitam, ad vitandum inconveniens. Quamvis enim ponamus minimum tempus, non tamen excludimus quin sit aliqua proportio huius minimi temporis ad tempus maius, eo quod hoc tempus minimum erit pars maioris temporis; sicut unitas est pars numeri, unde est aliqua proportio eius ad omnem numerum. Illud autem indivisibile non habet proportionem ad divisibile, quod non est pars eius; sicut punctum non est pars lineae, et ideo non est aliqua proportio puncti ad lineam. Accipiatur ergo alia gravitas finita e contrario, tanto maior gravitate finita quae movebat in maiori tempore quam gravitas infinita, in qua proportione tempus minimum gravitatis infinitae se habet ad tempus maius alterius gravitatis finitae. Puta, sit gravitas infinita e, tempus minimum in quo movet b, gravitas autem finita g, quae movet in maiori tempore quam b, scilicet in tempore d: accipiatur ergo alia gravitas tanto maior quam g, in qua proportione d excedit b, et sit haec gravitas f. Sic ergo, cum minoratio temporis sit secundum additionem gravitatis, sequetur quod gravitas f, quae est finita, moveat in eodem tempore cum gravitate infinita: quod est impossibile. He says therefore first [77] that even if there were a minimum time, it would not help in escaping the impossibility that follows from the assumption of infinite heaviness. For although we posit a minimum time, we do not exclude a ratio of this time to a greater time, for this minimum time will be a part of a greater time, just as one is part of number, which allows it to have a ratio to every number. But an indivisible which is not part of a divisible has no proportion to it, just as a point is not a part of a line and therefore there is no proportion of a point to a line. So let us take another heaviness which is finite and as much heavier proportionally than the finite heaviness that moved something in more time than the infinite heaviness, as the minimum time of the infinite heaviness is less than the greater time of the other finite heaviness. For example, let E be the infinite heaviness, and B the minimum time in which it moves, and let G be the finite heaviness that moves something in more time D than time B. Then let F be the other heaviness which is greater than G in the proportion that D exceeds B. Then, since the lessening of time corresponds to the increasing of heaviness, it will follow that the heaviness F, which is finite, will move something in the same time as the infinite heaviness. But this is impossible. Est autem attendendum quod, sicut non est proportio puncti ad lineam, ita etiam non est proportio instantis ad tempus; quia instans non est pars temporis. Sic ergo solum ista ratio tolleretur, si quis poneret quod gravitas infinita moveret in instanti: sed hoc est impossibile, ut probatum est in VI Physic., scilicet quod aliquis motus sit in instanti. It should be noted that, just as there is no proportion between a point and a line, so there is none between an instant and time, because an instant is not a part of time. Consequently, the only way Aristotle's argument could be destroyed, would be by positing that an infinite heaviness should move in an instant. But that is impossible, as was proved in Physics VI, namely, that any motion should occur in an instant. Deinde cum dicit: sed adhuc necesse etc., ostendit quod idem inconveniens sequitur in quocumque tempore ponamus gravitatem infinitam movere, etiam in tempore non minimo. Et hoc est quod dicit, quod si in qualicumque tempore finito, etiam non minimo, gravitas infinita movet, adhuc necesse est quod in ipso tempore aliqua gravitas finita moveat per finitum spatium; quia erit accipere excessum gravitatis secundum deminutionem temporis, ut praedictum est. Sic igitur patet quod impossibile est esse gravitatem infinitam: et eadem ratio est de levitate. Then at [78] he shows that the same impossibility follows in whatever time we assume an infinite heaviness to move. And this is what he says, namely, that if an infinite heaviness should move in any finite time whatever, even though it be not the minimum, it is still necessary that in that time a finite heaviness could move through a finite distance — for one will be able to take an excess of weight corresponding to a lessening of the time, as was said above. Consequently, it is clearly impossible for an infinite heaviness to exist; and the same argument holds for lightness.
Lecture 13:
A natural and demonstrative argument showing no natural body can be infiniteChapter 6 cont. Ἀδύνατον ἄρα ἄπειρον εἶναι βάρος, ὁμοίως δὲ καὶ κουφότητα. Καὶ σώματα ἄρ' ἄπειρον βάρος ἔχοντα καὶ κουφότητα ἀδύνατον. Ὅτι μὲν οὖν οὐκ ἔστιν ἄπειρον σῶμα, δῆλον διά τε τῶν κατὰ μέρος θεωροῦσι τοῦτον τὸν τρόπον, καὶ καθόλου σκοπουμένοις μὴ μόνον κατὰ τοὺς λόγους τοὺς ἐν τοῖς περὶ τὰς ἀρχὰς εἰρημένους ἡμῖν (διωρίσθη γὰρ κἀκεῖ καθόλου πρότερον περὶ ἀπείρου πῶς ἔστι καὶ πῶς οὐκ ἔστιν) ἀλλὰ καὶ νῦν ἄλλον τρόπον. 79 Infinite weight is therefore impossible, and the same reasoning applies also to infinite lightness. Bodies then of infinite weight and of infinite lightness are equally impossible. That there is no infinite body may be shown, as we have shown it, by a detailed consideration of the various cases. 80 But it may also be shown universally, not only by such reasoning as we advanced in our discussion of principles (though in that passage we have already determined universally the sense in which the existence of an infinite is to be asserted or denied), but also suitably to our present purpose in the following way. Μετὰ δὲ ταῦτ' ἐπισκεπτέον κἂν εἰ μὴ ἄπειρον μὲν τὸ σῶμα τὸ πᾶν, οὐ μὴν ἀλλὰ τοσοῦτόν γε ὥστ' εἶναι πλείους οὐρανούς τάχα γὰρ ἄν τις τοῦτ' ἀπορήσειεν, ὅτι καθάπερ ὁ περὶ ἡμᾶς κόσμος συνέστηκεν, οὐδὲν κωλύει καὶ ἑτέρους εἶναι πλείους μὲν ἑνός, μὴ μέντοι γε ἀπείρους. Πρῶτον δ' εἴπωμεν καθόλου περὶ τοῦ ἀπείρου. 81 That will lead us to a further question. Even if the total mass is not infinite, it may yet be great enough to admit a plurality of universes. The question might possibly be raised whether there is any obstacle to our believing that there are other universes composed on the pattern of our own, more than one, though stopping short of infinity. First, however, let us treat of the infinite universally. Chapter 7 Ἀνάγκη δὴ σῶμα πᾶν ἤτοι ἄπειρον εἶναι ἢ πεπερασμένον, καὶ εἰ ἄπειρον, ἤτοι ἀνομοιομερὲς ἅπαν ἢ ὁμοιομερές, κἂν εἰ ἀνομοιομερές, ἤτοι ἐκ πεπερασμένων εἰδῶν ἢ ἐξ ἀπείρων. Ὅτι μὲν τοίνυν οὐχ οἷόν τε ἐξ ἀπείρων, φανερόν, εἴ τις ἡμῖν ἐάσει μένειν τὰς πρώτας ὑποθέσεις πεπερασ(274b.) μένων γὰρ τῶν πρώτων κινήσεων οὐσῶν, ἀνάγκη καὶ τὰς ἰδέας τῶν ἁπλῶν σωμάτων εἶναι πεπερασμένας. Ἁπλῆ μὲν γὰρ ἡ τοῦ ἁπλοῦ σώματος κίνησις, αἱ δ' ἁπλαῖ πεπερασμέναι κινήσεις εἰσίν ἀνάγκη δὲ κίνησιν ἔχειν σῶμα πᾶν φυσικόν. 82 Every body must necessarily be either finite or infinite, and if infinite, either of similar or of dissimilar parts. If its parts are dissimilar, they must represent either a finite or an infinite number of kinds. 83 That the kinds cannot be infinite is evident, if our original presuppositions remain unchallenged. For the primary movements being finite in number, the kinds of simple body are necessarily also finite, since the movement of a simple body is simple, and the simple movements are finite, and every natural body must always have its proper motion. Ἀλλὰ μὴν εἴ γε ἐκ πεπερασμένων ἔσται τὸ ἄπειρον, ἀνάγκη καὶ τῶν μορίων ἕκαστον εἶναι ἄπειρον, λέγω δ' οἷον τὸ ὕδωρ ἢ τὸ πῦρ. Ἀλλ' ἀδύνατον δέδεικται γὰρ ὅτι οὔτε βάρος οὔτε κουφότης ἐστὶν ἄπειρος. 84 Now if the infinite body is to be composed of a finite number of kinds, then each of its parts must necessarily be infinite in quantity, that is to say, the water, fire, etc., which compose it. But this is impossible, because, as we have already shown, infinite weight and lightness do not exist. Ἔτι ἀναγκαῖον ἀπείρους τῷ μεγέθει εἶναι καὶ τοὺς τόπους αὐτῶν, ὥστε καὶ τὰς κινήσεις ἀπείρους εἶναι πάντων. Τοῦτο δ' ἀδύνατον, εἰ θήσομεν ἀληθεῖς εἶναι τὰς πρώτας ὑποθέσεις, καὶ μήτε τὸ κάτω φερόμενον εἰς ἄπειρον ἐνδέχεσθαι φέρεσθαι μήτε τὸ ἄνω κατὰ τὸν αὐτὸν λόγον. Ἀδύνατον γὰρ γίνεσθαι ὃ μὴ ἐνδέχεται γενέσθαι, ὁμοίως ἐπὶ τοῦ τοιόνδε καὶ τοσόνδε καὶ τοῦ ποῦ. Λέγω δ', εἰ ἀδύνατον γενέσθαι λευκὸν ἢ πηχυαῖον ἢ ἐν Αἰγύπτῳ, καὶ γίνεσθαί τι τούτων ἀδύνατον. Ἀδύνατον ἄρα καὶ φέρεσθαι ἐκεῖ οὗ μηθὲν δυνατὸν ἀφικέσθαι φερόμενον. 85 Moreover it would be necessary also that their places should be infinite in extent, so that the movements too of all these bodies would be infinite. But this is not possible, if we are to hold to the truth of our original presuppositions and to the view that neither that which moves downward, nor, by the same reasoning, that which moves upward, can prolong its movement to infinity. For it is true in regard to quality, quantity, and place alike that any process of change is impossible which can have no end. I mean that if it is impossible for a thing to have come to be white, or a cubit long, or in Egypt, it is also impossible for it to be in process of coming to be any of these. It is thus impossible for a thing to be moving to a place at which in its motion it can never by any possibility arrive. Ἔτι εἰ καὶ διεσπασμένα ἐστίν, οὐδὲν ἧττον ἐνδέχοιτ' ἂν τὸ ἐξ ἁπάντων [πῦρ] ἄπειρον εἶναι. Ἀλλὰ σῶμα ἦν τὸ πάντῃ διάστασιν ἔχον ὥστε πῶς οἷόν τε πλείω μὲν ἀνόμοια, ἕκαστον δ' αὐτῶν ἄπειρον εἶναι; πάντῃ γὰρ ἕκαστον δεῖ ἄπειρον εἶναι. 86 Again, suppose the body to exist in dispersion, it may be maintained none the less that the total of all these scattered particles, say, of fire, is infinite. 87 But a body we saw to be that which has extension every way. How can there be several dissimilar elements, each infinite? Each would have to be infinitely extended every way. Ἀλλὰ μὴν οὐδὲ πᾶν ὁμοιομερὲς ἐνδέχεται τὸ ἄπειρον εἶναι. Πρῶτον μὲν γὰρ οὐκ ἔστιν ἄλλη παρὰ ταύτας κίνησις. Ἕξει οὖν μίαν τούτων. Εἰ δὲ τοῦτο, συμβήσεται ἢ βάρος ἄπειρον ἢ κουφότητα εἶναι ἄπειρον. Ἀλλὰ μὴν οὐδ' οἷόν τε τὸ κύκλῳ σῶμα φερόμενον [εἶναι ἄπειρον]. Ἀδύνατον γὰρ τὸ ἄπειρον φέρεσθαι κύκλῳ οὐθὲν γὰρ διαφέρει τοῦτο λέγειν ἢ τὸ τὸν οὐρανὸν φάναι ἄπειρον εἶναι, τοῦτο δὲ δέδεικται ὅτι ἀδύνατον. 88 It is no more conceivable, again, that the infinite should exist as a whole of similar parts. For, in the first place, there is no other (straight) movement beyond those mentioned: we must therefore give it one of them. And if so, we shall have to admit either infinite weight or infinite lightness. Nor, secondly, could the body whose movement is circular be infinite, since it is impossible for the infinite to move in a circle. This, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible. Ἀλλὰ μὴν οὐδ' ὅλως γε τὸ ἄπειρον ἐνδέχεται κινεῖσθαι. Ἢ γὰρ κατὰ φύσιν κινηθήσεται ἢ βίᾳ καὶ εἰ βίᾳ, ἔστιν αὐτῷ καὶ ἡ κατὰ φύσιν, ὥστε καὶ τόπος ἄλλος ἴσος εἰς ὃν οἰσθήσεται. Τοῦτο δ' ἀδύνατον. 89 Moreover, in general, it is impossible that the infinite should move at all. If it did, it would move either naturally or by constraint: and if by constraint, it possesses also a natural motion, that is to say, there is another place, infinite like itself, to which it will move. But that is impossible.
Postquam philosophus ostendit de singulis corporibus naturalibus quod nullum eorum sit infinitum, hic ostendit communi ratione quod nullum corpus naturale sit infinitum: probatio enim quae est per medium commune, perfectiorem scientiam causat. 124. After showing that no single natural body is infinite, the Philosopher here shows by a general argument that no natural body is infinite — for a proof through a common medium causes more perfect science. Circa hoc ergo duo facit: About this, therefore, he does two things: primo dicit de quo est intentio;
secundo ostendit propositum, ibi: necesse itaque corpus omne et cetera.
First he mentions his intention;
Secondly, he proves his proposition, at 128.
Circa primum tria facit. 125. As to the first he does three things: Primo ostendit quasi epilogando quid prius sit dictum; dicens quod praedicto modo considerantibus manifestum est quod non est corpus infinitum, per ea quae sunt secundum partem, idest secundum proprias rationes singularium partium universi, scilicet corporis quod movetur circulariter, et quod movetur sursum aut deorsum. First he shows (as if summarizing) what has been previously said. And he states that for those who think according to the lines already laid down, it is clear that there is no infinite body, "by a detailed consideration of the various cases," i.e., on account of the reasons applied to the individual parts of the universe, namely, to the body that is moved circularly and to the bodies that are move upward or downward. Secundo ibi: et universaliter intendentibus etc., ostendit quid immediate restet dicendum. Et dicit quod idem potest esse manifestum si aliquis intendat universaliter, idest per medium commune. Et hoc non solum secundum illas rationes communes quae positae sunt in libro physicorum, ubi determinatum est de principiis communibus corporum naturalium (in tertio enim physicorum determinatur universaliter de infinito quomodo sit et quomodo non sit: ostensum est enim ibi quod infinitum est in potentia, sed non in actu). Nunc autem determinandum est alio modo de infinito, ostendendo scilicet universaliter quod nullum corpus sensibile potest esse infinitum in actu. 126. Secondly, at [801 he shows what immediately remains to be said. And he says that the same thing can be clear if someone looks at it universally, i.e., by a common medium. And this is in addition to those general arguments given in the book of the Physics where the common principles of all natural bodies were discussed — for in Physics III is a universal treatment of the infinite, as to how it exists and how not, it being shown there that the infinite exists in potency but not in act. Now, however, the infinite has to be treated in another way, by showing universally that no sensible body can be infinite in act. Tertio ibi: post haec autem intendendum etc., ostendit quid sit determinandum immediate post ista. Et dicit quod postquam ostenderimus hoc quod dictum est, intentio nostra erit inquirere, supposito quod totum corpus universi non sit infinitum, utrum tamen totum corpus sit tantae quantitatis, quod possint ex eo esse plures caeli, idest plures mundi. Forte enim potest de hoc aliquis dubitare, an sit possibile quod, sicut iste mundus est constitutus circa nos, ita etiam sint alii mundi plures uno, non tamen infiniti. Sed antequam hoc pertractemus, dicemus universaliter de infinito, ostendendo scilicet communibus rationibus quod nullum corpus sit infinitum. 127. Thirdly, at [81] he shows what must be determined immediately after these questions. And he says that after proving what has been proposed, our aim will be to inquire (on the supposition that the whole body of the universe is not infinite) whether the whole body is of such size that there can be made from it several heavens, i.e., many worlds. For perhaps someone could wonder whether it is possible that, just as our world is established about us, there might be other worlds, i.e., more than one though not an infinitude. But before dealing with that question, we shall speak universally of the infinite and show that from common reasons no body is infinite. Deinde cum dicit: necesse itaque etc., ostendit propositum: 128. Then at [82] he proves the proposition: et primo per rationes naturales demonstrativas;
secundo per rationes logicas, ibi: rationabilius autem et cetera.
First by natural demonstrative arguments;
Secondly, by logical arguments (L. 15).
Dico autem rationes demonstrativas et naturales, quae sumuntur ex propriis principiis scientiae naturalis; cuius consideratio consistit circa motum, et actionem et passionem, quae in motu consistunt, ut dicitur in III Physic. Now I call "demonstrative" and "natural" those arguments that are taken from the proper principles of natural science, whose consideration concerns motion, and action and passion which reside in motion, as is said in Physics III. Primo ergo ostendit nullum corpus esse infinitum, ex parte motus localis, qui est primus et communissimus motuum;
secundo universaliter ex parte actionis et passionis, ibi: quod autem omnino impossibile et cetera.
First, therefore, at [82] he shows that no body is infinite from the side of local motion, which is the first and most common of motions;
Secondly, universally on the part of action and passion (L. 14).
Circa primum duo facit: As to the first he does two things: primo praemittit quasdam divisiones;
secundo prosequitur singula membra, ibi: quod quidem igitur et cetera.
First he presents certain divisions, at 129;
Secondly, he examines the members individually, at 130.
Praemittit ergo primo tres divisiones. Quarum prima est, quod necesse est omne corpus aut esse finitum aut infinitum. Et si quidem sit finitum, habemus propositum: si autem sit infinitum, restat secunda divisio, scilicet quod aut est totum anomoeomerum, idest dissimilium partium, sicut corpus animalis, quod componitur ex carnibus, ossibus et nervis; aut est totum homoeomerum, idest similium partium, sicut aqua, cuius quaelibet pars est aqua. Si vero sit totum dissimilium partium, restat tertia divisio: utrum scilicet species partium talis corporis sint finitae numero aut infinitae. Si ergo probetur quod non sunt infinitae, neque iterum sunt finitae; et quod iterum nullum corpus similium partium sit infinitum: probatum erit quod nullum corpus universaliter est infinitum. 129. Therefore he first [82] presents three divisions: The first of these is that every body must be either finite or infinite. If it is finite, we have our proposition; but if it is infinite, a second division remains, namely, that it be a heterogeneous whole, i.e., having dissimilar parts, as an animal body which is composed of flesh, bones and sinews; or it is a homogeneous whole, i.e., having like parts, such as water, each part of which is water. But if it is a whole of dissimilar parts, a third division remains, namely, whether the species of the parts of such a body are finite or infinite in number. If it is proved that they are not infinite, nor again finite, and further that no body of parts that are alike is infinite, it will have been proved universally that no body is infinite. Deinde cum dicit: quod quidem igitur etc., prosequitur singula praedictorum. Et circa hoc tria facit: 130. Then at [83] he pursues each member. He does three things about this: primo ostendit quod non est possibile corporis dissimilium partium esse infinitas species partium eius;
secundo ostendit quod non est possibile esse corpus infinitum dissimilium partium, ita quod species partium sint finitae, ibi: sed tamen si quidem etc.;
tertio ostendit quod non est possibile esse aliquod corpus infinitum similium partium, ibi: sed adhuc neque totum et cetera.
First he shows that it is not possible in a body of unlike parts for the species of its parts to be infinite;
Secondly, that it is not possible for an infinite body of unlike parts to be such that the species of its parts be finite, at 131;
Thirdly, he shows that there can be no infinite body having parts that are alike, at 135.
Dicit ergo primo quod manifestum est quod non est possibile ex infinitis speciebus partium constitui aliquod corpus infinitum, si quis permittat manere in sua veritate primas hypotheses, idest suppositiones prius factas, scilicet quod sint solae tres species motuum simplicium. Si enim primi motus, scilicet simplices, sunt finiti, necesse est quod species corporum simplicium sint finitae: et hoc ideo, quia motus ipsius corporis simplicis est simplex, ut supra habitum est. Dictum est autem supra quod simplices motus sunt finiti: sunt enim tres, scilicet motus qui est ad medium, et motus qui est a medio, et motus qui est circa medium. Ideo autem oportet quod, si motus simplices sunt finiti, quod corpora simplicia sint finita, quia necesse est quod omne corpus naturale habeat proprium motum: si autem essent infinitae species corporum, motibus existentibus finitis, oporteret esse aliquas species corporum, quae non haberent motus: quod est impossibile. He says therefore first [83] that it is plainly not possible for an infinite body to be constituted from an infinite species of parts, so long as one is loyal to the "first hypotheses," i.e., the previously made suppositions that there are only three species of simple motion. For if the first motions, i.e. the simple motions, are finite, then the species of simple bodies must be finite, for the motion of a simple body is itself simple, as was had above. But it was also held above that simple motions are finite: for there are three, namely, motion to the middle, motion from the middle, and motion around the middle. Now the reason why simple bodies are finite, if simple motions are finite, is that every natural body must have its own proper motion — but if there were an infinite species of bodies, while the number of motions was finite, there would have to be some species of bodies without motions, which is impossible. Sic igitur ex hoc quod motus simplices sunt finiti, sufficienter probatur quod species corporum simplicium sint finitae. Omnia autem corpora mixta componuntur ex simplicibus. Unde si esset aliquod totum dissimilium partium, quod componeretur ex infinitis speciebus corporum mixtorum, tamen oporteret quod species primorum componentium sint finitae: quamvis etiam hoc non videatur possibile, quod finitorum elementorum diversificentur commixtiones in infinitum. Nec tamen aliquod corpus mixtum potest dici omnium similium partium: quia, etsi partes eius quantitativae sint similes specie, sicut quaelibet pars lapidis est lapis, partes tamen essentiales eius sunt diversae secundum speciem: componitur enim substantia corporis mixti ex corporibus simplicibus. Consequently, from the fact that simple motions are finite, it is sufficiently proved that the species of simple bodies are finite. Now it is from simple bodies that mixed bodies are composed. Hence, if there were a whole having unlike parts and composed of an infinite species of mixed bodies, the species of the first components would still have to be finite — though it does not even seem possible that mixtures from finite elements should be infinitely diversified. Neither can any compound body be called a mixture of all like parts, because, even if its quantitative parts be specifically alike, as each part of a stone is stone, yet its essential parts are specifically diverse, for the substance of a mixed body is composed of simple bodies. Deinde cum dicit: sed tamen si quidem etc., ostendit quod non est possibile esse corpus infinitum dissimilium partium, ita quod species partium sint finitae. Et ad hoc inducit quatuor rationes. Quarum prima est quod, si corpus dissimilium partium, infinitum existens, ex partibus finitis specie componeretur, oporteret quod quaelibet partium eius esset infinita secundum magnitudinem: puta, si aliquod corpus mixtum esset infinitum, elementis existentibus finitis, oporteret aerem esse infinitum et aquam et ignem. Sed hoc est impossibile: quia, cum quodlibet eorum sit grave vel leve, sequeretur secundum praemissa quod gravitas eius vel levitas esset infinita; ostensum est autem quod nulla gravitas vel levitas potest esse infinita. Ergo non est possibile quod corpus infinitum dissimilium partium componatur ex finitis speciebus partium. 131. Then at [84] he shows that it is impossible to have an infinite body of unlike parts, the species of which parts are finite. And he arrives at this with four arguments. The first is that, if a body of unlike parts is infinite and composed of parts that are finite with respect to species, each of the parts would have to be infinite in magnitude. For example, if a mixed body were infinite and composed of elements that were finite, air would have to be infinite, and so would the water and the fire. But this is impossible, because, since each of these is either heavy or light, it would follow according to what was previously said that its heaviness or lightness would be infinite. But it has been proved that no heaviness or lightness can be infinite. Therefore, it is not possible for an infinite body of unlike parts to be composed of a finite species of parts. Potest autem aliquis obiicere quod non sequitur, hac ratione facta, quod unaquaeque partium sit infinita: esset enim possibile totum esse infinitum, una parte existente infinita secundum magnitudinem, et aliis existentibus finitis. Sed hoc reprobatum est in III Physic.: si enim una pars esset infinita, consumeret alias partes finitas propter excessum virtutis. Potest tamen dici quod, etiam hoc posito, sequetur idem inconveniens, scilicet quod sit gravitas vel levitas infinita; et ideo de hoc Aristoteles non curavit. However, someone could object that it does not follow from this argument that each of the parts is infinite: for it could be possible for the whole to be infinite if one part were infinite in magnitude and the others finite. But this was rejected in Physics III — for if one part were infinite it would consume the other finite parts on account of its excessive power. Likewise it can be said that even in that case the same impossibility will follow, namely, that there would be an infinite heaviness or lightness. And therefore Aristotle was not concerned with it. Secundam rationem ponit ibi: adhuc necessarium et cetera. Si enim partes totius infiniti sint infinitae secundum magnitudinem, oportet etiam quod loca earum essent infinita secundum magnitudinem; quia loca oportet esse aequalia locatis. Sed motus mensuratur secundum magnitudinem loci in quem pertransit, ut probatur in VI Physic. Ergo sequitur quod motus omnium harum partium sint infiniti. Sed hoc est impossibile, si sint vera ea quae supra supposuimus, scilicet quod non contingit aliquid moveri deorsum in infinitum, neque etiam sursum; quia deorsum est determinatum, cum sit medium, et eadem ratione sursum est determinatum (si enim unum contrariorum est determinatum, et aliud). 132. The second argument is presented at [85]. For if the parts of an infinite whole were infinite in magnitude, their places would have to be infinite in magnitude, because places are necessarily equal to the things in them. But motion is measured according to the magnitude of the place into which it passes, as is proved in Physics VI. Therefore it follows that the motions of all these parts would be infinite. But this is impossible, if what we supposed above is true, namely, that nothing can be moved downward infinitely, nor upward either — because "down" is determinate, since it is the middle, and for the same reason "up" is determinate (for if one contrary is determinate, so is the other). Et hoc etiam hic ostendit per id quod est commune omnibus motibus. Videmus enim in transmutatione quae est secundum substantiam, quod impossibile est fieri illud quod non potest esse factum; sicut non potest fieri asinus rationalis, quia impossibile est asinum esse talem. Et simile est in tali, idest in motu qui est secundum qualitatem, et in tanto, idest in motu qui est secundum quantitatem, et in ubi, idest in motu qui est secundum locum. Si enim impossibile est quod aliquid nigrum sit factum album, sicut corvus, impossibile est quod fiat album; et si aliquid impossibile est quod sit cubitale, sicut formica, impossibile est quod ad hoc moveatur; et si impossibile est quod aliquid sit in Aegypto, puta Danubius, impossibile est quod illuc moveatur. Et huius ratio est, quia natura nihil facit frustra: esset autem frustra si moveret ad id ad quod impossibile est pervenire. Sic igitur impossibile est quod aliquid moveatur localiter illuc quo non est pervenire. Non est autem pertransire locum infinitum. Si igitur loca essent infinita, nullus esset motus. Quod cum sit impossibile, non potest esse quod partes corporis infiniti dissimilium partium, sint infinitae in magnitudine. And he also proves this by what is common to all motions. For in the transmutation according to substance, we see that it is impossible for a thing to become what it cannot be, as, for example, there cannot be made a rational ass, since it is impossible for an ass to be such. And the same goes for a motion in "such," i.e., with respect to quality and for a motion in "so much," i.e., with respect to quantity, and for a motion in "where," i.e., with respect to place. For if it is impossible for something black ever to have been made white, as a raven, it is impossible for it ever to become white. And if it is impossible for anything to be a foot long, as an ant, it is impossible for it to be moving toward that; and if it is impossible for something to be in Egypt, as the Danube, it is impossible for it to be moving thither. The reason for this is that nature does nothing in vain. But it would be in vain for a thing to be tending to what is impossible for it to reach. Consequently, it is impossible for a thing to be locally moved to a place where it cannot arrive. But it is impossible to traverse an infinite place. If, therefore, places were infinite, there would be no motion. But since that is impossible, it cannot be that the parts of an infinite body of unlike parts be infinite in magnitude. Tertiam rationem ponit ibi: adhuc si et discerpta et cetera. Posset enim aliquis dicere quod non est unum continuum infinitum, sunt tamen quaedam partes discerptae, idest disiunctae et non continuae, infinitae; sicut Democritus posuit infinita corpora indivisibilia, et sicut Anaxagoras posuit infinitas partes consimiles. 133. He presents the third argument at [86]. For someone could say that there is no infinite continuous unit, but that there are yet certain parts, disconnected and not continued, which are infinite, as Democritus posited infinite indivisible bodies, and as Anaxagoras posited infinite parts all similar to each other. Sed ipse dicit quod ex hac positione nihil minus sequitur inconveniens: quia, si sint infinitae partes ignis non continuae, nihil prohibet illas omnes coniungi, et sic fieri ex omnibus unum ignem infinitum. But Aristotle says that this position leads no less to an impossibility: for if infinite parts of fire are not joined, there is nothing to prevent all of them from joining and thus making one infinite fire from all of them. Quartam rationem ponit ibi: sed corpus est et cetera. Cum enim aliquid dicitur esse infinitum, oportet quod infinitum accipiatur secundum propriam eius rationem: puta, si dicamus lineam esse infinitam, intelligimus eam esse infinitam secundum longitudinem; si vero dicamus superficiem esse infinitam, intelligimus quod sit infinita secundum longitudinem et latitudinem. Corpus autem distenditur ad omnem partem, quia habet omnes dimensiones, ut supra dictum est: et sic, si corpus dicatur infinitum, oportet quod sit infinitum ad omnem partem; et ita ex nulla parte erit aliquid extra ipsum. Non ergo est possibile quod in corpore infinito sint plura dissimilia, quorum unumquodque sit infinitum: quia non est possibile esse plura infinita, secundum praedicta. 134. The fourth argument he presents at [87]. For when something is said to be infinite, the term should be taken according to its proper meaning. For example, if we say that a line is infinite, we understand it to be infinite in length; while, if we say that a surface is infinite, we understand that it is infinite in length and width. But a body stretches in every direction, because it has three dimensions, as was said above. Consequently, if a body is said to be infinite, it will have to be infinite in every direction, and so in no direction will there be anything outside it. It is therefore not possible that there be in an infinite body many things that are unlike, each of which is infinite, for according to the foregoing it is not possible for there to be a number of infinites. Deinde cum dicit: sed adhuc neque totum etc., ostendit quod corpus infinitum non potest esse similium partium: et hoc duabus rationibus. Quarum prima est, quia cuiuslibet corporis naturalis oportet esse aliquem motum localem; non est autem alius motus praeter istos qui supra dicti sunt, quorum scilicet unus est circa medium, alius a medio, et tertius ad medium; sequitur igitur quod habeat unum istorum motuum. Sed hoc est impossibile: quia si moveatur sursum vel deorsum, erit grave vel leve; et ita accidet gravitatem et levitatem esse infinitam, quod est impossibile secundum praemissa. Similiter etiam non est possibile quod moveatur circulariter, quia est impossibile infinitum circumferri: nihil enim differt hoc dicere, quam si dicatur caelum infinitum, quod impossibile est, ut supra ostensum est. Non ergo contingit totum corpus infinitum esse homoeomerum. 135. Then at [88] he shows that there cannot be an infinite body having like parts — and this with two arguments. The first of these is that every natural body must have some local motion; but there is no other except those mentioned above, one of which is around the middle, another from the middle, and a third to the middle. It follows, therefore, that it has one of these. But this is impossible — for if it moves upward or downward, it will be heavy or light, and, consequently, its heaviness or lightness will be infinite, which is impossible according to what has gone before. Likewise it cannot be moved circularly, because it is impossible for the infinite to turn in a circle. For there is no difference between saying this and saying that the heaven is infinite — which is impossible, as was proved above. Therefore a whole infinite body cannot be homogeneous. Secundam rationem ponit ibi: sed adhuc neque omnino etc.; quae sequitur ex communi ratione motus localis. Si enim sit corpus similium partium infinitum, sequitur quod nullo modo possit moveri. Quia si movetur, aut movebitur secundum naturam, aut secundum violentiam. Si autem sit ei aliquis motus violentus, sequitur quod etiam sit ei aliquis motus naturalis: quia motus violentus contrariatur motui naturali, ut supra habitum est. Si autem aliquis sit ei motus naturalis, sequitur quod etiam sit ei aliquis locus aequalis sibi, in quem naturaliter fertur: quia motus naturalis est eius quod fertur in proprium locum. Hoc autem est impossibile: quia sequeretur quod sint duo corporalia loca infinita; quod est aeque impossibile sicut quod sint duo corpora infinita; quia sicut corpus infinitum est undique infinitum, ita et locus infinitus. Non est igitur possibile quod corpus infinitum moveatur. Si ergo omne corpus naturale movetur, sequitur quod nullum corpus naturale sit infinitum. 136. The second argument is set down at [89] and it follows from the common notion of local motion. For if there should be an infinite body of parts that are alike, it follows that it cannot be moved at all. If it is moved, it will be moved either according to nature, or by compulsion. But if it has a compulsory motion, then must be a motion natural to it, because a compulsory motion is contrary to a natural motion, as was had above. But if there is a motion natural to it, it follows that there is a place equal to it, into which it is naturally moved, for natural motion belongs to what is moved to its own place. This, however, is impossible, because it would follow that there would be two infinite corporeal places, which is as impossible as that there should be two infinite bodies, for, just as an infinite body is infinite in every direction, so too is an infinite place. Therefore it is not possible for an infinite body to be moved. But if every natural body is moved, it therefore follows that no natural body is infinite. Est tamen attendendum quod haec ratio non procedit nisi de motu recto: nam id quod movetur circulariter, non mutat totum locum subiecto, sed solum ratione, ut probatur in VI Physic. Sed quod corpus infinitum non possit moveri circulariter, supra multipliciter est ostensum. It should be noted that this argument applies only to straight motion, for what is moved circularly does not change its place as to subject, but only in conception, as is proved in Physics VI. But that an infinite body cannot be moved circularly has already been proved above in many ways.
Lecture 14:
No sensible body is infinite — from action and passion, which follow upon motion.Chapter 7 cont. Ὅτι δ' ὅλως ἀδύνατον ἄπειρον ὑπὸ πεπερασμένου παθεῖν τι ἢ ποιῆσαι τὸ πεπερασμένον, ἐκ τῶνδε φανερόν. Ἔστω (275a.) γὰρ ἄπειρον ἐφ' οὗ Α, πεπερασμένον ἐφ' οὗ Β, χρόνος ἐν ᾧ ἐκίνησέ τι ἢ ἐκινήθη Γ. 90 That in general it is impossible for the infinite to be acted upon by the finite or to act upon it may be shown as follows. Εἰ δὴ ὑπὸ τοῦ Β τὸ Α ἐθερμάνθη ἢ ὤσθη ἢ ἄλλο τι ἔπαθεν ἢ καὶ ὁτιοῦν ἐκινήθη ἐν τῷ χρόνῳ ἐφ' οὗ Γ, ἔστω τὸ Δ τοῦ Β ἔλαττον, καὶ τὸ ἔλαττον ἐν τῷ ἴσῳ χρόνῳ ἔλαττον κινείτω ἔστω δὲ τὸ ἐφ' ᾧ Ε ὑπὸ τοῦ Δ ἠλλοιωμένον. Ὃ δή ἐστι τὸ Δ πρὸς τὸ Β, τὸ Ε ἔσται πρὸς πεπερασμένον τι. Ἔστω δὴ τὸ μὲν ἴσον ἐν ἴσῳ χρόνῳ ἴσον ἀλλοιοῦν, τὸ δ' ἔλαττον ἐν τῷ ἴσῳ ἔλαττον, τὸ δὲ μεῖζον μεῖζον, τοσοῦτον δὲ ὅσον ἀνάλογον ἔσται ὅπερ τὸ μεῖζον πρὸς τὸ ἔλαττον. Οὐκ ἄρα τὸ ἄπειρον ὑπ' οὐδενὸς πεπερασμένου κινηθήσεται ἐν οὐθενὶ χρόνῳ ἔλαττον γὰρ ἄλλο ἐν τῷ ἴσῳ χρόνῳ ὑπὸ ἐλάττονος κινηθήσεται, πρὸς ὃ τὸ ἀνάλογον πεπερασμένον ἔσται τὸ γὰρ ἄπειρον πρὸς τὸ πεπερασμένον ἐν οὐθενὶ λόγῳ ἐστίν. 91 (1. The infinite cannot be acted upon by the finite.) Let A be an infinite, B a finite, C the time of a given movement produced by one in the other. Suppose, then, that A was heated, or impelled, or modified in any way, or caused to undergo any sort of movement whatever, by in the time C. Let D be less than B; and, assuming that a lesser agent moves a lesser patient in an equal time, call the quantity thus modified by D, E. Then, as D is to B, so is E to some finite quantum. We assume that the alteration of equal by equal takes equal time, and the alteration of less by less or of greater by greater takes the same time, if the quantity of the patient is such as to keep the proportion which obtains between the agents, greater and less. If so, no movement can be caused in the infinite by any finite agent in any time whatever. For a less agent will produce that movement in a less patient in an equal time, and the proportionate equivalent of that patient will be a finite quantity, since no proportion holds between finite and infinite. Ἀλλὰ μὴν οὐδὲ τὸ ἄπειρον ἐν οὐθενὶ χρόνῳ κινήσει τὸ πεπερασμένον. Ἔστω γὰρ ἐφ' ᾧ τὸ Α ἄπειρον, τὸ δὲ Β πεπερασμένον, χρόνος ἐν ᾧ τὸ Γ. Οὐκοῦν τὸ Δ ἐν τῷ Γ ἔλαττον τοῦ Β κινήσει ἔστω τὸ Ζ. Ὃ δή ἐστι τὸ ΒΖ ὅλον πρὸς τὸ Ζ, τὸ Ε ἔχον τὸν λόγον τοῦτον ἔστω πρὸς τὸ Δ. Κινήσει ἄρα τὸ Ε τὸ ΒΖ ἐν τῷ Γ. Τὸ πεπερασμένον τοίνυν καὶ τὸ ἄπειρον ἐν τῷ ἴσῳ χρόνῳ ἀλλοιώσει. Ἀλλ' ἀδύνατον ἐν ἐλάττονι γὰρ τὸ μεῖζον ὑπέκειτο. Ἀλλ' ἀεὶ ὁ ληφθεὶς χρόνος ταὐτὸ ποιήσει, ὥστ' οὐκ ἔσται χρόνος οὐθεὶς ἐν ᾧ κινήσει. 92 (2. The infinite cannot act upon the finite.) Nor, again, can the infinite produce a movement in the finite in any time whatever. Let A be an infinite, B a finite, C the time of action. In the time C, D will produce that motion in a patient less than B, say F. Then take E, bearing the same proportion to D as the whole BF bears to F. E will produce the motion in BF in the time C. Thus the finite and infinite effect the same alteration in equal times. But this is impossible; for the assumption is that the greater effects it in a shorter time. It will be the same with any time that can be taken, so that there will no time in which the infinite can effect this movement. Ἀλλὰ μὴν ἐν ἀπείρῳ γε οὐκ ἔστι κινῆσαι οὐδὲ κινηθῆναι πέρας γὰρ οὐκ ἔχει, ἡ δὲ ποίησις καὶ τὸ πάθος ἔχει. 93 And, as to infinite time, in that nothing can move another or be moved by it. For such time has no limit, while the action and reaction have. Οὐδ' ἄπειρον δὴ ὑπ' ἀπείρου ἐνδέχεται οὐθὲν παθεῖν. Ἔστω γὰρ τὸ Α ἄπειρον καὶ τὸ Β, χρόνος δ' ἐν ᾧ ἔπαθε τὸ Β ὑπὸ τοῦ Α, ἐφ' ᾧ ΓΔ. Τὸ δὴ ἐφ' ᾧ τὸ Ε τοῦ ἀπείρου μέρος, ἐπεὶ ὅλον πέπονθε τὸ Β, οὐκ ἐν ἴσῳ χρόνῳ τὸ αὐτό ὑποκείσθω γὰρ ἐν ἐλάττονι κινεῖσθαι τὸ ἔλαττον χρόνῳ. Ἔστω τὸ Ε κεκινημένον ὑπὸ τοῦ Α ἐν τῷ Δ. Ὃ δὴ τὸ Δ πρὸς τὸ ΓΔ, τὸ Ε ἐστὶ πρός τι τοῦ Β πεπερασμένον. Τοῦτο τοίνυν ἀνάγκη ὑπὸ τοῦ Α κινηθῆναι ἐν τῷ ΓΔ χρόνῳ ὑπὸ γὰρ τοῦ αὐτοῦ ὑποκείσθω ἐν τῷ πλείονι καὶ ἐλάττονι (275b.) χρόνῳ τὸ μεῖζον καὶ τὸ ἔλαττον πάσχειν, ὅσα ἀνάλογον τῷ χρόνῳ διῄρηται. Ἐν οὐδενὶ ἄρα χρόνῳ δυνατὸν πεπερασμένῳ ἄπειρον ὑπ' ἀπείρου κινηθῆναι ἐν ἀπείρῳ ἄρα. Ἀλλ' ὁ μὲν ἄπειρος χρόνος οὐκ ἔχει τέλος, τὸ δὲ κεκινημένον ἔχει. 94 (3. There is no interaction between infinites.) Nor can infinite be acted upon in any way by infinite. Let A and B be infinites, CD being the time of the action A of upon B. Now the whole B was modified in a certain time, and the part of this infinite, E, cannot be so modified in the same time, since we assume that a less quantity makes the movement in a less time. Let E then, when acted upon by A, complete the movement in the time D. Then, as D is to CD, so is E to some finite part of B. This part will necessarily be moved by A in the time CD. For we suppose that the same agent produces a given effect on a greater and a smaller mass in longer and shorter times, the times and masses varying proportionately. There is thus no finite time in which infinites can move one another. Is their time then infinite? No, for infinite time has no end, but the movement communicated has. Εἰ τοίνυν πᾶν σῶμα αἰσθητὸν ἔχει δύναμιν ποιητικὴν ἢ παθητικὴν ἢ ἄμφω, ἀδύνατον σῶμα ἄπειρον αἰσθητὸν εἶναι. 95 If therefore every perceptible body possesses the power of acting or of being acted upon, or both of these, it is impossible that an infinite body should be perceptible. Ἀλλὰ μὴν καὶ ὅσα γε σώματα ἐν τόπῳ, πάντα αἰσθητά. Οὐκ ἔστιν ἄρα σῶμα ἄπειρον ἔξω τοῦ οὐρανοῦ οὐθέν. Ἀλλὰ μὴν οὐδὲ μέχρι τινός. Οὐθὲν ἄρα ὅλως σῶμα ἔξω τοῦ οὐρανοῦ. Εἰ μὲν γὰρ νοητόν, ἔσται ἐν τόπῳ τὸ γὰρ ἔξω καὶ ἔσω τόπον σημαίνει. Ὥστ' ἔσται αἰσθητόν. Αἰσθητὸν δ' οὐθὲν μὴ ἐν τόπῳ. 96 All bodies, however, that occupy place are perceptible. There is therefore no infinite body beyond the heaven. Nor again is there anything of limited extent beyond it. And so beyond the heaven there is no body at all. For if you suppose it an object of intelligence, it will be in a place—since place is what 'within' and 'beyond' denote—and therefore an object of perception. But nothing that is not in a place is perceptible.
Postquam philosophus ostendit corpus sensibile non esse infinitum, ratione accepta ex parte motus localis, hic ostendit idem ratione accepta ex parte actionis et passionis, quae consequuntur omnem motum. Et circa hoc duo facit: 137. After showing that a sensible body is not infinite with a reason based on local motion, the Philosopher here shows the same thing with a reason based on action and passion, which follow upon every motion. Concerning this he does two things: primo ostendit propositum;
secundo excludit quandam obviationem, ibi: sed tamen et quaecumque et cetera.
First he demonstrates the proposition;
Secondly, he excludes an objection, at 144.
Circa primum ponit talem rationem. Nullum corpus infinitum habet virtutem activam aut passivam aut utramque; sed omne corpus sensibile habet virtutem activam aut passivam aut utramque; ergo nullum corpus sensibile est infinitum. Circa hoc ergo duo facit: 138. With regard to the first, he gives the following argument: No infinite body has active or passive power or both; but every sensible body has active or passive power or both. Therefore, no sensible body is infinite. Then with regard to this he does two things: primo probat maiorem;
secundo ponit minorem et conclusionem, ibi: si igitur omne corpus et cetera.
First he proves the major premise;
Secondly, he presents the minor and conclusion, at 143.
Circa primum duo facit: About the first he does two things: primo proponit quod intendit, et dicit manifestum esse ex his quae dicentur, quod non solum impossibile est infinitum moveri localiter, sed universaliter est impossibile infinitum pati aliquid, vel etiam agere aliquid in corpus finitum. Secundo ibi: sit enim infinitum etc., probat propositum. First he proposes what he intends and says that it is clear from what will be said that not only is it impossible for something infinite to be moved locally but that universally it is impossible for something infinite to be acted upon or to act upon a finite body.
Secondly, at [91] he proves his proposition.
Et primo ostendit quod infinitum non patitur a finito; secundo ostendit quod finitum non patitur ab infinito, ibi: sed adhuc neque infinitum etc.;
tertio ostendit quod infinitum non patitur ab infinito, ibi: neque infinitum utique et cetera.
First he shows that the infinite is not acted upon by the finite, 139;
Secondly, that the finite is not acted upon by the infinite, at 140;
Thirdly, that the infinite is not acted upon by the infinite, at 142.
Dicit ergo primo quod, si corpus infinitum patitur a finito, sit corpus infinitum in quo est a, corpus autem finitum in quo est b: et quia omnis motus est in tempore, sit tempus g in quo b movit aut a motum est. Si ergo ponamus quod a quod est corpus infinitum, a b quod est corpus finitum, sit alteratum, puta calefactum, aut latum, idest motum secundum locum, aut aliquid aliud passum, puta infrigidatum aut humectatum aut quocumque modo motum, in tempore g: accipiamus unam partem b moventis, quae sit d (et nihil referret ad propositum si d esset quoddam aliud corpus minus quam b). Manifestum est autem quod minus corpus movet minus mobile in aequali tempore (hoc tamen supposito, quod in minori corpore sit minor virtus; quod oportet dicere si sit corpus similium partium; minor autem virtus in aequali tempore movet minus mobile). Sit ergo corpus e, quod alteratur aut qualitercumque movetur a d in tempore g; ita quod intelligamus corpus e esse partem totius infiniti quod est a. Sed quia tam d quam b est finitum, et quorumlibet duorum finitorum corporum est aliqua proportio ad invicem; secundum illam proportionem quam habet d ad b, accipiatur proportio corporis e ad quodcumque corpus maius finitum, puta quod sit f. 139. He says therefore first [91] that if an infinite body is acted upon by a finite, let A be an infinite body and B a finite body and, since every motion occurs in time, let G be the time in which B moves or A has been moved. If, therefore, we posit that A, which is the infinite body, is altered by B, which is the finite body, say heated or carried, i.e., moved locally, or affected in any other way, e.g., cooled or moistened, or moved in any way, in time G, let us take one part of the mover B, i.e., a part D (and it makes no difference, so far as the proposition is concerned, if D be some other body less than B). Now it is clear that a smaller body moves a smaller mobile in an equal time (supposing, of course, that there is in the smaller body less power — which must be said, if it is a body of like parts — hence the lesser power moves a smaller body in an equal time). Therefore, let E be a body which is altered or any other way moved by D in the time G, taking E as a part of the infinite whole A. But since both D and B are finite, and since any two finite bodies are mutually proportionate, then, according to the ratio of D to B, let there be taken the proportion of E to any other larger finite body, for example, F. Hac ergo positione facta, ponit quasdam suppositiones. Quarum prima est, quod alterans aequale in magnitudine et virtute, in aequali tempore alterabit aequale corpus. Secunda est, quod minus corpus alterans in aequali tempore alterabit minus; ita scilicet quod tantum erit corpus motum minus altero corpore moto, quantum erit analogum quodcumque maius ad minus, idest, quanta erit proportio excessus maioris corporis moventis ad minus. Having posited these preliminaries, he makes some suppositions. The first of these is that an altering cause which is equal in magnitude and power will alter an equal body in equal time. A second is that a smaller altering body will alter a smaller in equal time, the result being that one moved body will be less than the other moved body according to a ratio of something greater to something less, i.e., in the same proportion that the larger moving body exceeds the smaller moving body. Ex praemissis igitur concludit quod infinitum a nullo finito potest moveri secundum quodcumque tempus. Quia aliquid minus quam infinitum movebitur in aequali tempore ab illo minori quam sit corpus movens infinitum; scilicet e, quod est minus quam a, movebitur a d, quod est minus quam b, secundum praemissa. Id autem quod est analogum ad e, idest quod in eadem proportione se habet ad e sicut b ad d, est quoddam finitum: non enim potest dici quod ipsum infinitum quod est a, se habeat ad e sicut b se habet ad d, quia infinitum ad finitum nullam proportionem habet. Supposito autem quod aliquod finitum se habeat ad e sicut b ad d, erit commutatim dicere quod sicut d se habet ad e, ita b se habet ad illud finitum. Sed d movet e in tempore g: ergo b movet finitum in tempore g. Sed in hoc tempore positum est quod movet totum infinitum quod est a: ergo finitum in eodem tempore movebit finitum et infinitum. From these preliminaries, therefore, he concludes that the infinite cannot be moved by any finite in any time. For something less than the infinite will in an equal time be moved by that body which is less than the body moving the infinite; in other words, E, which is less than A, will be moved by D, which is less than B, according to our suppositions. But what is "analogous" to E, i.e., in the same ratio to E, as B to D, is finite, for it cannot be said that A, which is infinite, is to E, as B is to D, because the infinite has no proportion to the finite. Now on the assumption that something finite is to E as B is to D, then commutatively B is to that finite, as D is to E. But D moves E in time G; therefore B moves the finite in time G. But G was the time in which it was supposed that B moved the infinite whole A. Therefore the finite will move a finite and an infinite in the same time. Deinde cum dicit: sed adhuc neque infinitum etc., probat quod infinitum corpus non movet corpus finitum in aliquo tempore: 140. Then at [92] he proves that an infinite body does not move a finite body in any time. et primo ostendit quod non movet in tempore finito;
secundo quod non movet in tempore infinito, ibi: sed adhuc in infinito et cetera.
First he shows that it does not move it in finite time;
Secondly, not in infinite time, at 141.
Dicit ergo primo quod neque etiam corpus infinitum movebit corpus finitum in nullo tempore, scilicet determinato. Si enim detur contrarium, sit corpus infinitum in quo est a, corpus vero finitum quod ab eo movetur sit b vel bz, tempus autem in quo movetur sit g. D autem sit quaedam pars finita corporis infiniti quod est a: et quia minus in aequali tempore minus movet, consequens est quod corpus finitum quod est d, in g tempore moveat minus corpus eo quod est b; et sit id minus z, quod est pars eius. Quia igitur totum bz habet aliquam proportionem ad z, accipiatur quod sicut totum bz se habet ad z, ita e se habet ad d, quorum uterque est pars infiniti. Ergo commutatim quae est proportio d ad z, eadem est proportio e ad bz. Sed d movet z in g tempore: ergo e movebit bz in tempore g. Sed in hoc tempore, bz movebatur a corpore infinito quod est a: sequitur igitur quod infinitum et finitum alterent vel qualitercumque moveant in eodem tempore unum et idem mobile. Sed hoc est impossibile: supponebatur enim supra quod maius movens movet aequale mobile in minori tempore, quia velocius movet. Sic igitur impossibile est quod finitum moveatur ab infinito in tempore g; et idem sequitur quodcumque aliud tempus finitum sumatur. Nullum ergo tempus finitum est dare, in quo infinitum moveat finitum. He says therefore first [92] that neither will an infinite body move a finite body in any time, namely, determinate time. For if the contrary should be the case, let Abe the infinite body, and B or BZ the finite body moved by it, and G the time in which it is being moved. Let D be a finite part of the infinite body A. And because a lesser moves a smaller in equal time, then a finite body D in time G moves Z, a body smaller than B, but a part of B. Now because the whole BZ is proportionate to Z, let it be taken that the whole BZ is to Z, as E is to D, each of which is part of the infinite. Therefore, commutatively, E is to BZ in the same proportion as D is to Z. But D moves Z in time G; therefore E will move BZ in time G. But in time G, BZ was being moved by the infinite body A. It follows, therefore, than an infinite and a finite are altering or somehow moving one and the mane mobile in the same amount of time. But this is impossible — for it was supposed above that a greater mover moves an equal mobile in less time, because it moves more swiftly. Consequently, it is impossible for the finite to be moved by the infinite in time G; and the same follows no matter what finite time is taken. Hence there is no finite time possible in which the infinite moves the finite. Deinde cum dicit: sed adhuc in infinito etc., ostendit quod neque hoc potest esse in tempore infinito. Non enim contingit quod in tempore infinito aliquid moverit vel motum sit: quia tempus infinitum non habet finem, omnis autem actio vel passio habet finem: nihil enim agit vel patitur nisi ut perveniat ad aliquem finem. Relinquitur ergo quod infinitum non moveat finitum in tempore infinito. 141. Then at 1[93] he shows that this cannot occur in infinite time. For it is not possible that in an infinite time something shall have moved or shall have been moved — because infinite time has no end, whereas every action or passion does have an end, for nothing acts or is acted upon except in order to reach some end. What remains, therefore, is that an infinite does not move a finite in infinite time. Deinde cum dicit: neque infinitum utique etc., probat quod infinitum non moveat infinitum. Et dicit quod infinitum non contingit aliquid pati ab infinito secundum quamcumque speciem motus. Alioquin, sit corpus infinitum agens in quo est a, et corpus infinitum patiens in quo est b, tempus autem in quo b passum est ab a sit in quo dg; sit autem e pars infiniti mobilis quod est b. Quia ergo totum b passum est ab a in toto tempore quod est dg, manifestum est quod e, quod est pars eius, non movetur in toto hoc tempore: oportet enim supponere quod ab eodem movente minus mobile moveatur in minori tempore; quanto enim mobile magis vincitur a movente, tanto velocius movetur ab ipso. Sit ergo quod e, quod est minus quam b, moveatur ab a in tempore d, quod est pars totius temporis gd. D autem ad gd est aliqua proportio, cum utrumque sit finitum: accipiamus autem quod eandem proportionem habeat e ad aliquam partem ipsius mobilis infiniti maiorem, quam scilicet d habet ad gd. Sic ergo illud finitum maius quam e, necesse est quod moveatur ab a in gd tempore: oportet enim supponere quod ab eodem movente moveatur maius et minus mobile in maiori et minori tempore, ita quod divisio mobilium sit secundum proportionem temporum. Quia igitur proportio illius finiti ad e, est sicut proportio totius temporis gd ad d, oportet commutatim dicere quod proportio totius temporis gd ad illud mobile finitum maius, sit sicut proportio temporis d ad mobile e. Sed e movetur ab a in tempore d: ergo illud finitum maius movebitur ab a in tempore gd: et sic in eodem tempore movebitur finitum et infinitum, quod est impossibile. Et idem inconveniens sequitur, quodcumque tempus finitum accipiatur. Sic igitur impossibile est quod infinitum moveatur ab infinito in tempore finito. 142. Then at [94] he proves that the infinite does not move the infinite. And he says that an infinite cannot undergo anything from an infinite with respect to any species of motion at all. Otherwise let A be the infinite body which is acting, and B the infinite body acted upon, and DG the time in which B underwent something from A, and let E be a part of the infinite mobile B. Now, since the entire B has been modified by A in the entire time DG, it is clear that E, which is part of B, was not being moved in this whole time. For we must suppose that a smaller mobile is moved in less time by the same mover — for to the extent that a mobile is more overcome by a mover, the more swiftly is it moved by it. So let E, which is less than B, be moved by A in a time D which is part of the whole time GD. Now D is proportionate to GD, since both are finite. Let us assume, therefore, that E has the same ratio to some larger part of the infinite mobile as D has to GD. Then that finite mobile greater than E must be moved by A in time GD, for we must suppose that a larger and a smaller mobile are moved in more and less time when the same mover is acting, in such a way that the division of the mobiles corresponds to the ratio of the times. Since, therefore, the ratio of that finite to E equals the ratio of the entire time DG to D, then commutatively, we must say that the ratio of the entire time DG to that larger finite mobile is as the ratio of time D to mobile E. But E is moved by A in time D; therefore, that greater finite mobile will be moved by A in time DG. Hence the finite and the infinite will be moved in the same amount of time — which is impossible. And the same impossibility follows whatever be the finite time assumed. Consequently it is impossible for an infinite to be moved by an infinite in finite time. Relinquitur igitur, si moveatur, quod moveatur in infinito tempore. Sed hoc est impossibile, ut supra ostensum est, quia infinitum tempus non habet finem, omne autem quod movetur, habet finem sui motus: quia etsi totus motus caeli non haberet finem, una tamen circulatio habet finem. Sic igitur manifestum est quod infinitum non habet neque virtutem activam neque passivam. It remains, therefore, that if it is moved, it is moved in infinite time. But that, too, is impossible, as was proved above, because infinite time has no end, but everything which is moved has an end to its motion — for although the whole motion of the heaven does not have an end, one revolution does. It is therefore plain that the infinite has neither active nor passive power. Deinde cum dicit: si igitur etc., assumpta minori, infert conclusionem: dicens quod omne corpus sensibile habet virtutem activam aut passivam aut utramque. Dicitur autem hic corpus sensibile ad differentiam corporis mathematici: ita quod corpus sensibile dicatur omne corpus naturale, quod inquantum huiusmodi, natum est movere et moveri. Sic ergo concludit quod impossibile est aliquod corpus sensibile esse infinitum. 143. Then at [95], assuming the minor premise, he draws the conclusion and says that every sensible body has active or passive power or both.. He says "sensible body" here to differentiate from "mathematical body," so that the former means every natural body which, as such, is apt to cause motion or be moved. Thus he concludes that it is impossible for a sensible body to be infinite. Deinde cum dicit: sed tamen et quaecumque etc., excludit quandam obviationem: quia posset aliquis dicere quod sit aliquod corpus extra caelum intelligibile, quod sit infinitum. 144. Then at [96] he excludes a certain objection — for someone could say that there is outside the heavens an "intelligible body" which is infinite. Et dicit quod omnia corpora quae sunt in loco, sunt sensibilia. Non enim sunt corpora mathematica, quia talibus non debetur locus nisi secundum metaphoram, ut dicitur in I de Generat.: locus enim non quaeritur nisi propter motum, ut dicitur in IV Physic.; non autem moventur nisi corpora sensibilia et naturalia, nam mathematica sunt extra motum. Sic igitur manifestum est quod quaecumque corpora sunt in loco, sunt sensibilia. And he says that all bodies in place are sensible. For they are not mathematical bodies, because these do not have place except in a metaphorical sense, as is said in On Generation I. Now place is not needed except for motion, as is said in Physics IV, and only sensible and natural bodies are subject to motion — for mathematical things are outside of motion. Consequently, it is plain that all bodies in place are sensible. Et ex hoc concludit quod corpus infinitum non sit extra caelum; immo universalius, quod nullum corpus sit extra caelum, neque simpliciter, scilicet corpus infinitum, neque secundum quid (vel usque ad aliquid), idest corpus finitum; cum enim corpus omne sit finitum vel infinitum, sequitur quod nullum omnino corpus sit extra caelum. Quia si dicas quod sit intellectuale, sequetur quod sit in loco, ex quo ponitur extra caelum: extra enim et intra significant locum. Sic igitur sequitur quod, si aliquod corpus sit extra caelum, finitum vel infinitum, quod sit sensibile; eo quod nullum sensibile corpus est, quod non sit in loco (quia etiam caelum quodammodo est in loco, ut patet in IV Physic.). From this he concludes that there is not an infinite body outside the heaven; and indeed, more universally, that no body exists outside the heaven, either absolutely, i.e., namely, an infinite body, or in a certain respect (or up to a certain point), i.e., a finite body. Since bodies are either finite or infinite, it follows that no body at all exists outside the heaven. For if you should say that this body is intellectual, it will follow that it is in a place on account of your assuming that it is outside the heaven — because "outside" and "within" imply place. Consequently, it follows that if there is a body outside the heaven, then, whether it is finite or infinite, it is sensible, since there is no sensible body which does not exist in a place —for even the heaven is somehow in place, as is plain from Physics IV. Manifestum est autem secundum haec verba quod nullum corpus intelligibile, neque finitum neque infinitum, est extra caelum; quia extra significat locum, nihil autem est in loco nisi corpus sensibile. Manifestum est etiam quod nullum corpus infinitum sensibile est extra caelum: ostensum est enim supra quod nullum corpus sensibile est infinitum. Quod autem nullum corpus sensibile finitum sit extra caelum, non videtur hic probari, sed supponi: nisi forte per hoc quod omne corpus sensibile est in loco, omnia autem loca continentur infra caelum, quae determinantur tribus motibus localibus supra positis, scilicet qui sunt circa medium, a medio, et ad medium. So it is manifest according to these words that no intelligible body, finite or infinite, is outside the heaven, because "outside of" signifies place, and nothing is in place except a sensible body. It is also manifest that no infinite sensible body exists outside the heavens, for it was shown above that no sensible body is infinite. But the fact that no sensible finite body exists outside the heavens he does not prove here but supposes it, unless perhaps it is proved by the fact that every sensible body is in a place, and all places are contained within the heavens and determined by the three local motions mentioned above, namely, those around the middle, from the middle, and to the middle.
15 Lecture 15:
Logical reasons why no body is infinite.Chapter 7 cont. Λογικώτερον δ' ἔστιν ἐπιχειρεῖν καὶ ὧδε. Οὔτε γὰρ κύκλῳ οἷόν τε κινεῖσθαι τὸ ἄπειρον ὁμοιομερὲς ὄν μέσον μὲν γὰρ τοῦ ἀπείρου οὐκ ἔστι, τὸ δὲ κύκλῳ περὶ τὸ μέσον κινεῖται. Ἀλλὰ μὴν οὐδ' ἐπ' εὐθείας οἷόν τε φέρεσθαι τὸ ἄπειρον δεήσει γὰρ ἕτερον εἶναι τοσοῦτον τόπον ἄπειρον εἰς ὃν οἰσθήσεται κατὰ φύσιν, καὶ ἄλλον τοσοῦτον εἰς ὃν παρὰ φύσιν. 97 The question may also be examined in the light of more general considerations as follows. The infinite, considered as a whole of similar parts, cannot, on the one hand, move in a circle. For there is no centre of the infinite, and that which moves in a circle moves about the centre. Nor again can the infinite move in a straight line. For there would have to be another place infinite like itself to be the goal of its natural movement and another, equally great, for the goal of its unnatural movement. Ἔτι εἴτε φύσει ἔχει κίνησιν τοῦ εἰς εὐθὺ εἴτε βίᾳ κινεῖται, ἀμφοτέρως δεήσει ἄπειρον εἶναι τὴν κινοῦσαν ἰσχύν ἥ τε γὰρ ἄπειρος ἀπείρου καὶ τοῦ ἀπείρου ἄπειρος ἡ ἰσχύς ὥστ' ἔσται καὶ τὸ κινοῦν ἄπειρον (λόγος δ' ἐν τοῖς περὶ κινήσεως ὅτι οὐθὲν ἔχει ἄπειρον δύναμιν τῶν πεπερασμένων, οὐδὲ τῶν ἀπείρων πεπερασμένην). Εἰ οὖν τὸ κατὰ φύσιν καὶ παρὰ φύσιν ἐνδέχεται κινηθῆναι, ἔσται δύο ἄπειρα, τό τε κινοῦν οὕτω καὶ τὸ κινούμενον. 98 Moreover, whether its rectilinear movement is natural or constrained, in either case the force which causes its motion will have to be infinite. For infinite force is force of an infinite body, and of an infinite body the force is infinite. So the motive body also will be infinite. (The proof of this is given in our discussion of movement, where it is shown that no finite thing possesses infinite power, and no infinite thing finite power.) If then that which moves naturally can also move unnaturally, there will be two infinites, one which causes, and another which exhibits the latter motion. Ἔτι τὸ κινοῦν τὸ ἄπειρον τί ἐστιν; εἰ μὲν γὰρ αὐτὸ ἑαυτό, ἔμψυχον ἔσται. Τοῦτο δὲ πῶς δυνατόν, ἄπειρον εἶναι ζῷον; εἰ δ' ἄλλο [τι] τὸ κινοῦν, δύο ἔσται ἄπειρα, τό τε κινοῦν καὶ τὸ κινούμενον, διαφέροντα τὴν μορφὴν καὶ τὴν δύναμιν. 99 Again, what is it that moves the infinite? If it moves itself, it must be animate. But how can it possibly be conceived as an infinite animal? And if there is something else that moves it, there will be two infinites, that which moves and that which is moved, differing in their form and power. Εἰ δὲ μὴ συνεχὲς τὸ πᾶν, ἀλλ' ὥσπερ λέγει Δημόκριτος καὶ Λεύκιππος, διωρισμένα τῷ κενῷ, μίαν ἀναγκαῖον εἶναι πάντων τὴν κίνησιν. Διώρισται μὲν γὰρ τοῖς σχήμασιν τὴν δὲ φύσιν φασὶν αὐτῶν εἶναι μίαν, ὥσ(276a.) περ ἂν εἰ χρυσὸς ἕκαστον εἴη κεχωρισμένος. Τούτων δέ, καθάπερ λέγομεν, ἀναγκαῖον εἶναι τὴν αὐτὴν κίνησιν ὅπου γὰρ μία βῶλος, καὶ ἡ σύμπασα γῆ φέρεται, καὶ τό τε πᾶν πῦρ καὶ σπινθὴρ εἰς τὸν αὐτὸν τόπον. Ὥστ' οὔτε κοῦφον ἁπλῶς οὐθὲν ἔσται τῶν σωμάτων, εἰ πάντ' ἔχει βάρος εἰ δὲ κουφότητα, βαρὺ οὐδέν. 100 If the whole is not continuous, but exists, as Democritus and Leucippus think, in the form of parts separated by void, there must necessarily be one movement of all the multitude. They are distinguished, we are told, from one another by their figures; but their nature is one, like many pieces of gold separated from one another. But each piece must, as we assert, have the same motion. For a single clod moves to the same place as the whole mass of earth, and a spark to the same place as the whole mass of fire. So that if it be weight that all possess, no body is, strictly speaking, light: and if lightness be universal, none is heavy. Ἔτι εἰ βάρος ἔχει ἢ κουφότητα, ἔσται ἢ ἔσχατόν τι τοῦ παντὸς ἢ μέσον. Τοῦτο δ' ἀδύνατον ἀπείρου γ' ὄντος. 101 Moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region. But this is impossible while the world is conceived as infinite. Ὅλως δ', οὗ μή ἐστι μέσον μηδ' ἔσχατον, μηδὲ τὸ μὲν ἄνω τὸ δὲ κάτω, τόπος οὐθεὶς ἔσται τοῖς σώμασι τῆς φορᾶς. Τούτου δὲ μὴ ὄντος κίνησις οὐκ ἔσται ἀνάγκη γὰρ κινεῖσθαι ἤτοι κατὰ φύσιν ἢ παρὰ φύσιν, ταῦτα δ' ὥρισται τοῖς τόποις τοῖς τ' οἰκείοις καὶ τοῖς ἀλλοτρίοις. 102 And, generally, that which has no centre or extreme limit, no up or down, gives the bodies no place for their motion; and without that movement is impossible. A thing must move either naturally or unnaturally, and the two movements are determined by the proper and alien places. Ἔτι εἰ οὗ παρὰ φύσιν τι μένει ἢ φέρεται, ἀνάγκη ἄλλου τινὸς εἶναι τοῦτον τὸν τόπον κατὰ φύσιν (τοῦτο δὲ πιστὸν ἐκ τῆς ἐπαγωγῆς), ἀνάγκη δὴ μὴ πάντα ἢ βάρος ἔχειν ἢ κουφότητα, ἀλλὰ τὰ μὲν τὰ δὲ μή. 103 Again, a place in which a thing rests or to which it moves unnaturally, must be the natural place for some other body, as experience shows. Necessarily, therefore, not everything possesses weight or lightness, but some things do and some do not. Ὅτι μὲν τοίνυν οὐκ ἔστι τὸ σῶμα τοῦ παντὸς ἄπειρον, ἐκ τούτων φανερόν. From these arguments then it is clear that the body of the universe is not infinite.
Postquam philosophus ostendit universaliter non esse corpus infinitum rationibus physicis, idest quae sumuntur ex propriis scientiae naturalis, hic ostendit idem rationibus logicis, idest quae sumuntur ex aliquibus communioribus principiis, vel ex aliquibus probabilibus et non necessariis. Et hoc est quod dicit: est, idest contingit, conari ad propositum ostendendum rationabilius, idest magis per viam logicam, sic, idest secundum rationes sequentes. Unde alia littera planior est quae sic habet: magis autem logice est argumentari et sic. 145. After showing universally with Physica l reasons, i.e., with arguments taken from facts proper to natural science, that there is no infinite body, the Philosopher here shows the same thing with logical reasons, i.e., arguments taken from certain common principles or from things that are probable but not necessary. And this is what he says [97]: "It is," i.e., it is possible, "to try," to prove the proposition "more from reason, i.e., more according to the logical mode, "thus," i.e., according to the following arguments. Hence another MS is more plain when it says: "One can argue more logically [i.e., dialectically] as follows." Primo autem ostendit propositum de corpore infinito continuo;
secundo de infinito non continuo, ibi: si autem non continuum et cetera.
First he proves the proposition about an infinite continuous body;
Secondly, about one that is not continuous, at 150.
Circa primum duo facit. 146. Concerning the first he does two things: Primo ostendit quod corpus infinitum, similium partium existens, non potest moveri circulariter. Quod quidem probat per hoc, quod infiniti non est aliquod medium, sicut nec extremum: motus autem circularis est circa medium, ut supra habitum est: ergo et cetera. First he shows that an infinite body of like parts cannot be moved circularly. This he proves on the ground that there is neither a middle nor a boundary in an infinite body. But circular motion is around a middle, as was had above. Therefore.... Secundo ostendit tribus rationibus quod non est possibile quod tale corpus infinitum moveatur motu recto. Quarum prima talis est. Omne corpus quod movetur motu recto, potest moveri naturaliter et per violentiam. Quod autem movetur per violentiam, habet aliquem locum in quem movetur violenter; et omne quod movetur naturaliter, habet aliquem locum in quem movetur naturaliter. Locus autem omnis est aequalis locato. Sic ergo sequetur quod sint duo loca tanta quantum est corpus infinitum, in quorum unum movetur violenter, et in alium naturaliter. Hoc autem est impossibile, scilicet quod sint duo loca infinita, sicut et quod sint duo infinita corpora, ut supra habitum est. Relinquitur ergo quod nullum corpus naturale sit infinitum. 147. Secondly, with three arguments he shows that it is not possible for such an infinite body to be moved with a straight motion. The first of these is this: Every body that is moved with a straight motion can be moved naturally and through force. Now what is moved by force has a place to which it is forcefully moved, and whatever is moved naturally has a place to which it is moved naturally. But every place is equal to the thing in place. Consequently, it will follow that there are two places as large as the infinite body, to one of which it is forcefully moved, and to the other of which naturally. But it is no more possible that there be two infinite places than that there be two infinite bodies, as was had prove. It remains, therefore, that no natural body is infinite. Dicitur autem utraque ratio logica esse, quia procedit ex eo quod contingit corpori infinito inquantum est infinitum, sive sit mathematicum sive sit naturale, scilicet non habere medium, et non habere aliquid aequale extra se. Supra autem posuit aliqua similia, sed non tanquam principalia, sed tanquam assumpta ad manifestationem aliorum. Both of these reasons are called "logical," because they proceed from what occurs to an infinite body as infinite; whether it be mathematical or natural, namely, to have no middle and nothing equal to it outside of it. Above he posited similar statements, not, however, as principal premises but as assumptions used to manifest other things. Secundam rationem ponit ibi: adhuc sive natura habet etc.: quae talis est. Sive dicatur quod corpus infinitum moveatur motu recto naturaliter, sive per violentiam, utroque modo oportet dicere quod sit potentia movens corpus infinitum: ostensum est enim in VII et VIII Physic. quod omne quod movetur ab alio movetur, non solum in his quae moventur per violentiam, de quibus magis est manifestum, sed etiam in his quae moventur naturaliter, sicut corpora gravia et levia moventur a generante vel a removente prohibens. Cum autem fortius non moveatur a debiliori, impossibile est quod infinitum, cuius virtus est infinita, moveatur a potentia finita moventis: unde relinquitur quod oportet potentiam moventis esse infinitam. Manifestum est autem quod, si potentia sit infinita, erit rei infinitae: et e converso, si corpus sit infinitum, oportet quod virtus eius sit infinita. 148. The second argument is given at [98], and is as follows: Whether it be said that an infinite body is moved naturally with straight motion or by force, in either case there must be posited a power moving the infinite body — for it was shown in Physics VII and VIII that whatever is moved is moved by another, not only in things that are moved by force (where the principle is more evident), but also in things that are moved naturally, as heavy and light bodies are moved by the generator [or agent producing them], or by whatever removes an obstacle. But since the stronger is not moved by the weaker, it is impossible for an infinite, whose power is infinite, to be moved by the finite power of some mover. Hence it remains that the power of the mover must be infinite. Si ergo est corpus infinitum quod movetur, necesse est quod corpus movens sit etiam infinitum. Probatum est enim in his quae de motu, idest in VIII Physic., quod nullum finitorum habet virtutem infinitam, nec aliquod infinitorum habet virtutem finitam. Sic igitur patet quod, si sit corpus infinitum quod movetur motu recto, oportet quod moveatur a corpore infinito. But it is manifest that if a power is infinite, it will belong to an infinite thing; conversely, if a body is infinite, its power must be infinite. Therefore, if an infinite body is being moved, then the body moving it must be infinite. For it was proved "in the discussion on motion," i.e., in Physics VIII, that no finite thing has infinite virtue, and that no infinite has finite virtue. Consequently, it is plain that if an infinite body is being moved with straight motion, it must be being moved by an infinite body. Si ergo ponamus quod hoc corpus infinitum contingit moveri et secundum naturam et praeter naturam, similiter continget secundum utrumque motum quod sint duo infinita, scilicet illud quod movet sic, idest naturaliter vel violenter, et aliud quod movetur. Hoc autem est impossibile, quod sint duo corpora infinita, ut supra ostensum est. Ergo non est possibile esse corpus infinitum quod moveatur motu recto. Now, if we assume that this infinite body can be moved both according to nature and beside its nature, it will likewise happen, with respect to each motion, that there are two infinites, namely, one that moves thus, i.e., causes natural or compulsory motion, and one that is moved. But this is impossible, namely, that there be two infinite bodies, as was proved above. Therefore, it is not possible for an infinite body to be moved with a straight motion. Haec etiam ratio logica est, quia procedit ex communi proprietate infiniti corporis, quod scilicet non habeat extra se aliud corpus aequale. This argument is called "logical" because it proceeds from a common property of an infinite body, namely, that it does not have outside it another body equal to it. Potest autem ex hac ratione concludi non solum quod sint duo infinita, sed plura. Nam si corpus infinitum movetur naturaliter, corpus naturaliter ipsum movens erit infinitum; et quia contingit ipsum moveri violenter, corpus quod movet ipsum violenter erit infinitum; et sic erunt tria infinita. It can be concluded from this argument not only that there would be two infinites but more still. For if the infinite body is moved naturally, the body moving it naturally will be infinite; and because it can be moved by force, the body that moves it by force will be infinite. Thus there will be three infinites. Rursus, quia motus qui est violentus uni, est naturalis alteri, ut supra dictum est, sequetur etiam quod sit aliud corpus infinitum, quod naturaliter hoc modo moveatur a virtute infinita. Again, since a motion which is compulsory for one thing, is natural to another, as was stated above, it will follow, too, that there is another infinite body that is moved naturally in the aforesaid way by an infinite power. Tertiam rationem ponit ibi: adhuc movens et cetera. Et haec quidem ratio inducitur ad excludendum obviationem quandam ad praedictam rationem. Posset enim aliquis dicere quod corpus infinitum movetur naturaliter non quidem ab alio, sed a seipso, sicut animalia dicuntur seipsa movere: et sic non sequetur esse duo corpora infinita, quod praemissa ratio concludebat. 149. The third argument he gives at [99]. And this argument is adduced in order to exclude an objection to the preceding argument. For someone could say that an infinite body is naturally moved not by some other body but by itself, as animals are said to move themselves. Consequently, it will not follow that there are two infinite bodies, as the preceding argument concluded. Et ideo proponit quod necesse est dicere, si sit corpus infinitum, quod movens ipsum sit aliquid aliud: quia si moveret seipsum, esset animatum (hoc enim est proprium animalium, quod seipsa moveant). Si ergo corpus infinitum sit movens seipsum, sequetur quod sit animal infinitum. Sed hoc non videtur esse possibile, quia omne animal habet determinatam figuram et determinatam proportionem partium ad totum, quod non competit infinito. Sic igitur non potest dici quod infinitum moveat seipsum. Si autem dicatur quod aliquid aliud moveat ipsum, sequetur quod sint duo infinita, scilicet movens et quod movetur. Et ex hoc sequitur quod differunt secundum speciem et virtutem: quia movens comparatur ad mobile sicut actus ad potentiam. Hoc autem est impossibile, sicut prius dictum est. And therefore he proposes that it is necessary to say, that if there is an infinite body, whatever moves it is distinct from it. For if it moved itself, it would be animate—for it is proper to animals to move themselves. Consequently if the infinite body should move itself, it will be an infinite animal. But this does not seem possible, because every animal has a definite shape and a definite ratio between its parts and the whole, which factors do not belong to an infinite. Consequently, it cannot be said that the infinite moves itself. But if it be said that something else moves it, it will follow that there are two infinites, namely, the mover and the moved. And from this it follows that they differ in kind and in power: because the mover is related to the mobile as act to potency. But this is impossible, as was previously shown. Deinde cum dicit: si autem non continuum etc., ostendit non esse infinitum non continuum, sed distinctum per interpositionem vacui, sicut posuerunt Democritus et Leucippus. Et hoc ostendit tribus rationibus. Circa quarum primam dicit quod, si infinitum non sit unum totum continuum, sed, sicut dicunt Democritus et Leucippus, distinguatur vacuo intermedio (ponebant enim quod corpora indivisibilia non possunt invicem coniungi nisi vacuo mediante); secundum autem horum opinionem sequitur quod necessarium sit omnium esse unum motum. Dicebant enim quod illa corpora indivisibilia infinita sunt determinata, idest distincta ad invicem, solummodo per figuras, inquantum scilicet unum eorum est pyramidale, aliud sphaericum, aliud cubicum, et sic de aliis; et tamen dicunt naturam omnium eorum esse unam, sicut si aliquis dicat quod unumquodque eorum, per se separatum, sit de natura auri. Si autem eorum est una natura, necesse est quod sit unus et idem motus eorum, non obstante quod sint minimae partes corporum; quia idem est motus totius et partis, sicut totius terrae et unius boli (idest unius particulae), et totius ignis et unius scintillae. 150. Then at [100] he shows that there is no infinite which is non-continuous but distinguished by the interposition of voids, as Democritus and Leucippus posited. This he proves with three arguments. With regard to the first he says that if an infinite is not one continuous whole but is, as Democritus and Leucippus maintain, distinguished by an intermediate void — for they posited that the indivisible bodies cannot be mutually joined without an intervening void — then according to their opinion it follows that for all of them there is one motion. For they said that those infinite indivisible bodies are determined, i.e., mutually distinguished, only by their shape, namely, insofar as one is pyramidal, another spherical, another cubic, and so on. Yet they say that all of them are one with respect to their nature, as if, for example, someone said that each of them in isolation had the nature of gold. But if the nature of all is one, then, necessarily, all have one and the same motion in spite of their being the minimal parts of bodies — because the motion of the whole and of the part is the same, as is the motion of the whole earth and one clod, and of all fire and one spark. Si ergo omnia sunt eiusdem naturae et habent eundem motum, aut omnia moventur deorsum quasi habentia gravitatem, et sic nullum corpus erit simpliciter leve, cum omnia corpora dicantur esse ex his composita; aut omnia moventur sursum quasi habentia levitatem, et sic nullum corpus erit grave; quod est impossibile. Therefore, if all are of the same nature and have the same motion, then all are either moved downward as though having gravity — and thus there will be no body that is absolutely light, since all bodies are said to be composed of these; or else all are moved upward, as though having lightness, and thus no body will be heavy — which is impossible. Secundam rationem ponit ibi: adhuc si gravitatem etc.: quae talis est. Omne corpus grave movetur ad medium, omne autem corpus leve movetur ad extremum. Si ergo aliquod vel quodlibet praedictorum indivisibilium corporum haberet gravitatem aut levitatem, sequeretur quod totius spatii contenti ex indivisibilibus corporibus et vacuis intermediis, sit aliquod extremum aut medium. Sed hoc est impossibile, cum totum istud spatium sit infinitum. Relinquitur ergo hanc positionem esse impossibilem. 151. The second argument, given at [101], is this: Every heavy body is moved to the middle and every light body to the boundary. If, therefore, some or each of the aforesaid indivisible bodies had heaviness or lightness, it would follow that there would be a boundary and a center of that whole space contained by the indivisible bodies and the intermediate voids. But that is impossible, since all that space is infinite. It remains, therefore, that this position is impossible. Et quia haec ratio valet ad destruendum infinitum, qualitercumque infinitum ponatur, sive sicut continuum sive sicut non continuum, ideo hanc eandem rationem universalius ponit cum subdit: totaliterque et cetera. Et dicit quod universaliter possumus dicere quod ubi non est medium et extremum, ibi non est sursum, quod est extremum, neque deorsum, quod est medium. Quibus subtractis, nullus locus erit quo corpora ferantur motu recto: feruntur enim sursum vel deorsum. Sublato autem loco, nullus erit motus: quia omne quod movetur necesse est moveri aut secundum naturam aut praeter naturam, quod quidem determinatur per loca propria et aliena (nam motus naturales dicuntur quibus corpora moventur ad loca propria, motus autem violenti dicuntur quibus moventur ad loca aliena). Hoc autem est impossibile, quod motus auferatur a corporibus: ergo impossibile est ponere infinitum. 152. And since this argument effectively destroys the infinite howsoever assumed, i.e., whether continuous or non-continuous, he therefore presents this same argument in a more universal way at [102]. And he says that we can say universally that where there is no middle and no extreme boundary, there is no "up," which is the boundary, and no "down," which is the middle. And if these are removed, there is no place where bodies can be moved with straight motion; for they are moved upward or downward. But if place is removed, there will be no motion — for whatever is moved, must be moved either according to its nature or outside its nature, and this is judged by places that are proper and alien — for natural motions are those in which bodies are moved to their proper places, while compulsory motions are those in which they are moved to alien places. But this is impossible, namely, that motion be taken away from bodies. Therefore, it is impossible to posit an infinite. Tertiam rationem ponit ibi: adhuc si ubi et cetera. Et dicit quod locus ad quem movetur aliquid praeter naturam, vel in quo quiescit praeter naturam, necesse est quod sit cuiusdam alterius secundum naturam, ad quem scilicet naturaliter moveatur, et in quo naturaliter quiescat. Et hoc credibile fit ex inductione: nam terra movetur sursum praeter naturam, ignis vero secundum naturam; et e converso ignis deorsum praeter naturam, terra vero secundum naturam. Videmus autem quaedam moveri deorsum et quaedam sursum. Si autem illa quae moventur sursum, moventur praeter naturam, oportebit dicere aliqua alia esse quae moventur sursum secundum naturam; et similiter, si ponatur quod ea quae moventur deorsum, moventur praeter naturam, necesse est ponere alia quae moventur deorsum secundum naturam. Unde neque omnia habent gravitatem, neque omnia levitatem, secundum positionem praedictam: sed haec quidem habent gravitatem quae naturaliter moventur deorsum; haec autem non, quae naturaliter moventur sursum. 153. The third argument is given at [103]. And he says that the place to which something is moved outside its nature, or in which it rests outside its nature, must be according to nature for something else which is moved to it naturally and rests in it naturally. And this becomes credible by induction: for earth is moved upward outside its nature but fire according to nature; conversely, fire is moved downward outside its nature but earth according to nature. Now we observe certain things being moved downward and others upward. If the things being moved upward are moved outside their nature, we will be obliged to say that there are other things which are moved upward according to nature; likewise, if the things being moved downward are assumed to be moved outside their nature, it is necessary to posit other things that are moved downward according to nature. Hence not all things have heaviness and not all have lightness according to the foregoing position, but those naturally moved downward have heaviness, while those naturally moved upward do not have it. Ultimo autem epilogando concludit manifestum esse ex praedictis quod omnino non est corpus infinitum, scilicet infinitum continuum neque infinitum distinctum per interpositionem vacui. Finally in summary he concludes [104] that it is manifest from the foregoing that there is no infinite body at all, i.e., no infinite that is continuous and none that is distinguished by intervals of void. Dicuntur autem hae ultimae rationes logicae, quia procedunt ex quibusdam probabilibus nondum plene probatis. And these last arguments are called "logical," because they proceed. from probabilities not yet completely proved.
Lecture 16:
Two arguments for one universe, taken from lower bodies.Chapter 8 Διότι δ' οὐδὲ πλείους οἷόν τ' οὐρανοὺς εἶναι, λέγωμεν τοῦτο γὰρ ἔφαμεν ἐπισκεπτέον, εἴ τις μὴ νομίζει καθόλου δεδεῖχθαι περὶ τῶν σωμάτων ὅτι ἀδύνατον ἐκτὸς εἶναι τοῦ κόσμου τοῦδε ὁτιοῦν αὐτῶν, ἀλλὰ μόνον ἐπὶ τῶν ἀορίστως κειμένων εἰρῆσθαι τὸν λόγον. 105 We must now proceed to explain why there cannot be more than one heaven—the further question mentioned above. For it may be thought that we have not proved universal of bodies that none whatever can exist outside our universe, and that our argument applied only to those of indeterminate extent. Ἅπαντα γὰρ καὶ μένει καὶ κινεῖται καὶ κατὰ φύσιν καὶ βίᾳ, καὶ κατὰ φύσιν μέν, ἐν ᾧ μένει μὴ βίᾳ, καὶ φέρεται, καὶ εἰς ὃν φέρεται, καὶ μένει ἐν ᾧ δὲ βίᾳ, καὶ φέρεται βίᾳ, καὶ εἰς ὃν βίᾳ φέρεται, βίᾳ καὶ μένει. Ἔτι εἰ βίᾳ ἥδε ἡ φορά, ἡ ἐναντία κατὰ φύσιν. 106 Now all things rest and move naturally and by constraint. A thing moves naturally to a place in which it rests without constraint, and rests naturally in a place to which it moves without constraint. On the other hand, a thing moves by constraint to a place in which it rests by constraint, and rests by constraint in a place to which it moves by constraint. Further, if a given movement is due to constraint, its contrary is natural. Ἐπὶ δὴ τὸ μέσον τὸ ἐνταῦθα εἰ βίᾳ οἰσθήσεται ἡ γῆ ἐκεῖθεν, ἐντεῦθεν οἰσθήσεται ἐκεῖ κατὰ φύσιν 107 If, then, it is by constraint that earth moves from a certain place to the centre here, its movement from here to there will be natural, καὶ εἰ μένει ἐνταῦθα ἡ ἐκεῖθεν μὴ βίᾳ, καὶ οἰσθήσεται δεῦρο κατὰ φύσιν. Μία γὰρ ἡ κατὰ φύσιν. 108 and if earth from there rests here without constraint, its movement hither will be natural. And the natural movement in each case is one. Ἔτι ἀνάγκη πάντας τοὺς κόσμους ἐκ τῶν αὐτῶν εἶναι σωμάτων, ὁμοίους γ' ὄντας τὴν φύσιν. Ἀλλὰ μὴν καὶ τῶν σωμάτων ἕκαστον ἀναγκαῖον τὴν αὐτὴν (276b.) ἔχειν δύναμιν, οἷον λέγω πῦρ καὶ γῆν καὶ τὰ μεταξὺ τούτων εἰ γὰρ ὁμώνυμα ταῦτα καὶ μὴ κατὰ τὴν αὐτὴν ἰδέαν λέγονται τἀκεῖ τοῖς παρ' ἡμῖν, καὶ τὸ πᾶν ὁμωνύμως ἂν λέγοιτο κόσμος. Δῆλον τοίνυν ὅτι τὸ μὲν ἀπὸ τοῦ μέσου φέρεσθαι πέφυκε, τὸ δ' ἐπὶ τὸ μέσον αὐτῶν, εἴπερ πᾶν ὁμοειδὲς τὸ πῦρ τῷ πυρὶ καὶ τῶν ἄλλων ἕκαστον, ὥσπερ καὶ τὰ ἐν τούτῳ μόρια τοῦ πυρός. 109 Further, these worlds, being similar in nature to ours, must all be composed of the same bodies as it. Moreover each of the bodies, fire, I mean, and earth and their intermediates, must have the same power as in our world. For if these names are used equivocally, if the identity of name does not rest upon an identity of form in these elements and ours, then the whole to which they belong can only be called a world by equivocation. Clearly, then, one of the bodies will move naturally away from the centre and another towards the centre, since fire must be identical with fire, earth with earth, and so on, as the fragments of each are identical in this world. Ὅτι δ' ἀναγκαῖον οὕτως ἔχειν, ἐκ τῶν περὶ τὰς κινήσεις ὑποθέσεων φανερόν αἵ τε γὰρ κινήσεις πεπερασμέναι, ἕκαστόν τε τῶν στοιχείων λέγεται καθ' ἑκάστην τῶν κινήσεων. Ὥστ' εἴπερ καὶ αἱ κινήσεις αἱ αὐταί, καὶ τὰ στοιχεῖα ἀναγκαῖον εἶναι πανταχοῦ ταὐτά. 110 That this must be the case is evident from the principles laid down in our discussion of the movements, for these are limited in number, and the distinction of the elements depends upon the distinction of the movements. Therefore, since the movements are the same, the elements must also be the same everywhere. Πέφυκεν ἄρα φέρεσθαι καὶ ἐπὶ τόδε τὸ μέσον τὰ ἐν ἄλλῳ κόσμῳ τῆς γῆς μόρια, καὶ πρὸς τόδε τὸ ἔσχατον τὸ ἐκεῖ πῦρ. Ἀλλ' ἀδύνατον τούτου γὰρ συμβαίνοντος ἀνάγκη φέρεσθαι ἄνω μὲν τὴν γῆν ἐν τῷ οἰκείῳ κόσμῳ, τὸ δὲ πῦρ ἐπὶ τὸ μέσον, ὁμοίως δὲ καὶ τὴν ἐντεῦθεν γῆν ἀπὸ τοῦ μέσου φέρεσθαι κατὰ φύσιν πρὸς τὸ ἐκεῖ φερομένην μέσον, διὰ τὸ τοὺς κόσμους οὕτω κεῖσθαι πρὸς ἀλλήλους. Ἢ γὰρ οὐ θετέον τὴν αὐτὴν εἶναι φύσιν τῶν ἁπλῶν σωμάτων ἐν τοῖς πλείοσιν οὐρανοῖς, ἢ λέγοντας οὕτως τὸ μέσον ἓν ποιεῖν ἀνάγκη καὶ τὸ ἔσχατον τούτου δ' ὄντος ἀδύνατον εἶναι κόσμους πλείους ἑνός. 111 The particles of earth, then, in another world move naturally also to our centre and its fire to our circumference. This, however, is impossible, since, if it were true, earth must, in its own world, move upwards, and fire to the centre; in the same way the earth of our world must move naturally away from the centre when it moves towards the centre of another universe. This follows from the supposed juxtaposition of the worlds. For either we must refuse to admit the identical nature of the simple bodies in the various universes, or, admitting this, we must make the centre and the extremity one as suggested. This being so, it follows that there cannot be more worlds than one. Τὸ δ' ἀξιοῦν ἄλλην εἶναι φύσιν τῶν ἁπλῶν σωμάτων, ἂν ἀποσχῶσιν ἔλαττον ἢ πλεῖον τῶν οἰκείων τόπων, ἄλογον τί γὰρ διαφέρει τὸ τοσονδὶ φάναι μῆκος ἀπέχειν ἢ τοσονδί; Διοίσει γὰρ κατὰ λόγον, ὅσῳ πλεῖον μᾶλλον, τὸ δ' εἶδος τὸ αὐτό. 112 To postulate a difference of nature in the simple bodies according as they are more or less distant from their proper places is unreasonable. For what difference can it make whether we say that a thing is this distance away or that? One would have to suppose a difference proportionate to the distance and increasing with it, but the form is in fact the same.
Postquam philosophus ostendit quod universum non est infinitum magnitudine, hic ostendit quod non sunt plures mundi numero, nedum quod sint infiniti. 154. After showing that the universe is not infinite in magnitude, the Philosopher here shows that there are not numerically many worlds, much less an infinitude of them. Et primo dicit de quo est intentio;
secundo exequitur propositum, ibi: omnia enim et manent et cetera.
First he mentions his intention;
Secondly, he pursues his proposition, at 155.
Dicit ergo primo quod, quia ostensum est quod corpus totius universi non est infinitum, restat dicendum quod non est possibile esse plures caelos, idest plures mundos: iam enim supra diximus quod de hoc erat intendendum. He says therefore first [105] that because it has been proved that the body of the whole universe is not infinite, there remains for us to say that it is not possible that there be many heavens, i.e., many worlds: for we had already mentioned above that this was to be discussed. Est autem considerandum quod supra philosophus fecit mentionem quod extra caelum non est aliquod corpus neque finitum neque infinitum; ex quo sequitur quod non sit alius mundus praeter istum; esset enim aliquod corpus extra caelum. Et ideo, si sufficienter esset supra probatum quod extra caelum non sit aliquod corpus neque finitum neque infinitum, nihil restaret probandum. Sed si quis non putat quod in superioribus sit ostensum universaliter de corporibus, quod scilicet impossibile sit quodcumque eorum esse extra mundum, sed solum quod ratio supra sit inducta de corporibus quae ponuntur esse infinita; secundum hoc adhuc restat videndum an sit possibile esse plures caelos, sive plures mundos. It should be noted that above the Philosopher mentioned that outside the heavens there is no body either finite or infinite; from which it follows that there is not another world besides it, for that would put a body outside the heavens. Consequently, if it were sufficiently proved above that outside the heavens there exists no body either finite or infinite, nothing would remain to be proved. But if someone does not consider that it was proved for bodies universally, namely, that it is impossible for any of them to be outside the world, but considers that the argument given above refers only to bodies assumed infinite, then, according to this, it still remains to be seen whether it is possible that there be many heavens, i.e., many worlds. Deinde cum dicit: omnia enim et manent etc., probat propositum: 155. Then at [106] he proves his proposition: et primo ostendit quod sit tantum unus mundus;
secundo inquirit an possibile sit esse plures mundos, ibi: quod autem non solum unus et cetera.
First he shows that there is but one world;
Secondly, he inquires whether it is possible that there be many worlds (L. 19).
Circa primum duo facit: As to the first he does two things: primo ostendit esse tantummodo unum mundum, ratione sumpta ex inferioribus corporibus, ex quibus omnes ponebant mundum consistere;
secundo ostendit idem communiter ex utrisque corporibus, tam inferioribus quam caelestibus, ibi: adhuc autem et per eas et cetera.
First he shows that there is only one world and takes his argument from the lower bodies, of which everyone supposed the world to consist, at 156;
Secondly, he shows the same with a general argument based on both the lower and the celestial bodies (L. 18).
Circa primum duo facit: About the first he does two things: primo inducit rationes ad propositum ostendendum;
secundo probat quoddam quod supposuerat, ibi: quod autem est aliquid et cetera.
First he adduces arguments to prove his proposition;
Secondly, he proves something he had presupposed (L. 17).
Circa primum ponit tres rationes:
secunda incipit ibi: adhuc necesse etc.;
tertia ibi: sed adhuc et cetera.
With regard to the first he gives three arguments: The second one begins at 159;
The third one in Lecture 17.
Circa primum duo facit. 156. Regarding the first he does two things: Primo praemittit tres suppositiones. Quarum prima est, quod omnia corpora quiescunt et moventur tam secundum naturam, quam etiam secundum violentiam. Quod quidem habet veritatem in corporibus inferioribus, quae cum sint generabilia et corruptibilia, sicut per vim fortioris agentis possunt permutari a sua specie, ita etiam possunt removeri a suo loco per motum violentum vel quietem: in corporibus autem caelestibus nihil potest esse violentum et extra naturam, cum sint incorruptibilia. First he presents three suppositions. The first is that all bodies rest and are moved both according to nature and according to compulsion. This of course is true in lower bodies which, since they can be generated and corrupted, can not only be transmuted from their species by the power of a stronger agent, but can be removed from their place by a violent motion or by violent rest. But in celestial bodies, since they are incorruptible, nothing can be violent and outside their nature. Secunda suppositio est, quod in quocumque loco aliqua corpora manent secundum naturam et non per violentiam, in illum locum per naturam feruntur: et in quemcumque locum e converso aliqua per naturam feruntur, in illo loco naturaliter quiescunt. Et idem dicendum est circa violentiam: quia in quo loco aliqua quiescunt per violentiam, in illum locum feruntur per violentiam; et e converso, si ad aliquem locum feruntur per violentiam, in illo loco per violentiam quiescunt. Et huius suppositionis ratio est quia, cum quies in loco sit finis motus localis, oportet motum proportionari quieti, sicut finis proportionatur his quae sunt ad finem. The second supposition is that in whatever place certain bodies remain according to nature and not through compulsion, they are moved thither by nature, and into whatever place things are carried by nature they naturally rest there. And the same is to be said about violence: in whatever place things rest through violence, they are carried to that place by violence; conversely, if they are carried to a place through violence, they are at rest there through violence. The reason for this supposition is that since rest in a place is the end of local motion, the motion must be proportionate to the rest, just as the end is proportionate to the means. Tertia suppositio est, quod si aliqua loci mutatio sit per violentiam alicui corpori, contraria est ei secundum naturam, sicut patet ex his quae supra dicta sunt. The third supposition is that if any change of place is accomplished by violence to a body, the contrary change is according to nature for that body, as is plain from what was said above. Secundo ibi: ad medium itaque etc., ex praedictis suppositionibus argumentatur ad propositum. Primo quidem ex parte motus. Si enim sunt duo mundi, oportet esse in utroque aliquam terram. Terra ergo quae est in alio mundo, aut feretur ad medium huius mundi per naturam, aut per violentiam. Si per violentiam, oportebit dicere, secundum tertiam suppositionem, quod contraria loci mutatio, quae est ab isto mundo in medium illius mundi, sit ei secundum naturam. Et hoc patet esse falsum, quia a medio istius mundi nunquam terra movetur secundum naturam: ergo et primum est falsum, scilicet quod sint plures mundi. 157. Secondly, at [107] from these suppositions he argues to his proposition. First on the part of motion. For if there are two worlds, there must be earth in both. Therefore the earth in that other world will be moved to the middle of this world either by nature or by compulsion. If by the latter, we shall have to say, according to the third supposition, that the contrary change of place, i.e., from this world to the middle of that world is natural to it. And this is plainly false, since earth is never naturally moved from the middle of this world. Therefore, the first is also false, namely, that there is more than one world. Secundo ibi: et si manet etc., argumentatur ad idem ex parte quietis. Sicut enim manifestum est quod natura terrae non patitur quod moveatur secundum naturam a medio huius mundi, ita etiam terrae natura hoc habet, quod in medio huius mundi quiescat naturaliter. Si ergo inde huc delata terra manet hic non per violentiam, sed per naturam, sequitur per secundam suppositionem quod ab illo medio feretur huc secundum naturam. Et hoc ideo, quia unus est motus, vel una loci mutatio terrae secundum naturam: unde non potest esse quod uterque motus sit terrae naturalis, scilicet ab illo medio ad istud, et ab isto ad illud. 158. Secondly, at [108] he argues to the same on the part of rest. For just as it is plain that the nature of earth does not allow being moved naturally from the middle of this world, so, too, the nature of earth has this quality, that it be naturally at rest in the middle of this world. If then earth brought here from that world remains here not by violence but by nature, it follows, according to the second supposition, that it will be brought from that middle to here according to nature. And this is so because there is but one motion, or one change of place, that is according to nature for earth; hence both motions cannot be natural to earth, namely, from that middle to this or from this to that. Deinde cum dicit: adhuc necesse etc., ponit secundam rationem, quae excludit quendam defectum quem posset aliquis imponere primae rationi: posset enim aliquis ad primam rationem respondere quod terra quae est in illo mundo, est alterius naturae quam terra quae est in hoc mundo. 159. Then at [109] he presents a second argument which excludes a certain defect which someone can claim in the first argument: for someone could answer to the first that the earth in that world is different in nature from that in this world. Primo ergo Aristoteles hoc excludit;
secundo ex hoc argumentatur ad propositum, ibi: natae sunt igitur ferri etc.;
tertio excludit quandam obviationem, ibi: dignificare autem et cetera.
First, then, Aristotle dismisses this at 160;
Secondly, from this he argues to his proposition, at 162;
Thirdly, he excludes an objection, at 163.
Ostendit autem terram quae est in alio mundo, esse eiusdem naturae cum terra quae est in hoc mundo, He shows that the earth in the other world is of the same nature as that of this world: primo quidem ratione accepta ex parte mundi;
secundo ratione accepta ex parte motus, ibi: quod autem necesse sit et cetera.
First with an argument taken on the part of the world, at
Secondly, with one based on motion, at 161.
Dicit ergo primo quod, si plures mundi qui ponuntur sint similis naturae, necesse est quod sint ex eisdem corporibus: et adhuc ulterius necesse est quod unumquodque illorum corporum habeat eandem virtutem cum corpore quod est in hoc mundo: et sic oportet ignem et terram esse eiusdem virtutis in quolibet illorum mundorum, et eadem ratio est de intermediis corporibus, quae sunt aer et aqua. Quia si corpora quae sunt ibi in alio mundo, dicuntur aequivoce cum corporibus quae sunt apud nos in hoc mundo, et non secundum eandem ideam, idest non secundum eandem speciem, consequens erit quod etiam ipsum totum constans ex huiusmodi partibus aequivoce dicatur mundus: ex partibus enim diversis in specie necesse est et totum diversum in specie componi. Hoc autem non videntur intendere qui ponunt plures mundos; sed univoce utuntur nomine mundi. Unde sequitur secundum eorum intentionem quod corpora quae sunt in diversis mundis, habeant eandem virtutem. Et ita manifestum est quod etiam in aliis mundis, sicut et in isto, aliquod ipsorum corporum ex quibus constituitur mundus, natum sit ferri a medio, quod competit igni, aliud autem ad medium, quod competit terrae; si hoc verum est, quod omnis ignis omni igni est eiusdem speciei, in quocumque mundo sit ignis, sicut et diversae partes ignis in hoc mundo existentis sunt unius speciei. Et eadem est ratio de aliis corporibus. 160. He says therefore first [109] that if the several worlds posited are of a like nature, they must be composed of the same bodies; further, each of those bodies must have the same virtue as the body of this world. Consequently, fire and earth must have the same virtue in each of those worlds, and the same goes for the intermediate bodies, air and water. For if the bodies that are there in another world are spoken of equivocally in relation to the bodies that exist among us in this world and are not according to the same "idea," i.e., not of the same species, the consequence will be that the entire world consisting of such bodies will be only equivocally called a world. For wholes that are composed of parts diverse in species are themselves diverse. But this does not seem to be the intention of those who posit many worlds; rather they use the word "world" univocally. Hence it follows according to their intention that the bodies in these different worlds possess the same virtue. And thus it is manifest that even in those worlds, just as in this, some one of the bodies constituting the world is apt to be moved from the middle, which belongs to fire, and some other to the middle, which belongs to earth, if it is true that all fire is akin in species to all other fire in whatever world it exists, just as the various parts of fire in this world are of one species. And the same holds for the other bodies. Deinde cum dicit: quod autem necesse etc., ostendit idem ratione accepta ex parte motus. Et dicit manifestum esse quod necesse sit sic se habere sicut dictum est, de uniformitate corporum quae sunt in diversis mundis; et hoc ex suppositionibus quae accipiuntur circa motus. Vocat autem suppositiones ea quibus utitur ad propositum ostendendum, propter hoc quod hic supponuntur sicut principia, licet quaedam eorum supra fuerint probata. Est autem una suppositio quod motus sunt finiti, idest determinati secundum species: non enim sunt infinitae species motuum simplicium, sed tres tantum, ut supra probatum est. Secunda suppositio est quod quodlibet elementorum dicitur secundum quod habet naturam ad unum aliquem motuum; sicut terra dicitur gravis propter habitudinem ad motum deorsum, ignis dicitur levis propter aptitudinem ad motum sursum. 161. Then at [110] he shows the same thing with an argument taken from motion. And he says that it is manifestly necessary that things be as we have said concerning the uniformity of the bodies which are in the various worlds; and this from the suppositions which are assumed with respect to motions. And he calls "suppositions" the statements which he uses to show the proposition, because here they are being assumed as principles, although some of them have been previously proved. Now one of the suppositions is that motions are finite, i.e., determinate with respect to species; for there are not infinite species of simple notions, but three only, as was proved above. A second supposition is that each of the elements is described in terms of having a natural tendency toward some one of the motions; as earth is described as heavy on account of its tendency to downward motion, and fire light on account of its aptitude for upward motion. Quia igitur sunt determinatae species motus, necesse est quod sint iidem motus secundum speciem in quolibet mundo. Et quia unumquodque elementorum dicitur secundum aliquem motuum, necesse est ulterius quod elementa sint eadem secundum speciem ubique, idest in quolibet mundo. Hence, since the species of motion are determinate, the same specific motions must exist in every world. And because each of the elements is described with respect to some motion, it is further necessary that the elements are specifically the same everywhere, i.e., in each world. Deinde cum dicit: natae sunt igitur etc., ex praemissis argumentatur ad propositum. Si enim corpora quae sunt in quolibet mundo, sunt eiusdem speciei; videmus autem quod omnes partes terrae quae sunt in hoc mundo, feruntur ad hoc medium huius mundi, et omnes partes ignis ad extremum huius; consequens erit quod etiam omnes partes terrae quae sunt in quocumque alio mundo, feruntur ad medium huius mundi; et omnes partes ignis quae sunt in quocumque alio mundo, feruntur ad extremum huius mundi. Sed hoc est impossibile. Si enim hoc accideret, necesse esset quod terra quae est in alio mundo, ferretur sursum in proprio suo mundo, et quod ignis in illo mundo ferretur ad medium. Et simili ratione terra quae est in hoc mundo, ferretur secundum naturam a medio huius mundi in medium illius mundi. 162. Then at [111] from these premises he argues to the proposition. For if the bodies in every world are of the same species, and we see that all the parts of earth in this world are carried to the middle of this world, and all parts of fire to its boundary, then the consequence will be that also all the parts of earth in any other world are moved to the middle of this world, and all the parts of fire in any other world to the boundary of this world. But this is impossible. For if this should happen, the earth in another world would have to be carried upward in its own world and fire in that world would have to be carried to its middle. Similarly, the earth in this world would be naturally carried from the center of this world to the center of that world. Et hoc necesse est sequi propter dispositionem mundorum, qui talem situm habent ut medium unius mundi sit distans a medio alterius; et sic non potest terra ad medium alterius mundi moveri, nisi recedat a medio sui mundi mota versus extremum, quod est moveri sursum. Similiter, quia extrema diversorum mundorum habent diversum situm, necesse est quod si ignis debeat ferri ad extremum alterius mundi, quod recedat ab extremo proprii mundi, quod est moveri deorsum in proprio mundo. Haec autem sunt inconvenientia: quia aut ponendum est quod non sit eadem natura simplicium corporum in pluribus mundis, quod supra improbatum est; aut si dicamus esse eandem naturam, et velimus vitare praedicta inconvenientia quae sequuntur ex diversitate mediorum et extremorum, necesse est ponere unum solum medium, ad quod feruntur omnia gravia ubicumque sint, et unum extremum, ad quod feruntur omnia levia ubicumque sint. Quo posito, impossibile est esse plures mundos; quia ad unitatem medii et extremi sequitur unitas circuli seu sphaerae. And this must follow on account of the disposition of the worlds which have such a position that the middle of one world is at a distance from the middle of another; consequently, earth cannot be moved to the middle of another world without leaving the middle of its own world and moving to the boundary, which is to be moved upward. Likewise, because the boundaries of various worlds have different positions, then if fire is to be carried to the boundary of another world, it must leave the boundary of its own world, which is to be moved downward in its own world. But all these things are untenable — for either we must posit that the natures of the simple bodies are not the same in the several worlds (which was disproved above), or, if we say that they are of the same nature and wish to avoid the aforesaid inconsistencies which follow upon a diversity of middles and boundaries, we must admit but one middle to which all heavy bodies, wherever they are, are moved, and one boundary to which are moved all light things wherever they be. On this assumption, it is impossible that there be many worlds, because one middle and one boundary imply one circle or sphere. Deinde cum dicit: dignificare autem etc., excludit quandam obviationem, qua posset aliquis dicere quod corpora quae sunt in alio mundo, non moventur ad medium et extremum huius mundi, propter distantiam. 163. Then at [112] he excludes an objection, since someone could say that the bodies in another world are not moved to the center and boundaries of this world on account of the distance. Sed ipse hoc excludens dicit quod irrationabile est dignum reputare quod sit alia natura simplicium corporum, propter hoc quod distent plus vel minus a propriis locis, ita scilicet quod ad propria loca moveantur de propinquo et non de remoto. Non enim videtur differre quantum ad naturam corporis, quod per tantam longitudinem distet a suo loco vel per tantam: quia differentia mathematicorum non diversificat naturam. Est enim secundum rationem quod quanto plus corpus appropinquat ad suum locum, tanto magis velociter moveatur; ita tamen quod species sit eadem et motus et mobilis. Differentia enim velocitatis est secundum quantitatem, non secundum speciem; sicut et differentia longitudinis. But he rejects this and says that it is unreasonable to accept the postulate that the natures of simple bodies vary on the ground of their being more or less distant from their places, so as to be moved to their places when they are near but not when they are far away. For it does not seem to make any difference to the nature of the body whether it is this far or that far from its place, because mathematical differences do not vary the nature. For it is according to reason that the closer a body gets to its place the more swiftly is it moved, but yet the species of its motion and of the mobile are not varied. For a difference in velocity is according to quantity, not according to species, just as is a difference in length.
Lecture 17:
A third argument from lower bodies. Natural bodies have determinate placesChapter 8 cont. Ἀλλὰ μὴν ἀνάγκη γ' εἶναί τινα κίνησιν αὐτῶν ὅτι μὲν γὰρ κινοῦνται, φανερόν. Πότερον οὖν βίᾳ πάσας ἐροῦμεν κινεῖσθαι καὶ τὰς ἐναντίας; ἀλλ' ὃ μὴ πέφυκεν ὅλως κινεῖσθαι, ἀδύνατον τοῦτο κινεῖσθαι βίᾳ. Εἰ τοίνυν ἐστί τις κίνησις αὐτῶν κατὰ φύσιν, ἀνάγκη τῶν ὁμοειδῶν καὶ τῶν καθ' ἕκαστον πρὸς ἕνα ἀριθμῷ τόπον ὑπάρχειν τὴν κίνησιν, οἷον πρὸς τόδε τι μέσον καὶ πρὸς τόδε τι ἔσχατον. 113 Moreover, the bodies must have some movement, since the fact that they move is quite evident. Are we to say then that all their movements, even those which are mutually contrary, are due to constraint? No, for a body which has no natural movement at all cannot be moved by constraint. If then the bodies have a natural movement, the movement of the particular instances of each form must necessarily have for goal a place numerically one, i.e. a particular centre or a particular extremity. Εἰ δὲ πρὸς εἴδει ταὐτά, (277a.) πλείω δέ, διότι καὶ τὰ καθ' ἕκαστα πλείω μέν, εἴδει δ' ἕκαστον ἀδιάφορον, οὐ τῷ μὲν τῷ δ' οὐ τοιοῦτον ἔσται τῶν μορίων, ἀλλ' ὁμοίως πᾶσιν ὁμοίως γὰρ ἅπαντα κατ' εἶδος ἀδιάφορα ἀλλήλων, ἀριθμῷ δ' ἕτερον ὁτιοῦν ὁτουοῦν. Λέγω δὲ τοῦτο, ὅτι εἰ τὰ ἐνταῦθα μόρια πρὸς ἄλληλα καὶ τὰ ἐν ἑτέρῳ κόσμῳ ὁμοίως ἔχει, καὶ τὸ ληφθὲν ἐντεῦθεν οὐδὲν διαφερόντως πρὸς τῶν ἐν ἄλλῳ τινὶ κόσμῳ μορίων καὶ πρὸς τῶν ἐν τῷ αὐτῷ, ἀλλ' ὡσαύτως διαφέρουσι γὰρ οὐθὲν εἴδει ἀλλήλων. 114 If it be suggested that the goal in each case is one in form but numerically more than one, on the analogy of particulars which are many though each undifferentiated in form, we reply that the variety of goal cannot be limited to this portion or that but must extend to all alike. For all are equally undifferentiated in form, but any one is different numerically from any other. What I mean is this: if the portions in this world behave similarly both to one another and to those in another world, then the portion which is taken hence will not behave differently either from the portions in another world or from those in the same world, but similarly to them, since in form no portion differs from another. Ὥστ' ἀναγκαῖον ἢ κινεῖν ταύτας τὰς ὑποθέσεις, ἢ τὸ μέσον ἓν εἶναι καὶ τὸ ἔσχατον. Τούτου δ' ὄντος ἀνάγκη καὶ τὸν οὐρανὸν ἕνα μόνον εἶναι καὶ μὴ πλείους, τοῖς αὐτοῖς τεκμηρίοις τούτοις καὶ ταῖς αὐταῖς ἀνάγκαις. 115 The result is that we must either abandon our present assumption or assert that the centre and the extremity are each numerically one. But this being so, the heaven, by the same evidence and the same necessary inferences, must be one only and no more. Ὅτι δ' ἔστι τι οὗ πέφυκεν ἡ γῆ φέρεσθαι καὶ τὸ πῦρ, δῆλον καὶ ἐκ τῶν ἄλλων. 116 A consideration of the other kinds of movement also makes it plain that there is some point to which earth and fire move naturally. Ὅλως γὰρ τὸ κινούμενον ἔκ τινος εἴς τι μεταβάλλει, καὶ ταῦτα ἐξ οὗ καὶ εἰς ὃ εἴδει διαφέρει πᾶσα δὲ πεπερασμένη μεταβολή οἷον τὸ ὑγιαζόμενον ἐκ νόσου εἰς ὑγίειαν καὶ τὸ αὐξανόμενον ἐκ μικρότητος εἰς μέγεθος. Καὶ τὸ φερόμενον ἄρα καὶ γὰρ τοῦτο γίνεταί ποθέν ποι. Δεῖ ἄρα εἴδει διαφέρειν ἐξ οὗ καὶ εἰς ὃ πέφυκε φέρεσθαι, ὥσπερ τὸ ὑγιαζόμενον οὐχ οὗ ἔτυχεν, οὐδ' οὗ βούλεται ὁ κινῶν. Καὶ τὸ πῦρ ἄρα καὶ ἡ γῆ οὐκ εἰς ἄπειρον φέρονται, ἀλλ' εἰς ἀντικείμενα ἀντίκειται δὲ κατὰ τόπον τὸ ἄνω τῷ κάτω, ὥστε ταῦτα ἔσται πέρατα τῆς φορᾶς. 117 For in general that which is moved changes from something into something, the starting-point and the goal being different in form, and always it is a finite change. For instance, to recover health is to change from disease to health, to increase is to change from smallness to greatness. Locomotion must be similar: for it also has its goal and starting-point—and therefore the starting-point and the goal of the natural movement must differ in form—just as the movement of coming to health does not take any direction which chance or the wishes of the mover may select. Thus, too, fire and earth move not to infinity but to opposite points; and since the opposition in place is between above and below, these will be the limits of their movement. Ἐπεὶ καὶ ἡ κύκλῳ ἔχει πως ἀντικείμενα τὰ κατὰ διάμετρον, τῇ δ' ὅλῃ οὐκ ἔστιν ἐναντίον οὐδέν, ὥστε καὶ τούτοις τρόπον τινὰ ἡ κίνησις εἰς ἀντικείμενα καὶ πεπερασμένα. Ἀνάγκη ἄρα εἶναί τι τέλος καὶ μὴ εἰς ἄπειρον φέρεσθαι. 118 (Even in circular movement there is a sort of opposition between the ends of the diameter, though the movement as a whole has no contrary: so that here too the movement has in a sense an opposed and finite goal.) There must therefore be some end to locomotion: it cannot continue to infinity. Τεκμήριον δὲ τοῦ μὴ εἰς ἄπειρον φέρεσθαι καὶ τὸ τὴν γῆν μέν, ὅσῳ ἂν ἐγγυτέρω ᾖ τοῦ μέσου, θᾶττον φέρεσθαι, τὸ δὲ πῦρ, ὅσῳ ἂν τοῦ ἄνω. Εἰ δ' ἄπειρον ἦν, ἄπειρος ἂν ἦν καὶ ἡ ταχυτής, εἰ δ' ἡ ταχυτής, καὶ τὸ βάρος καὶ ἡ κουφότης ὡς γὰρ <�εἰ> τῷ κατωτέρω ταχὺ ἦν τι, ἕτερον τῷ βάρει ἂν ἦν ταχύ, οὕτως εἰ ἄπειρος ἦν ἡ τούτου ἐπίδοσις, καὶ ἡ τῆς ταχυτῆτος ἐπίδοσις ἄπειρος ἂν ἦν. 119 This conclusion that local movement is not continued to infinity is corroborated by the fact that earth moves more quickly the nearer it is to the centre, and fire the nearer it is to the upper place. But if movement were infinite speed would be infinite also; and if speed then weight and lightness. For as superior speed in downward movement implies superior weight, so infinite increase of weight necessitates infinite increase of speed.
Praemissis duabus rationibus ad ostendendum unitatem mundi, hic Aristoteles ponit tertiam rationem ad idem; quae quidem addit quoddam aliud, quod videbatur deficere ad primam rationem. Posset enim aliquis dicere quod corporibus non inest moveri naturaliter ad aliqua loca determinata: vel, si ad aliqua loca determinata moventur, ea quae sunt unius speciei et diversa secundum numerum, moventur ad loca diversa secundum numerum, quae conveniunt in specie; non autem ad eundem locum secundum numerum, sicut prima ratio supponebat. Ad haec igitur certificanda philosophus inducit hanc tertiam rationem. Circa quam tria facit: 164. Having given two arguments showing that the world is one, Aristotle here gives a third argument for the same. And this argument adds something which seemed to be lacking in the first argument. For someone could say that it is not inherent in bodies to be naturally moved to certain definite places, or, if they are moved to definite places, those that are one in species and diverse in number are moved to numerically diverse places, which agree in species. But they are not moved to the same numerical place as the first argument supposed. Therefore, in order to make these things sure, Aristotle adduces this third argument. With respect to this he does three things: primo ponit rationem;
secundo excludit quandam obviationem, ibi: si autem ad specie eadem etc.;
tertio infert principalem conclusionem, ibi: itaque necessarium et cetera.
First he gives the argument, at 165;
Secondly, he excludes an objection, at 166;
Thirdly, he infers the main conclusion, at 169.
Dicit ergo primo necessarium esse quod sit aliquis motus praedictorum corporum. Manifestum est autem quod moventur: quod quidem apparet et per sensum et per rationem, quia huiusmodi sunt corpora naturalia, quibus competit moveri. Potest ergo dubitatio remanere, utrum sit dicendum quod corpora naturalia moveantur per violentiam omnibus motibus quibus moventur, etiam si sint contrarii; puta quod ignis inducatur et sursum et deorsum per violentiam. Sed hoc est impossibile: quia quod non est omnino natum moveri, idest quod nullum motum habet ex sua natura, impossibile est quod moveatur per violentiam. Hoc enim dicimus violentiam pati, quod per vim fortioris agentis removetur a propria inclinatione: si igitur corporibus non inesset aliqua naturalis inclinatio ad quosdam motus, violentia in eis locum non haberet; sicut si animal non esset natum videre, non attribueretur ei caecitas. Oportet igitur dicere quod istorum corporum quae sunt partes mundi, sit aliquis motus secundum naturam. Eorum igitur quorum est una natura, est unus motus. Unus autem motus dicitur, qui est ad unum terminum, ut patet in V Physic. Necesse est ergo quod motus singulorum quae sunt unius speciei, sit ad unum numero locum: videlicet, si sint gravia, ad hoc medium quod est huius mundi; et si sint levia, ad hoc extremum huius mundi. Et ad hoc sequitur esse unum mundum. 165. He says therefore first [113] that the above-mentioned bodies must have some motion. For it is manifest that they are moved — this, indeed, is evident to sense and to reason, because such are natural bodies, i.e., bodies which it befits to be moved. Therefore there can remain the doubt whether it is to be said that natural bodies are moved violently with all the motions with which they are moved, even if they are contrary motions — for example, that fire is moved both upward and downward by compulsion. But this is impossible, because what is not apt to be moved at all, i.e., what of its nature has no motion cannot be moved by compulsion. For we say that a thing suffers compulsion if it is removed from its proper inclination by the force of a stronger agent. If, therefore, there is not a natural inclination to certain motions in bodies, compulsion has no place in them — any more than blindness would be attributed to an animal if it had no capacity to see. Consequently, we must admit that those bodies which are parts of the world have a motion according to nature, and among the bodies having a nature, the motion is one. Now motion is called "one" inasmuch as it is to one terminus, as is plain in Physics V. Therefore the motion of each thing belonging to the same species must be to one numerical place: namely, if they are heavy, it is to the middle, which is of this world; if they are light, it is to the boundary which is of this world. And upon this it follows that there is one world. Deinde cum dicit: si autem ad specie eadem etc., excludit quandam obviationem. Posset enim aliquis dicere quod omnia corpora quae habent eundem motum naturalem, moventur ad loca quae sunt eadem specie, sed plura numero: quia etiam ipsa singularia, idest singulae partes unius corporis naturalis, puta terrae vel aquae, sunt plura numero, sed non differunt specie. Non videtur autem plura requirere unitas naturae mobilium quae sunt unius speciei, quam quod eorum motus sit unus secundum speciem; ad quod videtur sufficere quod loca ad quae terminatur, sint similia in specie. 166. Then at [114] he excludes an objection. For someone could say that all bodies having the same natural motion are moved to places that are the same in species, but several numerically — since even the singulars, i.e., the individual parts of one natural body, e.g., earth or water, are numerically many but do not differ in species. But oneness of nature in the mobiles that are of the same species does not seem to require any more than that their motion be one in species; in keeping with this, it would seem to be enough if the places at which the motion is terminated were alike in species. Sed ipse ad hoc excludendum dicit quod tale accidens, scilicet moveri ad eadem loca secundum speciem, non videtur convenire huic partium, huic autem non (ut scilicet quaedam partes similes specie moveantur ad eundem locum numero, quaedam vero ad eundem locum secundum speciem); sed similiter oportet quod conveniat omnibus (ut scilicet vel omnes partes similes specie moveantur ad unum locum secundum numerum, vel omnes huiusmodi partes moveantur ad unum locum similem specie, numero tamen differentem); quia omnes huiusmodi similiter se habent quantum ad hoc quod non differunt specie ab invicem, sed unumquodque differt ab altero secundum numerum. Hoc autem ideo dicit, quia partes alicuius corporis, puta terrae, quae sunt in hoc mundo, similiter se habent ad invicem et cum partibus terrae quae sunt in alio mundo, ex quo terra hic et ibi est eiusdem speciei. Si ergo hinc, idest ex isto mundo, sumatur aliqua pars, puta terrae, nihil differt si comparetur ad aliquam partium quae sunt in aliquo alio mundo, vel si comparatur ad eas quae sunt in hoc mundo, sed similis est comparatio ad utrasque; quia non differunt specie ad invicem partes terrae quae sunt in hoc mundo, et quae sunt in alio mundo. Et eadem ratio est de aliis corporibus. Videmus autem quod omnes partes terrae quae sunt in hoc mundo, moventur ad unum numero locum; et similiter est in aliis corporibus. Ergo omnes partes terrae, in quocumque mundo sint, naturaliter moventur ad hoc medium huius mundi. 167. But in order to exclude this he says that such an accident, namely, being moved to the same specific places, does not seem to be congruent to one set of parts and not to another (i.e., such that some parts alike in species would be moved to the same numerical place and others to the same specific place); rather it should be congruent to all alike (i.e., either all the parts alike in species be moved to the same numerical place, or all such parts be moved to one place specifically similar but numerically different) — for all such parts are alike in not differing specifically, but each differs from the other numerically. The reason he says this is that the parts of any body, for example, earth, which are in this world are similarly related both to the parts of earth in this world and to the parts in another world, since earth here and earth there are specifically the same. If, then, a part, e.g., of earth, be taken hence, i.e., from this world, it makes no difference whether it is compared to parts in some other world or to parts in this world; rather the relationships are the same in both cases. For the parts of earth in this world and those in some other world do not differ in species. And the same holds for other bodies. But we see that all parts of earth in this world are moved to one numerical place; similarly for other bodies. Therefore all the parts of earth in whatever world they exist are naturally moved to this middle of this world. Ipsa igitur naturalis inclinatio omnium corporum gravium ad unum numero medium, et omnium levium corporum ad unum numero extremum, manifestat unitatem mundi. Non enim potest dici quod in pluribus mundis ordinentur corpora secundum diversa media et extrema, sicut et in pluribus hominibus sunt media et extrema diversa numero, sed in eadem specie. Quia natura membrorum hominis vel cuiuslibet animalis non determinatur secundum ordinem ad aliquem locum, sed magis secundum ordinem ad aliquem actum; talis autem situs partium animalis congruit decentiae operationis membrorum. Sed natura gravium et levium determinatur ad certa loca; ita scilicet quod omnia quae habent eandem naturam, ad unum numero locum unam numero habent naturalem inclinationem. 168. Therefore the very natural inclination of all heavy bodies to one numerical middle, and of all light bodies to numerically one boundary, manifests the unity of the world. For it cannot be said that in the many worlds, bodies would be arranged according to diverse middles and boundaries, as happens in the case of men in whom the centers and boundaries are numerically diverse but specifically the same. For the nature of man's members or those of any other animal is not determined with respect to their relationship to some place but rather with respect to their relationship to some act; indeed, the position occupied by the parts of animals is in keeping with a suitable operation of the members. But the nature of heavy and of light things is determined to definite places, such that all having the same nature also have numerically one natural inclination to numerically one place. Deinde cum dicit: itaque necessarium etc., infert principalem conclusionem. Cum enim conclusio secundum formam debitam infertur ex praemissis, necesse est vel conclusionem concedere, vel praemissas negare. Concludit ergo quod aut est necesse amovere, idest negare, has suppositiones, idest principia ex quibus conclusit propositum; aut necesse est concedere conclusionem, quod scilicet sit unum medium, ad quod feruntur omnia gravia, et unum extremum, ad quod feruntur omnia levia. Quo existente vero, necesse est ex consequenti quod sit unum caelum, idest unus mundus, et non plures; et hoc per argumenta, idest signa, praedicta, et per necessitates, idest necessarias rationes, praedictas. 169. Then at [115] he infers the principal conclusion. For when a conclusion according to due form is inferred from premises, either the conclusion must be concluded or the premises denied. He concludes, therefore, that either it is necessary to deny these suppositions, i.e., the principles from which he concluded the proposition, or to concede the conclusion, namely, that there is one middle to which all heavy things are moved, and one boundary to which all light things are carried. If this is true, then it is necessary as a consequence that there be one heaven, i.e., one world and not several, and this on account of the above-given "arguments," i.e., signs and "necessities," i.e., necessary arguments. Deinde cum dicit: quod autem est aliquid etc., ostendit quoddam quod supposuerat, scilicet quod corpora naturalia habent loca determinata, ad quae naturaliter ferantur. 170. Then at [116] he proves something he had assumed, namely, that natural bodies have definite places to which they are naturally borne. Et primo ostendit propositum;
secundo destruit opinionem contrariam, ibi: sed adhuc neque ab alio et cetera.
First he proves the proposition;
Secondly, he rejects a contrary opinion (L. 18).
Circa primum duo facit: About the first he does two things: primo ostendit propositum per rationem naturalem;
secundo per signum, ibi: argumentum autem et cetera.
First he shows the proposition by a natural argument;
Secondly, by a sign, at 173.
Circa primum tria facit. As to the first he does three things: Primo proponit quod intendit: et dicit manifestum esse tam ex aliis rationibus quam ex praemissis (vel etiam ex aliis motibus) quod est aliquis locus determinatus, quo naturaliter terra fertur. Et similiter dicendum est de aqua et de quolibet aliorum corporum. First he proposes what he intends, and says it is clear from other arguments than the foregoing — or even from other motions — that there is a definite place whither earth is naturally borne. And the same is to be said of water and of any of the other bodies. Secundo ibi: omnino enim quod movetur etc., ponit rationem: dicens omnino, idest universaliter, hoc esse verum, quod omne quod movetur, transmutatur ex quodam determinato in quoddam determinatum: dicitur enim in I Physic. quod album fit non ex quolibet non albo, sed ex nigro. Haec autem duo, scilicet ex quo motus procedit et in quod terminatur, differunt specie: sunt enim contraria, ut patet in V Physic.; contrarietas autem est differentia secundum formam, ut dicitur in X Metaphys. 171. Secondly, at [117] he gives his argument, saying that entirely, i.e., universally, this is true, that whatever is moved is changed from something determinate to something determinate: for it is said in Physics I that something white comes to be, not from any non-white at random, but from black. Now these two factors, namely, that from which a motion proceeds, and that into which it is terminated, differ in species — for they are contrary, as is plain in Physics V; but contrariety is a difference respecting form, as is said in Metaphysics X. Hoc autem quod dictum est, probat per hoc, quod omnis transmutatio est finita, ut probatur in VI Physic., et etiam per ea quae supra dicta sunt, scilicet quod nihil movetur ad id ad quod non potest pervenire; nihil autem potest pervenire ad infinitum; unde oportet omnem mutationem esse finitam. Si autem non esset aliquod determinatum in quod tendit motus, differens specie ab eo a quo motus incipit, oporteret motum esse infinitum: nulla enim ratio esset quare motus magis terminaretur hic quam alibi; sed eadem ratione qua incoepit illinc moveri, inciperet moveri et hinc. He proves what he has said by the fact that every change is finite, as was proved in Physics VI, and also by the facts cited above, namely, that nothing is moved to what it cannot attain; but nothing can attain to the infinite; hence every change must be finite. But if there were not something definite toward which a motion tends and something specifically different from that, at which it begins, the motion would have to be infinite; for there would be no reason why the motion should end here rather than elsewhere, but, for the same reason that it began to be moved thence, it would also begin to be moved hence. Manifestat etiam per exemplum quod dictum est. Illud enim quod sanatur, movetur ex infirmitate in sanitatem; et illud quod augmentatur, movetur ex parvitate in magnitudinem: oportet igitur etiam illud quod fertur, idest quod movetur secundum locum, moveri a quodam determinato in quoddam determinatum; et haec sunt locus unde incipit motus, et locus quo tendit. Sic igitur oportet quod specie differat locus a quo aliquid movetur localiter, et in quem naturaliter fertur; sicut id quod sanatur non tendit ubicumque contingit, quasi a casu, neque ex sola voluntate moventis, sed ad aliquid determinatum, ad quod natura inclinatur. Sic igitur et ignis et terra et alia corpora naturalia non feruntur ad infinitum, idest ad aliquod indeterminatum, sicut posuit Democritus; sed feruntur in loca opposita locis in quibus prius erant. Contrariatur autem sursum secundum locum ei quod est deorsum. Sequitur ergo quod sursum et deorsum sunt termini naturalium motuum corporum simplicium. He also explains what was said, by an example. For what is healed is moved from sickness to health; what is increased is moved from small to large. Hence, too, what is carried, i.e., moved according to place, is moved from something definite to something definite, and these are the place at which a motion begins, and the place to which it tends. Consequently, there must be a specific difference between the place from which something is locally moved and the place into which it is naturally borne, just as what is healed does not tend to just anything at random, as though by chance, or solely according to the will of the mover, but to something definite, to which it is inclined by nature. In the same way, therefore, fire and earth and other natural bodies are not borne ad infinitum, i.e., to something indefinite, as Democritus held; rather they are borne to places opposite to those in which they previously found themselves. But "up" is contrary to "down" in the realm of place. It follows, therefore, that "up" and "down" are the termini of the natural motions of simple bodies. Tertio ibi: quoniam autem et qui in circuitu etc., excludit quandam obviationem, qua posset aliquis obviare ex motu circulari, qui non videtur esse ex opposito in oppositum, sed magis ex eodem in idem. 172. Then at [118 he excludes an objection by which someone could object that circular motion does not seem to be from opposite to opposite, but more from the same to the same. Sed ipse dicit quod etiam motus circularis aliqualiter habet oppositum in termino. Dicit autem aliqualiter, propter duo. Primo quidem quia non invenitur oppositio in motu circulari secundum aliqua puncta in circulo designata, prout sunt puncta ipsius circuli, sed solum prout sunt extrema diametri, secundum quam mensuratur maxima distantia in circulo, ut supra dictum est: unde subdit: ea quae secundum diametrum, scilicet extrema, opposita sunt. Secundo quia, sicut totum corpus sphaericum non mutat locum subiecto sed solum ratione, partes autem eius variant locum etiam subiecto; ita si accipiatur totus motus circularis, non invenitur aliqua oppositio in terminis nisi secundum rationem, prout scilicet idem, a quo et in quod est motus circularis, accipitur ut principium et ut finis; sed accipiendo partes motus circularis, accipitur ibi oppositio secundum lineam rectam, ut supra dictum est; et ideo subdit quod toti circulationi non est aliquid contrarium. Sic ergo patet quod etiam in his quae circulariter feruntur, mutatio est aliquo modo in opposita et finita. But he says that even circular motion somehow involves opposition of termini. He says "somehow" for two reasons. First, because opposition in circular motion is not found with respect to points designated on the circle insofar as they are points of the circle, but only insofar as they are the extremities of the diameter — on the basis of which a maximum distance is reckoned in a circle, as was said above. Hence he adds: "What are according to the diameter," i.e., the extremities of the diameter, "are opposite." Secondly, because just as the whole spherical body does not change place as to subject but only in conception, although the parts change their place even as to subject, so also, if the entire circular motion is taken, there is no opposition in termini, except conceptually, namely, in the sense that the same [point], from which and to which circular motion is, is taken now as the beginning and now as the end. But if we take the parts of circular motion, we find opposition with respect to a straight line, as has been said. And therefore he adds that there is nothing contrary to a whole revolution. Consequently, it is plain that even in things circularly moved, the change is in a certain way toward things opposite and determinate. Et sic universaliter concludit quod intendit, scilicet quod necesse est esse aliquem finem motus localis; non autem in infinitum fertur corpus naturale, idest ad aliquod indeterminatum, sicut posuit Democritus motum atomorum. Thus he concludes universally to what he intended, namely, that there is necessarily an end involved in local motion and that a natural body is not moved in infinitum [i.e., to nothing definite], as Democritus posited about the motion of atoms. Deinde cum dicit: argumentum autem etc., probat idem per signum: quam quidem probationem vocat argumentum, eo quod talis probatio est quasi coniecturalis. Et dicit quod argumentum eius quod corpus naturale non feratur in infinitum sed ad aliquod certum, est quod terra, quanto magis appropinquat ad medium, velocius fertur (quod potuit deprehendi ex maiori eius impulsu, prout scilicet a gravi cadente fortius impellitur aliquid iuxta terminum sui motus): et eadem ratio est de igne, quod motus eius in tanto est velocior, quanto magis appropinquat ad locum sursum. Si ergo in infinitum ferretur terra vel ignis, in infinitum posset velocitas eius augeri. 173. Then at [119] he proves the same thing through a sign. This proof he calls an "argument" in the sense that it is, so to speak, conjectural. And he says that the argument for claiming that a natural body is not moved to infinity but to something certain is that earth, the closer it approaches the middle, the more swiftly it is moved (which can be perceived from its greater impetus, namely, as something is more strongly impelled by the heavy in its fall as it nears the terminus of its motion); and the same holds for fire whose motion is swifter, the closer it approaches an upward place. If, therefore, earth or fire were moved to infinity, their speed could increase indefinitely. Et ex hoc concludit quod in infinitum posset augeri gravitas vel levitas corporis naturalis. Sicut enim velocitas corporis gravis est maior, quanto grave corpus amplius descendit, quod quidem corpus grave est velox per suam gravitatem; sic etiam ita poterit esse additio infinita ad velocitatem, si sit additio infinita ad gravitatem vel levitatem. Ostensum est autem supra quod non potest esse gravitas vel levitas infinita, et quod non potest aliquid moveri ad id ad quod non potest pertingere. Sic igitur additio gravitatis non potest esse in infinitum; et per consequens nec additio velocitatis. Unde nec motus corporum naturalium potest esse in infinitum. And from this he concludes that the heaviness or lightness of a natural body could be increased infinitely. For just as the speed of a heavy body is greater according as the heavy body descends farther (and a heavy body is swift on account of its heaviness), so, too, an indefinite addition could be made to the speed if an infinite addition were made to heaviness or lightness. But it was shown above that there cannot be an infinite heaviness or lightness, and that nothing can be moved toward what it cannot attain. Consequently, addition of heaviness ad infinitum cannot occur, and, as a result, neither can addition of speed. Hence neither can the motion of natural bodies be tending toward what is infinite. Sciendum est autem quod causam huius accidentis, quod terra velocius movetur quanto magis descenderit, Hipparchus assignavit ex parte moventis per violentiam; a quo quantum elongatur motus, tanto minus remanet de virtute moventis, et sic motus fit tardior; unde motus violentus in principio quidem intenditur, in fine autem remittitur intantum quod finaliter grave non potest plus sursum ferri, sed incipit moveri deorsum, propter parvitatem eius quod remanserat de virtute motoris violenti; quae quanto magis minoratur, tanto motus contrarius fit velocior. 174. It should be noted that the cause of this accident that earth is moved more swiftly the more it descends was explained by Hipparchus in terms of an agent causing motion by compulsion. The farther the motion is from such an agent the less remains of that agent's power, so that the motion becomes slower. Hence in the beginning, a compulsory motion is intense but in the end it is weakened, until finally the heavy body can no longer be borne upward, but begins to be moved downward due to the small amount of the agent's virtue that remains, which, the less it becomes, so much the swifter becomes the contrary motion. Sed ista ratio est particularis solum in his quae moventur naturaliter post motum violentum; non autem habet locum in his quae moventur naturaliter eo quod generantur extra propria loca. But this explanation is applicable only to things that are moved naturally after a compulsory motion; it does not apply to things that are moved naturally on account of being generated outside their proper places. Alii vero assignaverunt huius causam ex quantitate medii per quod fit motus, puta aeris, qui minor restat quanto plus proceditur in motu naturali; et ideo minus potest impedire motum naturalem. Sed et haec ratio non minus competeret in motibus violentis quam naturalibus; in quibus tamen contrarium accidit, ut infra dicetur. Others explained this phenomenon in terms of the amount of the medium through which the motion takes place (for example, the amount of air): in such a motion, if it is natural, the farther a thing has been moved, the less is the amount remaining — and, therefore, the less is it able to impede a natural motion. But this explanation also, applies no less to compulsory motions than to natural motions, in which, nevertheless, the contrary happens, as will be said below. Et ideo dicendum est cum Aristotele quod causa huius accidentis est, quod quanto corpus grave magis descendit, tanto magis confortatur gravitas eius, propter propinquitatem ad proprium locum. Et ideo argumentatur quod si cresceret in infinitum velocitas, quod cresceret etiam in infinitum gravitas. Et eadem ratio est de levitate. Therefore, it must be said with Aristotle that the cause of this phenomenon is that, to the extent that a heavy body descends more, to that extent is its heaviness the more strengthened on account of its proximity to its proper place. And therefore he argues that if the speed increased infinitely, the heaviness, too, would increase indefinitely. And the same holds for lightness.
Lecture 18:
Exclusion of the opinion that natural bodies are not moved naturally to determined places. Unity of the world from higher bodies.Chapter 8 cont. Ἀλλὰ (277b.) μὴν οὐδ' ὑπ' ἄλλου φέρεται αὐτῶν τὸ μὲν ἄνω τὸ δὲ κάτω οὐδὲ βίᾳ, ὥσπερ τινές φασι τῇ ἐκθλίψει. 120 Further, it is not the action of another body that makes one of these bodies move up and the other down; nor is it constraint, like the 'extrusion' of some writers. Βραδύτερον γὰρ ἂν ἐκινεῖτο τὸ πλεῖον πῦρ ἄνω καὶ ἡ πλείων γῆ κάτω νῦν δὲ τοὐναντίον ἀεὶ τὸ πλεῖον πῦρ θᾶττον φέρεται καὶ ἡ πλείων γῆ εἰς τὸν αὑτῶν τόπον. 121 For in that case the larger the mass of fire or earth the slower would be the upward or downward movement; but the fact is the reverse: the greater the mass of fire or earth the quicker always is its movement towards its own place. Οὐδὲ θᾶττον ἂν πρὸς τῷ τέλει ἐφέρετο, εἰ βίᾳ καὶ ἐκθλίψει πάντα γὰρ τοῦ βιασαμένου πορρωτέρω γιγνόμενα βραδύτερον φέρεται, καὶ ὅθεν βίᾳ, 122 Again, the speed of the movement would not increase towards the end if it were due to constraint or extrusion; for a constrained movement always diminishes in speed as the source of constraint becomes more distant, ἐκεῖ φέρεται οὐ βίᾳ. Ὥστ' ἐκ τούτων θεωροῦσιν ἔστι λαβεῖν τὴν πίστιν περὶ τῶν λεγομένων ἱκανῶς. 123 and a body moves without constraint to the place whence it was moved by constraint. A consideration of these points, then, gives adequate assurance of the truth of our contentions. Ἔτι δὲ καὶ διὰ τῶν ἐκ τῆς πρώτης φιλοσοφίας λόγων δειχθείη ἄν, καὶ ἐκ τῆς κύκλῳ κινήσεως, ἣν ἀναγκαῖον ἀΐδιον ὁμοίως ἐνταῦθά τ' εἶναι καὶ ἐν τοῖς ἄλλοις κόσμοις. 124 The same could also be shown with the aid of the discussions which fall under First Philosophy, as well as from the nature of the circular movement, which must be eternal both here and in the other worlds. Δῆλον δὲ κἂν ὧδε γένοιτο σκοπουμένοις ὅτι ἀνάγκη ἕνα εἶναι τὸν οὐρανόν. Τριῶν γὰρ ὄντων τῶν σωματικῶν στοιχείων, τρεῖς ἔσονται καὶ οἱ τόποι τῶν στοιχείων, εἷς μὲν ὁ τοῦ ὑφισταμένου σώματος ὁ περὶ τὸ μέσον, ἄλλος δὲ ὁ τοῦ κύκλῳ φερομένου, ὅσπερ ἐστὶν ἔσχατος, τρίτος δ' ὁ μεταξὺ τούτων ὁ τοῦ μέσου σώματος. Ἀνάγκη γὰρ ἐν τούτῳ εἶναι τὸ ἐπιπολάζον. Εἰ γὰρ μὴ ἐν τούτῳ, ἔξω ἔσται ἀλλ' ἀδύνατον ἔξω. Τὸ μὲν γὰρ ἀβαρὲς τὸ δ' ἔχον βάρος, κατωτέρω δὲ ὁ τοῦ βάρος ἔχοντος σώματος τόπος, εἴπερ ὁ πρὸς τῷ μέσῳ τοῦ βαρέος. Ἀλλὰ μὴν οὐδὲ παρὰ φύσιν ἄλλῳ γὰρ ἔσται κατὰ φύσιν, ἄλλο δ' οὐκ ἦν. Ἀνάγκη ἄρα ἐν τῷ μεταξὺ εἶναι. Τούτου δ' αὐτοῦ τίνες εἰσὶ διαφοραί, ὕστερον ἐροῦμεν. 125 It is plain, too, from the following considerations that the universe must be one. The bodily elements are three, and therefore the places of the elements will be three also; the place, first, of the body which sinks to the bottom, namely the region about the centre; the place, secondly, of the revolving body, namely the outermost place, and thirdly, the intermediate place, belonging to the intermediate body. Here in this third place will be the body which rises to the surface; since, if not here, it will be elsewhere, and it cannot be elsewhere: for we have two bodies, one weightless, one endowed with weight, and below is place of the body endowed with weight, since the region about the centre has been given to the heavy body. And its position cannot be unnatural to it, for it would have to be natural to something else, and there is nothing else. It must then occupy the intermediate place. What distinctions there are within the intermediate itself we will explain later on. Περὶ μὲν οὖν τῶν σωματικῶν στοιχείων, ποῖά τ' ἐστὶ καὶ πόσα, καὶ τίς ἑκάστου τόπος, ἔτι δ' ὅλως πόσοι τὸ πλῆθος οἱ τόποι, δῆλον ἡμῖν ἐκ τῶν εἰρημένων. We have now said enough to make plain the character and number of the bodily elements, the place of each, and further, in general, how many in number the various places are.
Postquam ostendit philosophus quod corpora naturalia moventur naturaliter ad determinata loca, hic excludit opinionem contrariam. 175. After showing that natural bodies are by nature moved to definite places, the Philosopher here excludes a contrary opinion. Et primo proponit quod intendit;
secundo probat propositum, ibi: tardius enim et cetera.
First he proposes what he intends;
Secondly, he proves his proposition, at 176.
Quia vero per hoc quod falsitas excluditur, veritas comprobatur, inducit hic philosophus exclusionem erroris quasi quandam veritatis demonstrationem; dicens quod adhuc etiam quod dictum est manifestatur per hoc, quod corpora naturalia non feruntur sursum et deorsum neque sicut ab alio exteriori mota. Now, since truth is established by excluding falsehood, the Philosopher here induces the exclusion of an error as a certain demonstration of the truth. He says, therefore, that what has been said is manifested by the fact that natural bodies are not borne upward and downward as though moved by some external agent. Per quod quidem intelligendum est quod removet exteriorem motorem, qui per se huiusmodi corpora moveat postquam sunt formam specificam sortita. Moventur enim levia quidem sursum, gravia autem deorsum a generante quidem, inquantum dat eis formam quam consequitur talis motus; sed a removente prohibens, per accidens et non per se. Quidam vero posuerunt quod postquam speciem sunt adepta huiusmodi corpora, indigent ab aliquo extrinseco moveri per se: quod hic philosophus removet. By this is to be understood that he rejects an external mover which would move these bodies per se after they obtained their specific form. For light things are indeed moved upward, and heavy bodies downward, by the generator inasmuch as it gives them the form upon which such motion follows, but they are moved per accidens, and not per se, by whatever removes an obstacle to their motion. However, some have claimed that after bodies of this kind have received their form, they need to be moved per se by something extrinsic. It is this claim that the Philosopher rejects here. Neque etiam dicendum est quod huiusmodi corpora moveantur per violentiam; sicut quidam dixerunt quod moveantur per quandam extrusionem, inquantum scilicet unum corpus truditur ab alio fortiori. Ponebant enim quod omnium corporum erat naturaliter unus motus: sed dum quaedam eorum ab aliis impelluntur, fit quod quaedam eorum moventur sursum, quaedam autem deorsum. Neither should it be said that these bodies are moved by compulsion, which is the opinion of those who said that they are moved by a certain "extrusion," in the sense that one body is displaced by another, stronger, one. For they assumed that there was one motion natural to all bodies, but since some are given momentum by others, it comes to pass that a certain number are moved upward and a certain number downward. Deinde cum dicit: tardius enim etc., probat propositum tribus rationibus. Quarum prima principaliter inducitur ad ostendendum quod huiusmodi corpora in suis naturalibus motibus non moventur ab exterioribus motoribus. Manifestum est enim quod tanto tardior est motus, quanto movens minus vincit super mobile. Eadem autem virtus moventis minus vincit maius mobile quam minus. 176. Then at [121] he proves his proposition with three arguments. The first of these is adduced mainly to show that bodies of this kind in their natural motions are not moved by external movers. For it is clear that a motion is slower to the extent that the mover overcomes the mobile less. But a given virtue of the mover overcomes a larger mobile less than a smaller. Si ergo huiusmodi corpora moverentur ab aliquo exteriore movente, tardius moveretur maior ignis sursum et maior terra deorsum. Nunc autem contrarium accidit, quod maior ignis et maior terra velocius feruntur in propria loca. Per quod datur intelligi quod huiusmodi corpora habent intrinsecus principia sui motus; quorum virtutes motivae tanto sunt maiores, quanto corpora fuerint maiora; et ideo velocius feruntur. Sic ergo patet quod huiusmodi corpora suis motibus naturalibus moventur non per virtutem exteriorem, sed per virtutem intrinsecam, quam acceperunt a generante. If, then, these bodies were moved by an external mover, a greater amount of fire would be moved upward more slowly and a larger amount of earth downward more slowly. But just the opposite happens, for a greater quantity of fire and a greater quantity of earth are moved more swiftly to their places. This gives us to understand that these bodies have the principles of their motion within themselves, and their motive powers are greater according as the bodies are greater, and that is why they are moved more swiftly. Consequently, it is plain that such bodies in their natural motions are not moved by an exterior power but by an intrinsic one, which they have received from their generator. Secundam rationem ponit ibi: neque velocius etc.; quae quidem principaliter ad hoc inducitur, quod motus horum corporum non est per violentiam. Videmus enim quod omnia quae per violentiam moventur, tanto tardius feruntur, quanto magis elongantur a motore qui vim intulit; sicut patet in his quae proiiciuntur, quod eorum motus in fine est remissior, et tandem totaliter deficit. Si ergo corpora gravia et levia moverentur per violentiam, quasi mutuo se trudentia, sequeretur quod eorum motus ad propria loca non esset velocior in fine, sed magis tardior; cuius contrarium ad sensum apparet. 177. At [122] he gives a second argument which is adduced mainly to show that motion of these bodies is not through compulsion. For we see that all things moved by compulsion are moved more slowly according as their distance from the mover increases, as is plain in projectiles, whose motion slackens near the end and finally fails. If, then, heavy and light bodies were moved by compulsion as though mutually pushing one another, it would follow that their motion toward their proper places would not be faster but slower in the end. But the contrary of this is plain to our senses. Tertiam rationem ponit ibi: et unde vi etc.; quae potest respicere ad utrumque. Videmus enim quod nullum corpus illuc fertur per violentiam, unde per violentiam removetur. Ex hoc enim aliquod corpus a loco aliquo per violentiam removetur, quia natum est ibi esse: unde illuc naturaliter, et non per violentiam fertur. Si ergo ponatur quod motus aliqui corporum gravium et levium, quibus ab aliquibus locis removentur, sint violenti, non potest dici quod motus contrarii, quibus ad illa loca feruntur, sint violenti. Et ita non est verum quod omnes motus horum corporum sint ab alio et per violentiam. 178. He gives at [123] the third argument which can regard both. For we see that no body is moved by violence to a place whence it can be removed by violence. For it is because a body is apt to be in a certain place that it can be moved thence by violence; hence it was originally brought there naturally and not by violence. If, therefore, it is assumed that some motions of heavy and light bodies are violent by which they are moved from certain places, it cannot be said that the contrary motions which brought them there are violent. Thus it is not true that all the motions of these bodies are caused by another and by violence. Concludit autem ex dictis epilogando, quod per speculationem horum contingit accipere fidem de his quae dicta sunt. He concludes from the foregoing, in summary, that speculation on these points will testify to the truth of what has been said. Deinde cum dicit: adhuc autem et per eas etc., ostendit unitatem mundi per corpora superiora, quae circulariter feruntur: 179. Then at [124] he shows through the higher bodies which are moved circularly that the world is one: et primo specialiter per corpora superiora;
secundo communiter per superiora et inferiora, ibi: palam autem utique et cetera.
First in a special way by the higher bodies;
Secondly, in a general way by the higher and the lower, at 181.
Dicit ergo primo quod adhuc ostendi potest quod sit solum unus mundus, per rationes sumptas ex prima philosophia, idest per ea quae determinata sunt in metaphysica, et per hoc quod ostensum est in VIII Physic., quod motus circularis est sempiternus, quod quidem habet naturalem necessitatem et in hoc et in aliis mundis. Conclusit enim philosophus sempiternitatem motus caeli in VIII Physic. per ordinem mobilium et moventium; quod quidem necesse est similiter se habere in quolibet mundo, si mundus univoce dicatur. Si autem motus caeli sit sempiternus, oportet quod moveatur a virtute infinita, quae non sit virtus in magnitudine, ut probatur in VIII Physic. Talis autem virtus est immaterialis, et per consequens una numero, cum sit tantum forma et species, multiplicatio autem individuorum eiusdem speciei est per materiam. Et sic oportet quod virtus quae movet caelum, sit una numero. Unde oportet quod et caelum sit unum numero, et per consequens totus mundus. He says therefore first [124] that there is still another way of proving that there is but one world, by arguments taken from first philosophy, i.e., by using what has been determined in the Metaphysics, and from what has been shown in Physics VIII, namely, that circular motion is eternal, which, both in this and in other worlds, has a natural necessity. For the Philosopher concluded to the eternity of celestial motion in Physics VIII by considering the order between mobiles and movers, which must be similar in any world, if "world" is taken univocally. Now if celestial motion is eternal, it must be moved by an infinite power, such as cannot exist in a magnitude, as was proved in Physics VIII. Such a power is non-material and consequently numerically one, since it is a form and species only, whereas it is through matter that individuals are multiplied in the same species. Consequently, the power that moves the heavens must be numerically one. Hence the heavens too must be numerically one, and, consequently, the whole world. Potest autem aliquis dicere hanc rationem non ex necessitate concludere. Primum enim movens movet caelum sicut desideratum, ut dicitur in XII Metaphys.; nihil autem prohibet idem a pluribus desiderari; et ita videtur quod ex unitate primi moventis non possit ex necessitate concludi unitas caeli. 180. But someone can say that this argument does not conclude with necessity. For the first mover moves the heaven as that which is desired, as is said in Metaphysics XII. But there is nothing to prevent the same thing from being accidentally many. So it seems that we cannot from the unity of the first mover conclude necessarily to the unity of the heavens. Sed dicendum est quod multa possunt unum desiderare, non quidem quasi de pari, eo quod uni primo non immediate adiungitur absoluta multitudo; sed secundum quendam ordinem possunt multa desiderare unum, quaedam propinquius et quaedam remotius, quorum coordinatio in ordine ad unum ultimum, facit unitatem mundi. But it must be said that many can desire one thing, but not indeed in an identical way, since an absolute multitude is not joined immediately to one thing that is first; but many things can desire one thing according to a certain order, some being closer and some more remote, the coordination of which to one ultimate objective makes the unity of the world. Deinde cum dicit: palam autem utique etc., probat propositum ratione sumpta communiter ex corporibus superioribus et inferioribus. Et dicit quod etiam sic intendendo sicut dicetur, necesse est esse unum caelum, idest unum mundum. Ad quod probandum assumit quod, sicut sunt tria corporalia elementa, scilicet caelum et terra et medium, ita sunt et tria loca eis correspondentia: unus quidem locus qui est circa medium, qui est corporis subsistentis, idest corporis gravissimi quod substat omnibus, scilicet terrae; alius autem locus qui est extremus in altitudine, qui est corporis quod movetur circulariter; tertius autem locus qui est intermedius horum, qui est medii corporis. 181. Then at [125] he proves his proposition with an argument taken generally from higher and lower bodies. And he says that even the following consideration will show that it is necessary for the heaven, i.e., the world, to be one. To prove this he assumes that, just as there are three bodily elements, namely, heaven and earth and an intermediate, so there are three places corresponding to them: one is the place about the middle, that of the subsisting body, i.e., the place of the heaviest body which supports all, namely, earth; another is the place which is the highest in altitude, that of the circularly moved body; the third place is intermediate and corresponds to the intermediate body. Circa quae quidem verba primo considerandum est quod etiam caelum inter elementa computat, cum tamen elementum sit ex quo componitur res, ut dicitur in V Metaphys. With regard to these words it should be noted that Aristotle here reckons the heaven among the elements, although an element is something out of which things are composed, as is said in Metaphysics V. Caelum autem, etsi non veniat in compositionem corporis mixti, venit tamen in compositionem totius universi, quasi quaedam pars eius. Vel elementa large nominat quaecumque simplicia corpora: quae quidem vocat corporalia elementa, ad differentiam materiae primae, quae est elementum, non tamen corporale, sed absque omni forma, prout in se consideratur. However the heaven, even though it does not enter into the composition of a mixed body enters into the composition of the whole universe, as being a part of it. Or he is using the word "element" in a wide sense to designate any of the simple bodies which he calls "bodily elements" to distinguish them from prime matter, which, though an element, is not a bodily element, for considered in itself it is without any form. Secundo autem considerandum est de hoc quod dicit tria esse loca. Cum autem locus sit terminus corporis continentis, ut dicitur in IV Physic., satis potest esse manifestum quid sit locus medii elementi; quia superficies supremi corporis continentis ipsum. De primo autem corpore quomodo sit in loco, ostensum est in IV Physic. Sed quomodo medium, quod non habet rationem continentis sed contenti, sit locus corporis gravis, videtur dubitationem habere. Secondly, we should consider his statement that there are three places. Now since place is the boundary of a containing body, as is said in Physics IV, it can be clear what the place of the intermediate element is — for it is the surface of the supreme, body containing it. How the first body is in place has been explained in Physics IV. But how the middle [i.e., the center], which seems to be not a container but a contained, is the place of the heavy body seems to offer difficulty. Sed dicendum est quod, sicut dictum est in IV Physic., superficies corporis continentis non habet rationem loci secundum quod est superficies talis corporis, sed secundum ordinem situs quem habet ad primum continens, prout scilicet magis vel minus ei appropinquat. Corpus autem grave in sua natura est maxime elongatum a corpore caelesti propter eius materialitatem; et ideo debetur ei locus remotissimus a primo continente, qui est propinquissimus medio; et ita superficies continens corpus grave dicitur locus eius secundum propinquitatem ad medium. Unde signanter dicit quod locus qui est circa medium est corporis subsistentis. But it should be said that, as has been said in Physics IV, the surface of the containing body does not have the notion of place because it is the surface of such a body but with respect to the position it has in relation to the first container accordingly, namely, as it is nearer or farther from it. Now the heavy body in its nature is at a maximum distance from the celestial body on account of its materiality; therefore there is due it a place farthest from the first container and nearest to the middle. Consequently the surface containing the heavy body is called its place according to its nearness to the center. Hence he said advisedly that the place located around the middle is the place of the subsisting body. Ex his autem quae proposita sunt procedit ad propositum ostendendum ex corpore levi, sicut supra processerat ex corpore gravi. Necesse est enim corpus leve quod superfertur, esse in hoc loco medio: quia, cum omne corpus sit in aliquo loco, si corpus leve non esset in hoc loco medio, esset extra ipsum; quod est impossibile, quia extra hunc locum medium ex una parte est corpus caeleste, quod est sine gravitate et levitate, ex alia autem parte est corpus terrestre, quod habet gravitatem. Non autem potest dici quod sit aliquis locus magis deorsum quam locus qui est corporis habentis gravitatem; quia locus qui est apud medium, est proprius eius. Ex hoc autem patet quod impossibile est esse alium mundum quia oporteret ibi esse aliquod corpus leve; et sic, si mundus ille esset supra hunc mundum, corpus leve esset supra locum caeli; si autem esset infra hunc mundum, corpus leve esset infra locum corporis gravis, quod est impossibile. 182. From what has been set forth he goes on to prove his proposition from a light body, just as above he had proceeded from a heavy body. For it is necessary that a light body which is borne upwards be in this intermediate place: because, since every body is in some place, if the light body were not in this intermediate place, it would be outside it. But that is impossible, because outside this intermediate place there is, on the one side, celestial body which has no heaviness or lightness, and on the other side, terrestrial body which has heaviness. Now it cannot be said that there is a place more downward than the place of the body having heaviness, because the place about the middle is proper to it. But from this it is plainly impossible for another world to exist, because some light body would have to be there and thus, if that world were above this world, a light body would exist above the place of the heavens; if that world were below this world, a light body would be below the place of the heavy body — which is impossible. Sed huic rationi posset aliquis obviare, dicendo quod corpus leve est extra hunc locum medium, non secundum naturam, sed praeter naturam. Sed ad hoc excludendum, subdit quod neque etiam praeter naturam possibile est corpus leve esse extra hunc medium locum. Quia omnis locus qui est alicuius corporis praeter naturam, est alicuius corporis secundum naturam: non enim Deus vel natura fecit aliquem locum frustra, in quo scilicet non sit natum esse aliquod corpus. Non autem invenitur in rerum natura aliquod aliud corpus praeter ista tria, quibus tria loca praedicta deputantur, ut ex dictis patet. Unde neque secundum naturam, neque praeter naturam, potest esse corpus leve extra hunc medium locum: et sic impossibile est esse multos mundos. 183. But to this argument someone could object that the light body would be outside this intermediate place not according to nature but outside its nature. To exclude this he adds that not even outside its nature can a light body be outside this intermediate place. Because every place that is outside nature for some body is according to nature for some other body. For neither God nor nature has made any place in vain, i.e., a place in which no body is apt to be. Now, no other body is found in nature except the three mentioned and to which the aforesaid places are deputed, as is plain from what has been said. Hence neither according to nature nor beside nature can a light body exist outside this intermediate place. Consequently, it is impossible that there be many worlds. Quia vero locutus fuerat de medio elemento quasi de uno quodam corpore, subiungit quod posterius, scilicet in tertio et quarto, dicetur quae sunt differentiae istius medii. Dividitur enim in ignem, aerem et aquam, quae etiam est levis per respectum ad terram. Since he had spoken of an intermediate element as if it were one certain body, he adds that later, i.e., in the third and fourth books, he will speak about; the differences in that intermediate. For it is divided into fire, air and water, which is also light in relation to earth. Ultimo epilogando concludit quod ex dictis manifestum est de corporeis elementis, quae et quot sint, et quis sit locus cuiuslibet eorum, et universaliter quot sint loca corporalia. Finally in summary he concludes that from the foregoing it is manifest about the bodily elements, which and how many they are, and what is the place of each of them and, in general, how many bodily places exist.
Lecture 19:
Solution of the argument seeming to justify several worlds.Chapter 9 Ὅτι δ' οὐ μόνον εἷς ἐστίν, ἀλλὰ καὶ ἀδύνατον γενέσθαι πλείους, ἔτι δ' ὡς ἀΐδιος ἄφθαρτος ὢν καὶ ἀγένητος, λέγωμεν, πρῶτον διαπορήσαντες περὶ αὐτοῦ. 127 We must show not only that the heaven is one, but also that more than one heaven is and, further, that, as exempt from decay and generation, the heaven is eternal. We may begin by raising a difficulty. Δόξειε γὰρ ἂν ὡδὶ σκοπουμένοις ἀδύνατον ἕνα καὶ μόνον εἶναι αὐτόν ἐν ἅπασι γὰρ καὶ τοῖς φύσει καὶ τοῖς ἀπὸ τέχνης συνεστῶσι καὶ γεγενημένοις ἕτερόν ἐστιν αὐτή τε καθ' αὑτὴν ἡ μορφὴ καὶ μεμιγμένη μετὰ τῆς ὕλης οἷον τῆς σφαίρας ἕτερον τὸ εἶδος (278a.) καὶ ἡ χρυσῆ καὶ ἡ χαλκῆ σφαῖρα, καὶ πάλιν τοῦ κύκλου ἑτέρα ἡ μορφὴ καὶ ὁ χαλκοῦς καὶ ὁ ξύλινος κύκλος τὸ γὰρ τί ἦν εἶναι λέγοντες σφαίρᾳ ἢ κύκλῳ οὐκ ἐροῦμεν ἐν τῷ λόγῳ χρυσὸν ἢ χαλκόν, ὡς οὐκ ὄντα ταῦτα τῆς οὐσίας ἂν δὲ τὴν χαλκῆν ἢ χρυσῆν, ἐροῦμεν, καὶ ἐὰν μὴ δυνώμεθα νοῆσαι μηδὲ λαβεῖν ἄλλο τι παρὰ τὸ καθ' ἕκαστον. Ἐνίοτε γὰρ οὐθὲν κωλύει τοῦτο συμβαίνειν, οἷον εἰ μόνος εἷς ληφθείη κύκλος οὐθὲν γὰρ ἧττον ἄλλο ἔσται τὸ κύκλῳ εἶναι καὶ τῷδε τῷ κύκλῳ, καὶ τὸ μὲν εἶδος, τὸ δ' εἶδος ἐν τῇ ὕλῃ καὶ τῶν καθ' ἕκαστον. 128 From one point of view it might seem impossible that the heaven should be one and unique, since in all formations and products whether of nature or of art we can distinguish the shape in itself and the shape in combination with matter. For instance the form of the sphere is one thing and the gold or bronze sphere another; the shape of the circle again is one thing, the bronze or wooden circle another. For when we state the essential nature of the sphere or circle we do not include in the formula gold or bronze, because they do not belong to the essence, but if we are speaking of the copper or gold sphere we do include them. We still make the distinction even if we cannot conceive or apprehend any other example beside the particular thing. This may, of course, sometimes be the case: it might be, for instance, that only one circle could be found; yet none the less the difference will remain between the being of circle and of this particular circle, the one being form, the other form in matter, i.e. a particular thing. Ἐπεὶ οὖν ἐστὶν ὁ οὐρανὸς αἰσθητός, τῶν καθ' ἕκαστον ἂν εἴη τὸ γὰρ αἰσθητὸν ἅπαν ἐν τῇ ὕλῃ ὑπῆρχεν. 129 Now since the universe is perceptible it must be regarded as a particular; for everything that is perceptible subsists, as we know, in matter. Εἰ δὲ τῶν καθ' ἕκαστον, ἕτερον ἂν εἴη τῷδε τῷ οὐρανῷ εἶναι καὶ οὐρανῷ ἁπλῶς. Ἕτερον ἄρα ὅδε ὁ οὐρανὸς καὶ οὐρανὸς ἁπλῶς, καὶ τὸ μὲν ὡς εἶδος καὶ μορφή, τὸ δ' ὡς τῇ ὕλῃ μεμιγμένον. 130 But if it is a particular, there will be a distinction between the being of 'this universe' and of 'universe' unqualified. There is a difference, then, between 'this universe' and simple 'universe'; the second is form and shape, the first form in combination with matter; Ὧν δ' ἐστὶ μορφή τις καὶ εἶδος, ἤτοι ἔστιν ἢ ἐνδέχεται πλείω γενέσθαι τὰ καθ' ἕκαστα. 131 and any shape or form has, or may have, more than one particular instance. Εἴτε γὰρ ἔστιν εἴδη, καθάπερ φασί τινες, ἀνάγκη τοῦτο συμβαίνειν, εἴτε καὶ χωριστὸν μηθὲν τῶν τοιούτων, οὐθὲν ἧττον ἐπὶ πάντων γὰρ οὕτως ὁρῶμεν, ὅσων ἡ οὐσία ἐν ὕλῃ ἐστίν, πλείω καὶ ἄπειρα ὄντα τὰ ὁμοειδῆ. 132 On the supposition of Forms such as some assert, this must be the case, and equally on the view that no such entity has a separate existence. For in every case in which the essence is in matter it is a fact of observation that the particulars of like form are several or infinite in number. Ὥστε ἤτοι εἰσὶ πλείους οὐρανοὶ ἢ ἐνδέχεται πλείους εἶναι. Ἐκ μὲν δὴ τούτων ὑπολάβοι τις ἂν καὶ εἶναι καὶ ἐνδέχεσθαι πλείους εἶναι οὐρανούς 133 Hence there either are, or may be, more heavens than one. On these grounds, then, it might be inferred either that there are or that there might be several heavens. σκεπτέον δὲ πάλιν τί τούτων λέγεται καλῶς καὶ τί οὐ καλῶς. Τὸ μὲν οὖν ἕτερον εἶναι τὸν λόγον τὸν ἄνευ τῆς ὕλης καὶ τὸν ἐν τῇ ὕλῃ τῆς μορφῆς καλῶς τε λέγεται, καὶ ἔστω τοῦτ' ἀληθές. Ἀλλ' οὐδὲν ἧττον οὐδεμία ἀνάγκη διὰ τοῦτο πλείους εἶναι κόσμους, οὐδ' ἐνδέχεται γενέσθαι πλείους, εἴπερ οὗτος ἐξ ἁπάσης ἐστὶ τῆς ὕλης, ὥσπερ ἔστιν. 134 We must, however, return and ask how much of this argument is correct and how much not. Now it is quite right to say that the formula of the shape apart from the matter must be different from that of the shape in the matter, and we may allow this to be true. We are not, however, therefore compelled to assert a plurality of worlds. Such a plurality is in fact impossible if this world contains the entirety of matter, as in fact it does. Ὡδὶ δὲ μᾶλλον ἴσως τὸ λεγόμενον ἔσται δῆλον. Εἰ γάρ ἐστιν ἡ γρυπότης καμπυλότης ἐν ῥινὶ ἢ σαρκί, καὶ ἔστιν ὕλη τῇ γρυπότητι ἡ σάρξ, εἰ ἐξ ἁπασῶν τῶν σαρκῶν μία γένοιτο σὰρξ καὶ ὑπάρξειεν ταύτῃ τὸ γρυπόν, οὐθὲν ἂν ἄλλ' οὔτ' εἴη γρυπὸν οὔτ' ἐνδέχοιτο γενέσθαι. Ὁμοίως δὲ καὶ εἰ τῷ ἀνθρώπῳ ἐστὶν ὕλη σάρκες καὶ ὀστᾶ, εἰ ἐκ πάσης τῆς σαρκὸς καὶ πάντων τῶν ὀστῶν ἄνθρωπος γένοιτο ἀδυνάτων ὄντων διαλυθῆναι, οὐκ ἂν ἐνδέχοιτο εἶναι ἄλλον ἄνθρωπον. Ὡσαύ(278b.) τως δὲ καὶ ἐπὶ τῶν ἄλλων ὅλως γὰρ ὅσων ἐστὶν ἡ οὐσία ἐν ὑποκειμένῃ τινὶ ὕλῃ, τούτων οὐδὲν ἐνδέχεται γίγνεσθαι μὴ ὑπαρχούσης τινὸς ὕλης. 135 But perhaps our contention can be made clearer in this way. Suppose 'aquilinity' to be curvature in the nose or flesh, and flesh to be the matter of aquilinity. Suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. Then neither would there be, nor could there arise, any other thing that was aquiline. Similarly, suppose flesh and bones to be the matter of man, and suppose a man to be created of all flesh and all bones in indissoluble union. The possibility of another man would be removed. Whatever case you took it would be the same. The general rule is this: a thing whose essence resides in a substratum of matter can never come into being in the absence of all matter. Ὁ δ' οὐρανὸς ἔστι μὲν τῶν καθ' ἕκαστα καὶ τῶν ἐκ τῆς ὕλης ἀλλ' εἰ μὴ ἐκ μορίου αὐτῆς συνέστηκεν ἀλλ' ἐξ ἁπάσης, τὸ μὲν εἶναι αὐτῷ οὐρανῷ καὶ τῷδε τῷ οὐρανῷ ἕτερόν ἐστιν, οὐ μέντοι οὔτ' ἂν εἴη ἄλλος οὔτ' ἂν ἐνδέχοιτο γενέσθαι πλείους, διὰ τὸ πᾶσαν τὴν ὕλην περιειληφέναι τοῦτον. 136 Now the universe is certainly a particular and a material thing: if however, it is composed not of a part but of the whole of matter, then though the being of 'universe' and of 'this universe' are still distinct, yet there is no other universe, and no possibility of others being made, because all the matter is already included in this.
Postquam philosophus ostendit quod est unus solus mundus, hic ostendit quod impossibile est esse plures. Et hoc necessarium fuit ostendere: quia nihil prohibet aliquid esse falsum, quod tamen contingit esse verum. Circa hoc autem tria facit: 184. After showing that there is but one world, the Philosopher here shows that it is impossible for there to be many. And it was necessary to prove this, because nothing prevents the possibility of something's being false [now] which can yet be true [later]. Concerning this he does three things: primo ponit obiectionem, ex qua videtur ostendi quod possibile sit esse plures mundos;
secundo solvit eam, ibi: considerandum autem iterum etc.;
tertio probat quod in solutione supposuerat, ibi: hoc ipsum igitur restat ostendere et cetera.
First he presents an objection which seems to show that it is possible that many worlds exist;
Secondly, he answers it, at 194;
Thirdly, he proves something he had presupposed in his answer (L. 20).
Circa primum duo facit: About the first he does two things: primo dicit de quo est intentio, et quo ordine sit agendum;
secundo incipit exequi propositum, ibi: videbitur enim utique et cetera.
First he states his intention and his plan of treatment;
Secondly, he begins to prove his proposition, at 186.
Dicit ergo primo quod post praedicta restat ostendendum quod non solum sit unus mundus, sed quod etiam impossibile sit esse plures: et ulterius quod mundus sit sempiternus, ita scilicet quod sit incorruptibilis, tanquam nunquam desinens esse, et ingenitus, tanquam nunquam esse incipiens, secundum suam opinionem. Et hoc adiungit quia videtur prima consideratio aliqualiter dependere ex secunda. Si enim esset mundus generabilis et corruptibilis per compositionem et dissolutionem, secundum amicitiam et litem, ut Empedocles posuit, possibile esset esse multos mundos, ita scilicet quod, uno corrupto, alius postea generaretur, sicut ipse Empedocles posuit. Et quia tunc vere cognoscitur veritas, quando dubitationes sunt solutae, quae videntur esse contra veritatem; ideo prius oportet ponere dubitationes circa hoc ipsum, ex quibus scilicet videtur quod sint vel possint esse plures mundi; huius enim solutio est confirmatio veritatis. 185. He says therefore first [127] that after the foregoing, we must still prove that not only is there one world but that it is impossible for there to be more, and further that the world is eternal, so as to be imperishable, i.e. never ceasing to be, and unborn, i.e., never beginning to be, according to his opinion. He states this because the first consideration seems somehow to depend on the second. For if the world were generable and perishable by union and separation, according to friendship and strife, as Empedocles said, many worlds would be possible in the sense that when one had perished another would be generated later, as Empedocles believed. And because the truth is truly known when the difficulties which seem to be contrary to it are solved, therefore the first thing to do is bring forth the difficulties concerning this, i.e., which seem to indicate that there are or can be many worlds — for the solution to this difficulty will confirm the truth. Deinde cum dicit: videbitur enim utique etc., ponit rationem ex qua aliquis potest dubitare, aestimans possibile esse quod sint plures mundi. Unde praemittit quod sic intendentibus, scilicet secundum rationem quae sequitur, videbitur esse impossibile ipsum, scilicet mundum, esse unum et solum: subintelligendum est ex necessitate. Non enim sequens ratio probat quod necesse sit esse plures mundos, quod aequipollet ei quod est impossibile unum solum esse mundum: sed probat quod possibile est esse plures mundos, quod aequipollet ei quod est non necesse esse unum solum mundum. Ad hoc autem ostendendum inducit rationem quae continet duos syllogismos: 186. Then at [128] he presents the argument that could lead one to question whether it is not possible for more than one world to exist. Hence he prefaces the remark that, for those who hold this point of view, i.e., the one coinciding with the argument to follow, it will appear impossible that it, namely, the world, be one and unique, i.e., that there be necessarily just one world. For the following argument does not prove that it is necessary that there be several worlds, which is equivalent to its being impossible that there be but one; rather it proves that it is possible that there be more than one world, which is equivalent to its not being necessary that there be but one. Now in order to show this he induces an argument containing two syllogisms: quorum primum primo ponit;
secundo secundum, ibi: quorum autem est forma quaedam et cetera.
The first of these is at 187;
The second at 190.
Primus syllogismus talis est. In omnibus sensibilibus quae fiunt ab arte vel a natura, alia est consideratio formae secundum se consideratae, alia est consideratio formae prout est in materia; sed caelum est quoddam sensibile habens formam in materia; ergo alia est consideratio absoluta formae ipsius, prout consideratur in universali, et alia est consideratio formae ipsius in materia, prout consideratur in particulari. The first syllogism is this: In all sensible things that come to be by art or by nature, the consideration of the form considered in itself is one thing and the consideration of the form insofar as it is in matter is another. But the heaven is a sensible thing having a form in matter. Therefore, the absolute consideration of its form, i.e., as considered universally, is one thing, and the consideration of its form in matter, i.e., as considered in particular is another. Primo ergo ponit maiorem;
secundo minorem, ibi: quoniam igitur est caelum etc.;
tertio infert conclusionem, ibi: si autem singularium et cetera.
First, therefore, he presents the major, at 187;
Secondly, the minor, at 188;
Thirdly, he draws the conclusion, at 189.
Dicit ergo primo quod in omnibus existentibus et generatis, idest factis, vel a natura vel ab arte, alterum est secundum nostram considerationem ipsa forma secundum seipsam considerata; et alterum est ipsa forma mixta cum materia, idest secundum quod accipitur prout est coniuncta cum materia. 187. He says therefore first [128] that in all things that exist and were generated, i.e., made, either by nature or by art, the form considered according to itself is one thing according to our consideration, and the form mixed with matter, i.e., the form taken as joined with matter, is another. Et hoc primo manifestat per exemplum in mathematicis, in quibus est magis manifestum, eo quod in ratione eorum non ponitur materia sensibilis. Alterum est enim secundum considerationem nostram ipsa species sphaerae, et alterum forma sphaerae in materia sensibili, prout significatur cum dicitur aurea vel aerea sphaera: et similiter aliud est ipsa forma circuli, et aliud est quod dicitur aereus aut ligneus circulus. Et hoc manifestat quia, cum dicimus quod quid erat esse, idest definitivam rationem, sphaerae aut circuli, non ponimus in eius ratione aureum aut aereum; tanquam hoc quod dicimus aureum aut aereum, non sint de eorum substantia, quam scilicet significat definitio. He first explains this by an example in mathematical objects in which it is more evident, because sensible matter does not enter therein. For the species of a sphere is according to our consideration other than the form of the sphere in sensible matter, which is denoted when a sphere is called "golden" or "bronze"; similarly, the form of a circle is one thing, and what is meant by a golden or bronze circle is another. And this is evident, because when we give the quod quid erat esse, i.e., the defining notion, of a circle or a sphere, we make no mention therein of gold or bronze. This implies that to be "golden" or "bronze" does not pertain to their substance [essence], which the definition signifies. Sed videtur hoc magis esse dubium in rebus naturalibus, quarum formae non possunt esse nec intelligi sine materia sensibili; sicut simum non potest esse nec intelligi sine naso. Sed tamen formae naturales, quamvis non possint intelligi sine materia sensibili in communi, possunt tamen intelligi sine materia sensibili signata, quae est individuationis et singularitatis principium; sicut pes non potest intelligi sine carnibus et ossibus, potest tamen intelligi sine his carnibus et his ossibus. Et ideo subdit quod, si non possumus intelligere neque sumere in nostra consideratione aliquid aliud praeter singulare, idest praeter materiam, quae includitur in ratione singularis, scilicet prout est signata (quia quandoque nihil prohibet hoc accidere, ut scilicet non possit forma intelligi sine materia sensibili, sicut si intelligamus circulum sine materia sensibili): nihilominus tamen in naturalibus, in quibus hoc accidit quod non intelligitur forma sine materia, alia est ratio rei in communi acceptae et in singulari, sicut hominis et huius hominis; puta si dicamus quod aliud est esse circulo et huic circulo, idest alia est ratio definitiva utriusque. Et haec quidem, scilicet ratio rei in communi, est species, idest ipsa ratio speciei: haec autem, scilicet ratio rei in particulari, significat rationem speciei in materia determinata, et est de numero singularium. But there seems to be a difficulty in natural things, whose forms cannot exist or be understood without sensible matter, as "snub" cannot exist and be understood without "nose." Natural forms, however, although they cannot be understood without sensible matter in common, can be understood without signed sensible matter, which is the principle of individuation and of singularity. Thus, "foot" cannot be understood without flesh and bones, but it can be understood without this flesh and these bones. And therefore he adds that if we cannot understand and accept in our consideration anything outside the singular, i.e., outside the matter which is included in the notion of the individual, namely, as it is signate—because sometimes there is nothing to prevent this from happening (namely, that a form be able to be understood without sensible matter) in the same way that we understood a circle without sensible matter; nevertheless, in natural things, in which forms are not understood without matter, the notions of the thing taken in common and taken in the singular are not the same, any more than the notion of "man" and of "this man" are the same. Thus the essence of "circle" and "this circle," i.e., of the notions defining a circle, and this circle, are different. For the notion of a thing in common is the species, i.e., the notion of the species, but the notion of a particular thing signifies the notion of the species as found in determinate matter, and pertains to the singular. Deinde cum dicit: quoniam igitur est caelum etc., ponit minorem syllogismi inducti. Et dicit quod, cum caelum, idest mundus, sit quoddam sensibile, necesse est quod sit de numero singularium: et hoc ideo, quia omne sensibile habet esse in materia. Id autem quod est forma non in materia, non est sensibile, sed intelligibile tantum: qualitates enim sensibiles sunt dispositiones materiae. 188. Then at [129] he presents the minor of his syllogism. And he says that since the heaven, i.e., the world, is something sensible, it must be among the singulars, for every sensible thing exists in matter. For a form not in matter is not sensible but intelligible only — for sensible qualities are characteristics of matter. Deinde cum dicit: si autem singularium etc., ponit conclusionem. Et dicit quod si caelum, idest mundus, est de numero singularium, ut ostensum est, alterum erit esse huic caelo singulariter dicto, et caelo simpliciter, idest universaliter sumpto; idest alia erit ratio utriusque. Et sic sequitur quod alterum sit secundum considerationem hoc caelum singulariter dictum, et caelum universaliter sumptum: ita scilicet quod hoc caelum universaliter sumptum sit sicut species et forma; hoc autem, scilicet caelum singulariter sumptum, sit sicut forma coniuncta materiae. Quod non est sic intelligendum quod in ratione rei naturalis universaliter sumptae nullo modo cadat materia; sed quod non cadat ibi materia signata. 189. Then at [130] he presents the conclusion and says that if the heaven, i.e., the world, belongs among the singulars, as has been shown, its notion as a singular will differ from its notion absolutely, i.e., taken universally the two notions will differ. Consequently, it follows that "this heaven" taken singularly will be different in consideration from "heaven" taken universally, i.e., this latter heaven taken universally will be as a species and form, while the other, namely, that taken singularly, will be as form joined to matter. However, this is not to be taken as implying that in the definition of a natural thing taken universally no matter is mentioned at all, but rather that individual matter is not mentioned. Deinde cum dicit: quorum autem est forma quaedam etc., ponit secundum syllogismum, qui talis est. Quorumcumque est forma in materia, aut sunt aut contingit esse plura individua unius speciei; sed hoc caelum significat formam in materia, ut dictum est; ergo aut sunt aut possunt esse plures caeli. 190. Then at [131] he presents the second syllogism, as follows: Whatever things have their forms in matter, are, or are able to be, several individuals of one species. But "this heaven" signifies a form in matter, as was said. Therefore, there either are, or can be, many heavens. Circa hoc autem primo ponit maiorem;
secundo manifestat eam, ibi: sive enim sint species etc.;
tertio infert conclusionem, ibi: itaque aut sunt et cetera. Minorem supponit ex praemisso syllogismo.
Now in regard to this he first presents the major;
Secondly, he explains it, at 191;
Thirdly, [having taken the minor from the previous syllogism], he draws the conclusion at 192.
Dicit ergo primo quod omnia illa quorum est forma quaedam et species, idest quae non sunt ipsae formae et species, sed habent formas et species, aut sunt plura singularia unius speciei, aut contingit fieri plura: illa vero quae ipsamet sunt formae et species subsistentes, sicut substantiae separatae, non possunt esse plura unius speciei. He says therefore first [131] that all things of which there is a form and species, i.e., which are not themselves forms and species, but have forms and species, are either many individuals of one species or many can exist. But things that are themselves forms and subsistent species, as are separated substances, cannot have several members of one species. Deinde cum dicit: sive enim sint species etc., manifestat praedictam propositionem tam secundum opinionem Platonicam, quam secundum opinionem propriam. Et dicit quod sive sint species, idest ideae separatae, sicut Platonici dicunt, necesse est hoc accidere, scilicet quod sint plura individua unius speciei (quia species separata ponitur sicut exemplar rei sensibilis; possibile est autem ad unum exemplar fieri multa exemplata); sive etiam nullum talium, idest nulla specierum, separatim existat; nihilominus plura individua possunt esse unius speciei. Videmus enim in omnibus sic accidere, quorum substantia, idest essentia quam significat definitio, est in materia signata, quod sunt plura, immo infinita individua unius speciei. Et hoc ideo est, quia cum materia signata non sit de ratione speciei, ratio speciei indifferenter potest salvari in hac materia signata et in illa: et ita possunt esse plura individua unius speciei. 191. Then at [132] he explains the foregoing both according to Plato's opinion and according to his own. And he says that whether there are "species," i.e., separated ideas, as the Platonists assume, then this must happen, i.e., there must be several individuals of one species — because the separated species is posited as the exemplar of a sensible thing and it is possible to make many copies according to one exemplar; or whether no such species exist separately, there can still be several individuals of one species. For we see this happen in all things whose substance (i.e., whose essence, which is signified by the definition) exists in signate matter, namely, that there are several individuals, or even an infinitude of individuals, of one species. The reason for this is that, since signate matter does not enter the notion of the species, the notion of the species can be indifferently verified in this individual matter and in that; consequently, there can be many individuals of one species. Deinde cum dicit: itaque aut sunt etc., infert conclusionem intentam, scilicet quod aut sunt plures caeli, aut contingit esse factos plures caelos. 192. Then at [133] he draws the intended conclusion, namely, that either there are many worlds or many worlds can be made. Ultimo autem epilogat quod ex praemissis potest aliquis suspicari quod vel sint vel possint esse plures mundi. Finally he says in summary that from the foregoing someone can conjecture that either there are, or can be, many worlds. Sed videtur hic esse contrarietas inter Aristotelem et Platonem. Nam Plato in Timaeo ex unitate exemplaris probavit unitatem mundi: hic autem Aristoteles ex unitate speciei separatae concludit possibile esse quod sint plures mundi. 193. But there seems to be a conflict here between Aristotle and Plato. For Plato in the Timaeus proved the oneness of the world from the oneness of the exemplar; but here Aristotle from the oneness of the separated species concludes to the possibility of several worlds. Et potest dupliciter responderi. Uno modo ex parte ipsius exemplaris. Quod quidem si sic sit unum quod unitas sit essentia eius, necesse est exemplatum etiam imitari exemplar in sua unitate. Et tale est primum exemplar separatum: unde et mundum, qui est primum exemplatum, necesse est esse unum: et secundum hoc procedit probatio Platonis. Si vero unitas non sit essentia exemplaris, sed sit praeter essentiam eius, sic exemplatum poterit assimilari exemplari in eo quod pertinet ad eius speciem, puta in ratione hominis vel equi, non autem quantum ad ipsam unitatem: et hoc modo procedit hic ratio Aristotelis. But two answers can be given to this. First on the part of the exemplar, which, if it is one in such a way that oneness is its essence, then the copy must imitate the exemplar in this oneness. But the first separated exemplar is such. Hence also the world, which is the first copy thereof, must be one. This was the way Plato proceeded in his proof. But if oneness is not of the essence of the exemplar but is outside its essence, then the copy could be like the exemplar in respect to what belongs to its species — for example, in the notion of man or horse — but not in respect to oneness. And it is in this way that Aristotle's reasoning proceeds. Alio modo potest solvi ex parte exemplati, quod tanto est perfectius, quanto magis assimilatur exemplari. Alia ergo exemplata assimilantur exemplari uni secundum unitatem speciei, non secundum unitatem numeralem: sed caelum, quod est perfectum exemplatum, assimilatur suo exemplari secundum unitatem numeralem. Or it can be answered from the viewpoint of the copy, which is more perfect to the extent that it is more faithful to the exemplar. Therefore, some copies are like one exemplar in respect to oneness of species, but not in respect to numerical oneness. But the heaven, which is a perfect copy, is like its exemplar with respect to numerical oneness. Deinde cum dicit: considerandum autem iterum etc., solvit obiectionem praedictam. 194. Then at [134] he solves this objection: Et primo ponit solutionem;
secundo manifestat eam, ibi: sic autem forte et cetera.
First he gives the solution;
Secondly, he explains it, at 195.
Dicit ergo primo quod oportet iterum, ad solvendum dubitationem praedictam, considerare quid dicatur bene et quid non bene: si enim omnia praemissa sint vera, necesse est conclusionem esse veram. Dicit igitur quod bene dictum est quod altera sit ratio formae, ea scilicet quae est sine materia, et ea quae est cum materia, He says therefore first that in order to settle the above doubt we must once more consider what was said well and what not well. For if all the premises are true, the conclusion is necessarily true. He says, therefore, that it was correct to say that the notion of form differs, namely, in the case of that which is without matter and in the case of that which is with matter. et hoc concedatur tanquam verum; et sic concedatur conclusio primi syllogismi, quae est minor secundi. Sed non sequitur ex necessitate propter hoc quod sint multi mundi, vel quod possint esse plures, si verum sit quod iste mundus sit ex tota sua materia, sicuti est verum, ut infra probabitur: maior enim propositio secundi syllogismi, scilicet quod illa quae habent formam in materia possunt esse multa numero unius speciei, non habet veritatem nisi in illis quae non constant ex tota sua materia. This is to be granted as true. Consequently, the first conclusion which is the minor of the second syllogism is conceded. But from this it does not follow of necessity either that there are several worlds, or that there can be several, if it is true that this world consists of all its matter, as is true and as will be proved below. For the major proposition of the second syllogism, namely, that things which have a form in matter can be numerically many in one species, is not true except in things that do not consist of their entire matter. Deinde cum dicit: sic autem forte etc., manifestat quod dixerat per exemplum. 195. Then at [135] he explains what he had said with an example. Et primo ponit exempla;
secundo adaptat ad propositum, ibi: caelum autem est quidem singularium et cetera.
First he gives the examples;
Secondly, he adapts them to his proposition, at 196.
Dicit ergo primo quod per ea quae dicentur, magis fiet manifestum quod dictum est. Simitas enim est curvitas in naso aut in carne; et ita caro est materia simitatis. Si ergo ex omnibus carnibus fieret una caro, scilicet unius nasi, et in hac esset simitas, nihil aliud esset simum, neque posset esse. Et eadem ratio est de homine, cum carnes et ossa sint materia hominis, si ex omnibus carnibus et ossibus fieret unus homo, ita scilicet quod nullo modo possent dissolvi, non posset esse aliquis alius homo quam unus (si vero possent dissolvi, possibile esset, illo homine corrupto, alium hominem esse; sicut dissoluta arca, ex eisdem lignis fit alia arca). Et ita etiam est in aliis. Et huius rationem assignat, quia nihil eorum quorum forma est in materia, potest fieri, si non adsit propria materia; sicut domus non posset fieri si non sint lapides et ligna. Et ita, si non sint aliae carnes et ossa praeter ea ex quibus componitur unus homo, non poterit fieri alius homo praeter illum. He says therefore first [135] that what has been said will become clearer from what will be said. For snub-nosedness is curvature in a nose or in flesh; thus flesh is the matter of snub-nosedness. If then from all flesh one flesh were to be made, namely, the flesh of one nose, and snub-nosedness existed in it, nothing else would be snub-nosed nor could be. And the same holds for man, since flesh and bones are the matter of man: if one man were formed from all the flesh and all the bones, so that he could now not be destroyed, there could be no more than one man — but if he could be destroyed, it would be possible, after his corruption, for another man to exist, just as when a box is destroyed, another can be made from the same wood. And the same is true for other things. And the reason for this he assigns, namely, that none of the things whose form is in matter can come into being if the proper matter is not at hand, any more than a house could be made if there were not stones and wood. Consequently, if there were no bones and flesh other than those of which the one man is composed, no other man could come into being but him. Deinde cum dicit: caelum autem est quidem singularium etc., adaptat ad propositum. Et dicit verum esse caelum esse de numero singularium, et eorum quae ex materia constituuntur: non tamen est ex parte suae materiae, sed ex tota sua materia. Et ideo, quamvis sit alia ratio caeli et huius caeli, non tamen est aut potest esse aliud caelum, propter hoc quod tota materia caeli comprehensa est sub hoc caelo. 196. Then at [136] he adapts this to his proposition. And he says it is true that the heaven is a singular thing and one constituted of matter. But it is not constituted out of part of its matter, but out of all of it. And therefore, although there is a difference between the notions of "heaven" and "this heaven," there neither is, nor can be, another heaven, due to the fact that all the matter of heaven is comprehended under this heaven. Sciendum est autem quod quidam aliis modis probant possibile esse plures caelos. Uno modo sic. Mundus factus est a Deo; sed potentia Dei, cum sit infinita, non determinatur ad istum solum mundum; ergo non est rationabile quod non possit facere etiam alios mundos. 197. However, it should be realized that some prove the possibility of many worlds in other ways. In one way, as follows: The world was made by God; but the power of God, since it is infinite, is not limited to this world alone. Therefore it is not reasonable to say that He cannot make yet other worlds. Et ad hoc dicendum est quod, si Deus faceret alios mundos, aut faceret eos similes huic mundo, aut dissimiles. Si omnino similes, essent frustra: quod non competit sapientiae ipsius. Si autem dissimiles, nullus eorum comprehenderet in se omnem naturam corporis sensibilis: et ita nullus eorum esset perfectus, sed ex omnibus constitueretur unus mundus perfectus. To this it must be said that if God were to make other worlds, He would make them either like or unlike this world. If entirely alike, they would be in vain — and that conflicts with His wisdom. If unlike, none of them would comprehend in itself every nature of sensible body; consequently no one of them would be perfect, but one perfect world would result from all of them. Alio modo potest argui sic. Quanto aliquid est nobilius, tanto eius species est magis virtuosa; mundus autem est nobilior qualibet re naturali hic existente; cum igitur species rei naturalis hic existentis, puta equi aut bovis, possit perficere plura individua, multo magis species totius mundi potest plura individua perficere. In another way, as follows: To the extent that something is more noble, to that extent is its species more powerful. But the world is nobler than any natural thing existing here. Therefore, since the species of a natural thing existing here, for example, of a horse or cow, could perfect many individuals, much more so can the species of the whole world perfect many individuals. Sed ad hoc dicendum est quod maioris virtutis est facere unum perfectum, quam facere multa imperfecta. Singula autem individua rerum naturalium quae sunt hic, sunt imperfecta; quia nullum eorum comprehendit in se totum quod pertinet ad suam speciem. Sed mundus hoc modo perfectus est: unde ex hoc ipso eius species ostenditur magis virtuosa. But to this it must be answered that it takes more power to make one perfect than to make several imperfect. Now the single individuals of natural things which exist here are imperfect, because no one of them comprehends within itself the total of what, pertains to its species. But it is in this way that the world is perfect; hence, from that very fact its species is shown to be more powerful. Tertio obiicitur sic. Melius est multiplicari optima, quam ea quae sunt minus bona; sed mundus est optimus; ergo melius est esse plures mundos, quam plura animalia aut plures plantas. Thirdly, one objects thus: It is better for the best to be multiplied than for things not so good. But the world is the best. Therefore, it is better to have many worlds than many animals or many plants. Et ad hoc dicendum quod hoc ipsum pertinet ad bonitatem mundi, quod sit unus; quia unum habet rationem boni: videmus enim quod per divisionem aliqua decidunt a propria bonitate. To this it must be said that here it pertains to the goodness of the world to be one, because oneness possesses the aspect of goodness. For we see that through being divided some things lose their proper goodness.
Lecture 20:
The universe shown to consist of every natural and sensible body as its matterChapter 9 cont. Λείπεται ἄρα αὐτὸ τοῦτο δεῖξαι, ὅτι ἐξ ἅπαντος τοῦ φυσικοῦ καὶ τοῦ αἰσθητοῦ συνέστηκε σώματος. Εἴπωμεν δὲ πρῶτον τί λέγομεν εἶναι τὸν οὐρανὸν καὶ ποσαχῶς, ἵνα μᾶλλον ἡμῖν δῆλον γένηται τὸ ζητούμενον. 137 It remains, then, only to prove that it is composed of all natural perceptible body. First, however, we must explain what we mean by 'heaven' and in how many senses we use the word, in order to make clearer the object of our inquiry. Ἕνα μὲν οὖν τρόπον οὐρανὸν λέγομεν τὴν οὐσίαν τὴν τῆς ἐσχάτης τοῦ παντὸς περιφορᾶς, ἢ σῶμα φυσικὸν τὸ ἐν τῇ ἐσχάτῃ περιφορᾷ τοῦ παντός εἰώθαμεν γὰρ τὸ ἔσχατον καὶ τὸ ἄνω μάλιστα καλεῖν οὐρανόν, ἐν ᾧ καὶ τὸ θεῖον πᾶν ἱδρῦσθαί φαμεν. Ἄλλον δ' αὖ τρόπον τὸ συνεχὲς σῶμα τῇ ἐσχάτῃ περιφορᾷ τοῦ παντός, ἐν ᾧ σελήνη καὶ ἥλιος καὶ ἔνια τῶν ἄστρων καὶ γὰρ ταῦτα ἐν τῷ οὐρανῷ εἶναί φαμεν. Ἔτι δ' ἄλλως λέγομεν οὐρανὸν τὸ περιεχόμενον σῶμα ὑπὸ τῆς ἐσχάτης περιφορᾶς τὸ γὰρ ὅλον καὶ τὸ πᾶν εἰώθαμεν λέγειν οὐρανόν. 138 (a) In one sense, then, we call 'heaven' the substance of the extreme circumference of the whole, or that natural body whose place is at the extreme circumference. We recognize habitually a special right to the name 'heaven' in the extremity or upper region, which we take to be the seat of all that is divine. (b) In another sense, we use this name for the body continuous with the extreme circumference which contains the moon, the sun, and some of the stars; these we say are 'in the heaven'. (c) In yet another sense we give the name to all bodies included within extreme circumference, since we habitually call the whole or totality 'the heaven'. Τριχῶς δὴ λεγομένου τοῦ οὐρανοῦ, τὸ ὅλον τὸ ὑπὸ τῆς ἐσχάτης περιεχόμενον περιφορᾶς ἐξ ἅπαντος ἀνάγκη συνεστάναι τοῦ φυσικοῦ καὶ τοῦ αἰσθητοῦ σώματος διὰ τὸ μήτ' εἶναι μηδὲν ἔξω σῶμα τοῦ οὐρανοῦ μήτ' ἐνδέχεσθαι γενέσθαι. 139 The word, then, is used in three senses. Now the whole included within the extreme circumference must be composed of all physical and sensible body, because there neither is, nor can come into being, any body outside the heaven. Εἰ γὰρ ἔστιν ἔξω τῆς ἐσχάτης περιφορᾶς σῶμα φυσικόν, ἀνάγκη αὐτὸ ἤτοι τῶν ἁπλῶν εἶναι σωμάτων ἢ τῶν συνθέτων, καὶ ἢ κατὰ φύσιν ἢ παρὰ φύσιν ἔχειν. 140 For if there is a natural body outside the extreme circumference it must be either a simple or a composite body, and its position must be either natural or unnatural. Τῶν μὲν οὖν ἁπλῶν οὐθὲν ἂν εἴη. Τὸ μὲν γὰρ κύκλῳ φερόμενον δέδεικται ὅτι οὐκ ἐνδέχεται μεταλλάξαι τὸν αὑτοῦ τόπον. Ἀλλὰ μὴν οὐδὲ τὸ ἀπὸ τοῦ μέσου δυνατόν, οὐδὲ τὸ ὑφιστάμενον. Κατὰ φύσιν μὲν γὰρ οὐκ ἂν εἴησαν (ἄλλοι γὰρ αὐτῶν οἰκεῖοι τόποι), 141 But it cannot be any of the simple bodies. For, first, it has been shown that that which moves in a circle cannot change its place. And, secondly, it cannot be that which moves from the centre or that which lies lowest. Naturally they could not be there, since their proper places are elsewhere; παρὰ φύσιν δ' εἴπερ εἰσίν, ἄλλῳ τινὶ ἔσται κατὰ φύσιν ὁ ἔξω τόπος τὸν γὰρ τούτῳ παρὰ φύσιν ἀναγκαῖον ἄλλῳ εἶναι κατὰ φύσιν. Ἀλλ' οὐκ ἦν ἄλλο σῶμα παρὰ ταῦτα. 142 and if these are there unnaturally, the exterior place will be natural to some other body, since a place which is unnatural to one body must be natural to another: but we saw that there is no other body besides these. Then it is not possible that any simple body should be outside the heaven. Οὐκ ἄρ' ἐστὶ δυνατὸν οὐθὲν τῶν ἁπλῶν ἔξω εἶναι τοῦ (279a.) οὐρανοῦ σῶμα. Εἰ δὲ μὴ τῶν ἁπλῶν, οὐδὲ τῶν μικτῶν ἀνάγκη γὰρ εἶναι καὶ τὰ ἁπλᾶ τοῦ μικτοῦ ὄντος. 143 But, if no simple body, neither can any mixed body be there: for the presence of the simple body is involved in the presence of the mixture. Ἀλλὰ μὴν οὐδὲ γενέσθαι δυνατόν ἤτοι γὰρ κατὰ φύσιν ἔσται ἢ παρὰ φύσιν, καὶ ἢ ἁπλοῦν ἢ μικτόν. Ὥστε πάλιν ὁ αὐτὸς ἥξει λόγος οὐδὲν γὰρ διαφέρει σκοπεῖν εἰ ἔστιν ἢ εἰ γενέσθαι δυνατόν. 144 Further neither can any body come into that place: for it will do so either naturally or unnaturally, and will be either simple or composite; so that the same argument will apply, since it makes no difference whether the question is 'does A exist?' or 'could A come to exist?' Φανερὸν τοίνυν ἐκ τῶν εἰρημένων ὅτι οὔτ' ἔστιν ἔξω οὔτ' ἐγχωρεῖ γενέσθαι σώματος ὄγκον οὐθενός ἐξ ἁπάσης ἄρ' ἐστὶ τῆς οἰκείας ὕλης ὁ πᾶς κόσμος ὕλη γὰρ ἦν αὐτῷ τὸ φυσικὸν σῶμα καὶ αἰσθητόν. Ὥστ' οὔτε νῦν εἰσὶ πλείους οὐρανοὶ οὔτ' ἐγένοντο, οὔτ' ἐνδέχεται γενέσθαι πλείους ἀλλ' εἷς καὶ μόνος καὶ τέλειος οὗτος οὐρανός ἐστιν. 145 From our arguments then it is evident not only that there is not, but also that there could never come to be, any bodily mass whatever outside the circumference. The world as a whole, therefore, includes all its appropriate matter, which is, as we saw, natural perceptible body. So that neither are there now, nor have there ever been, nor can there ever be formed more heavens than one, but this heaven of ours is one and unique and complete.
Posita solutione inducta, hic philosophus probat quod supposuerat, scilicet quod mundus constet ex tota sua materia. 198. Having presented the solution brought forward, the Philosopher here proves what he had presupposed, namely, that the world consists of all its matter. Et primo dicit de quo est intentio, et quo ordine sit procedendum: dicens quod hoc ipsum restat ostendere ad complementum praemissae solutionis, quod mundus constet ex omni corpore naturali et sensibili, quod est materia eius. Sed antequam hoc ostendamus, oportet primo dicere quid significetur per hoc nomen caelum, et quot modis dicatur, ut illud quod quaeritur magis possit manifestari. First he tells his intention and order of procedure [137] and says that in order to complete the preceding solution, we must show that the world consists of every natural and sensible body, which is its matter. But before showing this, it is necessary to explain what is meant by this word "heaven," and in how many senses it is used, so that our question can be answered more clearly. Secundo ibi: uno quidem igitur modo etc., exequitur propositum: 199. Secondly he proves his proposition: et primo ostendit quot modis dicatur caelum;
secundo ostendit principale propositum, ibi: tripliciter autem et cetera.
First he shows the various senses of the word "heaven";
Secondly, he proves the main proposition, at 200.
Circa primum ponit tres significationes caeli. Uno enim modo dicitur caelum substantia quaedam quae est extremae circulationis totius, idest quae in toto universo est extrema, et circulariter movetur. Et quia exposuerat significationem nominis per substantiam, cuius ratio transcendit considerationem naturalem, cum pertineat ad considerationem metaphysici, adhibet aliam expositionem, in eadem tamen significatione, dicens quod caelum est corpus naturale quod est in extrema circumferentia totius: et haec expositio est magis propria scientiae naturali. With regard to the first [138] he gives three senses of heaven. In one way the heaven is called "the substance of the extreme circulation of the whole," i.e., that which is at the boundary of the whole universe and is moved circularly. And because he had explained the meaning of the word in terms of "substance," whose notion transcends natural philosophy, since it pertains to Metaphysics, he adds another explanation having the same meaning, saying that the heaven is "the natural body whose place is at the extreme circumference of the world," which explanation is more befitting to natural science. Probat autem hanc significationem ex consuetudine loquendi: quia nominibus est utendum ut plures, sicut dicitur in II Topic. Consueverunt enim homines vocare caelum illud quod est extremum totius mundi, et quod maxime est sursum: non quidem secundum quod sursum accipitur in scientia naturali, prout scilicet est terminus motus levium (sic enim nihil magis est sursum quam locus in quem fertur ignis): sed sumitur hic sursum secundum communem modum loquendi, prout id quod est remotius a medio, vocatur sursum. Consuevit etiam vocari sursum id quod est locus omnium divinorum (ut tamen divina non dicantur hic corpora caelestia, quae non omnia sunt in suprema sphaera; sed secundum quod divina dicuntur substantiae immateriales et incorporeae): dictum est enim supra quod omnes homines locum qui est sursum attribuunt Deo. He proves this meaning from the way people speak — since words are to be used in the sense most people use them, as is said in Topics II. For men are more likely to call "heaven" that which is the extreme of the entire world and which is most up, not, indeed, as "up" is taken in natural science, i.e., as being the terminus of the motion of light things (for in this sense nothing is farther "up" than the place to which fire is borne) but as taken according to common parlance, where "up" designates that which is farther from the middle. "Up" also refers to the place of all divine beings (where "divine" signifies not celestial bodies — not all of which are in the outermost sphere — but non-material and incorporeal substances), for it has been said above that all men attribute to God a place that is up. Secundo modo dicitur caelum non solum suprema sphaera, sed totum corpus quod continuatur cum extrema circumferentia totius universi, idest omnes sphaerae caelestium corporum, in quibus sunt luna et sol et quaedam stellarum, scilicet alii quinque planetae (nam stellae fixae sunt in suprema sphaera secundum opinionem Aristotelis, qui non posuit aliam sphaeram esse supra sphaeram stellarum fixarum). In a second way "heaven" means not only the outermost sphere but "the whole body continuous with the extreme circumference of the whole universe," i.e., all the spheres of celestial bodies, in which exist the moon and sun and certain of the stars, namely, the other five planets (for the fixed stars are in the supreme sphere according to the opinion of Aristotle, who did not posit another sphere above that of the fixed stars). Et hanc etiam significationem probat per communem usum loquendi: dicimus enim solem et lunam et alios planetas esse in caelo. Dicuntur autem haec corpora continuari cum suprema sphaera, propter convenientiam in natura, quia scilicet sunt incorruptibilia et circulariter mobilia; non autem ita quod ex omnibus sit unum corpus continuum; quia sic eorum non possent esse plures et diversi motus; continuum est enim cuius motus est unus, ut dicitur in V Metaphys. And he proves this meaning also on the basis of common parlance: for we say that the sun and moon and other planets exist in the heaven. Now these bodies are said to be continuous with the extreme sphere, because they are alike in nature, i.e., they are imperishable and movable circularly, and not because one continuous body is formed from all of them — for then they could not have several and different motions, a continuum being something whose motion is one, as is said in Metaphysics V. Tertio modo dicitur caelum totum corpus quod continetur ab extrema circumferentia, idest a suprema sphaera. Et hoc etiam probat ex usu loquendi: quia consuevimus totum mundum et omne, idest universum, vocare caelum. In a third way "heaven" means "the whole body contained within the extreme circumference," i.e., by the extreme sphere. This, too, he proves from the common use of the word — since we are wont to call the whole world and the totality, i.e., the universe, the "heaven." Est autem considerandum quod caelum his tribus modis dicitur non aequivoce, sed analogice, scilicet per respectum ad unum primum: primo enim et principaliter dicitur caelum suprema sphaera; secundo autem aliae sphaerae caelestes, ex continuitate quam habent ad supremam sphaeram; tertio modo universitas corporum, secundum quod continetur ab extrema sphaera. It should be noted that "heaven" is here used in these three ways not equivocally but analogically, i.e., in relation to one first. For it is the supreme sphere that is first and principally called "heaven"; secondly, the other celestial spheres from the continuity they have with the supreme sphere; thirdly, the universe of bodies insofar as they are contained by the extreme sphere. Deinde cum dicit: tripliciter autem etc., ostendit propositum. 200. Then at [139] he proves the proposition. Et primo ostendit quod non est aliquod corpus sensibile extra caelum tertio modo dictum, idest extra hunc mundum;
secundo ostendit quod non est extra ipsum aliquid eorum quae consequuntur ad corpora naturalia, ibi: simul autem manifestum et cetera.
First he shows that there is no sensible body outside the heaven taken in the third sense, i.e., outside this world;
Secondly, he shows that there is not outside it any of the things that are normally consequent upon natural bodies (L. 21).
Circa primum tria facit: As to the first he does three things: primo proponit quod intendit;
secundo probat propositum, ibi: si enim est etc.;
tertio concludit principale intentum, ibi: manifestum igitur ex dictis et cetera.
First he proposes what he intends;
Secondly, he proves his proposition, at 201;
Thirdly, he concludes to his main proposition, at 206.
Dicit ergo primo quod, cum tripliciter dicatur caelum, nunc intendimus de caelo tertio modo dicto, secundum quod caelum dicitur totum quod continetur ab extrema circumferentia: et hoc caelum necesse est quod constet ex omni corpore sensibili et naturali (quod est eius materia: et sic constat ex tota sua materia), propter hoc quod extra hoc caelum nullum corpus est, nec contingit esse. He says therefore first [139] that whereas "heaven" is said in three ways, we shall be discussing it now in its third sense, where heaven is taken as "the whole contained by the extreme circumference." Concerning this heaven it is necessary that it consist of every sensible and natural body — which is its matter, and thus it consists of all its matter — due to the fact that outside this heaven no body exists, nor can exist. Deinde cum dicit: si enim est etc., probat propositum. 201. Then at [140] he proves the proposition. Et primo ostendit quod nullum corpus est extra caelum;
secundo quod nullum potest ibi esse, ibi: sed et neque factum esse et cetera.
First he shows that there is no body outside the heaven;
Secondly, that none can be there, at 205.
Circa primum duo facit: About the first he does two things: primo praemittit quandam divisionem, per quam manifestat propositum;
secundo excludit singula membra divisionis, ibi: simplicium quidem igitur et cetera.
First he presents a division through which he manifests the proposition;
Secondly, he excludes each member of the division, at 202.
Dicit ergo primo quod, si est aliquod corpus physicum, idest naturale, extra extremam peripheriam, idest circumferentiam, necesse est quod illud corpus aut sit de numero simplicium corporum, aut de numero compositorum. Item necesse est quod vel sit ibi secundum naturam, vel praeter naturam. He says therefore first [140] that if there is a Physica l, i.e., natural, body outside the extreme periphery, i.e., circumference, it has to be either of the number of simple bodies, or of the number of composite bodies. Moreover, it must exist there according to nature, or outside its nature. Deinde cum dicit: simplicium quidem igitur etc., excludit singula membra praedictae divisionis. 202. Then at [141] he eliminates each member of this division. Et primo ostendit quod extra extremam sphaeram non est aliquod corpus simplex secundum naturam. Corporum enim simplicium quoddam est circulariter motum; quoddam est quod movetur a medio; quoddam quod movetur ad medium, et in medio subsistit omnibus aliis, ut supra habitum est. Nullum autem horum potest esse extra extremam circumferentiam. Ostensum est enim supra in VI Physic. quod corpus quod circulariter fertur, non permutat proprium locum secundum totum, nisi solum ratione. Sic igitur non est possibile quod corpus quod circulariter fertur, transferatur ad aliquem locum extra eum in quo est. Hoc autem sequeretur si esset aliquod corpus circulariter motum extra extremam circumferentiam, sicut in suo loco naturali. Quia per quam rationem esset naturalis illi corpori circulariter moto, per eandem rationem esset naturalis huic corpori quod in hoc mundo circulariter fertur; omne autem corpus naturaliter fertur ad suum locum naturalem; sequeretur ergo quod istud corpus circulariter motum transferretur extra suum locum ad alium locum, quod est impossibile. First he shows that outside the extreme sphere no simple body exists according to nature. For simple bodies are such that one is moved circularly, one from the middle, and one is moved to the middle and in the middle supports all the others, as was had above. But none of these bodies can exist outside the extreme circumference. For it has been shown above in Physics VI that the circularly moved body does not as to its whole being change its place except in conception. Consequently, it is not possible for that body which is moved circularly to be transferred to a place outside of that in which it exists. But this would follow, if there were a circularly moved body existing outside the extreme circumference as in its natural place. Since the reason that it would be natural to that circularly moved body would also make it natural to the body circularly moved in this world, and every body is naturally borne to its natural place, it would follow, therefore, that that latter circularly moved body would be transferred outside its proper place to another place — which is impossible. Similiter etiam non est possibile esse extra extremam circumferentiam corpus leve, quod movetur a medio, neque etiam corpus grave, quod substat aliis corporibus in medio. Si enim dicatur quod sint extra extremam circumferentiam naturaliter, hoc esse non potest, quia habent alia loca naturalia, scilicet infra extremam circumferentiam totius; ostensum est autem supra quod omnium gravium est unus numero locus, et similiter omnium levium. Unde non est possibile quod ista corpora sint naturaliter extra extremam circumferentiam totius. Similarly it is not possible for a light body which is moved from the center to be outside the extreme circumference or for a heavy body which supports the other bodies in the center. For if it is maintained that they exist naturally outside the extreme circumference, such a thing cannot be, since they have other natural places, namely, within the extreme circumference of the whole. For it was shown above that there is one numerical place for all heavy bodies and one for all light bodies. Hence it is not possible that those bodies be naturally outside the extreme circumference of the whole. Et est considerandum quod ista ratio, et quantum ad corpus circulariter motum, et quantum ad corpus quod movetur motu recto, habet necessitatem ex eo quod supra probatum est, quod est tantum unum extremum et unum medium. And it should be noted that this argument, both as to the body circularly moved, and as to the body moved with straight motion, possesses necessity on account of what was proved above, namely, that there is but one extreme and one middle. Secundo ibi: praeter naturam autem etc., ostendit quod nullum corpus simplex est extra caelum praeter naturam. Si enim esset ibi praeter naturam, ille locus alicui corpori esset naturalis: locus enim qui est uni corpori praeter naturam, necesse est quod sit alii corpori secundum naturam: quia si alicui loco deesset proprium corpus, locus ille esset frustra. Sed non potest esse quod ille locus sit naturalis alicui corpori: non enim est naturalis neque corpori circulariter moto, neque corpori levi aut gravi; ostensum est autem supra quod nullum aliud corpus est praeter ista. Sic igitur patet quod nullum corpus simplex est extra caelum, neque secundum naturam neque praeter naturam. 203. Secondly, at [142] he shows that no simple body is outside the heaven outside its nature. For if it were there in that manner that place would be natural to some other body; for a place outside nature for one body must be according to nature for some other — if a proper body were lacking to a place, that place would exist in vain. But it cannot be said that that place is natural to any body: for it is not natural to a circularly moved body, nor to a light or heavy body. But it has been shown above that there are no other bodies besides these. Consequently, it is plain that no simple body exists outside the heaven, either according to nature or outside nature. Tertio ibi: si autem non simplicium etc., probat quod non est ibi aliquod corpus mixtum. Quia si non est ibi aliquod simplicium corporum, sequitur quod non sit ibi etiam aliquod corpus mixtum: ubicumque enim est corpus mixtum, necesse est ibi esse corpora simplicia, eo quod corpora simplicia sunt in mixto; et mixtum sortitur locum naturalem secundum corpus simplex quod in eo dominatur. 204. Thirdly, at [143] he proves that there is no mixed body there. For if none of the simple bodies exists there, it follows that no mixed body is. Wherever there is a mixed body, simple bodies must be there, due to the fact that simple bodies are present in the mixed; and a mixed body gets its natural place according to the simple body predominant in it. Deinde cum dicit: sed et neque factum esse etc., ostendit quod etiam extra caelum non contingit esse aliquod corpus. Unde dicit quod non est possibile fieri aliquod corpus extra caelum. Quia aut esset ibi secundum naturam aut praeter naturam, et iterum aut esset simplex aut mixtum; et quidquid horum detur, erit eadem ratio quae est supra: quia non differt secundum rationes praemissas an sit aliquod corpus extra caelum, vel possit ibi fieri; quia rationes praemissae utrumque concludunt, et quia in sempiternis non differt esse et posse, ut dicitur in III Physic. 205. Then at [144] he shows that outside the heaven there cannot be any body. Hence he says that it is not possible for a body to come to be outside the heaven. For it would be there either according to nature or outside nature; again, it would be either simple or mixed. But no matter which of these is given, the same situation as above would prevail. For according to the above-stated reasons, it makes no difference whether the question concerns the existence of a body outside the heaven, or the possibility of its coming to be there, since the foregoing arguments conclude both, and since in sempiternal things to be and to be able to be do not differ, as is said in Physics III. Deinde cum dicit: manifestum igitur ex dictis etc., concludit conclusionem principaliter intentam. Et dicit manifestum esse ex dictis quod extra caelum neque est aliqua moles cuiuscumque corporis, neque contingit ibi tale aliquid fieri: quia totus mundus est ex tota materia sua propria, materia autem mundi est corpus naturale sensibile. 206. Then at [145] he draws the conclusion mainly intended. And he says it is manifest from what has been said that outside the heaven no mass of any sort of body exists, nor can exist, since the whole world consists of its entire proper matter and the matter of the world is the sensible natural body. Nec est intelligendum quod velit probare nullum corpus sensibile esse extra caelum, propter hoc quod est ex tota sua materia; sed potius e converso. Utitur autem illo modo loquendi propter hoc quod ista duo invicem convertuntur. However, it should be not understood that he wishes to prove that no sensible body exists outside the heaven on the ground that it consists of the totality of its matter; but rather the converse. Nevertheless, he uses that manner of speaking because the two are mutually convertible. Concludit igitur quod neque sunt in praesenti plures caeli, neque fuerunt in praeterito, neque unquam poterunt fieri in futuro: sed istud caelum est unum et solum et perfectum, utpote constans ex omnibus suis partibus, sive ex tota sua materia. He concludes, therefore, that there are not many worlds at present, nor were there many in the past, nor will there ever be able to be in the future. Rather the heaven is one and unique and perfect in the sense of consisting of all its parts or of its total matter.
Lecture 21:
Outside the heaven there is no place, time etc., consequent upon sensible bodies.Chapter 9 cont. Ἅμα δὲ δῆλον ὅτι οὐδὲ τόπος οὐδὲ κενὸν οὐδὲ χρόνος ἐστὶν ἔξω τοῦ οὐρανοῦ. 146 It is therefore evident that there is also no place or void or time outside the heaven. Ἐν ἅπαντι γὰρ τόπῳ δυνατὸν ὑπάρξαι σῶμα 147 For in every place body can be present; κενὸν δ' εἶναί φασιν ἐν ᾧ μὴ ἐνυπάρχει σῶμα, δυνατὸν δ' ἐστὶ γενέσθαι 148 and void is said to be that in which the presence of body, though not actual, is possible; χρόνος δὲ ἀριθμὸς κινήσεως κίνησις δ' ἄνευ φυσικοῦ σώματος οὐκ ἔστιν. Ἔξω δὲ τοῦ οὐρανοῦ δέδεικται ὅτι οὔτ' ἔστιν οὔτ' ἐνδέχεται γενέσθαι σῶμα. 149 and time is the number of movement. But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. Φανερὸν ἄρα ὅτι οὔτε τόπος οὔτε κενὸν οὔτε χρόνος ἐστὶν ἔξω. 150 It is clear then that there is neither place, nor void, nor time, outside the heaven. Διόπερ οὔτ' ἐν τόπῳ τἀκεῖ πέφυκεν, οὔτε χρόνος αὐτὰ ποιεῖ γηράσκειν, οὐδ' ἐστὶν οὐδενὸς οὐδεμία μεταβολὴ τῶν ὑπὲρ τὴν ἐξωτάτω τεταγμένων φοράν, 151 Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor is there any change in any of the things which lie beyond the outermost motion; ἀλλ' ἀναλλοίωτα καὶ ἀπαθῆ τὴν ἀρίστην ἔχοντα ζωὴν καὶ τὴν αὐταρκεστάτην διατελεῖ τὸν ἅπαντα αἰῶνα. 152 they continue through their entire duration unalterable and unmodified, living the best and most selfsufficient of lives. (Καὶ γὰρ τοῦτο τοὔνομα θείως ἔφθεγκται παρὰ τῶν ἀρχαίων. Τὸ γὰρ τέλος τὸ περιέχον τὸν τῆς ἑκάστου ζωῆς χρόνον, οὗ μηθὲν ἔξω κατὰ φύσιν, αἰὼν ἑκάστου κέκληται. Κατὰ τὸν αὐτὸν δὲ λόγον καὶ τὸ τοῦ παντὸς οὐρανοῦ τέλος καὶ τὸ τὸν πάντα χρόνον καὶ τὴν ἀπειρίαν περιέχον τέλος αἰών ἐστιν, ἀπὸ τοῦ αἰεὶ εἶναι τὴν ἐπωνυμίαν εἰληφώς, ἀθάνατος καὶ θεῖος). 153 As a matter of fact, this word 'duration' possessed a divine significance for the ancients, for the fulfilment which includes the period of life of any creature, outside of which no natural development can fall, has been called its duration. On the same principle the fulfilment of the whole heaven, the fulfilment which includes all time and infinity, is 'duration'—a name based upon the fact that it is always—duration immortal and divine. Ὅθεν καὶ τοῖς ἄλλοις ἐξήρτηται, τοῖς μὲν ἀκριβέστερον τοῖς δ' ἀμαυρῶς, τὸ εἶναί τε καὶ ζῆν. 154 From it derive the being and life which other things, some more or less articulately but others feebly, enjoy. Καὶ γάρ, καθάπερ ἐν τοῖς ἐγκυκλίοις φιλοσοφήμασι περὶ τὰ θεῖα, πολλάκις προφαίνεται τοῖς λόγοις ὅτι τὸ θεῖον ἀμετάβλητον ἀναγκαῖον εἶναι πᾶν τὸ πρῶτον καὶ ἀκρότατον ὃ οὕτως ἔχον μαρτυρεῖ τοῖς εἰρημένοις. 155 So, too, in its discussions concerning the divine, popular philosophy often propounds the view that whatever is divine, whatever is primary and supreme, is necessarily unchangeable. This fact confirms what we have said. Οὔτε γὰρ ἄλλο κρεῖττόν ἐστιν ὅ τι κινήσει (ἐκεῖνο γὰρ ἂν εἴη θειότερον) 156 For there is nothing else stronger than it to move it—since that would mean more divine— οὔτ' ἔχει φαῦλον οὐδέν, οὔτ' ἐνδεὲς τῶν αὑτοῦ καλῶν οὐδενός ἐστιν. 157 and it has no defect and lacks none of its proper excellences. (279b.) Καὶ ἄπαυστον δὴ κίνησιν κινεῖται εὐλόγως πάντα γὰρ παύεται κινούμενα ὅταν ἔλθῃ εἰς τὸν οἰκεῖον τόπον, τοῦ δὲ κύκλῳ σώματος ὁ αὐτὸς τόπος ὅθεν ἤρξατο καὶ εἰς ὃν τελευτᾷ. 158 Its unceasing movement, then, is also reasonable, since everything ceases to move when it comes to its proper place, but the body whose path is the circle has one and the same place for starting-point and goal.
Postquam philosophus ostendit quod extra caelum non est aliquod corpus sensibile, nec potest esse, hic ostendit quod extra caelum non est aliquod eorum quae consequuntur ad corpora sensibilia. After showing that there neither is, nor can be, any sensible body outside the heaven, the Philosopher here shows that outside the heaven there is none of the things that follow upon sensible bodies. Et primo ostendit propositum;
secundo ostendit qualia sint quae extra caelum nata sunt esse, ibi: propter quod quidem neque in loco et cetera.
First he proves the proposition;
Secondly, he describes the things that do exist outside the heaven, at 213.
Circa primum tria facit: About the first he does three things: primo proponit quod intendit;
secundo probat propositum, ibi: in omni enim loco etc.;
tertio infert conclusionem intentam, ibi: manifestum igitur et cetera.
First he proposes what he intends;
Secondly, he proves the proposition, at 208;
Thirdly, he draws the intended conclusion, at 212.
Dicit ergo primo quod simul cum hoc quod probatum est, extra caelum non esse corpus sensibile, manifestum est quod extra caelum neque est locus, neque vacuum, neque tempus: de his enim tribus determinatur in IV Physic. sicut de quibusdam consequentibus corpora naturalia. He says therefore first [146] that with the proof that outside the heaven there is no sensible body, it is also manifest that outside the heaven there is neither place nor void nor time — for these three things were discussed as being concomitants of natural bodies in Physics IV. Deinde cum dicit: in omni enim loco etc., probat propositum. 208. Then at [147] he proves the proposition. Primo quidem quantum ad locum. In omni enim loco possibile est existere corpus, alioquin locus esset frustra; sed extra caelum non est possibile existere aliquod corpus, ut probatum est; ergo extra caelum non est locus. First, as to place: In every place it is possible for a body to exist, otherwise it would be in vain. But outside the heaven it is not possible for any body to exist, as was proved. Therefore, outside the heaven there is no place.
Secundo ibi: vacuum autem etc., probat quod extra caelum non est vacuum. Illi enim qui ponunt vacuum, definiunt vacuum esse locum in quo non existit corpus, sed possibile est esse; sed extra caelum non est possibile corpus esse, ut ostensum est; ergo extra caelum non est vacuum. Secondly, at [148] he proves that outside the heaven there is not a void: Those who posit a void define it to be a place in which a body is not existing but can exist. But outside the heaven it is not possible for a body to exist, as has been shown. Therefore, outside the heaven there is not a void. Est autem sciendum quod Stoici posuerunt vacuum infinitum, in cuius quadam parte est mundus: et ita relinquitur secundum eos quod extra extremam circumferentiam sit vacuum. Quod quidem tali imaginatione probare volebant. Si enim esset aliquis in extrema circumferentia caeli, aut posset extendere manum suam extra aut non. Si non posset, ergo impediretur ab aliquo extrinseco existente; et redibit eadem quaestio de illo extrinseco, si in extremo eius aliquis existens posset ultra manum porrigere; et ita vel procedetur in infinitum, vel devenietur ad aliquod extremum corpus, ultra quod homo ibi existens posset manum porrigere. Quo dato, sequitur quod extra illud possit esse corpus et non sit; et ita extra erit vacuum. 209. But it should be noted that the Stoics posited an infinite void, in one part of which the world exists. Consequently, according to them, there is a void outside the heaven. They wanted to prove this with the following fantasy: If someone were on the extreme circumference of the heaven, he could either extend his hand beyond or not. If not, then it is being impeded by something existing beyond. The same question will return regarding that thing existing beyond, if anyone could, while on the extremity, reach out his hand beyond. Consequently we must go on infinitely, or come to an extreme body beyond which a man existing there could reach out his hand. In that case it follows that beyond that a body could exist and does not. Hence there will be a void beyond. Ad hoc autem respondet Alexander, dicens positionem esse impossibilem: cum enim corpus caeli sit impassibile, non est receptivum alicuius extranei. Unde si ex hac impossibili positione sequitur aliquod inconveniens, non est curandum. To this Alexander responds that the position is impossible. For since the body of the heaven cannot undergo anything, it cannot receive anything extraneous. Hence, if from this impossible assumption, something against the thesis follows, one should pay it no heed. Sed haec responsio non videtur esse sufficiens: quia impossibilitas huius positionis non est ex parte eius quod est extra caelum, sed ex parte ipsius caeli; nunc autem agitur de eo quod est extra caelum. Unde eadem ratio est si totum universum esset terra, in cuius extremo posset esse homo. Et ideo oportet aliter dicere, sicut ipse etiam dicit, quod manum suam extra extendere non posset homo in extrema circumferentia constitutus, non propter aliquod extrinsecum impediens, sed quia de natura omnium corporum naturalium est, quod contineantur infra extremam circumferentiam caeli; alioquin caelum non esset universum. Unde si esset aliquod corpus quod non dependeret a corpore caeli sicut a continente, illud nihil prohiberet esse extra caelum, sicut substantiae spirituales, ut infra dicetur. But this answer does not seem to be sufficient — since the impossibility of this position is not on the part of something outside the heaven but on the part of the heaven itself. But now we are dealing with what is outside the heaven. Hence it is the same argument if the whole universe were the earth, on whose boundary a man could exist. Consequently, we must state otherwise, just as he says, that a man situated on the extreme circumference could not extend his hand beyond, not because of something outside impeding it, but because it is of the very nature of all natural bodies that they be contained within the extreme circumference of the heaven — otherwise the heaven would not be the universe. Hence if there were a body not depending on the body of the heaven as on a container, there would be nothing to prevent it from existing outside the heaven, as in the case of the spiritual substances, as will be said below. Quod autem non sit vacuum extra caelum, probat Alexander quia aut illud vacuum erit finitum, aut infinitum: si finitum, oportet quod alicubi terminetur, et redibit eadem quaestio, utrum extra illud possit aliquis manum extendere; si autem sit infinitum, erit potens recipere corpus infinitum; aut ergo illa potentia vacui erit frustra, aut oportebit ponere corpus infinitum, quod possit recipi in vacuo infinito. 210. But that there is no void outside the heaven Alexander proves on the ground that such a void is either finite or infinite: If finite, then it is terminated somewhere and the same question will return: Could a person extend his hand beyond that? If it is infinite, it will be capable of receiving an infinite body: then either that power of the void will be in vain or it will be necessary to posit an infinite body capable of being received into the void of the infinite. Item, si sit vacuum extra mundum, similiter se habet mundus ad quamlibet partem vacui, quia in vacuo nulla est differentia: et ita haec pars vacui in qua est mundus, non est proprius locus eius. Nulla est ergo causa quare in hac parte vacui maneat. Si autem mundus feratur, non feretur magis ad unam partem quam ad aliam, quia in vacuo non est differentia: feretur ergo ad omnem partem; et ita mundus discerpetur. Likewise, if there is a void outside the world, the world will be related to each part of the void in exactly the same way, because in a void there are no differences. Consequently, this part of the void in which the world exists is not its proper place. Therefore there is no cause why it should remain in this part of the void. But if the world is in motion, it will not be moved to one part rather than to another, because in the void there are no differences. Therefore, it will be moved in every direction; and thus the world will be torn asunder. Tertio, ibi: est autem tempus etc. probat quod extra caelum non sit tempus. Tempus enim est numerus motus, ut patet in IV Physic.; motus autem non potest esse sine corpore naturali, corpus autem naturale nec est nec potest esse extra caelum, ut probatum est; ergo extra caelum non potest esse nec tempus nec motus. 211. Thirdly, at [149] he proves that outside the heaven there is no time. For time is the number of motion, as is plain in Physics IV. But motion cannot exist without a natural body, and a natural body neither exists nor can exist outside the heaven, as has been proved. Therefore, outside the heaven there neither is, nor can be, time. Deinde cum dicit: manifestum igitur etc., infert conclusionem intentam; concludens manifestum esse ex praedictis quod extra totum mundum nec est locus, neque vacuum, neque tempus. 212. Then at [150] he draws the conclusion intended, and concludes that it is manifest from the foregoing that outside the whole heaven there is neither place nor void nor time. Deinde cum dicit: propter quod quidem neque in loco etc., ostendit qualia sunt ea quae sunt extra mundum. Et circa hoc duo facit: 213. Then at [151] he describes what type of things are outside the heaven. About this he does two things: primo concludit ex praemissis eorum qualitatem;
secundo ostendit idem ex his quae communiter dicuntur, ibi: etenim quemadmodum in encycliis et cetera.
First he concludes their condition from the foregoing;
Secondly, he shows the same from common opinion, at 217.
Circa primum duo facit: About the first he does two things: primo removet ab eis conditionem eorum quae sunt hic;
secundo ostendit propriam conditionem eorum, ibi: sed inalterabilia et cetera.
First he removes from them the condition of things that exist here;
Secondly, he describes their proper condition, at 214.
Dicit ergo primo quod, quia extra caelum non est locus, sequitur quod ea quae ibi sunt nata esse, non sunt in loco. Et hoc quidem Alexander dicit posse intelligi de ipso caelo, quod quidem non est in loco secundum totum, sed secundum partes, ut probatur in IV Physic. He says therefore first [151] that because there is no place outside the heaven, it follows that things by nature apt to be there do not exist in place. And Alexander says that this can be understood about the heaven itself, which is not in place as a whole but with respect to its parts, as is proved in Physics IV. Et iterum, quia tempus non est extra caelum, sequitur quod non sint in tempore; et ita tempus non facit ea senescere. Quod etiam dicit Alexander posse caelo convenire, quod quidem non est in tempore, secundum quod esse in tempore est quadam parte temporis mensurari, ut dicitur in IV Physic. Et non solum talia non senescunt in tempore, sed neque est aliqua transmutatio eorum quae sunt super illam lationem quae est maxime extra ordinata, idest super motum localem corporum levium: motum enim rectum consuevit vocare lationem. Again, because time does not exist beyond the heaven, it follows that they do not exist in time; consequently, time does not make them grow old. And this, too, according to Alexander, can belong to the heaven, which, indeed, is not in time in the sense that to be in time consists in being measured by some part of time, as is said in Physics IV. Not only do such beings not grow old in time, but no change affects those things which lie "beyond the outermost motion [lationem]," i.e., beyond the local motion of light bodies — for he is accustomed to call rectilinear motion latio. Sed hoc non videtur esse verum, quod corporum caelestium non sit aliqua transmutatio, cum moveantur localiter: nisi forte exponamus de transmutatione quae est in substantia. Sed haec videtur extorta expositio, cum philosophus universaliter omnem mutationem excludat. Similiter etiam non potest dici proprie quod caelum sit ibi, idest extra caelum. Et ideo convenientius est quod hoc intelligatur de Deo et de substantiis separatis, quae manifeste neque tempore neque loco continentur, cum sint separatae ab omni magnitudine et motu. Huiusmodi autem substantiae dicuntur esse ibi, idest extra caelum, non sicut in loco, sed sicut non contenta nec inclusa sub continentia corporalium rerum, sed totam corporalem naturam excedentia. Et his convenit quod dicitur, quod eorum nulla sit transmutatio: quia superexcedunt supremam lationem, scilicet ultimae sphaerae, quae ordinatur sicut extrinseca et contentiva omnis mutationis. But it does not seem to be true that no change affects heavenly bodies, since they are moved locally, unless perhaps we limit "change" to one affecting the substance. But this seems to be a forced explanation, since the Philosopher excludes all change universally. Likewise, it cannot be properly said that the heaven is there, i.e., outside the heaven. Consequently, it is better to understand his words as applying to God and separated substances which plainly are not contained by time, nor place, since they are separated from all magnitude and motion. Such substances are said to be "there," i.e., outside the heaven, not as in a place, but as not contained nor included under the containment of bodily things, and as exceeding all of corporeal nature. It is such beings that the expression befits, namely, that they undergo no change; because they lie beyond the extreme motion, namely, that of the farthest sphere, which is ordered as extrinsic to and containing all change. Deinde cum dicit: sed inalterabilia etc., ostendit qualia sunt huiusmodi entia. 214. Then at [152] he explains the qualities of these beings. Et primo ostendit eorum conditionem;
secundo exponit quoddam nomen quo usus fuerat, ibi: etenim hoc nomen etc.;
tertio ostendit influentiam eorum in alia, ibi: unde et aliis et cetera.
First he describes their condition;
Secondly, he explains a word he used, at 215;
Thirdly, he shows the influence of these beings on others, at 216.
Dicit ergo primo quod illa entia quae sunt extra caelum, sunt inalterabilia et penitus impassibilia, habentia optimam vitam, inquantum scilicet eorum vita non est materiae permixta, sicut vita corporalium rerum. Habent etiam vitam per se sufficientissimam, inquantum non indigent aliquo vel ad conservationem suae vitae, vel ad executionem operum vitae. Habent etiam vitam non temporalem, sed in toto aeterno. He says therefore first [152] that those beings which are outside the heaven are unalterable and wholly impassible. They lead the best of lives, inasmuch as their life is not mingled with matter as is the life of corporeal beings. They also have a life that is most self-sufficient, inasmuch as they do not need anything in order to conserve their life or to perform the works of life, They have a life, too, which is not temporal but in total eternity. Horum autem quae hic dicuntur, quaedam possunt attribui corporibus caelestibus, puta quod sint impassibilia et inalterabilia: sed alia duo non possunt eis convenire, etiam si sint animata. Non enim habent optimam vitam, cum eorum vita sit ex unione animae ad corpus caeleste: nec etiam habent vitam per se sufficientissimam, cum per motum suum bonum consequantur, ut dicetur in secundo. Now, among the qualities here listed some can be attributed to heavenly bodies — for example, that they are impassible and unalterable. But the other two cannot belong to them, even if they are alive. For they do not have the best life, since their life would be one resulting from the union of a soul to a celestial body; neither do they have a most self-sufficient life, since they attain their good through motion, as will be said in Book II. Deinde cum dicit: etenim hoc nomen etc., exponit nomen aeterni, quo usus fuerat. Et dicit quod antiqui pronunciaverunt hoc nomen divine, idest convenienter rebus divinis. Hoc enim nomen dupliciter accipitur. 215. Then at [153] he explains the word "eternal" which he had used. And he says that the ancients pronounced this word as divine, i.e., as befitting divine things. Now this word has two meanings. Uno quidem modo secundum quid, quod scilicet est aeternum vel saeculum alicuius rei: idem enim apud Graecos utrumque significat. Dicit ergo quod aeternum vel saeculum uniuscuiusque rei vocatur finis, idest mensura quaedam terminans, quae continet tempus vitae cuiuslibet rei, ita quod nihil de tempore vitae quae est alicuius rei secundum naturam, est extra illum finem vel mensuram; sicut si dicamus quod spatium centum annorum est saeculum vel aeternum hominis. In one way it is used in a qualified sense as meaning the eternity or age [saeculum] of a thing: for in Greek the same word signifies both. He says, therefore, that the eternity or age of a thing is called an end, i.e., a certain terminal measure which contains the time of any thing's life, in such a way that no time of the life belonging to the thing according to nature exists outside that end or measure. It is like saying that the span of 100 years is the "age" or "eternity" of a man. Alio modo dicitur aeternum simpliciter, quod comprehendit et continet omnem durationem. Et hoc est quod dicit, quod secundum eandem rationem aeternum dicitur finis totius caeli, idest spatium continens totam durationem caeli, quod est spatium totius temporis. Et secundum hoc dicitur aeternum perfectio quaedam, quae continet omne tempus et omnem infinitatem durationis: non quidem sic quod ipsum aeternum distendatur secundum successionem praeteriti et futuri, sicut spatium temporis quantumcumque sit, quia talis successio sequitur motum, illa autem sunt penitus immobilia quae dixit habere vitam in aeterno; sed aeternum totum simul existens, comprehendit omne tempus et omnem infinitatem. Et denominatur in Graeco ab hoc quod est semper esse. Et talis finis, qui aeternum dicitur, est immortalis, quia vita illa non terminatur morte; et divinus, quia excedit omnem materiam, quantitatem et motum. In another way "eternity" is used in an absolute sense as comprehending and containing all duration. And this is what he says, namely, that according to the same notion, eternity is called the end of the entire heaven, i.e., it is the span containing the entire duration of the heaven, i.e., the span of all of time. In this sense, eternity refers to a certain perfection which contains all time and the entire infinitude of duration — not as though this eternity is stretched out according to the succession of past and future, as in the case of any span of time, because such succession follows upon motion, whereas the things he described as having life in eternity are completely immobile, but this eternity is a whole existing all at once and comprehending all time and all infinitude. (The Greek word [in English "aeon"] is derived from the words for "always existing".) Such an end, which is called "eternal" is immortal, because that life is not ended by death, and "divine," because it is beyond all matter, quantity, and motion. Deinde cum dicit: unde et aliis etc., ostendit influentiam eorum in alia. Est autem manifestum quod ab eo quod est perfectissimum, fit derivatio ad alia quae sunt minus perfecta; sicut calidum derivatur ab igne ad alia quae sunt minus calida, ut dicitur in II Metaphys. Unde cum ista entia habeant vitam optimam et per se sufficientissimam, et esse sempiternum, consequens est quod inde communicetur aliis esse et vivere. Non tamen aequaliter omnibus: sed his quidem clarius, idest evidentius et perfectius, scilicet his quae habent esse sempiternum eadem numero existentia, et his quae habent vitam rationalem; his autem obscurius, idest debilius et imperfectius, sicut his quae sunt sempiterna non secundum idem numero sed secundum idem specie, et quae habent vitam sensibilem vel nutritivam. 216. Then at [154] he shows the influence of these things on others. Now it is manifest that from what is most perfect there is a flowing to others that are less perfect, just as heat flows from fire to other things that are less hot, as is said in Metaphysics II. Hence, since those beings possess the best and most self-sufficient life and eternal existence, it is from them that existence and life are communicated to other things. But not equally to all; rather, to some "more luminously," i.e., more evidently and more perfectly, namely, to those that have individual eternal existence and to those that have rational life; to others "more darkly," i.e., in a lesser and more imperfect way, namely, to those things that are eternal, not in the same individuals, but according to sameness of species, and which have sense or nutritive life. Deinde cum dicit: etenim quemadmodum in encycliis etc., manifestat quod dixerat de conditione praedictorum entium quae sunt extra caelum. 217. Then at [155] he manifests what he had said about the condition of the aforesaid beings that exist outside the heaven. Et primo proponit quod intendit;
secundo inducit rationes, ibi: neque enim aliud et cetera.
First he proposes what he intends;
Secondly, he presents reasons, at 218.
Circa primum considerandum est quod apud philosophos erant duo genera dogmatum. Quaedam enim erant quae a principio secundum ordinem doctrinae multitudini apponebantur, quae quidem vocabantur encyclia: quaedam autem erant magis subtilia, quae proponebantur auditoribus iam provectis, quae vocabantur syntagmatica, idest coordinalia, vel acroamatica, idest auditionalia. Dogmata autem philosophorum dicuntur philosophemata. With respect to the first [155] it should be known that among the philosophers there were two kinds of teachings. For there were some which from the very beginning were proposed according to the order of doctrine to the multitude and these were called "encyclia"; others were more subtle, and were proposed to the more advanced hearers and were called "syntagmatica," i.e., co-ordinal, or "acromatica," i.e., hearable, teachings. The dogmas of the philosophers are called "philosophemata." Dicit ergo quod in huiusmodi encycliis philosophematibus circa res divinas, multoties philosophi rationibus manifestabant quod necesse est omne divinum esse intransmutabile, quasi non subiectum motui, et primum, quasi non subiectum tempori, et summum, quasi non contentum loco: divinum autem dicebant omnem substantiam separatam. Et hoc attestatur his quae dicta sunt de huiusmodi entibus. He says, therefore, that in the "encyclic" [or popular] philosophic discussions concerning divine things the philosophers very often in their arguments showed that everything divine must be "untransmutable," as not subject to motion, and "first," as not subject to time, and "highest," as not contained by place. And they called every separated substance "divine." And this confirms what has been said about such beings. Deinde cum dicit: neque enim aliud etc., ponit rationes ad ostendendum quod dixerat, scilicet quod primum et supremum sit intransmutabile. 218. Then at [156] he gives reasons to manifest what he had said, namely, that the first and highest is untransmutable. Et primo ostendit propositum;
secundo infert quandam conclusionem ex dictis, ibi: et incessabili itaque et cetera.
First he manifests the proposition;
Secondly, he draws a conclusion, at 220.
Circa primum ponit duas rationes: quarum prima talis est. Semper movens et agens est melius moto et passo; sed non est aliquid melius primo et summo divino, quod possit ipsum movere, quia illud esset adhuc divinius; primum ergo divinum non movetur, quia omne quod movetur necesse est ab alio moveri, ut probatur in VII et VIII Physic. In regard to the first he gives two arguments, the first of which is as follows: What is always causing motion and acting is better than what is moved and acted upon. But there is nothing better than the first and highest divinity, so as to be able to move it, because such a mover would be more divine. Therefore, the first divine being is not moved, since whatever is moved must be moved by another, as is proved in Physics VII and VIII. Secundam rationem ponit ibi: neque habet pravum etc.: quae talis est. Omne quod movetur, aut movetur ad hoc quod evadat aliquod malum, aut ad hoc quod acquirat aliquod bonum; sed primum non habet aliquod malum quod possit evadere, neque indiget aliquo bono quod possit acquirere, quia est perfectissimum; ergo primum non movetur. 219. The second argument is at [157]: Whatever is moved is moved either to avoid an evil or acquire a good. But what is first has no evil to avoid and lacks no good that it could acquire, because it is most perfect. Therefore, the first is not moved. Potest autem et sic formari ratio. Omne quod movetur, aut movetur ad melius aut ad deterius; sed neutrum potest Deo convenire, secundum ea quae hic dicuntur; ergo Deus nullo modo movetur. Et est attendendum quod haec secunda ratio potest induci ad hoc quod non moveatur a seipso. The argument could also be presented in the following way: Whatever is moved is moved either to better or to worse. But neither of these can belong to God according to what is said here. Therefore, God, is in no way moved. And one should note that this second argument may be introduced to show that He is not moved by Himself. Deinde cum dicit: et incessabili itaque etc., infert conclusionem ex dictis. Et dicit rationabiliter, idest probabiliter, sequi quod illud primum movens primum mobile, moveat motu incessabili. Quaecumque enim mota quiescunt, tunc quiescunt quando perveniunt ad proprium locum, sicut patet in gravibus et levibus; sed hoc non potest dici in primo mobili, quod circulariter movetur, quia idem est unde incipit motus eius et in quod terminatur; ergo primum mobile movetur a primo motore motu incessabili. 220. Then at [158] from the foregoing he draws a conclusion. And he says it "reasonably," i.e., probably, follows that that first mover of the first mobile acts with unceasable motion. For whatever things, after having been moved, rest, these do so when they reach their appropriate place, as is clear in heavy and light bodies. But this cannot be said of the first mobile which is moved circularly, because where its motion starts is the same as where it ends. Therefore, the first mobile is moved by the first mover with an unceasing motion. Et est attendendum quod haec ratio non ex necessitate concludit. Potest enim dici quod motus caeli non cessat, non propter naturam loci, sed propter voluntatem moventis. Et ideo non inducit eam tanquam necessariam, sed tanquam probabilem. And it should be noted that this argument does not conclude of necessity. For it can be said that the motion of the heaven does not cease, not on account of the nature of the place, but on account of the will of the mover. Therefore, he does not present this as a necessary, but as a probable, conclusion.
Lecture 22:
Whether the universe is infinite by eternal duration.Chapter 10 Τούτων δὲ διωρισμένων λέγωμεν μετὰ ταῦτα πότερον ἀγένητος ἢ γενητὸς καὶ ἄφθαρτος ἢ φθαρτός, διεξελθόντες πρότερον τὰς τῶν ἄλλων ὑπολήψεις 159 Having established these distinctions, we may now proceed to the question whether the heaven is ungenerated or generated, indestructible or destructible. Let us start with a review of the theories of other thinkers; αἱ γὰρ τῶν ἐναντίων ἀποδείξεις ἀπορίαι περὶ τῶν ἐναντίων εἰσίν. 160 for the proofs of a theory are difficulties for the contrary theory. Ἅμα δὲ καὶ μᾶλλον ἂν εἴη πιστὰ τὰ μέλλοντα λεχθήσεσθαι προακηκοόσι τὰ τῶν ἀμφισβητούντων λόγων δικαιώματα. 161 Besides, those who have first heard the pleas of our adversaries will be more likely to credit the assertions which we are going to make. Τὸ γὰρ ἐρήμην καταδικάζεσθαι δοκεῖν ἧττον ἂν ἡμῖν ὑπάρχοι καὶ γὰρ δεῖ διαιτητὰς ἀλλ' οὐκ ἀντιδίκους εἶναι τοὺς μέλλοντας τἀληθὲς κρίνειν ἱκανῶς. 162 We shall be less open to the charge of procuring judgement by default. To give a satisfactory decision as to the truth it is necessary to be rather an arbitrator than a party to the dispute. Γενόμενον μὲν οὖν ἅπαντες εἶναί φασιν, 163 That the world was generated all are agreed, ἀλλὰ γενόμενον οἱ μὲν ἀΐδιον, οἱ δὲ φθαρτὸν ὥσπερ ὁτιοῦν ἄλλο τῶν συνισταμένων, οἱ δ' ἐναλλὰξ ὁτὲ μὲν οὕτως ὁτὲ δὲ ἄλλως ἔχειν [φθειρόμενον], καὶ τοῦτο αἰεὶ διατελεῖν οὕτως, ὥσπερ Ἐμπεδοκλῆς ὁ Ἀκραγαντῖνος καὶ Ἡράκλειτος ὁ Ἐφέσιος. 164 but, generation over, some say that it is eternal, others say that it is destructible like any other natural formation. Others again, with Empedliocles of Acragas and Heraclitus of Ephesus, believe that there is alternation in the destructive process, which takes now this direction, now that, and continues without end. Τὸ μὲν οὖν γενέσθαι μὲν ἀΐδιον δ' ὅμως εἶναι φάναι τῶν ἀδυνάτων. Μόνα γὰρ ταῦτα θετέον ὐλόγως ὅσα ἐπὶ πολλῶν ἢ πάντων ὁρῶμεν ὑπάρχοντα, περὶ δὲ τούτου συμβαίνει τοὐναντίον ἅπαντα γὰρ τὰ γινόμενα καὶ φθειρόμενα φαίνεται. 165 Now to assert that it was generated and yet is eternal is to assert the impossible; for we cannot reasonably attribute to anything any characteristics but those which observation detects in many or all instances. But in this case the facts point the other way: generated things are seen always to be destroyed. Ἔτι δὲ τὸ μὴ ἔχον ἀρχὴν τοῦ ὡδὶ ἔχειν, ἀλλ' ἀδύνατον ἄλλως ἔχειν πρότερον τὸν ἅπαντα αἰῶνα, ἀδύνατον καὶ μεταβάλλειν ἔσται γάρ τι αἴτιον, ὃ εἰ ὑπῆρχε πρότερον, δυνατὸν ἂν ἦν ἄλλως ἔχειν τὸ ἀδύνατον ἄλλως ἔχειν. Εἰ δὲ πρότερον ἐξ ἄλλως ἐχόντων συνέστη ὁ κόσμος, εἰ μὲν ἀεὶ οὕτως ἐχόντων καὶ ἀδυνάτων ἄλλως ἔχειν, οὐκ ἂν ἐγένετο εἰ δὲ γέγονεν, ἀνάγκη δηλονότι κἀκεῖνα δυνατὰ εἶναι ἄλλως ἔχειν καὶ μὴ ἀεὶ οὕτως ἔχειν, ὥστε καὶ συνεστῶτα διαλυθήσεται καὶ διαλελυμένα συνέστη ἔμπροσθεν, καὶ τοῦτ' ἀπειράκις ἢ οὕτως εἶχεν ἢ δυνατὸν ἦν. Εἰ δὲ τοῦτ', οὐκ ἂν εἴη ἄφθαρτος, οὔτ' εἰ ἄλλως εἶχέ ποτε οὔτ' εἰ δυνατὸν ἄλλως ἔχειν. 166 Further, a thing whose present state had no beginning and which could not have been other than it was at any previous moment throughout its entire duration, cannot possibly be changed. For there will have to be some cause of change, and if this had been present earlier it would have made possible another condition of that to which any other condition was impossible. Suppose that the world was formed out of elements which were formerly otherwise conditioned than as they are now. Then (1) if their condition was always so and could not have been otherwise, the world could never have come into being. And (2) if the world did come into being, then, clearly, their condition must have been capable of change and not eternal: after combination therefore they will be dispersed, just as in the past after dispersion they came into combination, and this process either has been, or could have been, indefinitely repeated. But if this is so, the world cannot be indestructible, and it does not matter whether the change of condition has actually occurred or remains a possibility.
Postquam philosophus ostendit quod corpus totius mundi non est infinitum, et quod non est multiplex numero, hic inquirit utrum sit infinitum durationis aeternitate. 221. After the Philosopher showed that the body of the whole universe is not infinite, and that it is not multiple in number, here he inquires whether it is infinite by eternal duration. Et primo ponit opiniones aliorum;
secundo determinat propositum secundum propriam opinionem, ibi: primum autem dividendum et cetera.
And first he gives the opinions of others.
Secondly, he settles the question according to his own opinion
Circa primum tria facit: Regarding the first, he does three things: primo dicit de quo est intentio;
secundo ponit opiniones, ibi: genitum quidem igitur etc.; tertio improbat eas, ibi: factum esse quidem et cetera.
First he declares his intention.
Secondly he gives the opinions, at [163].
Thirdly he refutes them.
Circa primum duo facit: primo dicit de quo est intentio, et quo ordine sit agendum. Et dicit quod post determinationem praemissorum, dicendum est postea utrum mundus sit ingenitus aut genitus, idest utrum per generationem incoeperit esse a quodam principio temporis, aut non; et utrum sit incorruptibilis aut corruptibilis, idest utrum per corruptionem post aliquod tempus esse desinat, vel non. Prius tamen quam haec pertractemus secundum nostram opinionem, debemus pertranseuntes, idest breviter, dicere suspiciones aliorum, idest opiniones aliorum philosophorum circa hoc; quas suspiciones vocat, quia ex levibus rationibus ad haec dicenda movebantur. Difficile enim est ad hoc inducere efficaces rationes: unde et ipse Aristoteles dicit in I Topic. quod quaedam problemata sunt de quibus rationes non habemus, ut utrum mundus sit aeternus vel non. 222. Regarding the first, he does two things. First he states his intention and the order of procedure. And he says that after determining the previous matters, he must go on to say whether the universe is ungenerated or generated, that is whether it begin to exist at some beginning point of time or not, and whether it is incorruptible or corruptible, that is whether after some time it will cease to exist through corruption, or not. But before treating these matters according to our opinion, we must first briefly review the surmisals of others, that is the opinions of other philosophers on this matter. He calls them surmisals [ suspiciones ], because they were moved to these opinions by frivolous reasons. For it is difficult to adduce efficacious reasons; thus Aristotle said in Topics I that there are some problems about which we do not have reasons, such as whether the world is eternal or not. Secundo ibi: contrariorum enim etc., assignat rationes tres quare hic et alibi aliorum opiniones pertractet. Quarum prima est quia demonstrationes, idest probationes, contrariorum, idest contrariarum opinionum, sunt dubitationes de contrariis, scilicet opinionibus, idest sunt obiectiones ad contrarias opiniones: expedit autem ei qui vult cognoscere aliquam veritatem, ut sciat dubitationes quae sunt contra illam veritatem; quia solutio dubitatorum est inventio veritatis, ut dicitur in III Metaphys. Et ita ad sciendum veritatem multum valet videre rationes contrariarum opinionum. 223. Secondly, at "of contrary things", he assigns three reasons why here and elsewhere he reviews the opinions of others. The first reason is that "demonstrations", that is proofs, "of contrary things", that is, of contrary opinions, are critiques of "contraries", that is, contrary opinions. That is, they are objections against contrary opinions. Whoever wishes to know any truth, must know the critiques against that truth, because the solution of doubts is the finding of truth, as is said in III Metaphysica. And thus, to know the truth, it is very important to see the reasons for contrary opinions. Secundam rationem ponit ibi: simul autem et cetera. Et dicit quod simul cum praedicta ratione est alia ratio: quia ea quae dicenda sunt magis redduntur credibilia apud illos qui primo audiunt iustificationes, idest rectificationes, sermonum dubitatorum, idest solutiones rationum ex quibus dubitatio emergit: quia quandiu homo dubitat, antequam eius dubitatio solvatur, est mens eius similis ligato, qui non potest ire. 224. As for the second reason, he says that there is an additional reason. Because what must be said is made more credible to people who first hear the justification or defense of disputed opinions, that is solutions of the reasons which gave rise to the dispute. For as long as a man is in doubt, before his doubt is resolved, his mind is like someone bound, who cannot move. Tertiam rationem ponit ibi: gratis enim condemnare et cetera. Et dicit quod quando nos posuerimus opiniones aliorum, et induxerimus eorum rationes, et solverimus eas, et posuerimus rationes in contrarium, minus inerit nobis quod videamur condemnare dicta aliorum gratis, idest sine debita ratione, sicut qui reprobant dicta aliorum ex solo odio, quod non convenit philosophis, qui profitentur se inquisitores esse veritatis. Oportet enim eos qui volunt sufficienter iudicare de veritate, quod non exhibeant seipsos sicut inimicos eorum de quorum dictis est iudicandum; sed sicut arbitros, et disquisitores pro utraque parte. 225. The third reason is where he says "to condemn without reason" etc. And he says that when we cite the opinions of others and examine and solve their reasons, and give reasons for the contrary, we will not appear guilty of condemning the opinions of others gratuitously, that is, without proper reason, like those who condemn the opinions of others out of mere hatred. This is not becoming to philosophers, who profess to be searchers of the truth. For those who wish to be adequate judges of the truth must not show themselves enemies of those whose statements are to be judged, but as arbiters, and inquirers for both sides. Deinde cum dicit: genitum quidem igitur etc., ponit opiniones aliorum. Et primo ponit in quo omnes conveniunt: et dicit quod omnes qui fuerunt ante eum, dixerunt quod mundus sit genitus, idest a quodam principio temporis esse incipiens per generationem. 226. Then at [163] he gives the opinions of others. First he shows in what they all agree, and says that all who were before him stated that the world is generated, i.e., at a certain beginning of time it began to exist through generation. Secundo ibi: sed genitum etc., ponit in quo differunt. Et tangit tres opiniones. Quidam enim dicebant quod, quamvis incoeperit esse ab aliquo principio temporis, tamen in sempiternum durabit; sicut primo dixerunt quidam poetae, ut Orpheus et Hesiodus, qui dicti sunt theologi, quia res divinas poetice et fabulariter tradiderunt; quos in hac positione secutus est Plato, qui posuit mundum generatum, sed indissolubilem. 227. Secondly, he shows in what they differ. And he touches on three opinions. First of all, some said that, although it began to be at a certain beginning of time, yet it will endure forever, as first was said by certain poets, such as Orpheus and Hesiod, who are called "theologians" because they presented divine things under the form of poetry and myths. Plato followed them in this position, holding the world to be generated but indestructible. Secunda opinio fuit quorundam aliorum, qui posuerunt mundum corruptibilem esse eo modo quo quodlibet aliud generatorum, quae constituuntur ex multis; ita scilicet quod mundus post corruptionem nunquam reparabitur, sicut Socrates post corruptionem nunquam reparatur per naturam. Et haec fuit positio Democriti, qui posuit mundum generari casu per concursum atomorum semper mobilium, et ita etiam per eorum segregationem quandoque esse dissolvendum. The second opinion was that of certain others, that the world is destructible in the same way as any other generated thing composed of many parts, and that after being destroyed, it will never be repaired, just as Socrates, once corrupted, is never restored by nature. And this was the opinion of Democritus, who declared the world to be generated by a fortuitous gathering together of atoms ever mobile, and likewise to be destined to be dissolved at some time by the separation of these atoms. Tertia opinio est dicentium quod mundus quandoque vicissim generatur et quandoque corrumpitur, et ista vicissitudo semper duravit et durabit. Et hoc dixit Empedocles Agrigentinus: posuit enim quod, amicitia congregante elementa et lite dissolvente ea, mundus generabatur et corrumpebatur. Hoc etiam posuit Heraclitus Ephesius, qui posuit quod quandoque totus mundus exureretur per ignem, et post certos decursus temporum iterum totus mundus generaretur per ignem, quem ponebat esse principium omnium rerum. The third opinion is that of those who say the world is alternately generated and destroyed, and that this alternation has always endured and will always last. Such was the opinion of Empedocles of Agrigenta, for he posited that with friendship assembling the elements and strife separating them, the world was [continuously] generated and destroyed. This, too, was the opinion of Heraclitus of Ephesus, who posited that at some time the world would be consumed by fire and after a certain lapse of time would again be generated by fire, which he supposed was the principle of all things. Dicunt autem quidam quod isti poetae et philosophi, et praecipue Plato, non sic intellexerunt secundum quod sonat secundum superficiem verborum; sed suam sapientiam volebant quibusdam fabulis et aenigmaticis locutionibus occultare; et quod Aristotelis consuetudo fuit in pluribus non obiicere contra intellectum eorum, qui erat sanus, sed contra verba eorum, ne aliquis ex tali modo loquendi errorem incurreret, sicut dicit Simplicius in commento. Alexander tamen voluit quod Plato et alii antiqui philosophi hoc intellexerunt quod verba eorum exterius sonant; et sic Aristoteles non solum contra verba, sed contra intellectum eorum conatus est argumentari. Quidquid autem horum sit, non est nobis multum curandum: quia studium philosophiae non est ad hoc quod sciatur quid homines senserint, sed qualiter se habeat veritas rerum. 228. Now, some claim that these poets and philosophers, and especially Plato, did not understand these matters in the way their words sound on the surface, but wished to conceal their wisdom under certain fables and enigmatic statements. Moreover, they claim that Aristotle's custom in many cases was not to object against their understanding, which was sound, but against their words, lest anyone should fall into error on account of their way of speaking. So says Simplicius in his Commentary. But Alexander held that Plato and the other early philosophers understood the matter just as the words sound literally, and that Aristotle undertook to argue not only against their words but against their understanding as well. Whichever of these may be the case, it is of little concern to us, because the study of philosophy aims not at knowing what men feel, but at what is the truth of things. Deinde cum dicit: factum esse quidem etc., improbat praedictas positiones: 229. Then at [165] he refutes these opinions: et primo primam;
secundo tertiam, ibi: vicissim autem etc.;
tertio secundam, ibi: totaliter autem factum etc. (secunda enim opinio minus habet rationis).
First, the first one;
Secondly, the third one, at 234;
Thirdly, the second one, at 235 (for the second has less of an argument).
Circa primum duo facit: About the first he does two things: primo improbat positionem;
secundo excludit quandam excusationem, ibi: auxilium autem et cetera.
First he refutes the opinion;
Secondly, he rejects an excusing of it, at 231.
Circa primum ponit duas rationes. Circa quarum primam dicit quod impossibile est mundum esse factum vel genitum ex quodam principio temporis, et quod postmodum in sempiternum duret. Cum enim aliqua volumus sumere rationabiliter, idest probabiliter absque demonstratione, talia oportet ponere quae videmus esse vera in omnibus aut in multis: hoc enim est de ratione probabilis. Sed in proposito accidit contrarium, quia omnia quae generantur, videmus corrumpi. Non ergo est ponendum quod mundus sit generatus, et quod sit incorruptibilis. With respect to the first he presents two arguments, in the first of which he says that it is impossible for the world to have been made or generated from a certain beginning of time and then afterwards to endure forever. For when we want to assume something "reasonably," i.e., probably, without a demonstration, we must posit what we observe to be true in all or in many cases, for this is the very nature of the probable. But in this case the contrary happens, because all things that are generated we see to corrupt. Therefore one should not lay down that the world is generated and indestructible. Secundam rationem ponit ibi: adhuc autem et cetera. Et inducit primo quoddam principium: et dicit quod, si aliquid est quod non habet in se potentiam quae sit principium eius quod est sic et aliter se habere, sed impossibile est quod aliter se habuerit prius per omnia saecula, impossibile est quod talis res transmutetur. Et hoc probat ducendo ad impossibile. Quia si talis res transmutaretur, erit quando transmutatur aliqua causa faciens eam transmutari, scilicet sua potentia ad transmutationem: quae si prius fuisset, possibile erat illam rem aliter se habere, quae tamen ponebatur impossibile aliter se habere. Si autem prius non habuit potentiam ad hoc quod aliter se haberet, et postea habet eam, hoc ipsum est transmutari illam rem: et sic etiam antequam haberet potentiam transmutandi, erat potens transmutari, ad hoc scilicet quod acciperet potentiam transmutandi. 230. He gives the second argument at [166]. And first he states a principle and says that if a thing is such that it does not have within itself a potency which is a principle of its being thus and otherwise, but it is impossible for it to have been otherwise throughout all preceding ages, then such a thing cannot be transmuted. This he proves by leading to an impossibility. For if such a thing should be transmuted, it would be when it is transmuted by some cause producing its transmutation, i.e., by its potency to transmutation. This potency, if it had existed before, would have made it possible for that thing to be other than it was, which thing, however, was assumed to be incapable of being otherwise. But if it previously lacked this potency to be otherwise, and later has it, that itself would be a transmutation of that thing. Consequently, even before it had the potency to be changed, it was able to be changed, namely, by receiving the power to be changed. Ex his autem sic argumentatur ad propositum. Si enim mundus constitutus est ex quibusdam rebus, quae priusquam mundus fieret aliter se habebant; si ita sit quod illa ex quibus constitutus est mundus, semper sic se haberent sicut prius se habebant, et impossibile sit aliter ea se habere, non fieret mundus ex eis. Si ergo factus est mundus ex eis, necesse est quod illa ex quibus factus est mundus, sint possibilia aliter se habere, et quod non semper eodem modo se habeant. Unde sequitur quod etiam constantia, idest postquam fuerint adunata ad constitutionem mundi, iterum possunt dissolvi; et quando erant dissoluta, prius fuerunt composita; et quod infinities vicissim haec sic se habebant, aut possibile erat sic se habere. Et si hoc est verum, sequitur quod mundus non sit incorruptibilis, neque unquam erit incorruptibilis, si ea ex quibus constat mundus aliter se habebant, neque etiam si possibile erat quod aliter se haberent: quia ex utroque sequitur quod etiam nunc possibile sit ea aliter se habere. From this he argues thus to his proposition; If the world was made from certain things which, before the world was made, were otherwise constituted, then if it is true that those things from which the world was formed were never otherwise than they always were, and could never be otherwise, the world could not have been formed from them. But if the world was formed from them, then, necessarily, those things from which it was formed could be otherwise and do not remain always the same. Hence it follows that even as constituents, i.e., after being united to form the world, they can be separated again; and, when dispersed, they have been previously united, and they alternated thus infinitely, or could have. And if this is true, it follows that the world is not imperishable, nor ever will be imperishable, if the things of which the world consists were at one time otherwise, or even could have been: for in either case it follows that even now it is possible that they be otherwise.
Lecture 23:
A Platonic evasion rejected. Two remaining opinions disproved.Chapter 10 cont. Ἣν δέ τινες βοήθειαν ἐπιχειροῦσι φέρειν ἑαυτοῖς τῶν λεγόντων ἄφθαρτον μὲν εἶναι γενόμενον δέ, οὐκ ἔστιν ἀληθής ὁμοίως γάρ φασι τοῖς τὰ διαγράμματα γράφουσι καὶ σφᾶς εἰρηκέναι περὶ τῆς γενέσεως, οὐχ ὡς γενομένου ποτέ, ἀλλὰ (280a.) διδασκαλίας χάριν ὡς μᾶλλον γνωριζόντων, ὥσπερ τὸ διάγραμμα γιγνόμενον θεασαμένους. 167 Some of those who hold that the world, though indestructible, was yet generated, try to support their case by a parallel which is illusory. They say that in their statements about its generation they are doing what geometricians do when they construct their figures, not implying that the universe really had a beginning, but for didactic reasons facilitating understanding by exhibiting the object, like the figure, as in course of formation. Τοῦτο δ' ἐστίν, ὥσπερ λέγομεν, οὐ τὸ αὐτό ἐν μὲν γὰρ τῇ ποιήσει τῶν διαγραμμάτων πάντων τεθέντων εἶναι ἅμα τὸ αὐτὸ συμβαίνει, ἐν δὲ ταῖς τούτων ἀποδείξεσιν οὐ ταὐτόν, ἀλλ' ἀδύνατον τὰ γὰρ λαμβανόμενα πρότερον καὶ ὕστερον ὑπεναντία ἐστίν ἐξ ἀτάκτων γὰρ τεταγμένα γενέσθαι φασίν, ἅμα δὲ ἄτακτον εἶναι καὶ τεταγμένον ἀδύνατον, ἀλλ' ἀνάγκη γένεσιν εἶναι τὴν χωρίζουσαν καὶ χρόνον ἐν δὲ τοῖς διαγράμμασιν οὐδὲν τῷ χρόνῳ κεχώρισται. Ὅτι μὲν οὖν ἀδύνατον ἅμ' ἀΐδιον αὐτὸν εἶναι καὶ γενέσθαι, φανερόν. 168 The two cases, as we said, are not parallel; for, in the construction of the figure, when the various steps are completed the required figure forthwith results; but in these other demonstrations what results is not that which was required. Indeed it cannot be so; for antecedent and consequent, as assumed, are in contradiction. The ordered, it is said, arose out of the unordered; and the same thing cannot be at the same time both ordered and unordered; there must be a process and a lapse of time separating the two states. In the figure, on the other hand, there is no temporal separation. It is clear then that the universe cannot be at once eternal and generated. Τὸ δ' ἐναλλὰξ συνιστάναι καὶ διαλύειν οὐδὲν ἀλλοιότερον ποιεῖν ἐστὶν ἢ τὸ κατασκευάζειν αὐτὸν ἀΐδιον μέν, ἀλλὰ μεταβάλλοντα τὴν μορφήν, ὥσπερ εἴ τις ἐκ παιδὸς ἄνδρα γινόμενον καὶ ἐξ ἀνδρὸς παῖδα ὁτὲ μὲν φθείρεσθαι ὁτὲ δ' εἶναι οἴοιτο δῆλον γὰρ ὅτι καὶ εἰς ἄλληλα τῶν στοιχείων συνιόντων οὐχ ἡ τυχοῦσα τάξις γίγνεται καὶ σύστασις, ἀλλ' ἡ αὐτή, ἄλλως τε καὶ κατὰ τοὺς τοῦτον τὸν λόγον εἰρηκότας, οἳ τῆς διαθέσεως ἑκατέρας αἰτιῶνται τὸ ἐναντίον. Ὥστ' εἰ τὸ ὅλον σῶμα συνεχὲς ὂν ὁτὲ μὲν οὕτως ὁτὲ δ' ἐκείνως διατίθεται καὶ διακεκόσμηται, ἡ δὲ τοῦ ὅλου σύστασίς ἐστι κόσμος καὶ οὐρανός, οὐκ ἂν ὁ κόσμος γίγνοιτο καὶ φθείροιτο, ἀλλ' αἱ διαθέσεις αὐτοῦ. 169 To say that the universe alternately combines and dissolves is no more paradoxical than to make it eternal but varying in shape. It is as if one were to think that there was now destruction and now existence when from a child a man is generated, and from a man a child. For it is clear that when the elements come together the result is not a chance system and combination, but the very same as before—especially on the view of those who hold this theory, since they say that the contrary is the cause of each state. So that if the totality of body, which is a continuum, is now in this order or disposition and now in that, and if the combination of the whole is a world or heaven, then it will not be the world that comes into being and is destroyed, but only its dispositions. Τὸ δ' ὅλως γενόμενον φθαρῆναι καὶ μὴ ἀνακάμπτειν ὄντος μὲν ἑνὸς ἀδύνατόν ἐστιν πρὶν γὰρ γενέσθαι ἀεὶ ὑπῆρχεν ἡ πρὸ αὐτοῦ σύστασις, ἣν μὴ γενομένην οὐχ οἷόν τ' εἶναί φαμεν μεταβάλλειν ἀπείρων δ' ὄντων ἐνδέχεται μᾶλλον. If the world is believed to be one, it is impossible to suppose that it should be, as a whole, first generated and then destroyed, never to reappear; since before it came into being there was always present the combination prior to it, and that, we hold, could never change if it was never generated. If, on the other hand, the worlds are infinite in number the view is more plausible. Οὐ μὴν ἀλλὰ καὶ τοῦτο πότερον ἀδύνατον ἢ δυνατόν, ἔσται δῆλον ἐκ τῶν ὕστερον εἰσὶ γάρ τινες οἷς ἐνδέχεσθαι δοκεῖ καὶ ἀγένητόν τι ὂν φθαρῆναι καὶ γενόμενον ἄφθαρτον διατελεῖν, ὥσπερ ἐν τῷ Τιμαίῳ ἐκεῖ γάρ φησι τὸν οὐρανὸν γενέσθαι μέν, οὐ μὴν ἀλλ' ἔσεσθαί γε τὸν λοιπὸν ἀεὶ χρόνον. Πρὸς οὓς φυσικῶς μὲν περὶ οὐρανοῦ μόνον εἴρηται, καθόλου δὲ περὶ ἅπαντος σκεψαμένοις ἔσται καὶ περὶ τούτου δῆλον. 171 But whether this is, or is not, impossible will be clear from what follows. For there are some who think it possible both for the ungenerated to be destroyed and for the generated to persist undestroyed. (This is held in the Timaeus, where Plato says that the heaven, though it was generated, will none the less exist to eternity.) So far as the heaven is concerned we have answered this view with arguments appropriate to the nature of the heaven: on the general question we shall attain clearness when we examine the matter universally.
Praemissis rationibus contra opinionem Platonis, hic philosophus excludit quandam excusationem praedictae opinionis, quam Xenocrates et alii Platonici afferebant. Et circa hoc duo facit: 231. After presenting the arguments against Plato, the Philosopher here rejects a certain excusing of the aforesaid opinion, which Xenocrates and other Platonists proposed. About this he does two things: primo proponit excusationem;
secundo excludit eam, ibi: hoc autem est, quemadmodum dicimus et cetera.
First he proposes the explanation;
Secondly, he rejects it, at 232.
Dicit ergo primo quod non est verum illud auxilium, idest illa excusatio, quam quidam Platonicorum, dicentium mundum esse incorruptibilem sed tamen factum vel genitum, conantur ferre sibi ipsis, ut non irrationabiliter posuisse videantur. Dicunt enim se dixisse de generatione mundi ad similitudinem eorum qui describunt figuras geometricas, qui primo describunt quasdam partes figurae, puta trianguli, et postea alias, non quasi prius fuerint huiusmodi partes antequam talis figura ex huiusmodi partibus constitueretur, sed ut magis explicite demonstrent ea quae ad figuram requiruntur. Et similiter dicunt Platonem dixisse mundum factum esse ex elementis, non tanquam aliquo tempore determinato mundus sit generatus, sed causa doctrinae; ut facilius instruerentur aliqui de natura mundi, dum prius demonstrantur eis partes mundi, et quid habeant huiusmodi partes ex seipsis, postea demonstratur eis compositio quam habent a causa mundi, quae Deus est. Et ita aspiciunt, idest considerant, mundum esse genitum, ad modum descriptionis qua utuntur geometrae in descriptione figurarum. He says, therefore, first [167] that there is no truth in that "help," i.e., that excusing, by which some Platonists seek to justify their assertion —that the world is imperishable, but yet made or generated — and make it appear not unreasonable. For they say that their description of the world's generation was after the manner of those who describe geometric figures by first drawing certain parts of the figure, e.g., of a triangle, and later other parts, not implying that these parts existed before the figure was formed of them, but doing this in order to demonstrate more explicitly what things are required for the figure. They say that Plato in like manner declared that the world was made from elements, not as though the world was generated at some definite time, but for the purpose of presenting his doctrine, so that, namely, his hearers would be more easily instructed about the nature of the world, if first the parts of the world were demonstrated to them and what these parts possessed of themselves, and later the composition they had from the cause of the world, which is God. Consequently they look on, i.e., consider, the world as generated in the manner of the description which geometers use in describing figures. Deinde cum dicit: hoc autem est, quemadmodum dicimus etc., improbat quod dictum est. Et dicit quod non eodem modo se habet quod ipsi dicunt circa generationem mundi, et quod geometrae dicunt circa descriptiones figurarum, sicut manifestabitur per ea quae nunc dicemus. Quia in descriptionibus geometricalibus, idem accidit si omnes partes figurae simul accipiantur ut constituunt figuram, et si non accipiantur simul: quia quando non accipiuntur simul, nihil aliud dicitur de eis nisi quod sunt lineae vel anguli; et hoc etiam salvatur in eis quando accipiuntur omnia simul in figura constituta ex eis. Sed in demonstrationibus eorum qui ponunt generationem mundi, non idem accipitur cum sunt simul et cum non sunt simul; sed impossibile est quod idem ex utraque parte accipiatur, sicut impossibile est opposita esse simul; illa enim quae accipiuntur prius, scilicet ante constitutionem mundi, et posterius, scilicet mundo iam constituto, sunt subcontraria, idest habent quandam adiunctam et latentem contrarietatem. 232. Then at [168] he disproves this explanation. And he says that the way the generation of the world is described by them is not in the same manner as the descriptions of figures made by geometers, as will be clear from what we shall now say. For in geometric descriptions the same thing happens whether all the parts are considered together as constituting the figure, or whether they are not taken together. When they are taken separately, no more is said about them than that they are lines or angles, which is also true of them when they are taken all together in the figure made out of them. But in the demonstrations presented by those who posit the generation of the world, the same thing is not taken when the parts are considered together and when they are not. Rather, it is impossible that the same be taken in both instances, just as it is impossible for opposites to be together — for the things taken first, i.e., before the establishing of the world, and those taken later, i.e., after the world is now established, are "subcontraries," i.e., have a certain conjoined and latent contrariety. Dicunt enim quod ex elementis inordinatis facta sunt ordinata, Deo scilicet reducente inordinationem elementorum ad ordinem, ut Plato in Timaeo dicit: geometrae autem non dicunt quod ex lineis divisis componatur triangulus, sed simpliciter quod ex lineis. Et esset simile si isti solum dicerent quod mundus sit ex elementis: sed dicunt quod mundus ordinatus sit ex elementis inordinatis. Non est autem possibile quod aliquid sit simul ordinatum et inordinatum: sed necesse est dari aliquam generationem, per quam unum eorum ab altero separetur, ut scilicet ante generationem sit inordinatum, post generationem vero ordinatum; et per consequens necesse est dari aliquod tempus distinguens utrumque. Sed in descriptionibus figurarum non requiritur aliqua distinctio temporis: non enim oportet quod linea et triangulus tempore distinguantur, sicut ordinatum et inordinatum. For they say that out of unordered elements, ordered things were made, God reducing the disorder among the elements to order, as Plato says in the Timaeus. But geometers do not say that a triangle is composed out of separated lines but out of lines. The situation would be similar if those in question solely said that the world results from elements, but what they say is that the orderly world came about from disordered elements. Now it is not possible for something to be at once ordered and disordered, but a process of generation is required through which one is separated from the other, so that before generation it is disordered, and after generation ordered. Consequently it is necessary to suppose some time distinguishing the two. But no such distinction of time is required in the descriptions of figures — for it is not necessary that a line and a triangle be distinguished in the order of time as ordered and disordered are. Volunt autem quidam adhuc excusare Platonem, quasi non posuerit quod inordinatio prius tempore fuerit in elementis mundi, et postea aliquo tempore incoeperint ordinari; sed quia inordinatio semper quantum ad aliquid adiuncta est elementis mundi, licet quantum ad aliquid ordinentur; sicut etiam ipse Aristoteles ponit quod materiae semper adiungitur privatio, quamvis et semper sit secundum aliquid formata. Potest etiam intelligi Platonem dedisse intelligere quid elementa ex se haberent, si non essent ordinata a Deo; non quod prius tempore fuerint inordinata. 233. Still others desire to excuse Plato on the ground that he did not teach that there was a prior disorder in the elements which subsequently, at a later time, began to be ordered, but rather disorder is always present under some aspect in the elements of the world, although under another aspect there is order, as Aristotle himself posits that matter always has a concomitant privation, although it is always in some respect under form. It is also possible to interpret Plato as stressing what the elements would be of themselves if they had not been put in order by God, not that there was ever a time in which they existed disordered. Sed quidquid Plato intellexerit, Aristoteles, sicut dictum est, obiiciebat contra id quod verba Platonis exprimunt. Concludit ergo ex praemissis quod impossibile sit mundum factum esse per generationem, et tamen eum in sempiternum durare. But whatever Plato may have understood about the matter, Aristotle, as has been said, objected against what Plato's words express. He concludes, therefore, from the foregoing that it is impossible for the world to have been generated and yet able to go on forever. Deinde cum dicit: vicissim autem etc., prosequitur opinionem Empedoclis, quam tertio posuerat. Et dicit quod illi qui dicunt mundum vicissim componi et dissolvi, nihil aliud faciunt quam quod adstruunt mundum esse sempiternum secundum substantiam, sed se transmutare secundum formam, sive secundum eius dispositionem; sicut si aliquis videns aliquem ex puero factum virum, si ponatur quod videat vicissim eundem ex viro factum puerum, putet eum quandoque fieri et quandoque corrumpi. Et quod secundum hanc opinionem Empedoclis ponatur ipsa substantia mundi sempiterna, manifestat per hoc quod post separationem elementorum per litem, quando iterum convenient elementa, non fiet qualiscumque ordo mundi et qualiscumque eius constitutio, sed eadem quae nunc est. 234. Then at [169] he takes up the opinion of Empedocles which is the third one mentioned. And he says that those who maintain that the world alternates between being assembled and dissolved do nothing more than assert the substantial permanence of the world but its transmutability with respect to its form or its arrangement. It is as though someone seeing a boy becoming a man, if it should be posited that he sees the same person becoming from a man a boy again, should reckon this person as [alternately] at one time coming into existence and at one time ceasing to be. That the opinion of Empedocles is tantamount to positing the substance of the world as eternal, he manifests by the fact that after the elements shall have been separated by strife and later reassembled, it is not just any order and any new arrangement that will ensue but the very same one that now exists. Et hoc manifestum est et aliter, scilicet per rationem, quia ab eadem causa, scilicet amicitia, congregabuntur tunc elementa, ex qua et prius congregata sunt, et sic eadem constitutio mundi sequetur: sed etiam hoc manifestum est secundum eos qui hanc positionem ponunt, qui asserunt contrarietatem litis et amicitiae, quas ponunt causam contrariae dispositionis in elementis, ut scilicet quandoque sint coniuncta, quandoque separata. Unde concludit quod, si totum corpus mundi, continuum existens, idest coniunctum, quandoque disponatur et aptetur uno modo, quandoque alio modo; cum ipsa consistentia sive substantia omnium corporum vocetur mundus sive caelum, sequitur quod mundus non generetur et corrumpatur, sed solum dispositiones ipsius. And this is made clear "in another way," i.e., by reason, because the very same cause, namely, friendship, will assemble the elements which previously assembled them; consequently, the same arrangement of the world will result. And this is plain also from the teachings of those who hold this position and assert that friendship and strife are contrary and the causes of a contrary disposition in the elements, so that at one time they are assembled and at another separated. Hence he concludes that if the entire body of the world, while remaining "continuous," i.e., conjoined, is now disposed and arranged in one way and later in another way, then, since it is the "combination," or substance, of all bodies that is called the world or heaven, it follows that the world is not generated and destroyed but only its arrangements are. Deinde cum dicit: totaliter autem factum etc., prosequitur opinionem Democriti, quam supra secundo posuerat. 235. Then at [170] he takes Democritus' opinion, which was the second one mentioned. Et primo dicit qualiter se habeat ista opinio;
secundo ostendit quid circa hanc postmodum erit manifestum, ibi: sed tamen et cetera.
First he explains this opinion;
Secondly, he shows what will later be clear about it, at 236.
Dicit ergo primo quod, si aliquis ponat quod mundus sit factus, et totaliter corrumpatur absque regressu, ita scilicet quod nunquam iterum fiat, hoc quidem est impossibile, si ponatur unus tantum mundus. Et hoc ideo, quia si sit unus mundus qui quandoque est factus, cum non sit factus ex nihilo, priusquam fieret existebat substantia quae erat ante eum. Aut ergo ponemus quod illa substantia quae praeerat mundo, poterat subiici generationi, aut non. Et si quidem non poterat generationi subiici, non poterat ex ea fieri mundus: et hoc est quod dicit, qua non facta, vel non genita, idest qua non subiecta generationi, impossibile esse dicimus transmutari, idest non possibile esse quod transmutetur, ad hoc ut ex ea fiat mundus. Si vero in sua natura habebat quod posset transmutari, ad hoc quod fieret ex ea mundus, etiam post corruptionem mundi poterit transmutari, ut ex ea iterum fiat mundus. He says therefore first [170] that if someone should maintain that the world was made, and entirely ceases to be without returning, in such a way, namely, that it will never be restored again, such a thing is impossible, if there is but one world. The reason is that if there is but one world, made at some time, then, since it was not made from nothing, there was, previous to its being made, a substance which existed before it. Either we hold that that substance which pre-existed before the world could have been subject to generation, or that it could not. If not, then the world could not have been made from it. And this is what he says, namely, that if it was not made, or not generated, i.e., not subject to generation, we say it to be impossible of transmutation, i.e., not able to be transmuted in order for the world to be made out of it. But if it possessed in its nature the power to be transmuted, so that the world could be made from it, then also after the destruction of the world it could be transmuted and a world made again from it. Sed si aliquis ponat infinitos mundos, ita scilicet quod ex quibusdam atomis uno modo compositis fiat hic mundus, et ex eisdem vel aliis alio modo compositis fiat alius mundus, et hoc in infinitum; magis poterit sustineri quod dictum est, scilicet quod mundus semel corruptus nunquam iterum generetur; quia ex quo possibile est esse alios mundos, ex illis atomis poterit alius mundus constitui. Sed si non posset esse mundus nisi unus, sequeretur inconveniens: quia materia in quam mundus resolveretur, esset adhuc in potentia ut ex ea fieret mundus; unde si non posset esse alius mundus, oporteret quod idem ipse iterum fieret. But if someone posits infinite worlds, in the sense that from atoms arranged in one way this world comes to be, and from the same or other atoms differently arranged another world comes to be, and so on ad infinitum, such a position would be a better foundation for what was said, namely, that the world once destroyed is never again regenerated, because from the assumption that other worlds are possible, another world could be arranged from those atoms. However, if there could be but one world, something incompatible with the theory follows: the matter into which the world dissolved would still be in potency to have a world made from it. Hence if a different world were impossible, the very same one would have to be produced again. Deinde cum dicit: sed tamen etc., ostendit quid restet dicendum: et dicit quod ex posterioribus erit manifestum utrum hoc sit possibile vel impossibile. Et si quidem ly hoc referatur ad immediate dictum de opinione ponentium infinitos mundos, non est intelligendum quod posteriora hic nominet ea quae immediate sequuntur, in quibus nulla de hoc fit mentio; sed intelliguntur posteriora ea quae dicentur de opinione Democriti in tertio huius, et in I de generatione. Si vero ly hoc referatur ad totum praecedens, ubi actum est de opinione ponentium mundum esse genitum, per posteriora intelliguntur immediate sequentia. 236. Then at [171] he shows what remains to be said, and says that from what will follow, it will be clear whether this is possible or impossible. And if "this" refers to what was just said of the opinion about infinite worlds, the phrase "what will follow" refers, not to what follows immediately, in which nothing is said about this opinion, but to what will be said about the opinion of Democritus in On the Heavens III and in On Generation I. But if "this" refers to the whole preceding section, where there is treated the opinion of those who posit that the world was generated, then the phrase "what will follow" refers to what immediately follows. Et ad hoc concordat quod immediate subditur. Sunt enim quidam, quibus videtur esse contingens quod aliquid quod nunquam fuit generatum, quandoque corrumpatur, et quod aliquid de novo genitum, incorruptibile perduret; sicut in Timaeo dicit Plato non solum quod caelum sit factum de novo, sed etiam quod duret de cetero sempiterno tempore; et sic ponit utrumque dictorum, scilicet quod materia inordinata, quae nunquam incoepit esse inordinata, quandoque esse desinat; et quod mundus incipiat, et nunquam desinat. Et contra istos sic ponentes mundum generari, supra circa principium huius libri naturalibus rationibus processum est solum quantum ad caelum, quod probavit esse ingenitum et incorruptibile, tanquam non habens contrarium: sed nunc hoc manifestabitur universali consideratione de omnibus entibus. And this is confirmed by what he at once adds. For there are some who conceive it possible for something which was never generated to perish at some time, and for something newly generated to remain incorruptible, as Plato says in the Timaeus that the heaven was produced in being, but will nevertheless endure for eternity. Thus he posits both statements: that disarranged matter, which never became disarranged, at some time ceases to be, and that the world began, and never ceases to be. Against those who thus posit that the world began through generation, Aristotle argued above near the beginning of this book with natural reasons solely to the effect that the heaven was proved ungenerated and indestructible, on the ground that it has no contrary. But now this will be shown by a universal consideration of all beings.
Lecture 24:
Various meanings of "generable" and "ungenerable," "corruptible" and "incorruptible"Chapter 11 (280b.) Πρῶτον δὲ διαιρετέον πῶς ἀγένητα καὶ γενητά φαμεν καὶ φθαρτὰ καὶ ἄφθαρτα 172 We must first distinguish the senses in which we use the words 'ungenerated' and 'generated', 'destructible' and 'indestructible'. πολλαχῶς γὰρ λεγομένων, κἂν μηδὲν διαφέρῃ πρὸς τὸν λόγον, ἀνάγκη τὴν διάνοιαν ἀορίστως ἔχειν, ἄν τις τῷ διαιρουμένῳ πολλαχῶς ὡς ἀδιαιρέτῳ χρῆται ἄδηλον γὰρ κατὰ ποίαν φύσιν αὐτῶν συμβαίνει τὸ λεχθέν. 173 These have many meanings, and though it may make no difference to the argument, yet some confusion of mind must result from treating as uniform in its use a word which has several distinct applications. The character which is the ground of the predication will always remain obscure. Λέγεται δ' ἀγένητον ἕνα μὲν τρόπον ἐὰν ᾖ τι νῦν πρότερον μὴ ὂν ἄνευ γενέσεως καὶ μεταβολῆς, καθάπερ ἔνιοι τὸ ἅπτεσθαι καὶ τὸ κινεῖσθαι λέγουσιν οὐ γὰρ εἶναι γενέσθαι φασὶν ἁπτόμενον, οὐδὲ κινούμενον. Ἕνα δ' εἴ τι ἐνδεχόμενον γίνεσθαι ἢ γενέσθαι μή ἐστιν ὁμοίως γὰρ καὶ τοῦτο ἀγένητον, ὅτι ἐνδέχεται γενέσθαι. Ἕνα δ' εἴ τι ὅλως ἀδύνατον γενέσθαι, ὥσθ' ὁτὲ μὲν εἶναι ὁτὲ δὲ μή. (Τὸ δ' ἀδύνατον λέγεται διχῶς. Ἢ γὰρ τῷ μὴ ἀληθὲς εἶναι εἰπεῖν ὅτι γένοιτ' ἄν, ἢ τῷ μὴ ῥᾳδίως μηδὲ ταχὺ ἢ καλῶς.) 174 The word 'ungenerated' then is used (a) in one sense whenever something now is which formerly was not, no process of becoming or change being involved. Such is the case, according to some, with contact and motion, since there is no process of coming to be in contact or in motion. (b) It is used in another sense, when something which is capable of coming to be, with or without process, does not exist; such a thing is ungenerated in the sense that its generation is not a fact but a possibility. (c) It is also applied where there is general impossibility of any generation such that the thing now is which then was not. And 'impossibility' has two uses: first, where it is untrue to say that the thing can ever come into being, and secondly, where it cannot do so easily, quickly, or well. Τὸν αὐτὸν δὲ τρόπον καὶ τὸ γενητὸν ἕνα μὲν εἰ μὴ ὂν πρότερον ὕστερον ἔστιν, εἴτε γινόμενον εἴτ' ἄνευ τοῦ γίνεσθαι, ὁτὲ μὲν μὴ ὄν, πάλιν δ' ὄν. Ἕνα δ' εἰ δυνατόν, εἴτε τῷ ἀληθεῖ διορισθέντος τοῦ δυνατοῦ εἴτε τῷ ῥᾳδίως. Ἕνα δ' ἐὰν ἡ γένεσις αὐτοῦ ἐκ τοῦ μὴ ὄντος εἰς τὸ ὄν, εἴτ' ἤδη ὄντος, διὰ τοῦ γίνεσθαι δ' ὄντος, εἴτε καὶ μήπω ὄντος, ἀλλ' ἐνδεχομένου. 175 In the same way the word 'generated' is used, (a) first, where what formerly was not afterwards is, whether a process of becoming was or was not involved, so long as that which then was not, now is; (b) secondly, of anything capable of existing, 'capable' being defined with reference either to truth or to facility; (c) thirdly, of anything to which the passage from not being to being belongs, whether already actual, if its existence is due to a past process of becoming, or not yet actual but only possible. Καὶ φθαρτὸν δὲ καὶ ἄφθαρτον ὡσαύτως εἴτε γὰρ πρότερόν τι ὂν ὕστερον ἢ μή ἐστιν ἢ ἐνδέχεται μὴ εἶναι, φθαρτὸν εἶναί φαμεν, εἴτε φθειρόμενόν ποτε καὶ μεταβάλλον, εἴτε μή. Ἔστι δ' ὅτε καὶ τὸ διὰ τοῦ φθείρεσθαι ἐνδεχόμενον μὴ εἶναι φθαρτὸν εἶναί φαμεν, καὶ ἔτι ἄλλως τὸ ῥᾳδίως φθειρόμενον, ὃ εἴποι ἄν τις εὔφθαρτον. 176 The uses of the words 'destructible' and 'indestructible' are similar. 'Destructible' is applied (a) to that which formerly was and afterwards either is not or might not be, whether a period of being destroyed and changed intervenes or not; and (b) sometimes we apply the word to that which a process of destruction may cause not to be; and also (c) in a third sense, to that which is easily destructible, to the 'easily destroyed', so to speak. Καὶ περὶ τοῦ ἀφθάρτου ὁ αὐτὸς λόγος Ἢ γὰρ τὸ ἄνευ φθορᾶς ὁτὲ μὲν ὂν ὁτὲ δὲ μὴ ὄν, οἷον τὰς ἁφάς, ὅτι ἄνευ τοῦ φθείρεσθαι πρότερον οὖσαι ὕστερον οὐκ εἰσίν. Ἢ τὸ ὂν μέν, δυνατὸν δὲ μὴ εἶναι, ἢ καὶ οὐκ ἐσόμενόν ποτε, νῦν δ' ὄν σὺ γὰρ εἶ, καὶ ἡ ἁφὴ νῦν ἀλλ' ὅμως φθαρτόν, ὅτι ἔσται ποτὲ ὅτε οὐκ ἀληθὲς εἰπεῖν ὅτι εἶ, οὐδὲ ταῦτα ἅπτεσθαι. Τὸ δὲ μάλιστα κυρίως, τὸ ὂν μέν, ἀδύνατον δὲ φθαρῆναι οὕτως ὥστε νῦν ὂν ὕστερον μὴ εἶναι ἢ ἐνδέχεσθαι μὴ εἶναι. Ἢ καὶ τὸ μήπω ἐφθαρμένον, ἐνδεχόμενον δ' ὕστερον μὴ εἶναι. Λέγεται δ' (281a.) ἄφθαρτον καὶ τὸ μὴ ῥᾳδίως φθειρόμενον. 177 Of the indestructible the same account holds good. It is either (a) that which now is and now is not, without any process of destruction, like contact, which without being destroyed afterwards is not, though formerly it was; or (b) that which is but might not be, or which will at some time not be, though it now is. For you exist now and so does the contact; yet both are destructible, because a time will come when it will not be true of you that you exist, nor of these things that they are in contact. Thirdly (c) in its most proper use, it is that which is, but is incapable of any destruction such that the thing which now is later ceases to be or might cease to be; or again, that which has not yet been destroyed, but in the future may cease to be. For indestructible is also used of that which is destroyed with difficulty.
Postquam philosophus prosecutus est opiniones aliorum circa propositam quaestionem de mundo, an sit genitus et corruptibilis, hic prosequitur praedictam quaestionem secundum suam opinionem. 237. After discussing others' opinions about whether the world is generated and destructible [corruptible], the Philosopher here pursues this question according to his own opinion. Et primo praemittit quaedam quae sunt necessaria ad investigationem propositi;
secundo prosequitur propositam quaestionem, ibi: determinatis autem his et cetera.
First he presents pre-notes needed in his investigation of the question;
Secondly, he pursues the question (L. 26).
Circa primum duo facit: About the first he does two things: primo distinguit multiplicitatem horum nominum, quibus utitur in quaestione, scilicet geniti et ingeniti, corruptibilis et incorruptibilis;
secundo distinguit multiplicitatem quorundam nominum, quae in praedictorum definitione cadunt, scilicet possibilis et impossibilis, ibi: si itaque haec sic habent et cetera.
First he distinguishes various senses of the following words used in the question: namely, "generated" and "ungenerated," "destructible" and "indestructible";
Secondly, he distinguishes various senses of certain words used in the definitions of the foregoing: namely, "possible" and "impossible" (L. 25).
Circa primum duo facit: About the first he does two things: primo dicit de quo est intentio;
secundo propositum prosequitur, ibi: dicitur autem ingenitum et cetera.
First he reveals his intention;
Secondly, he carries it out, at 239.
Circa primum duo facit. About the first he does two things: Primo dicit de quo est intentio: et dicit quod circa inquisitionem praedictae quaestionis, primo oportet distinguere quibus modis aliqua dicuntur generabilia et ingenerabilia, et iterum corruptibilia et incorruptibilia. First he reveals his intention [172] and says that in investigating the foregoing question it is first of all necessary to distinguish the various ways in which things are said to be "generable" and "ungenerable," "destructible" and "indestructible."
Deinde cum dicit: multipliciter enim dictis etc., assignat rationem suae intentionis. Et dicit quod quando aliqua multipliciter dicuntur, contingit quandoque quod illa multiplicitas nullam differentiam inducat quantum ad rationem quae proponitur, quando scilicet in illa ratione sumitur nomen solum in una significatione: tunc enim multiplicitas differentiam facit in ratione, quando nomen sumitur in diversis significationibus. Sed tamen, licet nulla differentia fiat quantum ad rationem, tamen intellectus audientis confuse se habet, si aliquis utatur nomine quod multipliciter potest distingui, tanquam distingui non posset: quia quando aliquis utitur indistincte nomine multiplici, non est manifestum secundum quam naturam significatam accidit conclusio. 238. Secondly, at [173] he reveals the reason for his intention and says that when things are said in a number of ways, it sometimes happens that this multiplicity produces no difference with regard to the argument proposed, i.e., when a particular word is restricted to one meaning in the course of the argument. But when a particular word is used with different meanings, such a multiplicity does make a difference. Even where there is no difference as to the argument, the intellect of the hearer becomes confused, if someone uses a word which can be distinguished in many ways as though it could not — for when someone uses a word of multiple meaning, it is not evident according to which signified essence the conclusion occurs. Deinde cum dicit: dicitur autem ingenitum etc., distinguit praedicta nomina: 239. Then at [174] he distinguishes the aforesaid words: et primo ingenitum et genitum;
secundo corruptibile et incorruptibile, ibi: et corruptibile autem et cetera.
First, "ungenerated" and "generated";
Secondly, "destructible" and "indestructible," at 243.
Circa primum duo facit: About the first he does two things: primo distinguit hoc nomen ingenitum;
secundo hoc nomen genitum, ibi: eodem autem modo et cetera.
First he distinguishes the word "ungenerated";
Secondly, the word "generated," at 241.
Ponit autem primo quod hoc nomen ingenitum dicitur tribus modis. Quorum primus est prout dicitur aliquid ingenitum, quod quidem nunc est, sed prius non erat, ita tamen quod hoc contingat sine generatione et transmutatione eius quod esse incipit; sicut aliqui ponunt exemplum de eo quod est tangi et moveri; dicunt enim quod tactum et motum non contingit generari. Et hoc probatum est in V Physic., quia, cum generatio sit quaedam species motus sive transmutationis, si motus generaretur, sequeretur quod mutationis esset mutatio. Sic ergo tactus et motus, licet esse incipiant, tamen dicuntur ingenita, quia non generantur, nec nata sunt generari. He declares first [174] that this word "ungenerated" is used in three ways. The first of these is when something is called "ungenerated" which now exists but previously did not, yet this occurs without its having been begotten or transmuted. Some give the example of being touched or moved: for they assert that contact and motion are not generated. And this was proved in Physics V because, since generation is a kind of motion or transmutation, if motion were generated, it would follow that there would be a change of a change. Consequently, contact and motion, although they begin to be, are called "ungenerated," because they are not generated and are not apt to be generated. Secundo modo dicitur aliquid esse ingenitum, quod quidem contingit fieri vel non fieri, et tamen nondum est factum; sicut hominem qui nascetur cras, contingit in futurum fieri vel non fieri, et tamen dicitur ingenitus, quia nondum est natus. Similiter enim et hoc potest dici ingenitum, quasi non genitum, quod contingit generari, quia nondum est generatum, sicut et illud quod non contingit generari. In a second way something is said to be "ungenerated," if it is able to either come to be or not come to be and still it has not yet come to be. For example, a man to be born tomorrow is able, as far as the future is concerned, to come to be and not come to be, and yet he is said to be "ungenerated," because he has not yet been born. For "ungenerated," in the sense of "not generated," can be applied similarly to what is able to come to be, because it is not yet generated, and to what is not able to be generated. Tertio modo dicitur aliquid ingenitum, quod omnino impossibile est fieri hoc modo ut quandoque sit et quandoque non sit, sive per generationem sive quocumque alio modo; et secundum hoc ingenita dicuntur quae non possunt esse, vel quae non possunt non esse. Hic autem modus distinguitur in duos: nam impossibile esse seu fieri dicitur dupliciter; uno modo absolute, quando scilicet simpliciter non est verum dicere quod hoc aliquando fiat; secundo modo prout dicitur aliquid impossibile fieri, quia non de facili potest fieri; et hoc quia non cito potest fieri, vel quia non est bene factibile, sicut si dicamus aliquod malum ferrum non esse bene fabricabile. In a third way something is said to be "ungenerated," when it is entirely impossible for it, through generation or any other way, to come into existence as being able either to exist or not exist. In this sense the word "ungenerated" describes things that cannot be or things that cannot not be. Now this third way is distinguished into two other ways, for there are two ways in which something is "impossible" to be or become: first, absolutely, when it is in no sense true to say that this may at some time come to be; secondly, when a thing is described as impossible to come about because it is not easy for it to come about, either because it does not come about quickly or because its coming into existence cannot be conveniently managed, as when we say that bad iron is not easy to fashion. Ad evidentiam autem horum modorum, considerandum est quod generatio importat aliquid commune, quod est incipere esse; et etiam importat determinatum modum essendi, scilicet per transformationem. Negatio igitur quae importatur hoc nomine ingenitum, uno modo potest negare utrumque, scilicet incoeptionem et modum incipiendi; vel potest solum negare modum incipiendi. Et utrumque contingit dupliciter: uno modo secundum actum, alio modo secundum potentiam. Si igitur praedicta negatio non neget incoeptionem, sed solum modum incipiendi, sic est primus modus, secundum quem dicitur aliquid ingenitum, quod potest incipere esse, sed non per generationem. Si vero neget non potentiam, sed solum actum, ut puta quia potest incipere esse et potest generari, non tamen adhuc incoepit esse vel est generatum, sic est secundus modus. Si vero non solum neget modum incipiendi, sicut in primo modo, nec solum actum generationis, sicut in secundo, sed simul modum incoeptionis et incoeptionem, et quantum ad actum et quantum ad potentiam; sic est tertius modus, qui est perfectissimus, secundum quem proprie et simpliciter dicitur aliquid ingenitum; quamvis et hic modus distinguatur secundum quod possibile dicitur aliquid vel simpliciter vel secundum quid. 240. In order to understand these three ways it should be noted that generation has the common note of something's beginning to exist, and also implies a definite way of existing, namely, through transformation. Therefore the negation implied by the word "ungenerated" may either negate both, namely, both a beginning and the way of beginning, or it can negate only the way of beginning. And both can occur in two ways: in one way in the sphere of act, and in the other in the sphere of potency. Therefore, if the negation does not deny a beginning but merely the manner of beginning, we have the first meaning of the word according to which something is said to be "ungenerated," if it can begin to be but not through generation. But if it does not deny the possibility but merely the actual state, for example, because it can begin to be and can be generated, but has not yet begun to be or been generated, then it is the second sense of the word. But if it does not only deny the manner of its beginning, as in the first sense, or only the actual state of existence, as in the second sense, but both the manner of its beginning and the very beginning itself, both as to its actual state and even its possibility, then it is the third and most perfect sense, according to which something is said to be ungenerated in the strict and absolute sense. This sense, however, is still distinguished according to whether something is said to be "possible" either absolutely or in a qualified sense. Deinde cum dicit: eodem autem modo etc., distinguit significationem huius nominis genitum. Et dicit quod eodem modo genitum dicitur tribus modis. Quorum primus est si aliquid prius non fuit et postea incoepit esse, sive per generationem, sicut homo, sive sine generatione, sicut tactus; dummodo illud quod dicitur genitum, quandoque non sit, et iterum postea sit. 241. Then at [175] he distinguishes the meanings of the word "generated," and says that it is also in three senses that "generated" is used. The first of these occurs if something previously did not exist and later began to exist, either through generation, as man, or without generation, as contact, provided that the thing described as generated is something that one time is not and later is. Secundo modo dicitur aliquid genitum, si possibile sit illud incipere esse; sive possibile determinetur per verum, ut scilicet dicatur possibile quod potest esse, sive determinetur per facile, ut scilicet dicatur possibile fieri quod de facili potest. In a second way, something is described as "generated," if it is possible for it to begin to exist, where "possible" refers either to the truth, i.e., to what can exist, or to what is easy, i.e., can easily be made to exist. Tertio modo dicitur aliquid genitum, cuius potest esse generatio, ut per hoc procedat de non esse in esse: et hoc indifferenter sive iam esse incoeperit, et hoc per fieri, idest per modum generationis; sive nondum esse incoeperit, sed contingat illud esse incipere per modum generationis. In the third way, something is described as "generated," if it can be the subject of generation and proceeds thus from non-existence to existence. In this third sense it makes no difference whether the thing has already begun to be, and this by being made, i.e., through the process of generation, or whether it has not yet begun to be, but may come to be through generation. Apparet etiam secundum praemissa ratio horum modorum. Quia cum dicitur genitum secundum primum modum, asseritur actualis incoeptio, non autem modus determinatus incipiendi, quem significat generatio. Secundum autem modum secundum, asseritur possibilitas incoeptionis absque determinato modo incipiendi: et hic modus potest distingui in duos secundum distinctionem potentiae. Secundum autem modum tertium, asseritur non solum incoeptio, sed determinatus modus incipiendi: et hic modus potest distingui in duos, quia vel asseritur determinatus modus incipiendi secundum actum, ut quia sit aliquid iam generatum; aut secundum potentiam, ut quia aptum natum sit generari. In keeping with what has been said, the notion of these ways is apparent. Because when something is called "generated" in the first sense, its actual inception is asserted but not a definite mode of inception that the word "generation" signifies. But in the second sense the possibility of inception is asserted without asserting the definite way it began, which sense is distinguished according to the way "potency" is distinguished. However, the third way asserts not only inception but a definite kind of inception. And this third way can be further distinguished into two: for it asserts either a definite kind of inception that is actual, as when something is already generated, or one that is potential, as indicating something is naturally apt to be generated. Et si quis recte consideret modos quos posuit circa genitum, differunt a modis quos posuit circa ingenitum dupliciter: uno modo secundum distinctionem, alio modo secundum ordinem. 242. Now if anyone rightly considers the senses he has set down of the word "generated," he will see that they differ from the senses of "ungenerated" in two ways: first with respect to distinction, and, secondly, with respect to order. Secundum distinctionem quidem, quia in distinctione modorum ingeniti, sub alio modo comprehendebatur negatio determinati modi incipiendi secundum potentiam, et in alio secundum actum: nam in primo modo dicebatur ingenitum, quod non poterat incipere per generationem; in secundo autem quod poterat incipere per generationem, sed nondum erat generatum. With respect to distinction: In distinguishing the senses of "ungenerated," the denial of a definite kind of inception as possible was included under one sense and the denial of the same kind of inception as actual, was included under another sense — for in the first sense "ungenerated" referred to what could not begin to be through generation, but in the second it referred to what could begin to be through generation but had not yet been generated. Sed quantum ad negationem incoeptionis in communi, sub eodem modo comprehendebat negationem potentiae et actus: dicebatur enim tertio modo ingenitum, quod nec incoepit esse, nec potest incipere. Sed circa modos geniti, e converso ex parte incoeptionis in communi distinguit modos secundum potentiam et actum: nam primus modus est quod actu incipit esse quocumque modo; secundus modus est quod potest incipere quocumque modo, licet nondum incoeperit. Sed ex parte determinati modi incipiendi, sub uno modo comprehendit potentiam et actum: dicitur enim tertio modo genitum, quod vel est generatum vel potest generari. Et sic patet quod isti tres modi non directe contraponuntur tribus primis: quia quod ibi distinguebatur, hic remanet indistinctum, et e converso. But in regard to the denial of inception in common, both the possibility and the actuality of inception are included under the same sense — for the third sense of "ungenerated" referred to what has both not begun to be and cannot begin to be. But conversely, in the senses of "generated" it is on the part of a beginning in common that he distinguishes the modalities according to potency and act — for the first sense refers to what actually begins to be in any way whatever, while the second sense refers to what can begin in any way, although it has not yet begun. However, with regard to a definite kind of inception, the actuality and possibility are included under one mode —for in the third sense something is described as "generated" which either has been generated or can be generated. Thus it is plain that the last three senses are not exactly parallel to the first three, because what was distinguished in the first remains undistinguished in the second, and vice versa. Secundum ordinem autem differunt isti modi. Nam in modis ingeniti praemittebatur id quod pertinet ad determinatum modum incoeptionis, ei quod pertinet ad incoeptionem in communi: sed circa modos geniti praemittitur id quod est ex parte incoeptionis in communi. Et hoc subtili ratione Aristoteles fecit. Voluit enim primo ponere modos imperfectos, et ultimo modos perfectos: differenter autem se habent negatio et affirmatio circa proprium et commune. Nam negatio quae negat proprium, est imperfecta; negatio autem quae negat commune, est perfecta, quia negato communi negatur proprium: et ideo ultimum modum ingeniti quasi perfectum posuit, quo negatur incoeptio in communi. Et quia negatio particularis modi incipiendi est imperfecta, ideo ex hac parte posuit partiales modos distinctos secundum potentiam et actum. With respect to order these senses are different: For in presenting the modes of "ungenerated," that which pertains to a definite kind of inception was placed before that which pertains to inception in common, whereas in presenting the modes of "generated," that which pertains to inception in common was mentioned first. And Aristotle had a subtle reason for so doing. For he wanted to list the imperfect senses first and the perfect ones last. Now denial and affirmation are related to the proper and to the common in different ways: for a denial of what is proper is imperfect, but a denial of what is common is perfect, because when the common is denied, the proper is denied. Consequently, the last sense of "ungenerated" is presented as the perfect sense, because it denies inception in general. And because the denial of a particular kind of inception is imperfect, he presents the partial modes as distinguished according to potency and act. Sed affirmatio proprii est perfecta, quia posito proprio ponitur commune; affirmatio autem communis est imperfecta: et ideo ultimum modum geniti posuit tanquam perfectum, quod incoepit esse per generationem; et comprehendit sub hoc modo, tanquam sub perfecto, et potentiam et actum. Modos autem pertinentes ad incoeptionem in communi, praemisit tanquam imperfectos: non enim perfecte dicitur aliquid genitum ex hoc solo quod incoepit esse. Et ideo ex hac etiam parte distinxit hos modos, tanquam partiales, secundum potentiam et actum. But the affirming of what is proper is perfect, because in affirming what is proper that which is common is also affirmed, while the affirming of what is common is imperfect. Accordingly, the last sense of "generated" is presented as the perfect one, namely, when something begins to be through generation, and he includes under this sense, as under the perfect sense, both the possibility and the actuality. However, the senses pertaining to inception in general are presented first, as the imperfect senses: for a thing is not said to be "generated" in the perfect sense just because it has begun to be. For this reason he distinguished these modes, as partial, into one referring to possibility and another referring to actuality. Deinde cum dicit: et corruptibile autem etc., distinguit modos corruptibilis et incorruptibilis: 243. Then at [176] he distinguishes the senses of "destructible" and "indestructible": et primo corruptibilis;
secundo incorruptibilis, ibi: et de incorruptibili et cetera.
First, "destructible";
Secondly, "indestructible," at 245.
Dicit ergo primo quod corruptibile et incorruptibile similiter dicuntur multipliciter: et ponit tres modos corruptibilis. Ubi considerandum est quod, sicut generatio importat incoeptionem cum determinato modo, ita corruptio importat desitionem cum determinato modo, scilicet transmutationis. Primus ergo modus corruptionis ponit desitionem in communi, absque distinctione potentiae et actus. Et est eadem ratio ordinis quae est supra de genito: sicut enim non dicitur aliquid perfecte genitum ex hoc quod incipit esse, ita non dicitur aliquid perfecte corruptum ex hoc quod desinit esse, nec perfecte corruptibile ex hoc quod potest desinere esse. He says therefore first [176] that "destructible" and "indestructible" are also said in many senses, and he presents three senses of "destructible." Now it should be noted that, just as generation implies inception in a definite way, so, too, destruction implies extinction in a definite way, namely, through transmutation. Consequently, the first sense of "destruction" is that of extinction in common without any distinction between possibility and actuality. And the reason for this order is the same as that used above for the word "generated": just as a thing is not said perfectly to be "generated" just because it begins to be, so a thing is not said perfectly to be "destroyed" just because it ceases to be, nor "destructible" just because it can cease to be. Est ergo primus modus, secundum quem dicimus aliquid esse corruptibile, quod, cum prius sit aliquid, posterius vel non est vel contingit non esse; sive hoc contingat per corruptionem et transmutationem, sicut homo est corruptibilis; sive non per corruptionem et transmutationem desinat esse, sicut tactus et motus. Therefore the first sense in which we describe something as "destructible" is when it previously existed but later it either is not, or is able not to be, whether this is due to perishing and transmutation, as a man is perishable, or not through perishing and transmutation, as contact and motion cease to be. Secundo modo dicimus aliquid esse corruptibile, quod contingit non esse, idest quandoque potest desinere esse, per specialem modum corruptionis. In the second sense we describe something as "destructible," if it can not be, i.e., able at some time to cease to be, on account of a specific way of ceasing to be. Tertio modo dicitur aliquid corruptibile, quod de facili corrumpitur: quod potest dici euphtharton, idest bene corruptibile. In the third sense, something is said to be "destructible," because it is easily destroyed, and can be called "euphtharton," i.e., well destructible. Est autem considerandum quod, licet modi corruptibilis cum modis geniti conveniant quantum ad ordinem, quia sicut ibi praemittitur generalis incoeptio, ita hic praemittitur generalis desitio; est tamen differentia quantum ad distinctionem. Nam ibi distinguebantur modi secundum actum et potentiam: hic autem distinguuntur modi secundum potentiam absolutam, et perfectam; quod est ultimus modus, tanquam perfectissimus; perfectissime enim corruptibile est quod de facili potest corrumpi. Et huius ratio est, quia genitum dicitur secundum actum, corruptibile autem dicitur secundum potentiam: unde genitum potest intelligi secundum actum et secundum potentiam, sed corruptibile non potest intelligi nisi secundum potentiam. 244. It should be observed that although the senses of "destructible" agree with those of "generated" as far as the order is concerned for just as in the latter there is placed first inception in general, so here there is placed first destruction in general, there is a difference in the way their modes are distinguished. For there the modes were distinguished according to possibility and actuality, but here they are distinguished according to absolute, and perfect, possibility, which latter is the last, as the most perfect mode — for the most perfectly destructible is what is easily destroyed. The reason for this is that "generated" is said according to act, while "destructible" according to potency. Hence "generated" can refer to both actuality and possibility, but "destructible" to possibility only. Ideo autem posuit genitum secundum actum, et corruptibile secundum potentiam, quia cum generatio sit de non esse in esse, corruptio de esse in non esse, illud quod est generabile nondum est ens, sed solum illud quod iam est genitum: e converso autem id quod est corruptibile est ens, non autem id quod iam est corruptum. Intendit autem philosophus facere quaestionem de entibus, non autem de non entibus: et ideo utitur nomine geniti et corruptibilis. The reason he set down "generated," which is according to act, and "corruptible," which is according to potency, is this: Since generation is from non-being to being, and corruption from being to non-being, that which is "generable" is not yet a being, but only that which has been "generated" is; on the other hand, that which is "corruptible" is a being, but that which has been "corrupted" is no longer a being. Now the intention of the Philosopher is to discuss a question, not of non-beings but of beings. And that is why he employs the words "generated" and "corruptible." Deinde cum dicit: et de incorruptibili etc., distinguit modos incorruptibilis. Et dicit quod de incorruptibili etiam est eadem distinctionis ratio. Ponit enim tres modos. Quorum primus est secundum negationem determinati modi desitionis; secundum scilicet quod incorruptibile dicitur, quod quidem potest desinere sic quod quandoque sit ens et postmodum non ens, sed hoc sine corruptione; sicut tactus et motus, qui cum primo sint, posterius non sunt, sed hoc est sine corruptione eorum, quia eorum non est corruptio, sicut nec generatio. Unde hic modus respondet primo modo ingeniti. 245. Then at [177] he distinguishes the senses of "indestructible." And he presents three senses. The first of these denies a definite kind of extinguishing process, insofar as that is said to be "indestructible" which can cease to be in such a way that at one time it exists and later does not, but this without corruption. Examples are contact and motion which, after first existing do not later, but this is without their corruption, since things are subject neither to generation nor corruption. Consequently, this sense corresponds to the first sense of "ungenerated." Secundo modo dicitur aliquid incorruptibile secundum negationem desitionis in communi: et sic dicit quod illud quod nunc est ens, et est impossibile quod postea non sit, vel quandoque non sit futurum, dicitur incorruptibile. Et hic modus incorruptibilitatis non competit alicui rei quae possit desinere esse per corruptionem: tu enim qui potes desinere esse per corruptionem, es nunc in praesenti; et similiter tactus, qui potest desinere esse, sed non per corruptionem, est nunc; sed tamen utrumque horum dicitur aliquo modo corruptibile, scilicet secundum primum modum corruptibilis; quia scilicet erit aliquando quando non erit verum dicere quod tu sis, nec erit verum dicere quod hoc tangatur. Et ideo illud maxime proprie dicitur incorruptibile, quod quidem est ens, sed impossibile est illud corrumpi hoc modo ut, cum modo sit ens, posterius non sit ens aut contingat non esse, et quamvis nondum sit corruptum, tamen contingat postremo illud non esse: illud enim quod non hoc modo se habet, dicitur proprie incorruptibile. In a second sense something is called "indestructible," when extinction in common is denied. And he says that "indestructible" in this sense refers to what is now a being and it is impossible for it later not to be a being, or not to be in the future. This kind of indestructibility does not belong to any thing that can cease to be through corruption. For you, who can cease to be through corruption, exist now, and so does contact, which can cease to be, but not by corruption — yet both of these are called "corruptible" in a certain way, since a time will come when it will not be true to say that you exist, or that this is in contact. And, therefore, that is most properly called "indestructible" which is, indeed, a being but cannot be destroyed in such a way that, while it is a being now, later it will not be, or is able not to be, and although not yet destroyed can, nevertheless, eventually become non-existent. What is not so constituted is properly called "indestructible." Tertio modo dicitur aliquid incorruptibile, quod non de facili corrumpitur. Quod etiam respondet tertio modo corruptibilis, sicut et secundus secundo, et primus primo. In a third sense, something is called "indestructible" which is not destroyed easily. And this corresponds to the third sense of "destructible," just as the second corresponds to the second, and the first to the first.
Lecture 25:
How something is said to be "possible" and "impossible".Chapter 11 cont. Εἰ δὴ ταῦθ' οὕτως ἔχει, σκεπτέον πῶς λέγομεν τὸ δυνατὸν καὶ ἀδύνατον 178 This being so, we must ask what we mean by 'possible' and 'impossible'. τό τε γὰρ κυριώτατα λεγόμενον ἄφθαρτον τῷ μὴ δύνασθαι ἂν φθαρῆναι, μηδ' ὁτὲ μὲν εἶναι ὁτὲ δὲ μή λέγεται δὲ καὶ τὸ ἀγένητον τὸ ἀδύνατον καὶ μὴ δυνάμενον γενέσθαι οὕτως ὥστε πρότερον μὲν μὴ εἶναι ὕστερον δὲ εἶναι, οἷον τὴν διάμετρον σύμμετρον. 179 For in its most proper use the predicate 'indestructible' is given because it is impossible that the thing should be destroyed, i.e. exist at one time and not at another. And 'ungenerated' also involves impossibility when used for that which cannot be generated, in such fashion that, while formerly it was not, later it is. An instance is a commensurable diagonal. Εἰ δή τι δύναται κινηθῆναι [στάδια ἑκατὸν] ἢ ἆραι βάρος, ἀεὶ πρὸς τὸ πλεῖστον λέγομεν, οἷον τάλαντα ἆραι ἑκατὸν ἢ στάδια βαδίσαι ἑκατόν (καίτοι καὶ τὰ μόρια δύναται τὰ ἐντός, εἴπερ καὶ τὴν ὑπεροχήν), ὡς δέον ὁρίζεσθαι πρὸς τὸ τέλος καὶ τὴν ὑπεροχὴν τὴν δύναμιν. Ἀνάγκη μὲν οὖν τὸ δυνατὸν καθ' ὑπεροχὴν τοσαδὶ καὶ τὰ ἐντὸς δύνασθαι, οἷον εἰ τάλαντα ἑκατὸν ἆραι, καὶ δύο, κἂν εἰ στάδια ἑκατόν, καὶ δύο δύνασθαι βαδίσαι. 180 Now when we speak of a power to move or to lift weights, we refer always to the maximum. We speak, for instance, of a power to lift a hundred talents or walk a hundred stades—though a power to effect the maximum is also a power to effect any part of the maximum—since we feel obliged in defining the power to give the limit or maximum. A thing, then, which is within it. If, for example, a man can lift a hundred talents, he can also lift two, and if he can walk a hundred stades, he can also walk two. But the power is of the maximum, Ἡ δὲ δύναμις τῆς ὑπεροχῆς ἐστίν κἂν εἴ τι ἀδύνατον τοσονδὶ καθ' ὑπερβολὴν εἰπόντων, καὶ τὰ πλείω ἀδύνατον, οἷον ὁ χίλια βαδίσαι στάδια μὴ δυνάμενος δῆλον ὅτι καὶ χίλια καὶ ἕν. 181 and a thing said, with reference to its maximum, to be incapable of so much is also incapable of any greater amount. It is, for instance, clear that a person who cannot walk a thousand stades will also be unable to walk a thousand and one. Μηδὲν δ' ἡμᾶς παρενοχλείτω διωρίσθω γὰρ κατὰ τῆς ὑπεροχῆς τὸ τέλος λεγόμενον τὸ κυρίως δυνατόν. Τάχα γὰρ ἐνσταίη τις ἂν ὡς οὐκ ἀνάγκη τὸ λεχθέν ὁ γὰρ ὁρῶν στάδιον οὐ καὶ τὰ ἐντὸς ὄψεται μεγέθη, ἀλλὰ τοὐναντίον μᾶλλον ὁ δυνάμενος ἰδεῖν στιγμὴν ἢ ἀκοῦσαι μικροῦ ψόφου καὶ τῶν μειζόνων ἕξει αἴσθησιν. 182 This point need not trouble us, for we may take it as settled that what is, in the strict sense, possible is determined by a limiting maximum. Now perhaps the objection might be raised that there is no necessity in this, since he who sees a stade need not see the smaller measures contained in it, while, on the contrary, he who can see a dot or hear a small sound will perceive what is greater. Ἀλλ' οὐδὲν διαφέρει πρὸς τὸν λόγον διωρίσθω γὰρ ἤτοι ἐπὶ τῆς δυνάμεως ἢ ἐπὶ τοῦ πράγματος ἡ ὑπερβολή. Τὸ γὰρ λεγόμενον δῆλον ἡ μὲν γὰρ ὄψις ἡ τοῦ ἐλάττονος ὑπερέχει, ἡ δὲ ταχυτὴς ἡ τοῦ πλείονος. 183 This, however, does not touch our argument. The maximum may be determined either in the power or in its object. The application of this is plain. Superior sight is sight of the smaller body, but superior speed is that of the greater body.
Postquam philosophus ostendit quot modis dicitur genitum et ingenitum, corruptibile et incorruptibile, hic exponit significationem huius quod dicitur possibile et impossibile. 246. After pointing out the various senses of "generated" and "ungenerated," "destructible" and "indestructible," the Philosopher here explains the meaning of what is called "possible" and "impossible." Et primo dicit de quo est intentio;
secundo exequitur propositum, ibi: si itaque aliquid potest et cetera.
First he reveals his intention;
Secondly, he executes his plan, at 248.
Circa primum duo facit. About the first he does two things: Primo dicit de quo est intentio: et dicit quod, cum ita se habeant ea quae dicta sunt circa significationem geniti et ingeniti, corruptibilis et incorruptibilis, oportet considerare quomodo dicatur aliquid possibile et impossibile. First he states what his intention is concerned with [178], and says that since the situation is thus with regard to the meanings of "generated" and "ungenerated," "destructible" and "indestructible," it is necessary to consider how something is said to be "possible" and "impossible." Secundo ibi: propriissime enim etc., assignat rationem suae intentionis, quia scilicet possibile et impossibile includuntur in ratione praedictorum. Quia, ut supra dictum est, propriissime dicitur aliquid esse incorruptibile, quod non solum non potest corrumpi, sed nec etiam quocumque modo aliquando esse et postea non esse. Et similiter ingenitum proprie dicitur quod est impossibile, scilicet esse et non esse, et quod non potest fieri quocumque tali modo quod prius non sit et postea sit; sicut diametrum quadrati esse symmetrum, idest commensuratum lateri quadrati, est ingenitum, quia nullo modo potest incipere esse. 247. Secondly, at [179] he gives the reason for his intention, namely, that "possible" and "impossible" are included in the definition of the aforesaid. For, as has been said above, that is most appropriately called "indestructible" which not only cannot be destroyed but can in no way exist at one time and later not exist. Similarly, "ungenerated" is appropriately applied to what is impossible, namely, to be and not to be, and which cannot come to be in any way such that previously it does not exist and later does exist. Thus, for the diagonal of a square to be symmetric, i.e., commensurate, to the side, is ungenerated, because it never can begin to be. Deinde cum dicit: si itaque aliquid potest etc., ostendit quomodo aliquid dicatur possibile et impossibile. Et est notandum quod, sicut dicit philosophus in V Metaphys., possibile et impossibile uno modo dicitur absolute, quia scilicet secundum se est tale quod possit esse verum vel non possit esse verum, propter habitudinem terminorum ad invicem; alio modo dicitur possibile et impossibile alicui, quod scilicet potest vel secundum potentiam activam vel passivam. Et sic accipitur hic possibile et impossibile, scilicet quod aliquod agens aut patiens potest aut non potest: haec enim significatio maxime congruit rebus naturalibus. 248. Then at [180] he shows how something is described as possible and impossible. And it should be noted that, as the Philosopher says in Metaphysics V, possible and impossible are said in one way absolutely, namely, because in themselves they can be true or cannot be true by reason of the relationship existing between the terms; in another way a thing is said to be possible or impossible to something, namely, what it is able for with respect to its active or passive power. And it is in this sense that "possible" and "impossible" are taken here, namely, as what is, or is not, within the power of an agent or patient — for this is the meaning that is most appropriate to natural things. Primo ergo ostendit quomodo dicatur aliquid esse possibile vel impossibile;
secundo excludit obiectionem, ibi: nihil autem nos turbet et cetera.
First, then, he shows how something is said to be "possible" or "impossible";
Secondly, he excludes an objection, at 251.
Circa primum duo facit: With respect to the first he does two things: primo manifestat quomodo dicatur aliquid esse possibile;
secundo ostendit quomodo dicatur aliquid esse impossibile, ibi: et utique si quid et cetera.
First he manifests how some thing is said to be "possible";
Secondly, how something is called "impossible," at 250.
Ad primi autem manifestationem dicit quod, si contingat aliquam rem posse in aliquid magnum, puta quod aliquis homo ambulet per centum stadia, aut possit levare aliquod magnum pondus, semper determinamus sive denominamus eius potentiam per respectum ad plurimum in quod potest; sicut dicimus potentiam huius hominis esse quod potest levare pondus centum talentorum, aut quod potest ire per spatium centum stadiorum, quamvis possit omnes partes infra istam quantitatem contentas, siquidem potest in id quod superabundat. Nec tamen denominatur ab illis partibus, puta quod determinetur eius potentia quia potest ferre quinquaginta talenta, aut ire quinquaginta stadia; sed per id quod est maximum: ita scilicet ut potentia uniuscuiusque denominetur per respectum ad finem, idest per ultimum et per maximum ad quod potest, et per virtutem suae excellentiae; sicut etiam et magnitudo cuiuslibet rei determinatur per id quod est maximum, sicut quantitatem tricubiti notificantes, non dicimus quod sit bicubitum. Et similiter rationem hominis assignamus per rationale, et non per sensibile: quia semper id quod est ultimum et maximum, est completivum et dans speciem rei. 249. To explain the first [180] he says that if a thing is capable of something great, for example, if a man can walk 100 stades or can lift a great weight, we always determine or describe his power in terms of the most he can do. For example, we say that the power of this man is that he can lift a weight of 100 talents or can walk a distance of 100 stades, even though he is capable of all the partial distances included in that quantity, since he can do what exceeds. But his power is not described by these parts — we do not determine his power as being able to carry 50 talents or walk 50 stades, but by the most he can do. Consequently, the power of each thing is described with respect to the end, i.e., with respect to the ultimate, and to the maximum of which it is capable, and with respect to the strength of its excellence. Thus, too, the size of a thing is determined by what is greatest —for example, in describing the size of something that is three cubits, we do not say that it is two cubits. Similarly, we assign as the notion of man that he is rational, not that he is sensible, because what is the ultimate and greatest in a thing is what completes it and puts upon it the stamp of its species. Sic igitur patet quod ille qui potest in ea quae excellunt, necesse est quod possit etiam in ea quae sunt infra; puta si aliquis potest portare centum talenta, poterit etiam portare duo, et si potest ire per centum stadia, potest ire per duo: sed tamen virtus rei non attribuitur nisi excellentiae, idest, secundum id attenditur virtus rei, quod est excellentissimum omnium eorum in quae potest. Consequently, it is plain that one who can do what exceeds, necessarily can do what is less. For example, if a person can carry 100 talents, he can also carry two, and if he can walk 100 stades, he can also walk two; yet it is to what is excelling that the virtue of a thing is attributed, i.e., the virtue of a thing is gauged in terms of what is most excellent of all the things that can be done. Et hoc est quod dicitur in alia translatione, virtus est ultimum potentiae, quia scilicet virtus rei determinatur secundum ultimum in quod potest. Et hoc etiam habet locum in virtutibus animae: dicitur enim virtus humana, per quam homo potest in id quod est excellentissimum in operibus humanis, scilicet in opere quod est secundum rationem. This is what is said in another translation, "the virtue is the limit of a power," because, namely, the virtue of a thing is determined according to the ultimate it can do. And this applies also to the virtues of the soul: for a human virtue is that through which a man is capable of what is most excellent in human actions, i.e., in an action which is in accordance with reason. Deinde cum dicit: et utique si quid etc., ostendit quomodo dicatur aliquid alicui esse impossibile. Et dicit quod, si aliquod tantum est impossibile alicui, si aliquis accipiat ea quae excellunt, manifestum est quod impossibile erit ei portare vel facere plura; sicut ille qui non potest ire per mille stadia, manifestum est quod non potest ire per mille et unum. Unde patet quod, sicut determinatur id quod est possibile alicui per maximum in quod potest, in quo attenditur virtus eius; ita id quod est impossibile alicui determinatur per minimum eorum in quae non potest, in quo consistit eius debilitas. Puta si maximum in quod potest aliquis, est ire viginti stadia, minimum eorum in quae non potest, est viginti et unum; et ab hoc oportet determinare eius debilitatem, non autem ex eo quod non potest ire per centum vel per mille. 250. Then at [181] he tells how something is said to be "impossible" to a thing. And he says that if some amount is impossible to someone if one takes what excels, it is plain that it will be impossible for him to carry or do more. For example, a person who cannot walk 100 stades clearly cannot walk 101. Hence, it is plain that just as the possibility is determined by the greatest that a thing can do — which determines its virtue — so what is impossible is determined by the least that it cannot do, and this determines its weakness. For example, if the most that someone can do is to go 20 stades, the least that he cannot go is 21 — and it is from this that his weakness is to be determined, and not from his inability to walk 100 or 1,000 stades. Deinde cum dicit: nihil autem nos turbet etc., excludit quandam obiectionem. 251. Then at [182] he excludes an objection. Et primo movet eam;
secundo solvit, ibi: sed nihil differt et cetera.
First he proposes it;
Secondly, he solves it, at 252.
Dicit ergo primo quod nihil debet nos turbare, quin id quod proprie dicitur possibile, sit determinandum secundum terminum excellentiae. Potest enim aliquis instare, quasi non sit necessarium in omnibus id quod dictum est: videtur enim habere instantiam in visu et in aliis sensibus. Ille enim qui videt aliquam magnam quantitatem, puta unius stadii, non potest propter hoc videre magnitudines minoris quantitatis, quae infra illam quantitatem continentur: sed magis accidit contrarium, quia ille qui potest videre punctum, idest aliquod minimum sensu perceptibile, aut etiam qui potest audire parvum sonum, potest et maiora sentire. He says therefore first [182] that nothing should disturb us in connection with the fact that what is properly called "possible" is determined according to the limit of excellence. Someone could, indeed, object that what has been said is not necessary in all matters — for there seems to be an objection in the case of sight and other senses. For a person who sees some large quantity, for example, something a stadium long, cannot for that reason see magnitudes of smaller size contained below that quantity. Rather it is more the opposite that occurs — for one who can see a "point," i.e., some smallest thing perceptible to sense, or hear a faint sound, can sense what is greater. Deinde cum dicit: sed nihil differt etc., solvit praedictam obiectionem. Et dicit quod hoc quod dictum est, nihil differt ad rationem qua determinabatur quod possibile determinatur secundum excellentiam: quia huiusmodi excellentia, secundum quam attenditur virtus rei, potest determinari vel secundum virtutem vel secundum rem. Secundum rem quidem, quando in ipsa re est excellentia, sicut dictum est de centum stadiis vel centum talentis: et secundum hanc excellentiam oportet determinari virtutem activam; quia quod potest agere in rem maiorem, potest etiam in rem minorem. Secundum virtutem autem attenditur excellentia, quando aliquid quod non excellit in quantitate, requirit excellentiam virtutis: et hoc maxime videtur accidere circa potentias passivas; quanto enim aliquid est passibilius, tanto a minori potest moveri. Et quia sensus sunt potentiae passivae, ideo in sensibilibus accidit ut qui potest sentire minus, potest sentire maius. 252. Then at [183] he answers this objection and says that what was stated does not affect the argument whereby it is shown that the possible is determined by excellence. For the excellence according to which the virtue of a thing is measured can be determined according to the virtue, or according to the thing. According to the thing, when there is an excellence right in it, as was said about the 100 stades or the 100 talents. According to this excellence the active virtue is determined, because whatever can act on a greater thing can act on a lesser. But with respect to virtue, there is excellence when something which is not outstanding in quantity requires an excellence of virtue. And this is seen to occur especially with passive powers — for the more a thing is passible, the more it can be moved by what is less. And since the senses are passive powers, it happens in sensible things that one who can sense what is less can sense what is greater. Illud autem quod dictum est, hoc modo manifestat: quia visus qui est sensitivus minoris corporis, excedit in virtute, et sic attenditur hic excellentia in virtute, non in re; sed velocitas est excellentior quae est maioris magnitudinis (illud enim est velocius, quod in eodem tempore per maius spatium movetur), et talis excellentia non solum est in virtute, sed etiam in re. What he has just said he explains as follows: a vision capable of perceiving a smaller body excels in virtue; hence the excellence in this case is an excellence in the virtue and not in the thing. But that speed is more excellent which is of a greater magnitude — for that is speedier which can traverse a greater distance in the same time — and such excellence is an excellence not only in the virtue, but also in the thing.
Lecture 26:
Everything eternal is indestructible and ungeneratedChapter 12 Διωρισμένων δὲ τούτων λεκτέον τὸ ἐφεξῆς. Εἰ δή ἐστιν ἔνια δυνατὰ καὶ εἶναι καὶ μή, ἀνάγκη χρόνον τινὰ ὡρίσθαι τὸν πλεῖστον καὶ τοῦ εἶναι καὶ τοῦ μή, λέγω δ' ὃν δυνατὸν τὸ πρᾶγμα εἶναι καὶ ὃν δυνατὸν μὴ εἶναι καθ' ὁποιανοῦν κατηγορίαν, οἷον ἄνθρωπον ἢ λευκὸν ἢ τρίπηχυ ἢ ἄλλ' ὁτιοῦν τῶν τοιούτων. Εἰ γὰρ μὴ ἔσται ποσός τις, ἀλλ' ἀεὶ πλείων τοῦ προτεθέντος καὶ οὐκ ἔστιν οὗ ἐλάττων, ἄπειρον (281b.) ἔσται χρόνον δυνατὸν εἶναι, καὶ μὴ εἶναι ἄλλον ἄπειρον ἀλλὰ τοῦτ' ἀδύνατον. 184 Having established these distinctions we car now proceed to the sequel. If there are thing! capable both of being and of not being, there must be some definite maximum time of their being and not being; a time, I mean, during which continued existence is possible to them and a time during which continued nonexistence is possible. And this is true in every category, whether the thing is, for example, 'man', or 'white', or 'three cubits long', or whatever it may be. For if the time is not definite in quantity, but longer than any that can be suggested and shorter than none, then it will be possible for one and the same thing to exist for infinite time and not to exist for another infinity. This, however, is impossible. Ἀρχὴ δ' ἔστω ἐντεῦθεν τὸ γὰρ ἀδύνατον καὶ τὸ ψεῦδος οὐ ταὐτὸ σημαίνει. Ἔστι δὲ τὸ ἀδύνατον καὶ δυνατὸν καὶ ψεῦδος καὶ ἀληθὲς τὸ μὲν ἐξ ὑποθέσεως (λέγω δ', οἷον τὸ τρίγωνον ἀδύνατον δύο ὀρθὰς ἔχειν, εἰ τάδε, καὶ ἡ διάμετρος σύμμετρος). Ἔστι δ' ἁπλῶς καὶ δυνατὰ καὶ ἀδύνατα καὶ ψευδῆ καὶ ἀληθῆ. 185 Let us take our start from this point. The impossible and the false have not the same significance. One use of 'impossible' and 'possible', and 'false' and 'true', is hypothetical. It is impossible, for instance, on a certain hypothesis that the triangle should have its angles equal to two right angles, and on another the diagonal is commensurable. But there are also things possible and impossible, false and true, absolutely. Οὐ δὴ ταὐτό ἐστι ψεῦδός τέ τι εἶναι ἁπλῶς καὶ ἀδύνατον ἁπλῶς. Τὸ γάρ σε μὴ ἑστῶτα φάναι ἑστάναι ψεῦδος μέν, οὐκ ἀδύνατον δέ. Ὁμοίως δὲ τὸν κιθαρίζοντα, μὴ ᾄδοντα δέ, ᾄδειν φάναι ψεῦδος, ἀλλ' οὐκ ἀδύνατον. Τὸ δ' ἅμα ἑστάναι καὶ καθῆσθαι, καὶ τὴν διάμετρον σύμμετρον εἶναι, οὐ μόνον ψεῦδος, ἀλλὰ καὶ ἀδύνατον. 186 Now it is one thing to be absolutely false, and another thing to be absolutely impossible. To say that you are standing when you are not standing is to assert a falsehood, but not an impossibility. Similarly to say that a man who is playing the harp, but not singing, is singing, is to say what is false but not impossible. To say, however, that you are at once standing and sitting, or that the diagonal is commensurable, is to say what is not only false but also impossible. Οὐ δὴ ταὐτόν ἐστιν ὑποθέσθαι ψεῦδος καὶ ἀδύνατον. Συμβαίνει δ' ἀδύνατον ἐξ ἀδυνάτου. 187 Thus it is not the same thing to make a false and to make an impossible hypothesis, and from the impossible hypothesis impossible results follow. Τοῦ μὲν οὖν καθῆσθαι καὶ ἑστάναι ἅμα ἔχει τὴν δύναμιν, ὅτι ὅτε ἔχει ἐκείνην, καὶ τὴν ἑτέραν ἀλλ' οὐχ ὥστε ἅμα καθῆσθαι καὶ ἑστάναι, ἀλλ' ἐν ἄλλῳ χρόνῳ. 188 A man has, it is true, the capacity at once of sitting and of standing, because when he possesses the one he also possesses the other; but it does not follow that he can at once sit and stand, only that at another time he can do the other also. Εἰ δέ τι ἄπειρον χρόνον ἔχει πλειόνων δύναμιν, οὐκ ἔστιν ἐν ἄλλῳ χρόνῳ, ἀλλὰ τοῦθ' ἅμα. Ὥστ' εἴ τι ἄπειρον χρόνον ὂν φθαρτόν ἐστι, δύναμιν ἔχοι ἂν τοῦ μὴ εἶναι. Εἰ δὴ ἄπειρον χρόνον, ἔστω ὑπάρχον ὃ δύναται. Ἅμα ἄρ' ἔσται τε καὶ οὐκ ἔσται κατ' ἐνέργειαν. Ψεῦδος μὲν οὖν συμβαίνοι ἄν, ὅτι ψεῦδος ἐτέθη. Ἀλλ' εἰ μὴ ἀδύνατον ἦν, οὐκ ἂν καὶ ἀδύνατον ἦν τὸ συμβαῖνον. Ἅπαν ἄρα τὸ ἀεὶ ὂν ἁπλῶς ἄφθαρτον. 189 But if a thing has for infinite time more than one capacity, another time is impossible and the times must coincide. Thus if a thing which exists for infinite time is destructible, it will have the capacity of not being. Now if it exists for infinite time let this capacity be actualized; and it will be in actuality at once existent and non-existent. Thus a false conclusion would follow because a false assumption was made, but if what was assumed had not been impossible its consequence would not have been impossible. Anything then which always exists is absolutely imperishable. Ὁμοίως δὲ καὶ ἀγένητον εἰ γὰρ γενητόν, ἔσται δυνατὸν χρόνον τινὰ μὴ εἶναι—φθαρτὸν μὲν γάρ ἐστι τὸ πρότερον μὲν ὄν, νῦν δὲ μὴ ὂν ἢ ἐνδεχόμενόν ποτε ὕστερον μὴ εἶναι γενητὸν δὲ ὃ ἐνδέχεται πρότερον μὴ εἶναι—ἀλλ' οὐκ ἔστιν ἐν ᾧ χρόνῳ δυνατὸν τὸ ἀεὶ ὂν ὥστε μὴ εἶναι, οὔτ' ἄπειρον οὔτε πεπερασμένον καὶ γὰρ τὸν πεπερασμένον χρόνον δύναται εἶναι, εἴπερ καὶ τὸν ἄπειρον. Οὐκ ἄρα ἐνδέχεται τὸ αὐτὸ καὶ ἓν ἀεί τε δύνασθαι εἶναι καὶ ἀεὶ μὴ εἶναι. Ἀλλὰ μὴν οὐδὲ τὴν ἀπόφασιν, οἷον λέγω μὴ ἀεὶ εἶναι. Ἀδύνατον ἄρα καὶ ἀεὶ μέν τι εἶναι, φθαρτὸν (282a.) δ' εἶναι. Ὁμοίως δ' οὐδὲ γενητόν δυοῖν γὰρ ὅροιν εἰ ἀδύνατον τὸ ὕστερον ἄνευ τοῦ προτέρου ὑπάρξαι, ἐκεῖνο δ' ἀδύνατον ὑπάρχειν, καὶ τὸ ὕστερον. Ὥστ' εἰ τὸ ἀεὶ ὂν μὴ ἐνδέχεταί ποτε μὴ εἶναι, ἀδύνατον καὶ γενητὸν εἶναι. 190 It is also ungenerated, since if it was generated it will have the power for some time of not being. For as that which formerly was, but now is not, or is capable at some future time of not being, is destructible, so that which is capable of formerly not having been is generated. But in the case of that which always is, there is no time for such a capacity of not being, whether the supposed time is finite or infinite; for its capacity of being must include the finite time since it covers infinite time. It is therefore impossible that one and the same thing should be capable of always existing and of always not-existing. And 'not always existing', the contradictory, is also excluded. Thus it is impossible for a thing always to exist and yet to be destructible. Nor, similarly, can it be generated. For of two attributes if B cannot be present without A, the impossibility A of proves the impossibility of B. What always is, then, since it is incapable of ever not being, cannot possibly be generated.
Postquam philosophus exposuit significationem nominum quae in quaestione proponuntur, hic incipit argumentari ad quaestionem propositam, utrum scilicet aliquid possit esse genitum et incorruptibile, vel ingenitum et corruptibile. 253. After explaining the meanings of the words proposed in the question, the Philosopher here begins to argue on the question proposed, namely, whether something can be generated and indestructible, or ungenerated and destructible. Et primo ostendit hoc esse impossibile per rationes communes;
secundo per rationem propriam scientiae naturalis, ibi: et naturaliter et cetera.
First he shows with general arguments that this is impossible;
Secondly, with arguments proper to natural science, at 286 (L. 29).
Circa primum duo facit: About the first he does two things: primo ostendit quid sequitur ex praemissis circa propositum;
secundo incipit argumentari ad propositum ostendendum, ibi: principium autem sit hinc et cetera.
First he shows what follows from the preceding with respect to the present question;
Secondly, he begins to argue to his proposition, at 255.
Dicit ergo primo quod, determinatis praemissis circa significationem nominum, oportet nunc dicere illud quod consequenter se habet in hac consideratione. Dictum est enim supra quod possibile dicitur secundum aliquod determinatum, puta potens currere dicitur aliquis secundum centum stadia. Sunt autem in rebus quaedam quae possunt esse et non esse. Necesse est ergo ex praemissis quod sit determinatum aliquod plurimum tempus et respectu ipsius esse, ita scilicet quod non possit ampliori tempore esse, et respectu ipsius non esse, ita scilicet quod non possit ampliori tempore non esse. 254. He says therefore first [184] that, the preceding having been determined as to the meanings of certain words, it is now time to state what follows in this treatment. For it has been said above that the "possible" is described in terms of something definite — for example, someone's power to run is described in terms of 100 stades. But there exist in external reality some things that can both exist and not exist. Therefore it is necessary according to the foregoing that there be determined some maximum time both affecting existence, such that it is not possible to exist for a greater time, and affecting non-existence, such that it is not possible not to exist for a greater time. Et ne hoc intelligatur solum de esse substantiali, subiungit quod, cum dicimus possibile vel non possibile rem esse, vel id quod est possibile non esse, potest intelligi secundum quamcumque praedicationem, idest secundum quodcumque praedicamentum: puta hominem esse vel non esse, quod pertinet ad genus substantiae; aut album esse aut non esse, quod pertinet ad genus qualitatis; aut bicubitum esse vel non esse, quod pertinet ad genus quantitatis; aut de quocumque alio consimili. And lest this be understood as applying only to substantial existence, he adds that, when we say that it is possible or not possible for a thing to exist, or that which is able not to exist, such expressions can be understood with regard to any predication, i.e., with regard to any predicament: for example, that a man exist or not exist, which pertains to the genus of substance; or that white exist or not exist, which pertains to the genus of quality; or that "two cubits" exist or not exist, which pertains to the genus of quantity; or any other similar thing. Et quod oporteat intelligi secundum aliquod determinatum tempus, cum dicitur aliquid posse esse vel non esse, probat ducendo ad impossibile. Quia, sicut ipse dicit, si non est aliquod tempus determinatae quantitatis, in quo possit esse vel non esse, sed semper accipiatur maius tempore proposito (puta si potest esse in quinquaginta annis, et adhuc plus, et iterum plus), et non sit devenire ad aliquod tempus respectu cuius omne tempus in quo potest esse sit minus; cum idem possit esse et non esse, ut dictum est, sequitur quod idem possit esse in tempore infinito, et non esse in tempore infinito; quia eadem ratio est circa hoc quod est non esse, et circa hoc quod est esse. That when something is said to be able to be or not be, that expression must be understood in terms of some determinate time, he now proves by leading to an impossibility. For, as he says, if there is not a time of determinate quantity in which it could be or not be, but a time greater than a given time is always assumed (for example, if it can be for fifty years and then more and again still more), and no limit is reached with respect to which every time in which it can be is less, then, since it is the same thing that can be and not be, as was said, it follows that the same thing can be for an infinite time, and not be for an infinite time, because the same reasoning applies to the non-existence as applies to the existence. Non tamen ita quod illud tempus respectu cuius aliquid potest non esse, quod concluditur esse infinitum, sit idem cum illo tempore infinito respectu cuius aliquid dicitur posse esse; quia sic posset esse et non esse in eodem tempore, quod est impossibile, ut infra dicetur: sed quod aliud tempus infinitum sit eius quod est non esse, et aliud eius quod est esse. Quod est impossibile: non enim possunt esse duo tempora infinita, quia sic essent duo tempora simul. Hoc autem impossibile sequitur ex hoc quod dicitur quod possibile esse vel possibile non esse non intelligitur respectu determinati temporis: hoc ergo oportet primo esse manifestum, quod possibile esse dicitur respectu determinati temporis, et similiter possibile non esse: quod etiam consonat his quae sunt praemissa de significatione possibilis. This does not mean that the time in respect to which something is able not to be, and which was concluded to be infinite, is the same as the time in respect to which the thing is able to be — because then the same thing would be able to be and not be during the same time, which is impossible, as will be said below. It means rather that there is one infinite time for the thing as non-existing, and another for it as existing. Now this is impossible: for there cannot be two infinite times, because then two times would be simultaneous. But this impossibility follows from saying that the possibility to be or the possibility not to be are not reckoned with respect to some determinate time. Therefore the first thing that must be clear is that the possibility of being is said with respect to a determinate time, and similarly the possibility of not being. And this agrees with what has been already laid down about the meaning of "possible." Deinde cum dicit: principium autem sit hinc etc., incipit argumentari ad propositum. Et circa hoc duo facit: 255. Then at [185] he begins to argue to his proposition. About this he does two things: primo argumentatur ad propositum per communes rationes;
secundo per propriam rationem scientiae naturalis, ibi: et naturaliter et cetera.
First he argues to it with general reasons;
Secondly, with an argument proper to natural science, at 286 (L. 29).
Circa primum duo facit: About the first he does two things: primo ostendit veritatem, scilicet quod incorruptibile et ingenitum se consequuntur, et similiter corruptibile et genitum;
secundo improbat positionem contrariam, ibi: dicere itaque nihil et cetera.
First he shows the truth, namely, that indestructible and unproduced follow one upon the other; and likewise, destructible and generated;
Secondly, he disproves the contrary of this (L. 29).
Circa primum duo facit: Regarding the first he does two things: primo ostendit propositum, ostendendo quomodo se habeat sempiternum ad ingenitum et incorruptibile, et ad genitum et corruptibile;
secundo quomodo ista se habeant ad invicem, ibi: palam autem et ex determinatione et cetera.
First he proves his proposition by showing how what is eternal is related to the ungenerated and indestructible, and to the generated and destructible;
Secondly, how they are related to one another (L. 28).
Circa primum tria facit: About the first he does three things: primo ostendit quod omne sempiternum est incorruptibile et ingenitum;
secundo ostendit quod nullum sempiternum est genitum vel corruptibile, neque e converso, ibi: quoniam autem negatio etc.;
tertio concludit quod omne ingenitum et incorruptibile est sempiternum, ibi: igitur si et ingenitum et cetera.
First he shows that everything eternal is indestructible and ungenerated;
Secondly, that nothing eternal is generated or destructible, nor conversely (L. 27);
Thirdly, he concludes that everything ungenerated and indestructible is eternal, at 265 (L. 27).
Circa primum duo facit: About the first he does two things: primo praemittit quaedam necessaria;
secundo argumentatur ad propositum, ibi: si itaque aliquid et cetera.
First he presents some needed pre-notes;
Secondly, he argues to his proposition, at 257.
Dicit ergo primo quod oportet hinc sumere principium ad propositum ostendendum, quod impossibile et falsum non significant idem. 256. He says therefore first [185] that in order to prove the proposition, it is necessary to start from the fact that "impossible" and "false" do not mean the same. Circa quod quatuor ponit. Quorum primum est quod tam impossibile quam possibile, tam verum quam falsum, dicuntur dupliciter. Uno modo ex suppositione, quod scilicet necesse est esse verum vel falsum, possibile vel impossibile, suppositis quibusdam: sicut triangulum secundum rei veritatem necesse est habere tres angulos aequales duobus rectis, sed tamen hoc est impossibile suppositis quibusdam, puta si supponamus quod triangulus sit quadratum, ad quod sequitur triangulum habere quatuor rectos. Similiter etiam diametrum quadrati sequetur esse commensurabilem lateri, si quaedam supposita sint vera, puta si ponamus quod quadratum diametri sit quadruplum quadrati lateris: sic enim sequetur quod proportio diametri ad latus sit sicut proportio numeralis, quae est ratio commensurabilis. Alio modo dicuntur aliqua simpliciter, scilicet absolute et secundum se possibilia et impossibilia, falsa et vera. Regarding this he posits four reflections. The first is that both "possible" and "impossible," as well as "true" and "false," are used in two ways. In one way, conditionally, i.e., in the sense that a thing must be true or false, possible or impossible, if certain things are assumed; for example, a triangle must in fact have three angles equal to two right angles, but nevertheless such a property is impossible if certain things are assumed — thus, if we should suppose a triangle to be a square, it would follow that a triangle would have four right angles. In like manner, it will follow that the diagonal of a square is commensurate to the side if certain assumptions are true — for example, if we should assume that the square of the diagonal is 4 times the square of the side — for then it will always follow that the ratio of the diagonal to the side is a numerical proportion, which is a commensurable ratio. In a second way things are said to be simpliciter, i.e., absolutely and in themselves, "possible" and "impossible," "false" and "true.". Secundum ponit ibi: non autem idem et cetera. Et dicit quod non est idem aliquid esse falsum simpliciter, idest absolute, et esse impossibile absolute. Si enim dicam te stare, qui non stas sed sedes, falsum erit quod dicitur, non autem impossibile; et similiter falsum erit et non impossibile, si quis dicat cantare eum qui citharizat sed non cantat; sed quod aliquis simul stet et sedeat, vel quod diameter sit commensurabilis lateri, non solum est falsum, sed et impossibile. The second he gives at [186], and he says that to be false simpliciter, i.e. absolutely, and to be impossible absolutely, are not the same. For if I say that you are standing, whereas you are not standing but sitting, then what is said will be false but not impossible; likewise it will be false and not impossible if I say that the person playing the harp is singing, whereas he is not singing. But for someone to be standing and sitting at the same time, or for the diagonal to be commensurable with the side, is not only false, but impossible as well. Tertium ponit ibi: non itaque etc.: quod concluditur ex praemissis. Cum enim non idem sit falsum et impossibile, sequitur quod non sit idem supponere falsum et impossibile: nam ex falso non sequitur impossibile, sed ex impossibili sequitur impossibile. The third he gives at [187] and he concludes it from the foregoing. For since the false and the impossible are not the same, it follows that it is not the same thing to assume what is false and to assume what is impossible: from the false there does not follow the impossible, but from the impossible there follows the impossible. Quartum ponit ibi: hoc quidem igitur et cetera. Et quia dictum est quod simul stare et sedere est impossibile, concludit quod, licet aliquid simul habeat virtutem ad opposita (puta ad sedere et stare), tali ratione, quia quandoque una potentia reducitur in actum, quandoque altera; nihil tamen hanc habet potentiam ut simul habeat opposita (puta ut simul sedeat et stet), sed oportet hoc in alio et alio tempore esse. He gives the fourth at [188]. And because it has been said that to stand and sit at the same time is impossible, he concludes that, although something may have at the same time the power to do the opposite things — for example, to sit and to stand — in the sense that now one power is actualized and now the other, nevertheless nothing has the power to have both simultaneously (for example, to stand and sit at the same time) but this must be at different times. Deinde cum dicit: si itaque aliquid etc., ostendit propositum, scilicet quod omne sempiternum sit incorruptibile et ingenitum. 257. Then at [189] he proves the proposition, namely, that everything eternal is indestructible and ungenerated. Et primo ostendit quod omne sempiternum sit incorruptibile;
secundo quod omne sempiternum sit ingenitum, ibi: similiter autem et ingenitum et cetera.
First he shows that everything eternal is indestructible;
Secondly, that everything eternal is ungenerated, at 259.
Dicit ergo primo, concludens ex praemissis, in quibus dictum est possibile determinari ad aliquod tempus, quod si aliquid habet virtutem ad plura tempore infinito, non potest dici quod possit aliquid eorum respectu unius temporis, et aliud respectu alterius temporis; sed quidquid potest, potest respectu huius temporis, quia non est aliquod tempus extra tempus infinitum. Si ergo ponamus quod aliquid existens in infinito tempore sit corruptibile, sequitur ex hoc quod est corruptibile, quod habeat virtutem ad hoc quod quandoque non sit; quod quidem oportet intelligi respectu eiusdem temporis infiniti in quo est, vel respectu alicuius partis eius. Quia ergo est in infinito tempore, et tamen ponitur potens non esse, eo quod est corruptibile, sit existens quod potest non esse, idest ponatur non esse ex quo dicis quod potest non esse. Et quia poterat non esse respectu infiniti temporis vel alicuius partis eius, sequitur quod simul secundum actum sit et non sit: quia in infinito tempore ponebatur esse, et postea ponitur non esse respectu eiusdem temporis. He says therefore first [189], as a conclusion from the foregoing (in which it was said that the "possible" is determined for some certain time), that if something is capable of several things during an infinite time, it cannot be said that one of them is possible at one time and another at another time, but whatever it is capable of is possible with respect to this time, because there is no time outside the infinite time. If therefore we should posit something existing in an infinite time to be destructible, from its destructibility it follows that it has the power not to exist at some time; and this must be understood with respect to the same infinite time in which it exists or in respect to some part of that time. Now since it exists in an infinite time and yet is supposed capable of not existing (since it is destructible), then let what is capable of not existing be such, i.e., let it be assumed not to exist, since you say that it is able not to exist. And because it had this capability (of not existing) with respect to infinite time, or some part of it, it follows that it simultaneously actually exists and does not exist —since it is assumed to be existing in infinite time, and later not to exist with respect to the same time. Manifestum est igitur quod hoc falsum accidit ex falso posito, scilicet ex hoc quod tu ponebas istud existens in infinito tempore non esse quandoque. Sed si hoc falsum non esset impossibile, non sequeretur impossibile; sequitur autem impossibile, scilicet idem simul esse et non esse; ergo impossibile fuit illud non esse. Non ergo poterat non esse; et ita non erat corruptibile. Sic ergo patet quod omne quod est semper ens, non potest esse corruptibile; et ita simpliciter est incorruptibile. It is plain that this falsity occurs on account of the false assumption that the thing existing in infinite time does not exist at some time. But if this falsehood were not something impossible, an impossibility would not follow. However an impossibility does follow, namely, that the same thing exists and does not exist at the same time. Therefore it was impossible for it not to exist. It had not been able, therefore, not to exist — and thus it was not destructible. Consequently it is plain that whatever is always an existing being cannot be destructible, and thus is absolutely indestructible. Sed videtur quod iste processus Aristotelis necessitatem non habeat. Quamvis enim nullius potentia sit ad hoc quod duo opposita sint in eodem tempore in actu, tamen nihil prohibet quod potentia alicuius sit ad duo opposita respectu eiusdem temporis sub disiunctione, aequaliter et eodem modo: sicut potentia mea est ad hoc quod cras in ortu solis vel sedeam vel stem; non tamen ut utrumque sit simul, sed aequaliter possum vel stare non sedendo, vel sedere non stando. Sic igitur posset aliquis obviare rationi Aristotelis. Ponamus enim aliquid semper ens, ita tamen quod istud esse suum sempiternum sit contingens et non necessarium. Poterit ergo non esse respectu cuiuscumque partis temporis infiniti, in quo ponitur semper esse: nec propter hoc sequetur quod aliquid sit simul ens et non ens. Eadem enim ratio videtur in toto infinito tempore, et in aliquo toto tempore finito. Etsi enim ponamus quod aliquis sit in domo semper per totam diem, tamen non est impossibile eum in domo non esse in quacumque parte diei: quia non ex necessitate est in domo per totam diem, sed contingenter. 258. But it seems that this reasoning of Aristotle does not conclude with necessity. For although nothing has the power to have two opposite things in existence at the same time, yet nothing prevents a thing from being at the same time capable of two opposites disjunctively, equally and in the same way For example, I have the power to sit or to stand tomorrow at sun-up; not that both might take place at the same time but I am equally capable either of standing without sitting, or of sitting without standing. Hence someone could object to the argument of Aristotle thus: Let us suppose something always existing, yet in such a way that its eternity is contingent and not necessary. It would have the power therefore not to exist with respect to any part of the infinite time in which it is posited as always existing — yet it will not follow because of this that something is existing and not existing at the same time. For the same notion seems to be valid in infinite time and in some finite time. For although we might say that someone is always in his house throughout the whole day, it is not impossible for him not to be in the house at any part of the day — for he is not of necessity in the house throughout the whole day, but contingently. Sed dicendum est quod non est eadem ratio utrobique. But it must be answered that the same notion does not apply in both cases. Nam illud quod semper est, scilicet per infinitum tempus, habet potentiam ut sit in infinito tempore: potentia autem existendi non est ad utrumque respectu temporis in quo quis potest esse; omnia enim appetunt esse, et unumquodque tantum est quantum potest esse. Et hoc praecipue patet in his quae sunt a natura, quia natura est determinata ad unum. Et sic quidquid semper est, non contingenter semper est, sed ex necessitate. For what exists always, i.e., through infinite time, has the power to exist in infinite time. But the power to exist is not undetermined to either alternative with respect to the time in which someone is able to exist — for all things seek to exist and each thing exists as long as it can. And this is particularly true in things of nature, because nature is determined to one. Consequently whatever exists always, does so not contingently but of necessity. Deinde cum dicit: similiter autem et ingenitum etc., ostendit idem ex parte geniti vel ingeniti: et dicit quod similiter illud quod est semper, scilicet in infinito tempore, necesse est esse ingenitum. Quia si esset genitum, esset possibile quod quodam tempore non esset, sicut de corruptibili dictum est: sicut enim corruptibile est quod, cum prius fuerit, nunc non est, vel contingit non esse quandoque in futurum, ita genitum est quod nunc est, sed prius non fuit. Non est autem dare aliquod tempus in quo id quod semper est, possibile sit non esse, neque in tempore finito neque in tempore infinito: quia quod potest esse tempore infinito, sicut id quod semper est, potest esse quolibet tempore finito, quod includitur a tempore infinito; et ita sequetur, secundum praedictam deductionem, quod aliquid simul sit et non sit, quod est impossibile. Non igitur contingit quod unum et idem possit semper esse et semper non esse: quia hoc esset semper esse et semper non esse tempore infinito. 259. Then at [190] he proves the same on the part of the generated or ungenerated. And he says that in like manner what exists always, i.e., in an infinite time, is necessarily ungenerated. If it were generated, it would be possible that at some time it not exist, as was said of the destructible — for just as the destructible is what, although previously existing, does not now exist or is able at some future time not to exist, so the generated is what now exists but previously was not. But there is, neither in finite time nor in infinite time, any time in which what always exists is able not to exist — for what can exist in infinite time, just as what always exists, can exist in any finite time, which is included by infinite time. Accordingly, it will follow, according to the aforesaid deduction, that something simultaneously exists and does not exist, which is impossible. Therefore it does not happen that one and the same thing is able always to exist and always not to exist — since this would be the same as always to exist and always not to exist for an infinite time. Similiter etiam non est possibilis negatio eius quod est semper esse, puta ut si dicamus quod id quod semper est, possit non semper esse: hoc enim esset posse non esse ad minus tempore finito. Likewise it is not possible to deny the existence of what always exists, for example, to say that what always exists is able not always to exist: for this would imply the possibility of not existing at least for a finite time. Sic igitur patet quod impossibile est aliquid semper esse, et quod sit corruptibile, vel etiam quod sit genitum. Quia si sint duo termini ita se habentes quod posterius non possit esse sine primo, sicut homo non potest esse sine animali; si illud, scilicet primum, est impossibile esse, sequitur quod posterius etiam sit impossibile esse; sicut si impossibile est lapidem esse animal, impossibile est lapidem esse hominem. Hoc autem quod est aliquando non esse, sequitur ad corruptibile et genitum sicut quoddam communius, ut ex dictis patet. Si ergo illud quod semper est, non contingit quandoque non esse, sequitur etiam quod impossibile sit id quod semper est, esse genitum; et similiter impossibile est illud esse corruptibile. Et sic patet quod omne quod est sempiternum, est ingenitum et incorruptibile. Thus it is plain that it is impossible for something always to exist and to be destructible, or also to be generated. If there are two terms so related that the second cannot exist without the first, as man cannot be without being an animal, then, if the first cannot be, it follows that the second cannot be — just as, if it is impossible for a stone to be animal, it is impossible for a stone to be man. Now not to be at some time follows the destructible and the generated as something more common, as is plain from what was said. Therefore, if what exists always cannot at some time not exist, it follows also that it is impossible for what always exists to be generated, and likewise that it is impossible for it to be destructible. Consequently, it is plain that everything eternal is ungenerated and indestructible.
Lecture 27:
Nothing eternal generated and corrupted, and conversely.Chapter 12 cont. Ἐπεὶ δ' ἀπόφασις τοῦ μὲν ἀεὶ δυναμένου εἶναι τὸ μὴ ἀεὶ δυνάμενον εἶναι, τὸ δ' ἀεὶ δυνατὸν μὴ εἶναι ἐναντίον, οὗ ἀπόφασις τὸ μὴ ἀεὶ δυνάμενον μὴ εἶναι, 191 But since the contradictory of 'that which is always capable of being' 'that which is not always capable of being'; while 'that which is always capable of not being' is the contrary, whose contradictory in turn is 'that which is not always capable of not being', ἀνάγκη τὰς ἀποφάσεις ἀμφοῖν τῷ αὐτῷ ὑπάρχειν, καὶ εἶναι μέσον τοῦ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος τὸ δυνάμενον εἶναι καὶ μὴ εἶναι 192 it is necessary that the contradictories of both terms should be predicable of one and the same thing, and thus that, intermediate between what always is and what always is not, there should be that to which being and not-being are both possible; ἡ γὰρ ἑκατέρου ἀπόφασίς ποτε ὑπάρξει, εἰ μὴ ἀεί. Ὥστ' εἰ τὸ μὴ ἀεὶ μὴ ὂν ἔσται ποτὲ καὶ οὐκ ἔσται, καὶ τὸ μὴ ἀεὶ δυνάμενον εἶναι δηλονότι, ἀλλά ποτε ὄν, ὥστε καὶ μὴ εἶναι. Τὸ αὐτὸ ἄρ' ἔσται δυνατὸν εἶναι καὶ μή, καὶ τοῦτ' ἔστιν ἀμφοῖν μέσον. 193 for the contradictory of each will at times be true of it unless it always exists. Hence that which not always is not will sometimes be and sometimes not be; and it is clear that this is true also of that which cannot always be but sometimes is and therefore sometimes is not. One thing, then, will have the power of being, and will thus be intermediate between the other two. Λόγος δὲ καθόλου ὅδε. Ἔστω γὰρ τὸ Α καὶ τὸ Β μηδενὶ τῷ αὐτῷ δυνάμενα ὑπάρχειν, ἅπαντι δὲ τὸ Α ἢ τὸ Γ καὶ τὸ Β ἢ τὸ Δ. Ἀνάγκη δὴ ᾧ μήτε τὸ Α ὑπάρχει μήτε τὸ Β, παντὶ ὑπάρχειν τὰ ΓΔ. Ἔστω δὴ τὸ Ε τὸ μεταξὺ τῶν ΑΒ ἐναντίων γὰρ τὸ μηθέτερον μέσον. Τούτῳ δὴ ἀνάγκη ἄμφω ὑπάρχειν τό τε Γ καὶ τὸ Δ. Παντὶ γὰρ ἢ τὸ Α ἢ τὸ Γ, ὥστε καὶ τῷ Ε ἐπεὶ οὖν τὸ Α ἀδύνατον, τὸ Γ ὑπάρξει. Ὁ δ' αὐτὸς λόγος καὶ ἐπὶ τοῦ Δ. 194 Expresed universally our argument is as follows. Let there be two attributes, A and B, not capable of being present in any one thing together, while either A or C and either B or D are capable of being present in everything. Then C and D must be predicated of everything of which neither A nor B is predicated. Let E lie between A and B; for that which is neither of two contraries is a mean between them. In E both C and D must be present, for either A or C is present everywhere and therefore in E. Since then A is impossible, C must be present, and the same argument holds of D. Οὔτε δὴ τὸ ἀεὶ ὂν γενητὸν οὐδὲ φθαρτόν, οὔτε τὸ ἀεὶ μὴ ὄν. Δῆλον δ' ὅτι καὶ εἰ γενητὸν ἢ φθαρτόν, οὐκ ἀΐδιον. Ἅμα γὰρ ἔσται δυνάμενον ἀεὶ εἶναι καὶ δυνάμενον μὴ ἀεὶ εἶναι τοῦτο δ' ὅτι ἀδύνατον, δέδεικται πρότερον. 195 Neither that which always is, therefore, nor that which always is not is either generated or destructible. And clearly whatever is generated or destructible is not eternal. If it were, it would be at once capable of always being and capable of not always being, but it has already been shown that this is impossible.
ἀεὶ ὄν ἀεὶ μὴ ὄν Α Β γενητόν Ε μὴ ἀεὶ ὄν μὴ ἀεὶ μὴ ὄν Γ Δ Ἆρ' οὖν εἰ καὶ ἀγένητον, ὂν δέ, τοῦτ' ἀνάγκη ἀΐδιον εἶναι, ὁμοίως δὲ καὶ εἰ ἄφθαρτον, ὂν δέ; (Λέγω δὲ τὸ ἀγένητον καὶ ἄφθαρτον τὰ κυρίως λεγόμενα, ἀγένητον μὲν ὃ ἔστι νῦν, καὶ πρότερον οὐκ ἀληθὲς ἦν εἰπεῖν τὸ μὴ εἶναι, ἄφθαρτον δὲ ὃ νῦν ὂν ὕστερον μὴ ἀληθὲς ἔσται εἰπεῖν μὴ εἶναι). 196 Surely then whatever is ungenerated and in being must be eternal, and whatever is indestructible and in being must equally be so. (I use the words 'ungenerated' and 'indestructible' in their proper sense, 'ungenerated' for that which now is and could not at any previous time have been truly said not to be; 'indestructible' for that which now is and cannot at any future time be truly said not to be.) Ἢ εἰ μὲν ταῦτα ἀλλήλοις ἀκολουθεῖ καὶ τό τε ἀγένητον ἄφθαρτον καὶ τὸ ἄφθαρτον ἀγένητον, ἀνάγκη καὶ τὸ ἀΐδιον ἑκατέρῳ ἀκολουθεῖν, καὶ εἴτε ἀγένη (282b.) τον, ἀΐδιον, εἴτε ἄφθαρτον, ἀΐδιον. 197 If, again, the two terms are coincident, if the ungenerated is indestructible, and the indestructible ungenearted, then each of them is coincident with 'eternal'; anything ungenerated is eternal and anything indestructible is eternal.
Postquam philosophus ostendit quod omne sempiternum est ingenitum et incorruptibile, hic comparat sempiternum ad corruptibile et genitum, ostendens quod simul esse non possunt. 260. After showing that everything eternal is ungenerated and indestructible, the Philosopher here compares the eternal to the destructible and the generated, and shows that they cannot be at the same time. Et primo praemittit quaedam ex quibus procedit ratio;
secundo ex illis argumentatur ad propositum, ibi: neque itaque semper existens et cetera.
First he prefaces certain things from which the argument proceeds;
Secondly, from these he argues to his proposition, at 264.
Circa primum tria proponit. Primo quidem declarat oppositionem eius quod est semper esse et semper non esse: et quamvis adiungat hoc, quod est possibile, non tamen tradit oppositionem quae attenditur secundum possibile et non possibile, sed secundum semper esse et non semper esse. Dicit ergo primo quod huius affirmativae quae est possibile semper esse, negatio contradictorie ei opposita est possibile non semper esse: non quidem ex parte ipsius possibilis, respectu cuius haec est affirmativa possibile non semper esse; sed quantum ad ipsum quod est non semper esse. Sed hoc quod est possibile semper non esse, opponitur contrarie secundum eundem modum ei quod est possibile semper esse. Negativa autem huius est possibile non semper non esse. Regarding the first he proposes three things. First, indeed, he sets out the opposition between "always to be" and "always not to be" [191]; and although he includes "possible," he does not discuss the opposition according to "possible" and "not possible," but only that between "always being" and "not always being." He says therefore first that the contradictory denial of the affirmation "possible always to be" is "possible not always to be": this negation is taken not on the part of "possible," in regard to which "possible not always to be" is affirmative, but on the part of "not always to be." But "possible always, not to be" is opposed contrarily (according to the same mode) to what is "possible always to be," the negative of which is "possible not always not to be." Et huius ratio est quia hoc adverbium semper designat universalitatem temporis, sicut hoc signum omnis designat universalitatem suppositorum. Unde sicut huic enuntiationi omnis homo est, contradictoria est non omnis homo est, aequipollens ei quae est aliquis homo non est; contraria vero huic omnis homo est, dicitur omnis homo non est, aequipollens huic nullus homo est; huius autem contradictoria est non omnis homo non est, aequipollens huic aliquis homo est: ita huic quod dico semper esse, contradictorie opponitur non semper esse, quod aequipollet ei quod est aliquando non esse; sed ei quod est semper esse, contrarie opponitur semper non esse, quod aequipollet huic quod est nunquam esse; huic vero contradictorie opponitur non semper non esse, quod aequipollet ei quod est aliquando esse. The reason for this is that this adverb, always, designates universality of time, just as the sign, every, designates a universality of subjects. Hence, just as the contradictory of the statement, "Every man is," is "Not every man is," which is equivalent to "Some man is not," whereas the contrary of "Every man is," is "Every man is not," which is equivalent to "No man is," whose contradictory is "Not every man is not," which is equivalent to "Some man is"; so the contradictory of "always to be" is "not always to be," which is equivalent to "not to be at some time"; whereas the contrary of "always to be" is "always not to e," which is equivalent to "never to be," whose contradictory is "not always, o be," which is equivalent to "sometime to be." Secundo cum dicit: necesse negationes etc., concludit ex praedicto modo oppositionis quod oportet eidem subiecto inesse negationes ambarum, scilicet eius quod est semper esse et eius quod est semper non esse; quae scilicet negationes sunt non semper esse et non semper non esse. Quae quidem negationes eodem modo insunt eidem, ut illud sit medium inter semper ens et semper non ens quod quidem potest quandoque esse et quandoque non esse; sicut si dicamus quod inter omnem hominem esse et nullum hominem esse, medium est aliquem hominem esse et aliquem hominem non esse. 261. Secondly, at [192] he concludes from the aforesaid manner of opposition that the same subject must possess the negations of both, i.e., of "always to be" and "always not to be," which negations are "not always to be" and "not always not to be." These negations are present in the same way in the same subject which is the medium between always being and always not being, which indeed can at one time be and at another time not be, as if we should say that between "Every man is," and "no man is," the medium is "Some man is" and "Some man is not." Tertio ibi: utriusque enim negatio etc., probat hanc conclusionem sequi ex praemissis. Et primo ratione propria, quae scilicet sumitur ex ratione terminorum in quaestione positorum, dicens: utriusque enim negatio, scilicet tam eius quae est semper esse quam eius quae est semper non esse, quandoque existet, idest ponit aliquid quandoque esse, si non semper sit, idest si per negationem non ponitur aliquid semper: verbi gratia, ista negatio non semper ens, non ponit sempiternitatem neque circa esse neque circa non esse, et ideo ponit quandoque esse et quandoque non esse; et simile est de hac negatione non semper non esse. Concludit ergo quod illud quod non semper est non ens, erit quandoque et quandoque non erit: quia sic negatur semper non esse, quod non ponitur semper esse. Et similiter ista negatio quae est non semper possibile esse, quia removet sempiternitatem circa esse ita quod non ponit sempiternitatem circa non esse, ponit ens quandoque; et quia non ponit esse semper, nihil prohibet illud non esse. Sic ergo idem erit possibile esse quandoque et non esse quandoque. Et hoc est medium inter duo contraria quae sunt semper esse et semper non esse. 262. Thirdly, he proves that this conclusion follows from the foregoing. First, by a proper argument based on the notion of the terms appearing in the question, to the effect that the negation of both, namely, both of that which is "always to be" and that which is "always not to be," will at some time exist, i.e., posits something existing at some time, if it does not always exist, i.e., if by negation something is not posited always. For example, this negation "not always to exist" does not posit an eternal state either of being or of non-being; consequently, it posits to exist at some time, and at some time not to exist. And the same applies to the negation, "not always not to exist." He concludes therefore that what is not always non-existent will at one time be and at another time not be, because thus is denied "always not to exist" without positing the thing in question always to exist. Likewise the negation, "not always able to be," since it removes eternity of existence in such a way as not to posit eternity of non-existence, does posit "existence at some time." And because it does not posit eternal existence, there is nothing to prevent its not existing. Therefore "possible to be at some time" and "not to be some time" will be the same. And this is the medium between the two contraries, "always to be" and "always not to be." Secundo ibi: ratio autem etc., probat idem ratione communi, quae scilicet in quibuslibet terminis locum habet. Sint enim duo termini a et b, ita se habentes quod nulli eidem possint inesse quia sunt contrarii, sicut semper ens et semper non ens. Accipiatur autem alius terminus, scilicet g, qui ita se habeat ad a quod omni subiecto insit vel a vel g: habent enim se sicut affirmatio et negatio, ut semper ens et non semper ens. Sit autem alius terminus, scilicet d, qui eodem modo se habeat ad b, sicut semper non ens et non semper non ens. Necesse est ergo quod omni ei quod neque est a neque b, idest quod neque est semper ens neque semper non ens, insint et g et d, quae sunt negationes amborum: quia a quo removetur semper esse et semper non esse, necesse est quod attribuatur ei non semper esse, idest quandoque non esse, et non semper non esse, idest quandoque esse. Et sic illud subiectum a quo removetur utraque affirmatio, et cui attribuitur utraque negatio, est quod est medium inter a et b: quia illud quod negat utrumque extremum, est medium inter duo contraria; sicut quod neque est album neque nigrum, est medium inter album et nigrum. Huic ergo medio necesse est quod ambae negationes insint, scilicet g et d. Quia sicut dictum est, oportet quod cuicumque insit g aut a; unde oportet quod alterum eorum insit ei quod est e; quia igitur ei quod est e impossibile est quod insit a, sequitur quod insit ei g. Et eadem ratione probatur quod insit ei d. Sic igitur et g et d praedicantur de e, a quo removetur et a et b: quia scilicet aliquid est quandoque ens, quandoque non ens, quod neque est semper ens neque semper non ens. Et hoc est quod probare intendit. 263. Secondly, at [194] he proves the same thing with a common reason which, namely, applies to any terms. Let then A and B be two terms such that they can be found in no same thing, because they are contrary, in the case of "always to be" and "always not to be." Take another term G, which is so related to A, that in every subject there must be either A or G — they being related as affirmation and negation, as, for example, "always existing" and "not always existing." Then take another term D which is related to B in the same way as "always not existing"[B] is related to "not always not existing" [D]. It is necessary, therefore, that in everything which is neither A nor B, i.e., everything which neither always exists nor always does not exist, there inhere both G and D, which are the negations of both — since to that from w hich is removed "always existing" and "always not existing," there is necessarily attributed "not always existing" (i.e., "at some time not to be"), and "not always not existing (i.e., "to be some time"). Consequently that subject from which both affirmations are removed and to which both negations are applied is a medium between A and B — for what denies both extremes is a medium between two contraries, as, for example, what is neither white nor black, is intermediate between white and black. In such a medium must necessarily exist both negations, namely, G and D. For, as was said, either G or A exists in everything whatsoever; consequently, one of them exists in E. Since, then, A cannot exist in E, it follows that G exists in E. And arguing on the same lines, D must exist in E. Thus, therefore, both G and D are predicates of E, from which both A and B are removed, since, namely, that at one time exists, and at another time does not, which neither always exists nor always does not exist. And this is what he intended to prove. Deinde cum dicit: neque itaque semper existens etc., ex praemissis argumentatur ad propositum. Si enim est aliquid semper existens, neque est genitum neque corruptibile: similiter etiam si est semper non existens, neque est genitum neque corruptibile. Manifestum est autem quod etiam e converso, si aliquid est genitum aut corruptibile, non est sempiternum, neque quantum ad esse neque quantum ad non esse. Si enim detur oppositum, scilicet quod aliquid sit simul sempiternum et genitum et corruptibile, sequetur quod aliquid sit simul potens semper esse et non semper esse; quia sempiternum potest semper esse, generabile autem et corruptibile non semper est. Quod autem hoc sit impossibile, ostensum est prius: quia dictum est quod semper esse et non semper esse opponuntur contradictorie. Unde relinquitur impossibile esse quod aliquid sit simul sempiternum et corruptibile vel genitum. 264. Then at [195] from these premises he argues to his proposition. For if something always exists it is neither generated nor destructible; similarly, if something is always non-existent, it is neither generated nor destructible. Now it is manifest that also conversely, if something is generated or destructible, it is not eternal, either in respect to existing or in respect to non-existing. For if we assume the opposite as true, namely, that something is at once eternal and generated and destructible, it will follow that something is at once capable of always being and not always being, because the eternal can always exist but the generated and corruptible does not always exist. Now the impossibility of this was pointed out before: it was said that "always to exist" and "not always to exist" are opposed as contradictories. Hence what is left is that it is impossible for anything to be at once eternal and corruptible or generated. Deinde cum dicit: igitur si et ingenitum etc., ostendit quod omne ingenitum et incorruptibile est sempiternum. Et primo concludit hoc ex praemissis, dicens quod necesse est quod ingenitum omne sit sempiternum, et similiter incorruptibile omne sit sempiternum, dummodo sit ens; ita tamen quod accipiamus ingenitum et incorruptibile secundum quod proprie dicuntur; prout scilicet ingenitum dicitur quod ita est nunc quod non erat prius verum dicere de ipso quod non erat, et secundum quod incorruptibile dicitur quod ita nunc est quod posterius non erit verum dicere de ipso quod non sit; sicut patet ex his quae supra dicta sunt in distinctione horum nominum. 265. Then at [196] he shows that everything ungenerated and indestructible is eternal. First he concludes this from the premises and says that it is necessary for everything ungenerated to be eternal, and likewise for everything indestructible to be eternal, provided it be being, and provided that "ungenerated" and "indestructible" are taken in their proper sense. The proper sense of "ungenerated" denotes something which now exists in such a way that it was not previously true to say that it did not exist; and "indestructible" denotes what now exists in such a way that it will not later be true to say of it that it does not exist. This is clear from what was said in distinguishing these words above. Secundo ibi: aut si quidem etc., probat idem ex his quae infra ostendentur: dicens quod, si ingenitum et incorruptibile consequuntur se invicem hoc modo quod omne ingenitum sit incorruptibile et e converso, necesse est quod sempiternum consequatur ad utrumque; ut scilicet omne ingenitum et omne incorruptibile sit sempiternum. 266. Secondly, he proves the same point from what will be shown below. And he says that if "ungenerated" and "indestructible" are so related that everything ungenerated is indestructible and vice versa, then "eternal" must follow both, i.e., whatever is indestructible is eternal. Ex omnibus autem praemissis talis potest colligi ratio: nullum sempiternum est genitum neque corruptibile; omne ingenitum et omne incorruptibile est sempiternum; ergo nullum ingenitum est corruptibile, et nullum incorruptibile est genitum. From all the foregoing the following argument can be formed: Nothing eternal is generated or destructible. Everything ungenerated and everything incorruptible is eternal. Therefore nothing ungenerated is destructible, and nothing indestructible has been generated.
Lecture 28:
Generated and corruptible, ungenerated and incorruptible, follow on each otherChapter 12 cont. Δῆλον δὲ καὶ ἐκ τοῦ ὁρισμοῦ αὐτῶν καὶ γὰρ ἀνάγκη, εἰ φθαρτόν, γενητόν. Ἢ γὰρ ἀγένητον ἢ γενητόν εἰς δὲ ἀγένητον, ἄφθαρτον ὑπόκειται. 198 This is clear too from the definition of the terms, Whatever is destructible must be generated; for it is either ungenerated, or generated, but, if ungenerated, it is by hypothesis indestructible. Καὶ εἰ γενητὸν δή, φθαρτὸν ἀνάγκη ἢ γὰρ φθαρτὸν ἢ ἄφθαρτον ἀλλ' εἰ ἄφθαρτον, ἀγένητον ὑπέκειτο. 199 Whatever, further, is generated must be destructible. For it is either destructible or indestructible, but, if indestructible, it is by hypothesis ungenerated. Εἰ δὲ μὴ ἀκολουθοῦσιν ἀλλήλοις τὸ ἄφθαρτον καὶ τὸ ἀγένητον, οὐκ ἀνάγκη οὔτε τὸ ἀγένητον οὔτε τὸ ἄφθαρτον ἀΐδιον εἶναι. 200 If, however, 'indestructible' and 'ungenerated' are not coincident, there is no necessity that either the ungenerated or the indestructible should be eternal. Ὅτι δ' ἀνάγκη ἀκολουθεῖν, ἐκ τῶνδε φανερόν. Τὸ γὰρ γενητὸν καὶ τὸ φθαρτὸν ἀκολουθοῦσιν ἀλλήλοις. 201 But they must be coincident, for the following reasons. The terms 'generated' and 'destructible' are coincident; Δῆλον δὲ καὶ τοῦτο ἐκ τῶν πρότερον τοῦ γὰρ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος ἐστὶ μεταξὺ ᾧ μηδέτερον ἀκολουθεῖ, τοῦτο δ' ἐστὶ τὸ γενητὸν καὶ φθαρτόν. Δυνατὸν γὰρ καὶ εἶναι καὶ μὴ εἶναι ὡρισμένον χρόνον ἑκάτερον λέγω δ' ἑκάτερον καὶ εἶναι ποσόν τινα χρόνον καὶ μὴ εἶναι. Εἰ τοίνυν ἐστί τι γενητὸν ἢ φθαρτόν, ἀνάγκη τοῦτο μεταξὺ εἶναι. 202 this is obvious from our former remarks, since between what always is and what always is not there is an intermediate which is neither, and that intermediate is the generated and destructible. For whatever is either of these is capable both of being and of not being for a definite time: in either case, I mean, there is a certain period of time during which the thing is and another during which it is not. Anything therefore which is generated or destructible must be intermediate. Ἔστω γὰρ τὸ Α τὸ ἀεὶ ὄν, τὸ δὲ Β τὸ ἀεὶ μὴ ὄν, τὸ δὲ Γ γενητόν, τὸ δὲ Δ φθαρτόν. Ἀνάγκη δὴ τὸ Γ μεταξὺ εἶναι τοῦ Α καὶ τοῦ Β. Τῶν μὲν γὰρ οὐκ ἔστι χρόνος ἐπ' οὐδέτερον τὸ πέρας ἐν ᾧ ἢ τὸ Α οὐκ ἦν ἢ τὸ Β ἦν τῷ δὲ γενητῷ ἀνάγκη ἢ ἐνεργείᾳ εἶναι ἢ δυνάμει, τοῖς δὲ ΑΒ οὐδετέρως. Ποσὸν ἄρα τινὰ καὶ ὡρισμένον χρόνον καὶ ἔσται καὶ πάλιν οὐκ ἔσται. Ὁμοίως δὲ καὶ ἐπὶ τοῦ Δ. Γενητὸν ἄρα καὶ φθαρτὸν ἑκάτερον. Ἀκολουθοῦσιν ἄρα ἀλλήλοις τὸ γενητὸν καὶ τὸ φθαρτόν. 203 Now let A be that which always is and B that which always is not, C the generated, and D the destructible. Then C must be intermediate between A and B. For in their case there is no time in the direction of either limit, in which either A is not or B is. But for the generated there must be such a time either actually or potentially, though not for A and B in either way. C then will be, and also not be, for a limited length of time, and this is true also of D, the destructible. Therefore each is both generated and destructible. Therefore 'generated' and 'destructible' are coincident.
ἀεὶ ὄν γενητόν Α Γ φθαρτόν ἀεὶ μὴ ὄν Δ Β Ἔστω δὴ τὸ ἐφ' ᾧ Ε ἀγένητον, τὸ δ' ἐφ' ᾧ Ζ γενητόν, τὸ δ' ἐφ' ᾧ Η ἄφθαρτον, τὸ δ' ἐφ' ᾧ Θ φθαρτόν. Τὰ δὴ ΖΘ δέ) δεικται ὅτι ἀκολουθεῖ ἀλλήλοις. Ὅταν δ' ᾖ οὕτω κείμενα ὡς ταῦτα, οἷον τὸ μὲν Ζ καὶ τὸ Θ ἀκολουθοῦντα, τὸ δὲ Ε καὶ τὸ Ζ μηθενὶ τῷ αὐτῷ, ἅπαντι δὲ θάτερον, ὁμοίως δὲ καὶ τὰ ΗΘ, ἀνάγκη καὶ τὰ ΕΗ ἀκολουθεῖν ἀλλήλοις. Ἔστω γὰρ τῷ Η τὸ Ε μὴ ἀκολουθοῦν. Τὸ ἄρα Ζ ἀκολουθήσει παντὶ γὰρ τὸ Ε ἢ τὸ Ζ. Ἀλλὰ μὴν ᾧ τὸ Ζ, καὶ τὸ Θ. Τῷ ἄρα Η τὸ Θ ἀκολουθήσει. Ἀλλ' ὑπέκειτο ἀδύνατον (283a.) εἶναι. Ὁ δ' αὐτὸς λόγος καὶ ὅτι τὸ Η τῷ Ε. Now let E stand for the ungenerated, F for the generated, G for the indestructible, and H for the destructible. As for F and H, it has been shown that they are coincident. But when terms stand to one another as these do, F and H coincident, E and F never predicated of the same thing but one or other of everything, and G and H likewise, then E and G must needs be coincident. For suppose that E is not coincident with G, then F will be, since either E or F is predictable of everything. But of that of which F is predicated H will be predicable also. H will then be coincident with G, but this we saw to be impossible. And the same argument shows that G is coincident with E. Ἀλλὰ μὴν οὕτως ἔχει τὸ ἀγένητον, ἐφ' ᾧ Ε, πρὸς τὸ γενητόν, ἐφ' ᾧ Ζ, καὶ τὸ ἄφθαρτον, ἐφ' ᾧ Η, πρὸς τὸ φθαρτόν, ἐφ' ᾧ Θ. Now the relation of the ungenerated (E) to the generated (F) is the same as that of the indestructible (G) to the destructible (H).
ἀγένητον γενητόν Ε Ζ ἄφθαρτον φθαρτόν Η Θ
Supra philosophus ostendit propositum ex parte sempiterni, nunc autem ostendit propositum ex parte geniti et ingeniti, corruptibilis et incorruptibilis. 267. After proving his proposition above on the part of what is eternal, the Philosopher now proves the same thing on the part of the generated and ungenerated, the destructible and indestructible. Et primo probat propositum ex suppositione;
secundo ex necessitate, ibi: quod autem necesse consequi et cetera.
First he proves it from a supposition;
Secondly, with necessity, at 271.
Circa primum duo facit: About the first he does two things: primo ex suppositione huius quod ingenitum et incorruptibile convertantur, probat quod genitum et corruptibile convertuntur;
secundo ostendit unde sit supponenda conversio ingeniti et incorruptibilis, ibi: si autem non consequuntur et cetera.
First, on the supposition that ungenerated and indestructible are convertible terms, he proves that generated and destructible are convertible;
Secondly, he shows whence the conversion of ungenerated and indestructible is to be supposed, at 270.
Dicit ergo primo quod id quod intendimus potest fieri manifestum ex determinatione ipsorum, idest ex distinctione et habitudine horum terminorum ad invicem. Et primo ostendit quod genitum sequatur ad corruptibile, ita scilicet quod si aliquid sit corruptibile, ex necessitate sit genitum. Oportet enim id quod est corruptibile aut esse genitum aut ingenitum, quia de quolibet existentium alterum horum oportet praedicari: si ergo aliquid sit corruptibile quod non sit genitum, sequitur quod sit ingenitum. Supponimus autem quod ingenitum et incorruptibile convertantur: et ita si aliquid est ingenitum, erit incorruptibile. Si ergo aliquod corruptibile non sit genitum, sequitur quod aliquod corruptibile sit incorruptibile. 268. He says therefore first [198] that what we are pursuing can be made clear from their determination, i.e., from the way these terms are distinguished one from the other and related one to the other. First he shows that "generated" follows upon "corruptible," in such a way that if something is corruptible, then necessarily it was generated. For the corruptible must be either generated or ungenerated, because one of these two must be predicated of anything that exists. If, therefore, something is destructible which was not generated, it follows that it is ungenerated. But we are assuming that "ungenerated" and "indestructible" are convertible, i.e., that if something is ungenerated, it will be indestructible. Consequently, if there exists a destructible thing that was not generated, it follows that something destructible is indestructible. Secundo ibi: et si genitum autem etc., probat eodem modo quod necesse sit, si aliquid est genitum, quod sit corruptibile. Oportet enim id quod est genitum aut esse corruptibile aut incorruptibile; sed hoc supponitur, quod si aliquid est incorruptibile, quod sit ingenitum, propter eorum convertibilitatem; sequitur ergo quod sit aliquid genitum quod sit ingenitum, quod est impossibile. 269. Secondly, he proves in the same way that if something is generated, it is necessarily destructible. For what is generated must be either destructible or not. But we are supposing that if something is indestructible it is ungenerated, because these are convertible. It follows, therefore, that there is something generated which is ungenerated, which is impossible. Et sic probatum est quod omne corruptibile est genitum, et e converso: supposito tamen quod ingenitum et incorruptibile convertantur. Thus is proved that whatever is destructible is generated and vice versa, on the supposition, of course, that ungenerated and indestructible are convertible terms. Deinde cum dicit: si autem non consequuntur etc., ostendit unde hoc oporteat supponi. Et dicit quod si non consequuntur se invicem incorruptibile et ingenitum, non ex necessitate hoc quod est esse sempiternum, erit consequens ad hoc quod est ingenitum et ad incorruptibile: quod tamen supra ostensum est. 270. Then at [200] he shows why this must be supposed. And he says that if "indestructible" and "ungenerated" do not follow one upon the other, then "to be eternal" will not necessarily follow upon being ungenerated and being indestructible. But it has been proved above that it does. Deinde cum dicit: quod autem necesse consequi etc., probat propositum ex necessitate. 271. Then at [201] he proves his proposition from necessity. Et primo ostendit quod genitum et corruptibile convertantur;
secundo ex hoc ulterius ostendit quod etiam ingenitum et incorruptibile convertantur, ibi: sit itaque in quo est e et cetera.
First he shows that "generated" and "destructible" are convertible;
Secondly, from this he further shows that "ungenerated" and "indestructible" are also convertible, at 275.
Circa primum tria facit. Concerning the first he does three things: Primo proponit quod intendit: et dicit quod ex his quae dicentur, manifestum erit quod necesse est praedicta se invicem consequi; quia primo hoc manifestabitur, quod genitum et corruptibile se invicem consequuntur. First he reveals his intention, and says that from what will be said, it will be plain that the foregoing things follow one upon the other. It will first be shown that generated and destructible follow one upon the other. Secundo ibi: palam autem etc., inducit rationem ad hoc ostendendum. Et dicit quod sicut convertibilitas incorruptibilis et ingeniti manifestatur ex prius dictis, ita etiam hoc quod genitum et corruptibile sint convertibilia, manifestatur ex prioribus. Quia inter semper ens et semper non ens est medium, sicut supra dictum est, id ad quod neutrum consequitur, idest quod neque est semper ens neque semper non ens: tale autem est genitum et corruptibile, quia utrumque eorum est possibile esse et non esse secundum aliquod tempus determinatum, ita scilicet quod aliquo tempore finito utrumque eorum sit, et iterum non sit quodam alio tempore: si ergo est aliquid quod sit genitum aut quod sit corruptibile, necesse est quod huiusmodi sit medium inter semper ens et semper non ens; et sic utrumque eorum eidem attribuitur, et se invicem consequi videntur. 272. Secondly, at [202] he presents an argument to prove this, and says that just as the convertibility of "indestructible" and "ungenerated" is plain from what was previously said, so, too, the convertibility of "generated" and "destructible." For between "always existing" and "always not existing" there is a middle (as was said above), namely, that which follows neither, i.e., what neither always is nor always is not. Now such are the "generated" and "destructible," because both are able to be and not to be with respect to some determinate time, in such a way, namely, that for some finite time both exist and for some other finite time both do not exist. If then there is something which is generated or is destructible, such a thing must be a middle between what always exists and what is always non-existent. Consequently both terms will apply to the same thing and they are found to follow one upon the other. Tertio ibi: sit enim a etc., manifestat praemissam rationem in terminis, dicens: sit a semper ens, et b sit semper non ens, g autem sit genitum, d autem sit corruptibile. Necesse est ergo g, quod est genitum, esse medium inter a et b, idest inter semper ens et semper non ens: quia his, scilicet a et b, non est aliquod tempus ad neutrum terminum, idest nec ante nec post, in quo vel a, quod est semper ens, non sit, aut b, quod est semper non ens, sit; sed ipsi genito necesse est quod sit tempus in quo non sit, ad utrumque extremum vel ad alterum, et similiter in quo sit, et hoc vel secundum actum vel secundum potentiam; cum tamen his quae sunt a et b neutro modo existat tempus ad oppositum, idest nec secundum actum nec secundum potentiam. Relinquitur ergo quod genitum quod est g, in quodam determinato tempore est, et quodam determinato tempore non est; et similis ratio est de d. Sequitur igitur quod utrumque eorum sit et genitum et corruptibile; ita scilicet quod genitum sit utrumque, et corruptibile sit utrumque. Sic ergo patet quod genitum et corruptibile se invicem consequuntur. 273. Thirdly, at [203] he manifests the foregoing argument by using terms, and says: Let Abe something that always exists, and B something that is always non-existent, whereas G is something generated and D something destructible. Then G is necessarily intermediate between A and B, i.e., between what always exists and what always is non-existent; for in regard to A and B there is no time at either terminus, i.e., either before or after, in which A, which is always existing, does not exist, or B, which is always non-existent, exists. But in regard to the generated, there must be some time in which it does not exist, either at both termini or at one of them, and likewise some time in which it does, and this either actually or potentially; but with regard to A and B there can be no opposite time in either way, i.e., either actually or potentially. That is left, therefore, is that the generated G exists for some definite time and for some definite time does not exist; and the same goes for D. It follows, therefore, that both are generated and destructible, i.e., in such a way that the generated thing is both, and the destructible is both. Thus it is plain that "generated" and "destructible" follow one upon the other. Sed videtur quod haec ratio non sit efficax: non enim est necesse quod quidquid est medium inter duo contraria, sit unum et idem. Nam inter album et nigrum medium quidem est quod neque est album neque nigrum, et tamen hoc dicitur de diversis quae se invicem non consequuntur: quia et rubeum et pallidum et quilibet mediorum colorum neque est album neque nigrum, et tamen isti colores non se invicem consequuntur. Et ita posset aliquis dicere quod medium inter semper ens et semper non ens est quod neque est semper ens neque semper non ens, sed alio modo hoc convenit corruptibili et alio modo generabili: nam genitum habet non esse antequam sit, corruptibile autem habet non esse postquam fuit. 274. But this argument does not seem to be valid: for it is not necessary that a middle between two contraries be one and the same thing. For the middle between white and black is indeed something neither white nor black; yet this is said of many different things which do not follow one upon the other. For red and pale and any of the intermediate colors are neither white nor black, and yet they do not follow one upon the other. Consequently, someone could say that the intermediate between "always existing" and "always not existing" is something which neither always exists nor always does not exist, but that this belongs to the "destructible" in one way and to the "generable" in some other way: for the "generated" has no existence before it exists, while the "destructible" has no existence after it has existed. Sed haec obiectio excluditur per hoc quod dicit, quod utrumque eorum est et non est quodam determinato tempore: et ita oportet quod utrumque eorum habeat esse post non esse et ante non esse. Et hoc magis manifestabitur in sequentibus. But this objection is excluded by the very fact that he says that it is in some definite time that each of them exists and does not exist. Thus both of them have to have existence after non-existence, and before non-existence. And this will be made clearer in the following lecture. Deinde cum dicit: sit itaque in quo est e etc., ostendit ex hoc quod etiam ingenitum et incorruptibile convertantur, dicens: sit e ingenitum, z genitum, I incorruptibile, t corruptibile. Quia igitur ostensum est quod genitum et corruptibile se invicem consequuntur, planum est quod z et t se invicem consequuntur. Quando igitur positum fuerit quod z et t se consequuntur, scilicet genitum et corruptibile; et quod e et z, idest genitum et ingenitum, nulli eidem insunt, sed cuilibet oportet inesse alterum eorum; et eadem ratio est de t et I, scilicet de corruptibili et incorruptibili, scilicet quod nulli eidem insunt, sed omni alterum: quando igitur haec ita ponuntur, necesse est quod I et e, idest ingenitum et incorruptibile, se invicem consequantur. 275. Then at [204] he shows from the foregoing that "ungenerated" and "indestructible" are also convertible, saying: Let E be ungenerated, Z generated, I indestructible and T destructible. Since it has been shown that "generated" and "destructible" follow upon each other, it is plain that Z and T follow upon each other. Now supposing that Z and T follow upon one another, namely, "generated" and "destructible," and assuming that E and Z, i.e., the "generated" and "non-generated," are not present in the same subject, but that one of them must be present in every subject, and the same for T and I, i.e., the "destructible" and "indestructible," namely, that they are not both present in any same subject, but one of them must be present in any subject, then, such suppositions having been made, it is necessary that I and E, i.e., the "non-generated" and "indestructible," follow one upon the other. Et hoc probat ducendo ad impossibile. Si enim ad I, quod est incorruptibile, non ex necessitate consequatur e, quod est ingenitum, sequetur quod z, quod est genitum, simul possit stare cum I, quod est incorruptibile: quia iam dictum est quod de quolibet praedicatur aut e, idest ingenitum, aut z, idest genitum. Insuper dictum est quod cui inest z, idest genitum, ei inest et t, idest corruptibile. Sic igitur sequetur quod t, idest corruptibile, insit ei quod est I, idest incorruptibili. Quod est contra positum: positum enim erat quod t et I nunquam eidem inessent: nihil enim est corruptibile et incorruptibile. Et eadem ratio est quod I, idest incorruptibile, consequatur ad id quod est e, scilicet ingenitum: quia eodem modo se habet ingenitum quod est e, ad genitum quod est z, sicut incorruptibile quod est I, ad corruptibile quod est t. Sic igitur patet ex praedictis quod omne corruptibile est genitum et e converso, et omne incorruptibile ingenitum et e converso. This he proves by leading to an impossibility. For if E, which is to be non-generated, does not follow necessarily upon I, which is to be indestructible, it will follow that Z, which is generated, can co-exist with I, which is indestructible, because it has already been established that of everything is predicated either E, i.e., non-generated, or Z, i.e., generated. Moreover it has been stated that whatever is Z, i.e., generated, is also T, i.e., destructible. Consequently, it will follow that T, i.e., destructible, is found in that which is I, i.e., indestructible. But that is contrary to the assumption that T and I are never present in the same thing — for nothing is destructible and indestructible. And the same reasoning shows that I, i.e., indestructible, follows upon E, i.e., non-generated, because the non-generated, E, is related to generated, Z, in the same way as indestructible, I, is related to destructible, T. Thus it is plain from the foregoing that whatever is destructible was generated and vice versa; and that what is indestructible is non-generated and vice versa.
Lecture 29:
Refutation of corruptible ungenerated and incorruptible generated. Argument from natural scienceChapter 12 cont. Τὸ δὲ φάναι μηδὲν κωλύειν γινόμενόν τι ἄφθαρτον εἶναι καὶ ἀγένητον ὂν φθαρῆναι, ἅπαξ ὑπαρχούσης τῷ μὲν τῆς γενέσεως τῷ δὲ τῆς φθορᾶς, ἀναιρεῖν ἐστι τῶν δεδομένων τι. Ἢ γὰρ ἄπειρον ἢ ποσόν τινα ὡρισμένον χρόνον δύναται ἅπαντα ἢ ποιεῖν ἢ πάσχειν, ἢ εἶναι ἢ μὴ εἶναι * * καὶ τὸν ἄπειρον διὰ τοῦτο, ὅτι ὥρισταί πως ὁ ἄπειρος, οὗ οὐκ ἔστι πλείων. Τὸ δὴ πῇ ἄπειρον οὔτ' ἄπειρον οὔθ' ὡρισμένον. 205 To say then that there is no reason why anything should not be generated and yet indestructible or ungenerated and yet destroyed, to imagine that in the one case generation and in the other case destruction occurs once for all, is to destroy part of the data. For (1) everything is capable of acting or being acted upon, of being or not being, either for an infinite, or for a definitely limited space of time; and the infinite time is only a possible alternative because it is after a fashion defined, as a length of time which cannot be exceeded. But infinity in one direction is neither infinite or finite. Ἔτι τί μᾶλλον ἐπὶ τῷδε τῷ σημείῳ ἀεὶ ὂν πρότερον ἐφθάρη ἢ μὴ ὂν ἄπειρον ἐγένετο; εἰ γὰρ μηθὲν μᾶλλον, ἄπειρα δὲ τὰ σημεῖα, δῆλον ὅτι ἄπειρον χρόνον ἦν τι γενητὸν καὶ φθαρτόν. Δύναται ἄρα μὴ εἶναι ἄπειρον χρόνον ἅμα γὰρ ἕξει δύναμιν τοῦ μὴ εἶναι καὶ εἶναι, τὸ μὲν πρότερον, εἰ φθαρτόν, τὸ δ' ὕστερον, εἰ γενητόν. Ὥστ' ἐὰν ὑπάρχειν θῶμεν ἃ δύναται, τὰ ἀντικείμενα ἅμα ὑπάρξει. 206 (2) Further, why, after always existing, was the thing destroyed, why, after an infinity of not being, was it generated, at one moment rather than another? If every moment is alike and the moments are infinite in number, it is clear that a generated or destructible thing existed for an infinite time. It has therefore for an infinite time the capacity of not being (since the capacity of being and the capacity of not being will be present together), if destructible, in the time before destruction, if generated, in the time after generation. If then we assume the two capacities to be actualized, opposites will be present together. Ἔτι δὲ καὶ τοῦθ' ὁμοίως ἐν ἅπαντι σημείῳ ὑπάρξει, ὥστ' ἄπειρον χρόνον τοῦ μὴ εἶναι καὶ τοῦ εἶναι ἕξει δύναμιν ἀλλὰ δέδεικται ὅτι ἀδύνατον τοῦτο. 207 (3) Further, this second capacity will be present like the first at every moment, so that the thing will have for an infinite time the capacity both of being and of not being; but this has been shown to be impossible. Ἔτι εἰ πρότερον ἡ δύναμις ὑπάρχει τῆς ἐνεργείας, ἅπανθ' ὑπάρξει τὸν χρόνον, καὶ ὃν ἀγένητον ἦν καὶ μὴ ὄν [τὸν ἄπειρον χρόνον], γίγνεσθαι δὲ δυνάμενον. Ἅμα δὴ οὐκ ἦν καὶ τοῦ εἶναι δύναμιν εἶχε, καὶ τοῦ τότε εἶναι καὶ ὕστερον ἄπειρον ἄρα χρόνον. 208 (4) Again, if the capacity is present prior to the activity, it will be present for all time, even while the thing was as yet ungenerated and non-existent, throughout the infinite time in which it was capable of being generated. At that time, then, when it was not, at that same time it had the capacity of being, both of being then and of being thereafter, and therefore for an infinity of time. Φανερὸν δὲ καὶ ἄλλως ὅτι ἀδύνατον φθαρτὸν ὂν μὴ φθαρῆναί ποτε. Ἀεὶ γὰρ ἔσται ἅμα καὶ φθαρτὸν καὶ ἄφθαρτον ἐντελεχείᾳ, ὥστε ἅμα ἔσται δυνατὸν ἀεί τε εἶναι καὶ μὴ ἀεί φθείρεται ἄρα ποτὲ τὸ φθαρτόν. Καὶ εἰ γενητόν, γέγονεν δυνατὸν γὰρ γεγονέναι, καὶ μὴ ἀεὶ ἄρα εἶναι. 209 It is clear also on other grounds that it is impossible that the destructible should not at some time be destroyed. For otherwise it will always be at once destructible and in actuality indestructible, so that it will be at the same time capable of always existing and of not always existing. Thus the destructible is at some time actually destroyed. The generable, similarly, has been generated, for it is capable of having been generated and thus also of not always existing. Ἔστι δὲ καὶ ὧδε θεωρῆσαι ὅτι ἀδύνατον ἢ γενόμενόν ποτε ἄφθαρτον διατελεῖν, ἢ ἀγένητον ὂν καὶ ἀεὶ πρότερον ὂν φθαρῆναι. Οὐδὲν γὰρ ἀπὸ τοῦ αὐτομάτου οὔτ' ἄφθαρτον οὔτ' ἀγένητον οἷόν τ' εἶναι. Τὸ μὲν γὰρ αὐτόματόν ἐστι καὶ τὸ ἀπὸ τύχης παρὰ τὸ ἀεὶ καὶ τὸ ὡς ἐπὶ (283b.) τὸ πολὺ ἢ ὂν ἢ γινόμενον τὸ δ' ἄπειρον χρόνον ἢ ἁπλῶς ἢ ἀπό τινος, ἢ ἀεὶ ἢ ὡς ἐπὶ τὸ πολὺ ὑπάρχει ὄν. Ἀνάγκη τοίνυν φύσει τὰ τοιαῦτα ὁτὲ μὲν εἶναι ὁτὲ δὲ μή. Τῶν δὲ τοιούτων ἡ αὐτὴ δύναμις τῆς ἀντιφάσεως, καὶ ἡ ὕλη αἰτία τοῦ εἶναι καὶ μή. Ὥστ' ἀνάγκη ἅμα ὑπάρχειν ἐνεργείᾳ τὰ ἀντικείμενα. 210 We may also see in the following way how impossible it is either for a thing which is generated to be thenceforward indestructible, or for a thing which is ungenerated and has always hitherto existed to be destroyed. Nothing that is by chance can be indestructible or ungenerated, since the products of chance and fortune are opposed to what is, or comes to be, always or usually, while anything which exists for a time infinite either absolutely or in one direction, is in existence either always or usually. That which is by chance, then, is by nature such as to exist at one time and not at another. But in things of that character the contradictory states proceed from one and the same capacity, the matter of the thing being the cause equally of its existence and of its non-existence. Hence contradictories would be present together in actuality. Ἀλλὰ μὴν οὐδέν γ' ἀληθὲς εἰπεῖν νῦν ὅτι ἔστι πέρυσιν, οὐδὲ πέρυσιν ὅτι νῦν ἔστιν. Ἀδύνατον ἄρα μὴ ὄν ποτε ὕστερον ἀΐδιον εἶναι ἕξει γὰρ ὕστερον καὶ τὴν τοῦ μὴ εἶναι δύναμιν, πλὴν οὐ τοῦ τότε μὴ εἶναι ὅτε ἔστιν (ὑπάρχει γὰρ ἐνεργείᾳ ὄν), ἀλλὰ τοῦ πέρυσιν καὶ ἐν τῷ παρελθόντι χρόνῳ. Ἔστω δὴ οὗ ἔχει τὴν δύναμιν ὑπάρχον ἐνεργείᾳ ἔσται ἄρα ἀληθὲς εἰπεῖν νῦν ὅτι οὐκ ἔστι πέρυσιν. Ἀλλ' ἀδύνατον οὐδεμία γὰρ δύναμις τοῦ γεγονέναι ἐστίν, ἀλλὰ τοῦ εἶναι ἢ ἔσεσθαι. Ὁμοίως δὲ καὶ εἰ πρότερον ὂν ἀΐδιον ὕστερον μὴ ἔσται ἕξει γὰρ δύναμιν οὗ ἐνεργείᾳ οὐκ ἔστιν. Ὥστ' ἂν θῶμεν τὸ δυνατόν, ἀληθὲς ἔσται εἰπεῖν νῦν ὅτι τοῦτ' ἔστι πέρυσιν καὶ ὅλως ἐν τῷ παρελθόντι χρόνῳ. 211 Further, it cannot truly be said of a thing now that it exists last year, nor could it be said last year that it exists now. It is therefore impossible for what once did not exist later to be eternal. For in its later state it will possess the capacity of not existing, only not of not existing at a time when it exists—since then it exists in actuality—but of not existing last year or in the past. Now suppose it to be in actuality what it is capable of being. It will then be true to say now that it does not exist last year. But this is impossible. No capacity relates to being in the past, but always to being in the present or future. It is the same with the notion of an eternity of existence followed later by non-existence. In the later state the capacity will be present for that which is not there in actuality. Actualize, then, the capacity. It will be true to say now that this exists last year or in the past generally. Καὶ φυσικῶς δὲ καὶ μὴ καθόλου σκοποῦσιν ἀδύνατον ἢ ἀΐδιον ὂν πρότερον φθαρῆναι ὕστερον, ἢ πρότερον μὴ ὂν ὕστερον ἀΐδιον εἶναι. Τὰ γὰρ φθαρτὰ καὶ γενητὰ καὶ ἀλλοιωτὰ πάντα ἀλλοιοῦται δὲ τοῖς ἐναντίοις, καὶ ἐξ ὧν συνίσταται τὰ φύσει ὄντα, καὶ ὑπὸ τῶν αὐτῶν τούτων φθείρεται. 212 Considerations also not general like these but proper to the subject show it to be impossible that what was formerly eternal should later be destroyed or that what formerly was not should later be eternal. Whatever is destructible or generated is always alterable. Now alteration is due to contraries, and the things which compose the natural body are the very same that destroy it.
Postquam philosophus ostendit quod generabile et corruptibile se invicem consequuntur, et similiter ingenitum et incorruptibile, hic reprobat opinionem contrariam, per hoc quod ex contraria opinione necesse est aliqua principiorum suppositorum destrui. 276. After showing that "generable" and "destructible" follow one upon the other and likewise "non-generated" and "indestructible," the Philosopher here refutes the contrary opinion, on the ground that from such a contrary opinion some of the assumed principles must be destroyed. Et primo ostendit quomodo per hanc positionem destruitur id quod suppositum est, virtutem omnem referri ad determinatum tempus;
secundo ostendit quod per hanc positionem destruitur quod suppositum est, quod non contingit simul idem esse et non esse, ibi: adhuc quid magis et cetera.
First he shows how such a position destroys the supposition that every power is referred to a determinate time;
Secondly, he shows that it destroys the supposition that the same thing cannot simultaneously be and not be, at 279.
Dicit ergo primo quod, cum ostensum sit demonstrative ex praesuppositis quibusdam principiis quod omne genitum est corruptibile, et omne ingenitum est incorruptibile, et e converso, consequens est quod qui dicit nihil prohibere quod aliquid quod est factum seu genitum sit incorruptibile, et aliquid quod est ingenitum possit corrumpi; ita scilicet quod uni eorum, scilicet genito, adsit semel tantum generatio, et alteri adsit semel tantum corruptio, sine vicissitudine generationis et corruptionis: per hoc necesse est destruere aliquod principiorum suppositorum. Si enim conclusio syllogistice sequitur ex praemissis, non potest interimi conclusio ex necessitate consequens ex praemissis, nisi interimatur aliquod praemissorum. 277. He says therefore first [205] that since it has been demonstrated from certain presupposed principles that every generated thing is destructible, and every non-generated is indestructible, and vice versa, consequently, whoever declares there is nothing to prevent a thing that was made or generated from being indestructible, or something non-generated from being destroyed, in such a way, however, that one of these, namely, the generated, is generated but once, and the other, namely, the destructible, is destroyed but once, without their being alternately generated and destroyed, necessarily destroys thereby one or the other of the principles that were presupposed. For if a conclusion follows syllogistically from the premises, the conclusion which follows with necessity from the premises cannot be destroyed, unless one of the premises be destroyed. Hoc autem videtur dicere contra Platonem, qui posuit mundum genitum sed incorruptibilem, et ex consequenti posuit quod illud inordinatum ex quo mundus est genitus, fuerit ingenitum sed corruptibile: quamvis quidam dicant hoc Platonem non sic intellexisse sicut sonant verba eius, contra quae hic Aristoteles disputat. Sed quantum pertinet ad expositionem huius libri, non refert utrum sic vel aliter Plato senserit, dummodo videatur qualiter haec positio improbetur per rationes Aristotelis. Now he seems to state this against Plato, who posited that the world was made but is indestructible, and consequently posited that the disorder from which the world was generated was ungenerated but destructible — although some say that Plato did not understand this in the way his words sound, against which meaning Aristotle is here disputing. But so far as the exposition of this book is concerned it makes no difference whether Plato felt this way or that, provided it becomes clear how this position is being refuted by the arguments of Aristotle. Resumit autem unum principiorum datorum, ex cuius suppositione argumentabatur ad propositum ostendendum: et dicit quod omnia habentia aliquam virtutem, possunt facere vel pati, vel esse vel non esse ea quorum habent virtutem, vel in tempore infinito vel in quodam tempore determinatae quantitatis, quod sit simpliciter finitum. Et quia supra non fecerat mentionem quod virtus diceretur nisi respectu determinati temporis, subiungit quod propter hoc habentia virtutem possunt aliqua facere vel esse tempore infinito, quia etiam ipsum tempus infinitum est aliqualiter determinatum, scilicet secundum rationem, ut non possit in eo diversitas inveniri: quia scilicet infinitum est cuius non est plus, idest quo non potest maius accipi. Nec obstat quod Aristoteles in III Physic. improbat hanc definitionem infiniti, dicens eam magis esse definitionem perfecti et totius, cum tamen infinitum sit imperfectum et in modum partis se habens: quia philosophus ibi loquitur de infinito secundum id quod de eo est in actu, cui semper potest additio fieri; hic autem loquitur de infinito secundum totum quod est de eo in potentia, cui non potest additio fieri. Et talis etiam est dispositio temporis, de quo nunc loquitur: quia tempus non est totum simul, sed est successivum. 278. So he takes up again one of the given principles from the assumption of which he had argued to the proof of his proposition. And he says that all things having a certain power can do something or be acted upon, or be or not be, in accordance with their power, either for an infinite time, or for some time of definite quantity, i.e., for a period of time that is absolutely finite. And because he had previously mentioned the meaning of power only with respect to a determinate time, he adds that the reason why things having power can do or be something for an infinite time is that even infinite time is in a sense determinate, namely, by reason, in such a way that no diversity can be found in it — since the infinite is "that of which there is not more," i.e., than which something greater cannot be taken. This is notwithstanding the fact that in Physics III Aristotle refutes this definition of the infinite, saying that it is rather a definition of the whole and of the perfect, whereas the infinite is imperfect and after the manner of a part. For there Aristotle is speaking of the infinite with respect to that of it is in act, to which addition can always be made; but here he is speaking of it with respect to all that is of it in potency, and to which nothing can be added. And such is also the condition of time, about which we are now speaking — since time is not all at once but successive. Illud autem tempus quod est infinitum quo, idest secundum aliquid, scilicet secundum principium vel secundum finem, neque est infinitum simpliciter, quia potest eo aliquid esse plus, neque simpliciter determinatum, quia non habet aliquam certam quantitatem. Et ideo, secundum praedictam suppositionem, non potest esse quod aliquid habeat virtutem faciendi vel patiendi, sive essendi vel non essendi, aliquo tempore quod sit finitum ex una parte et infinitum ex alia. Quicumque autem ponit quod aliquid est ingenitum et corruptibile, vel genitum et incorruptibile, ponit quod aliquid habeat potentiam essendi vel non essendi tempore secundum quid infinito et secundum quid finito: ergo destruit praedictum principium suppositum. Now a time which is infinite in some respect, i.e., in a qualified sense, namely, with respect to its beginning or its end, is neither absolutely infinite, because there can be more of it, nor absolutely determinate, because it does not have some certain quantity. And therefore, according to the aforesaid supposition, it cannot be that something have the power of doing or being acted upon, or of being or not being, for a time that is finite at one end and infinite at the other. But whoever declares that something is non-generated but destructible, or generated and indestructible, is positing that something has the power to be or not be for a time that is in one respect infinite and in another respect finite. Therefore he is destroying the aforesaid supposed principle. Deinde cum dicit: adhuc quid magis etc., ostendit quod praedicta positio destruit aliud principium suppositum, scilicet quod impossibile est idem esse et non esse. Et circa hoc duo facit: 279. Then at [206] he shows that the above-mentioned position destroys still another principle that was assumed, namely, that it is impossible for the same thing to be and not to be. About this he does two things: primo ostendit propositum ex parte potentiae eius quod ponitur generari vel corrumpi;
secundo ex parte causae ipsius, ibi: est autem et sic videre et cetera.
First he proves his proposition from the viewpoint of the potency existing in what is assumed to be generated or destroyed;
Secondly, from the cause of the same, at 284.
Circa primum duo facit: About the first he does two things: primo ostendit quod ponentibus aliquod ingenitum corrumpi, vel aliquod genitum incorruptibile, sequitur quod aliquid possit simul esse et non esse;
secundo ostendit quod idem inconveniens sequitur ponentibus aliquid esse corruptibile quod non corrumpitur, ibi: manifestum autem et aliter et cetera.
First he shows that to suppose the non-generated to be destroyed, or something generated to be indestructible, implies that something can at the same time be and not be;
Secondly, he shows that the same impossibility follows from the supposition that something destructible exists which is not destroyed, at 283.
Circa primum ponit tres rationes. Circa quarum primam dicit: si ponamus quod aliquid ingenitum prius semper fuit, et postea corrumpatur in aliquo signo temporis, idest in aliquo instanti, nulla ratio potest assignari quare magis possit corrumpi in isto instanti quam in aliquo infinitorum praecedentium. Et similiter si aliquid sit genitum quod prius non erat tempore infinito, et postea factum est in aliquo instanti, nulla ratio potest assignari quare magis possit esse vel fieri in hoc instanti quam in aliquo praecedentium infinitorum. In regard to the first he presents three arguments. With respect to the first of these he says: If we posit that something ungenerated first always existed and later was destroyed at a certain sign of time, i.e., at some certain instant, no reason can be assigned why it should be destroyed in that instant rather than in any other of the infinite previous instants. Likewise if for an infinite time something was not existing and then came to be at a certain instant, no reason can be assigned why it could be or come to be more in that instant than in any of the infinite preceding ones. Posset autem ratio assignari si tempus praecedens poneretur finitum, quia posset dici quod haberet virtutem ad esse vel non esse in tanto tempore, et non in pluri: sed ex quo ponitur fuisse vel non fuisse tempore infinito, praedicta ratio cessat. Et ideo necesse est ponere quod ingenitum potuerit non esse in quolibet instantium praecedentis temporis; et similiter quod genitum potuerit esse in quolibet instantium praecedentis temporis. Si enim nihil magis, idest si nulla maior ratio est quare possit incipere esse vel non esse in isto instanti quam in aliquo praecedentium, cum infinita signa, idest infinita instantia, praecesserint, manifestum est quod in illo infinito tempore erit aliquid generabile, ita quod in quolibet instanti illius temporis infiniti potuerit generari. Et similiter est dicendum quod in quolibet instanti illius temporis erat corruptibile illud quod ponitur ingenitum et postea corruptum. Sic igitur patet quod illud quod ponitur praeextitisse tempore infinito, potuit etiam non esse toto illo tempore infinito. Sequetur igitur quod aliquid habebit virtutem simul, idest respectu eiusdem temporis, eius quod est esse et eius quod est non esse: ita tamen quod ex parte eius quod est ingenitum et corruptibile, accipiatur esse prius quam non esse; ex parte autem geniti et incorruptibilis accipiatur esse posterius quam non esse. Nihil autem prohibet ponere id quod est possibile. Si ergo ponamus quod illud quod est ingenitum, pro illo tempore in quo erat et poterat non esse, quod tunc non fuerit, sequetur opposita simul esse, scilicet quod illud simul sit et non sit. Sic igitur praedicta positio removet hoc quod suppositum est, scilicet quod impossibile est idem simul esse et non esse. If the preceding time were supposed finite, a reason could be assigned, because it could be said that the thing had the power to exist or not exist for such and such a time and no more. But due to the fact that the thing is described as having existed or not having existed for an infinite time, the above-reason ceases. And therefore it is necessary to posit that the ungenerated could have not existed in each of the instants of the preceding time, and similarly that the generated thing was able to exist in each of the instants of the preceding time. For if there is nothing more, i.e., no better reason why it was able to be or not to be in that instant rather than any of the preceding, since infinite signs, i.e., an infinitude of instants preceded, it is plain that during that infinite time something will be generable in the sense that it could have been generated at any instant of that infinite time. And similarly it must be said that in each instant of that time the thing assumed ungenerated and later destroyed was destructible. Consequently it is plain that the thing assumed as pre-existing for an infinite time also had the potency not to be in that whole infinite time. It will follow therefore that something will simultaneously, i.e., at one and the same time, have the power to be and not be, in such a way, however, that on the part of what is ungenerated and destructible the existence preceded the non-existence, whereas on the part of what is generated and indestructible, the existence is after the non-existence. Now there is nothing to prevent us from assuming what is possible. If, then, we assume with regard to the ungenerated that it did not exist during that time in which it existed and was able not to exist, it will follow that opposites co-exist, namely, that it existed and did not exist at the same time. Consequently, the aforesaid supposition destroys what had been presupposed, namely, that it is impossible for the same thing to be and not be at the same time. Sed videtur quod ista ratio non cogat. Nihil enim prohibet aliquid esse simpliciter possibile, quod tamen est impossibile aliquo posito: sicut si ponamus Socratem sedere pro aliquo tempore, possibile est simpliciter illum pro illo tempore non sedere, tamen non est compossibile. Ita etiam potest dici quod illud quod fuit tempore infinito, pro tempore illo poterat non esse: non tamen hoc quod est ipsum non esse, est compossibile posito, ut scilicet simul possit poni cum eo quod est ipsum esse. 280. But this reason does not seem compelling. For nothing prevents what is possible, absolutely speaking, from being impossible under certain conditions. For example, if we suppose that Socrates is at some time seated, it is possible, absolutely speaking, for him not to be seated at that time, although it is not compossible. In like manner, it can be said that what has been existing for an infinite time had the power not to exist during that time — but not, however, in the sense that its non-existence is compossible with what was posited, namely, that it could be simultaneously with its actual being. Sed dicendum est quod illud quod est incompossibile ei quod est contingenter, nihil prohibet simpliciter possibile esse: sed illud quod est incompossibile ei quod simpliciter necesse est esse, est simpliciter impossibile. Id autem quod naturaliter est per tempus infinitum, necesse est esse: quia necesse est quod unumquodque tantum sit quantum natura rerum habet; non enim aliquid deficit esse nisi quando iam non potest esse, eo quod omnia appetunt esse. Si igitur aliquid ponitur possibile esse, ex hoc ipso necesse est quod ponatur compossibile ei quod necesse est esse. Et ideo si ponamus illud quod semper fuit, fuisse possibile non esse pro illo tempore, sequitur quod possit simul esse et non esse. Now it should be stated that nothing prevents what is incompossible to that which is contingent from being absolutely possible, yet what is incompossible to that which absolutely must be, is absolutely impossible. That which exists naturally through an infinite time exists necessarily — since it is necessary that each thing be to the extent that the nature of things provides for it, for nothing ceases to be except when it can no longer be, since all things long to be. Hence if something is presented as possible to be, then by that very fact it is necessary to posit it as compossible to that which must be. Therefore if we posit that what has always existed was able not to exist all during that time, it follows that it was able at once to be and not be. Secundam rationem ponit ibi: adhuc autem et hoc et cetera. Et dicit quod illud quod semper fuit vel semper non fuit, secundum praemissa ponitur habuisse potentiam oppositi eius quod ei inerat, non secundum aliquod signum vel instans, sed simpliciter in omni signo, idest in omni instanti: et sic sequitur quod aliquid habeat potentiam ut sit et non sit tempore infinito, quod est impossibile, ut supra ostensum est. 281. He gives the second argument at [207] and says that what always existed, or always did not exist, is according to the foregoing presumed to have possessed a power opposite to what was in it, not at some sign or instant, but absolutely at every sign, i.e., at every instant. Consequently, it follows that for an infinite time something would have the power to be and not be, which is impossible, as was proved above. Tertiam rationem ponit ibi: adhuc si prius etc., quae talis est. In eo quod incipit esse postquam non fuerat, vel non esse postquam fuerat, prius est virtus vel potentia quam actus: et ita si aliquod ens est ingenitum quod semper fuit, sequitur quod etiam semper habuit virtutem vel potentiam ad non esse; nulla enim est ratio quare advenerit ei ista potentia non essendi post tempus infinitum. Similiter etiam si sit aliquid genitum quod prius non fuerit tempore infinito, sequitur quod toto illo tempore fuerit possibile fieri: ita quod simul dum non erat, habebat potentiam essendi et non essendi hoc, et quod esset posterius secundum infinitum tempus, ex quo ponitur quod habet esse incorruptibile. 282. He gives the third argument at [208] which is this: In that which begins to be after it had not been, or not to be after it had been, the power or potency precedes the act. Accordingly, if something that always existed was ungenerated, it follows that it always had the potency not to exist —for there is no reason why that potency of non-being should have come to it after an infinite time. Similarly, even if there be something generated which for an infinite time did not exist, it follows that during that entire time it was able to come into existence, so that at the same time that it was not existing, it had the power to be and not be this, and that it would be later for an infinite time, since we are assuming that it is indestructible. Sic igitur ex quo in infinitum antequam esset, habebat potentiam ut esset in futurum in infinito tempore, nulla ratio erat quare potuerit esse in tali instanti et non prius, ex quo non est in potentia ad hoc quod est esse in tempore determinato. Relinquitur ergo quod potuerit esse etiam in aliquo tempore antequam fuerit: et ita poterat esse in illo tempore in quo non erat, et sic sequitur, secundum praemissa, quod potuerit simul esse et non esse. Et eadem ratio est de eo quod ponitur semper fuisse et quandoque corrumpi. Consequently, since for the infinite time before it existed it had the power to exist for an infinite time in the future, there was no reason why it could exist in that instant and not before, since it is not in potency to exist in a determinate time. What is left, therefore, is that it could have existed even at some time before it existed; thus it had the power to exist in that time in which it was not existing, and so it follows, according to the premises, that it was able to be and not be at the same time. And the same argument applies to what is assumed to have always been and is at a certain time destroyed. Deinde cum dicit: manifestum autem et aliter etc., concludit secundum eandem rationem quod impossibile est quod aliquid sit corruptibile, quod quandoque non corrumpatur. Posset enim aliquis obviare praedictis rationibus, dicendo quod omne genitum est corruptibile secundum suam naturam, sed potest contingere quod illud quod est corruptibile nunquam corrumpatur, propter aliquam causam conservantem ipsum in esse; sicut Plato posuit quod mundus est genitus et corruptibilis secundum seipsum, sed semper manebit propter voluntatem Dei (quamvis quidam dicant quod Plato non sic intellexerit mundum esse corruptibilem sicut ea quae in se habent necessariam causam corruptionis, sed per hoc voluerit designare dependentiam sui esse ab alio, quia scilicet necessitas essendi non est ei a seipso, sed a Deo. Sed quicumque fuerit intellectus Platonis non refert ad propositum, quia Aristoteles obiicit contra verba ipsius). Unde dicit manifestum esse quod impossibile est id quod est corruptibile, quandoque non corrumpi. Quia si quandoque non corrumpetur, potest non corrumpi, et ita erit incorruptibile: et tamen ponitur sempiterno tempore corruptibile existens: semper igitur, idest infinito tempore, erit simul actu corruptibile et incorruptibile. Sed quod corrumpitur non semper est, quod autem est incorruptibile, semper est: ergo erit aliquid simul possibile et semper esse et non semper esse, quod est impossibile, ut patet ex his quae supra dicta sunt; quia quod potest semper esse, ex necessitate semper est, unde non potest non semper esse. Sic igitur patet quod omne corruptibile quandoque corrumpetur. 283. Then at [209] he concludes according to the same reasoning that it is impossible for something to be destructible and not be destroyed at some time. For someone could object to the foregoing arguments and say that everything generated is destructible according to its nature, but it can happen that what is destructible may never be destroyed, because some cause is preserving its existence, as Plato assumed that the world is in itself generated and destructible, but will always remain, because God wills it. (Some say that Plato did not understand that the world is destructible, as though it had within itself the necessary cause of its destruction, but that he described it in that way because he wanted to point out that it depends for its existence on another, i.e., that the necessity of its existence is not in it of itself but from God. But whatever Plato may have understood makes no difference to the present undertaking, since Aristotle is objecting to his words.) Hence he says that it is plainly impossible for something destructible not to be at some time destroyed. Because if it will not be destroyed at some time, it has the power not to be destroyed and thus will be indestructible; and yet it is assumed to be a destructible thing existing for an infinite time. Consequently, it will be always, i.e., for an infinite time, simultaneously actually destructible and indestructible. But what is destroyed does not exist forever, whereas the indestructible does exist forever. Therefore there will be something capable at the same time of always existing and not always existing. But that is impossible, as is plain from what was said above, because what can always exist, necessarily exists always, and hence cannot be not always existing. Consequently, it is clear that everything destructible will be destroyed sometime. Et similiter si aliquid est generabile in sui natura, necesse est quod factum sit. Quod quidem non est sic intelligendum, quod omnia quae possunt generari quandoque generentur; multa enim possunt fieri quae nunquam fient: sed hoc non potest esse, quod aliquid iam existens in sua natura sit generabile, et tamen non sit generatum, sed ab aeterno praeextiterit. Illud enim quod est generabile non habet potentiam naturalem ad semper essendum, sed ut possit esse postquam aliquando est factum. Et ideo non dicit, si generabile est fiet, sed factum est. Similarly, if something is of its very nature generable, it is necessary that it be made. This does not mean that everything that can be generated will be generated at some time, for there are many things possible that will never be generated. But it cannot be that something now existing have a nature that is generable, and not have been generated, but have pre-existed from eternity. For what is generable does not have the natural power of always existing but of being able to be after it was at some time made. That is why he does not say that if it is generable, it will be made, but has been made. Deinde cum dicit: est autem et sic videre etc., ostendit idem ex parte causae eius quod ponitur ingenitum vel incorruptibile. 284. Then at [210] he proves the same from the viewpoint of the cause of what is assumed ungenerated and indestructible. Et primo ponit rationem;
secundo excludit quandam obviationem, ibi: sed adhuc neque verum et cetera.
First he presents his argument;
Secondly, he rejects an objection, at 286.
Dicit ergo primo quod etiam sic sicut dicetur, contingit videre quod impossibile est aut quod id quod quandoque factum est, sit incorruptibile, aut quod est ingenitum et semper prius existens, corrumpatur. Illud enim quod est incorruptibile vel ingenitum, non potest esse a casu: quia illud quod est a casu vel a fortuna, neque sicut semper neque sicut frequenter aut est aut fit; illud autem quod est in infinito tempore, sive simpliciter infinito sive infinito ex una parte, scilicet ante vel post, vel est sicut semper, sicut illud quod est in infinito tempore simpliciter, vel sicut frequenter, sicut illud quod est in infinito tempore ex una parte. Necesse est ergo quod talia quae vel generantur vel corrumpuntur post infinitum tempus, a natura habeant quod quandoque sint et quandoque non sint. Sed eorum quae naturaliter quandoque sunt quandoque non sunt, eadem potentia est ad contradictoria, scilicet ad esse et non esse: quia quod aliqua quandoque sint et quandoque non sint, habent ex materia, inquantum subiicitur privationi vel formae. Sic igitur idem sequitur quod prius, scilicet quod opposita possint simul inesse eidem. In eo enim quod est generatum, remanet materia potens non esse: et ita, cum sit incorruptibile, simul erit potens esse et potens non esse. Et eadem ratio est ex parte ingeniti. He says therefore first that, as will be said, we may also see in the following way that it is impossible either for a thing which is at some time generated to be thenceforward indestructible, or for a thing which is ungenerated and has always hitherto existed, to be destroyed. What is indestructible or ungenerated cannot exist by chance — since the product of chance or fortune neither exists nor comes to be as that which is always or usually. Meanwhile, anything which exists in infinite time, either absolutely finite or infinite in one direction, namely, before or after, is in existence either always, as is that which exists in infinite time absolutely, or for the most part, as is that which is in infinite time as to one part. Therefore it is necessary that such things which are either generated or corrupted after an infinite time, have from nature that they will at some time be and at some time not be. But in things which at one time naturally are and at another are not, the same power is directed to contradictories, namely, to being and not being, since this characteristic of at some time being, and at some time not being, is had from matter inasmuch as it is subject to privation or form. Thus the same thing follows as before, namely, that opposites could exist in the same thing at the same time. For in what has been generated a matter in potency to non-existence remains — and so, since it is indestructible, it will at the same time be able to be and able not to be. And the same holds for the ungenerated. Deinde cum dicit: sed adhuc neque verum etc., excludit quandam obviationem. Posset enim aliquis dicere quod illud incorruptibile quod est genitum, habet potentiam ad non esse, non quidem in futurum, sed respectu praeteriti: et similiter illud quod est ingenitum sed corruptibile, habet potentiam ad esse respectu praeteriti. 285. Then at [211] he excludes a certain objection. For someone could say that that indestructible thing which is generated has the power of not existing, not indeed with respect to the future, but with respect to the past; similarly what is ungenerated but destructible possesses a potency to existence with respect to the past. Sed hoc ipse excludit, dicens quod non est verum dicere nunc quod modo sit annus prior, vel aliquid eorum quae in praeterito tempore fuerunt; neque etiam potest dici quod id quod est nunc, fuerit in anno praeterito: sic enim aliqua sunt secundum tempus distincta, ut ordo temporis perverti non possit, ut scilicet ea quae sunt praeterita vertantur in praesentia, et ea quae sunt praesentia attribuantur tempori praecedenti. Ex quo patet quod impossibile est illud quod aliquando non fuit, quod posterius habeat esse in sempiternum, sicut iam conclusum est ex praemissa ratione. Quia ratione materiae ex qua genitum est, etiam postquam est, habet virtutem ad non esse: sed non potest dici quod habeat potentiam ad non esse tunc, quia iam existit actu ens, et sic opposita essent simul, ut in praemissis rationibus concludebatur; sed sequitur quod habeat potentiam ad non esse respectu prioris anni vel praeteriti temporis. Quod autem hoc sit impossibile, sic patet. Quia illud ad quod habet aliquid potentiam vel virtutem, potest poni esse in actu: si ergo possibile est aliquid respectu praeteriti temporis vel esse vel non esse, poterit poni quod annus prior non sit, idest quod illud quod fuit in anno priori tunc non fuerit: sed hoc est impossibile, ut praemissum est; et hoc ideo, quia nulla potentia respicit id quod factum est in praeterito, sed id quod est in praesenti vel quod futurum est. But he excludes this by saying that it is not true to assert now that it is at the present time last year, or any of the things which were in past time; nor can it be said that what exists now existed in the past year — for things are distinguished in time in such a way that the order of time cannot be reversed so as to make the past the present or attribute present things to the past. From this it is plainly impossible for something which at one time did not exist, later to have existence forever, as we have already concluded from the preceding argument. For by reason of the matter from which it was made it has the potency not to exist even after it does exist: but it cannot be said that it has the potency not to exist now, because it is already existing in act and thus opposites would co-exist, as was concluded in the previous arguments. But it follows that it has the potency to non-existence in regard to the past year or past time. But this is impossible as the following argument shows: That for which a thing has the potency or power can be made actual. If, therefore, it is possible for something with respect to past time either to be or not be, we can posit that last year was not, i.e., that what existed last year was not existing then. But this is impossible, as was set down previously, for no potency looks to what was made in the past, but to what is in the present or what will be. Et quod dictum est circa genitum quod ponitur incorruptibile, eadem etiam ratio est si aliquid ponatur prius existens in sempiterno tempore, et postea ponatur non existens per corruptionem. Sequetur enim quod postquam corruptum est, ratione materiae habeat potentiam ad illud quod non potest poni in actu, scilicet ad esse in priori tempore. Quod si ponatur esse possibile, verum erit dicere quod nunc est annus prior, et quod nunc est quidquid fuit in praeterito tempore, ex quo potentia non est nisi respectu praesentis, ut dictum est. And what has been said in regard to something generated but assumed incorruptible applies also if something is assumed as previously existing for sempiternal time and then assumed non-existent through having been corrupted. For it will follow that after it has been corrupted, it still possesses by reason of the matter a potency to something that cannot be reduced to act, namely, to existence in a previous time. If this is assumed possible, it will be true to say that it is now last year and that whatever existed in the past exists now, from the fact that a potency regards the present alone, as has been said. Virtus igitur huius rationis in hoc consistit quod, cum potentia non sit nisi respectu praesentis vel futuri, si aliquid dicatur habere potentiam respectu praeteriti, sequitur quod praeteritum convertatur, et fiat praesens vel futurum. The force of this argument consists in the fact that, since a potency looks only to the present or future, then if something is said to have a potency with respect to the past, it follows that the past is converted and made present or future. Deinde cum dicit: et naturaliter etc., ostendit propositum principale per rationem propriam scientiae naturali. Et dicit quod etiam per rationem naturalem, et non per rationem universalem, idest logicam vel metaphysicam, sicut in praecedentibus, potest considerari quod impossibile est id quod semper fuit postea corrumpi, vel id quod prius non fuit postea esse sempiternum. Et hoc probat quia omnia corruptibilia et generabilia sunt alterabilia; generatio autem et corruptio est terminus alterationis; alteratio autem fit de contrario in contrarium. Et sic patet quod ex illis contrariis ex quibus aliqua fiunt cum prius non essent, ab illis etiam postea corrumpuntur, et in eadem reducuntur per corruptionem; sicut si aliquid ex calido factum sit frigidum, potest iterum a calido calefieri. Et sic patet quod illud quod est generatum, potest iterum corrumpi; et illud quod est corruptum, fuit quandoque generatum. 286. Then at [212] he proves his main proposition with an argument proper to natural science. And he says that also with a natural argument, and not a "universal" one, i.e., one that is logical or Metaphysica l, as the preceding were, it can be considered that it is impossible for that which always existed to be later destroyed, or for that which previously did not exist to be afterwards eternal. And this he proves because all destructible and generable things are alterable. For generation and destruction are the termini of alteration, and alteration passes from contrary to contrary. Consequently, it is plain that by the very contraries from which things come to be when previously they did not exist, such things are later destroyed and reduced back to the same by corruption. Thus, for example, if something from being hot is made cold, it can again be made hot by what is hot. And so it is plain that what has been generated, can again be destroyed; and that what was destroyed, was at one time generated. Est autem considerandum quod praedictae rationes Aristotelis procedunt contra positionem ponentem mundum esse factum per generationem, et etiam esse incorruptibilem vel per se vel per voluntatem Dei. Nos autem secundum fidem Catholicam ponimus quod incoepit esse, non quidem per generationem quasi a natura, sed effluens a primo principio, cuius potentia non erat alligata ad dandum ei esse infinito tempore, sed secundum quod voluit, postquam prius non fuerat, ut manifestetur excellentia virtutis eius supra totum ens; quod scilicet totum ens tantum dependet ab ipso, et eius virtus non est alligata vel determinata ad productionem talis entis. Ea vero quae ab eo sic producta sunt ut in sempiternum sint, habent potentiam et virtutem ad semper essendum, et nullo modo ad hoc quod aliquando non sint. Quando enim non erant, talem potentiam non habebant: quando autem iam sunt, non habent potentiam respectu non esse quod prius fuit, sed respectu esse quod nunc est vel erit; quia potentia non respicit praeteritum, sed praesens vel futurum, ut philosophus dicit. 287. It should be noted that these arguments of Aristotle are directed against the position that posits a world produced by generation and indestructible either of its very nature or through the will of God. But according to the Catholic faith, we hold that it began to be, not through a process of generation as from nature, but by flowing from a first principle whose power was not bound to give it existence in infinite time but as it willed, after previous non-existence, in order to manifest the excellence of its power over the totality of being, namely, that the totality of being depends entirely on it and its power is not confined or determined to the production of some given being. Now the things produced by it so as to exist forever have the potency and power to exist forever, and in no way at some time not to exist. For as long as they did not exist, they had no such power; but when they now exist, they have no power with respect to non-existence in the past but to the existence which now prevails or will be — for potency does not look to the past, but to the present or future, as the Philosopher says. Sic igitur patet quod rationes praemissae in nullo impugnant sententiam Catholicae fidei. Et in hoc terminatur sententia primi libri. Thus it is clear that the preceding arguments in no way impugn the judgment of the Catholic faith. And with this the doctrine of the first book is brought to an end.
| Postquam in primo libro philosophus determinavit de toto mundo, in quo ostendit esse quaedam corpora quae moventur circulariter, quaedam quae moventur motu recto, hic incipit determinare de corporibus quae moventur circulariter. | 288. After having determined in Book I concerning the world as a whole, in which he showed to exist some bodies that are circularly moved and some that are moved with a straight motion, the Philosopher here begins to determine about the bodies that are circularly moved. |
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Et primo determinat de ipsis corporibus circulariter motis; secundo determinat de centro super quod circulariter moventur, ibi: reliquum autem de terra dicere et cetera. |
First he determines the question of the bodies themselves that are circularly moved; Secondly, he determines the question of the center about which they are circularly moved (Lecture 20). |
| Circa primum duo facit: | As to the first he does two things: |
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primo determinat de caelo, quod est corpus circulariter motum; secundo de stellis quae sunt in caelo, ibi: de vocatis autem astris et cetera. |
First he discusses the heaven, which is the circularly moved body; Secondly, the stars which are in the heaven (L. 10). |
| Circa primum duo facit: | About the first he does two things: |
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primo determinat de his quae pertinent ad substantiam caeli; secundo de his quae pertinent ad motum eius, ibi: quoniam autem est dupliciter et cetera. |
First he determines what pertains to the substance of the heaven; Secondly, what pertains to its motion (L. 7). |
| Circa primum tria facit: | As to the first he does three things: |
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primo determinat de duratione caeli; secundo de diversitate partium eius, ibi: quoniam autem quidam sunt etc.; tertio determinat de figura ipsius, ibi: figuram autem sphaericam et cetera. |
First he determines about the duration of the heaven; Secondly, about the variety of its parts (L. 2); Thirdly, about its shape (L. 5). |
| Circa primum duo facit: | Regarding the first he does two things: |
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primo infert conclusionem in praecedentibus manifestatam; secundo ex illa conclusione arguit ad propositum, ibi: propter quod bene se habet et cetera. |
First he draws a conclusion made clear in what has gone before; Secondly, from that conclusion he argues to his proposition, at 290. |
| Dicit ergo primo quod ex praemissis possumus accipere credulitatem quod totum caelum neque sit factum, neque contingat ipsum corrumpi, sicut quidam dicunt. | 289. He says therefore first [213] that from what has gone before [LL. 22 ff. of Book I], we can believe that the entire heaven neither was made nor is able to be corrupted as some say. |
| Dicit autem totum caelum esse ingenitum et incorruptibile, eo quod maxima pars corporum mundi est substantia caelestis corporis, quod est ingenitum et incorruptibile per modum quo in primo libro probatum est. Vel hoc dicit ad differentiam quarundam partium mundi, quae sunt generabiles et corruptibiles secundum partes, licet non secundum totum, sicut patet de elementis. Vel quia huiusmodi corpora quae sunt generabilia et corruptibilia, sicut animalia et plantae et lapides, non proprie sunt partes mundi (alioquin mundus nunquam perfectus esset, cum non habeat omnia huiusmodi simul): sed huiusmodi sunt quidam effectus partium mundi; et ideo, licet huiusmodi res subiaceant generationi et corruptioni non solum secundum partem, sed secundum totum, nihilominus tamen totus mundus caret generatione et corruptione. | He says that the whole heaven is ungenerated and indestructible on the ground that the major part of the bodies of the world is the substance of heavenly body, which is neither generated nor destructible, in the sense explained in Book I. Or else he is saying this to differentiate it from those parts of the world that are generable and destructible with respect to their parts, although not wholly, as is plain in the elements. Or else because those bodies which are generable and destructible, for example, plants and animals and stones, are not in the strict sense parts of the world (otherwise the world would never be perfect, since it would never possess all such things at once); rather they are effects of the parts of the world. Therefore, although such things are subject to generation and corruption not only with respect to a part but also as a whole, nevertheless the whole world is neither generated nor corrupted. |
| Et est notandum quod dicit caelum omne non est factum; sed non dicit neque corruptum, sed neque contingit corrumpi, propter illos qui dicebant mundum ex natura sua esse corruptibilem, et tamen nunquam corrumpetur propter voluntatem Dei; et ideo signanter dicit quemadmodum quidam dicunt. | It should be noted that he says "the whole heaven was not generated," and then, instead of saying, "it is not corrupted," he says, "it cannot be corrupted." He uses this way of stating it for the sake of those who said that the world is of its very nature corruptible but that on account of God's will it never will be corrupted. He therefore specifically says, "as some say". |
| Sed probatum est supra quod est unum tantum et sempiternum (quod dicit ne crederetur sempiternum esse non unum numero, sed specie); ita scilicet quod non habet principium neque finem totius aeterni, idest totius suae durationis infinitae. | But it has been proved above that the world is one only and eternal (which he says lest anyone suppose that the eternal be not numerically one but one in species only), in such a way as to have neither a beginning nor an end "of the whole eternal," i.e., of its whole infinite duration. |
| Et ne aliquis putaret mundum corporeum sic dici aeternum sicut Deus, cuius esse et vivere est totum simul, scilicet absque successione prioris et posterioris, subiungit habens autem infinitum tempus; quia scilicet eius duratio extenditur secundum successionem temporis. Non tamen totus mundus habet hoc modo durationem temporalem, sicut aliquod singulare generabile et corruptibile, cuius duratio comprehenditur a tempore, non tamen continet tempus: sed tempus continetur a toto mundo, tum quia tempus non extenditur ultra durationem mundi, tum quia tempus causatur ex motu primi corporis mundi, ut in IV Physic. habitum est. Unde tempus continetur a mundo, sicut effectus a causa. Habet autem tempus quod mensuret motum caeli, non quidem inquantum continetur ab eo sicut effectus a causa (non enim continens mensuratur per contentum, sed e converso): sed hoc, inquam, habet tempus inquantum est imago quaedam derivata ab aeternitate divina, sicut et Boethius dicit: qui tempus ab aevo ire iubes. | Now, lest anyone suppose that he means the corporeal world is eternal as God is eternal, Whose existence and life are totally all at once, i.e., without any succession of before and after, he adds that the world "possesses an infinitude of time," since, namely, its duration extends according to the succession of time. Yet the whole world does not possess temporal duration in the same way as some generable and destructible singular, whose duration is comprehended. by time but does not encompass time; rather time is encompassed by the whole world, both because time does not extend beyond the duration of the world and because time is produced from the motion of the first body of the world, as was explained in Physics IV. Thus time is contained by the world as an effect by its cause. Now time is the measure of a celestial motion not through the latter's being contained by it as an effect by its cause (for the container is not measured by the content, but the other way around), but through its being a certain image of God's eternity as Boethius says, "Who dost command time to proceed from the aeon." |
| Haec igitur quae dicta sunt, non solum credibilia redduntur per rationes supra positas, sed etiam per opiniones aliter dicentium, qui attribuunt mundo generationem et corruptionem. Si enim ita sit, quod et contingit mundum sic se habere sicut nos dicimus, absque hoc quod aliquod inconveniens sequatur, non autem contingit se habere secundum modum quo illi dicunt mundum factum esse, hoc iam habebit magnam inclinationem, idest magnam vim persuasivam, ad hoc quod aliquis credat immortalitatem caeli et sempiternitatem ipsius (ut immortalitas referatur ad perpetuitatem vitae, sempiternitas autem ad perpetuitatem essendi: ponebant enim caelum non solum esse, sed etiam vivere, tanquam animatum). | Therefore the foregoing statements are worthy of belief not only on account of the arguments previously cited, but also on account of the contrary opinions of those who attribute generation and corruption to the world. For if the world turns out to be as we have described it, with no paradoxes arising, and it cannot have come about in the manner described by those who claim that the world was generated, then our description will have a "great inclination," i.e., great power to persuade one to believe in the immortality of the heaven and in its eternity — where "immortality" refers to the perpetuity of life and "eternity" to the perpetuity of its existence — for they maintained that the heaven not only existed but also lived, as something animated. |
| Ex hoc autem quod hic dicit, apparet quod Aristoteles induxit praedictas rationes ad probandum sempiternitatem mundi, non tanquam ostendentes ex necessitate quod mundus non incoeperit, sed tanquam ostendentes quod non incoepit illo modo quo ab aliis incoepisse ponebatur. | From what he says here, it is plain that Aristotle presented his previous arguments in proof of the eternity of the world not with the intention of showing with necessity that the world could not have begun but as showing that it did not begin in the manner described by others. |
| Deinde cum dicit: propter quod bene se habet etc., ex praemissa conclusione, quae erat de sempiternitate totius mundi, concludit propositum, scilicet sempiternitatem corporis caelestis. Et circa hoc tria facit: | 290. Then at [214], from the preceding conclusion as to the eternity of the entire world, he concludes to his proposition, namely, to the eternity of the heavenly body. And concerning this he does three things: |
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primo infert conclusionem in generali; secundo manifestat eam in speciali, ibi: caelum autem etc.; tertio ex veritate manifestata excludit contrarias opiniones, ibi: propter quod quidem et cetera. |
First he infers the conclusion in a general way; Secondly, he explains it in detail, at 292; Thirdly, from the truth shown he excludes certain contrary opinions, 295. |
| Circa primum duo facit: | About the first he does two things: |
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primo infert conclusionem intentam; secundo ponit rationem ipsius, ibi: etenim finis et cetera. |
First he draws his intended conclusion; Secondly, he presents its argument, at 291. |
| Dicit ergo primo quod, quia ex praemissis inclinamur ad credendum sempiternitatem mundi, consequens est quod homo se exhibeat de facili persuasibilem a dictis antiquorum: non tamen quantum ad quoscumque antiquos errantes, sed praecipue quantum ad patres nostros, qui scilicet nos in cultu divino instruxerunt; ut scilicet credamus eorum sermones esse veros, quantum ad hoc quod credamus aliquid esse immortale et divinum, non solum de numero substantiarum immobilium, quae sunt penitus a materia separatae, sed etiam quantum ad corpora quae habent motum, talem tamen ut ipsius motus corporis divini et immortalis non sit aliquis finis, quo scilicet iste motus terminetur, sed magis iste motus sit finis omnium aliorum motuum. Ideo autem hoc attribuit antiquis sermonibus patrum, quia omnes illi qui apud gentiles cultum divinum instituerunt, hoc intendebant, quod cultus divinus exhiberetur caelo tanquam divino et immortali corpori et quod semper movetur: unde et a thein, quod est semper currere, in Graeco Theon, idest Deum, nominaverunt. | He says therefore first [214] that, because we are inclined to believe in the eternity of the world from what has preceded, it follows that a man shows himself easily persuasable by the dictums of the ancients — not, however, by those of any who erred but principally by those of our fathers, who, namely, schooled us in divine worship. We should be inclined to believe their words to be true, to the effect that there is something immortal and divine, not only among the number of the immobile substances, which are totally separated from matter, but also among bodies which have motion, such, however, that of the motion of the divine and immortal body there be no end, by which, namely, it might be terminated; rather its motion is the end of all other motions. Now the reason he attributed this to the ancient sayings of the ancestors is because all those who established a form of divine worship among the gentiles sought to have divine worship given to the heaven as to a divine and immortal body whose motion is endless. Accordingly they derive from theirs, which means "to run forever," their name for the deity, theos. |
| Deinde cum dicit: etenim finis etc., ponit rationem praedictae conclusionis, quantum ad hoc quod dixerat, quod motus caeli sit finis aliorum motuum. Omne enim continens habet rationem finis, inquantum contentum terminatur ad suum continens. Manifestum est autem quod imperfectum natum est contineri a perfecto. Sicut autem in primo ostensum est, motus circularis est perfectus, motus autem recti sunt imperfecti: quia non redeunt ad suum principium, sicut motus circularis, sed habent terminum maxime distantem et contrarium principio; unde sicut in principio incipiunt moveri, ita cum sunt in termino, incipiunt quiescere. Unde oportet quod motus circularis contineat alios motus, sicut perfectum continet imperfectum. Et propter hoc motus circularis est finis aliorum motuum, ita scilicet quod ipse motus circularis nullum habeat principium neque finem, quo incipiat moveri neque desinat, sed quod incessabiliter moveatur tempore infinito. Omne autem quod incipit aut desinit moveri, hoc patitur per aliquem motum praecedentem, qui est causa motus ipsius: si enim in eadem dispositione se haberet movens et mobile, non magis inciperet motus postea quam prius, in his quae a natura moventur; unde si aliquis motus incipit de novo, oportet praeexistere aliquem motum qui causet novitatem huius motus. Si autem mundus est sempiternus, oportet quod semper fuerit motus. Unde oportebat ponere aliquem motum sempiternum, qui contineat alios motus non sempiternos, tanquam finis ipsorum; ita tamen quod horum quidem mobilium sit causa quod incipiant moveri, illorum autem quae desinunt moveri, suscipiat quietem. | 291. Then at [2153 he presents his argument for that part of the foregoing conclusion which stated that the motion of the heaven is the end of other motions. For everything that contains has the notion of end inasmuch as the contents end at the limits of the container. Now it is clear that the imperfect is disposed to be contained by the perfect. As was proved in Book I, circular motion is perfect and straight motions imperfect, for these do not return to their beginning as a circular motion does; rather their terminus is most remote from the beginning and contrary to it — wherefore, just as they begin to move at the start, so, they begin to rest when at the end. Consequently, circular motion must contain other motions as the perfect contains the imperfect. And for this reason circular motion is the end of other motions, in such a way, namely, that the former has neither a beginning nor an end at which to start or cease; rather, it moves without cease in infinite time. For whatever begins or ceases to be moved, does so under the influence of some previous motion, which is the cause of its motion. If the mover and moved were in the same relationship, there would be no more reason for a motion to begin later than before. Hence, if some motion begins newly, there must pre-exist some motion to cause the newness of this motion. Now if the world is eternal, motion would have to have always been. Hence it was necessary to posit some eternal motion which would contain other motions that were not eternal and be their end in such a way as to be a cause of motion in these mobiles which begin to be moved, and to receive the rest of those which cease to be moved. |
| Non autem dicit causet quietem, sed suscipiat: quia de intentione causae universalis est quod imprimat suam similitudinem effectibus, qui tamen non possunt adaequare causam universalem, sed recipiunt similitudinem eius secundum suum modum; sicut patet quod haec inferiora non recipiunt uniformiter a Deo sempiternitatem divini esse, ut scilicet maneant semper eadem numero, sed manent eadem specie per generationem et corruptionem individuorum; unde Deus ipse quidem dat esse rebus, sed earum corruptionem recipit, quasi ea utens ad generationem aliorum. Et similiter inferiores motus recipiunt similitudinem sempiternitatis motus caelestis non uniformiter, sed secundum alternationem quietis et motus. Unde id quod est in eis de motu, causatur ex motu caelesti; quod autem est in eis de defectu motus, idest de quiete, causatur ex defectu ipsorum, in quorum natura non est ut semper moveantur; sed motus caeli dicitur suscipere quietem horum corporum, sicut ordinatam ad finem. Et sic etiam Plato in Timaeo Deum mundi conditorem inducit dicentem caelestibus diis: alimentum dantes augete, et detrimentum passa iterum suscipite. | He does not say "causes the state of rest" but "receives," because a universal cause aims at impressing its likeness on its effects which, however, cannot be equated to the universal cause but receive its likeness according to their condition. Thus lower things do not uniformly receive from God the eternity of the divine being so as to remain forever the same in number, but they remain the same in species through the generation and corruption of individuals. Hence God gives existence to things but receives their corruption, using it, as it were, for the generation of other things. In like manner, the lower motions receive a likeness of the eternity of the heavenly motion not in a uniform manner but according to the alternation of motion and rest. Here, whatever there is in them of motion is caused by the heavenly motion; but whatever is in them of defect of motion, i.e., of rest, is due to their defect, because it is not in their nature to be in eternal motion. So the motion of the heaven is said to accept the state of rest of these bodies as something ordained to an end. Wherefore Plato in the Timaeus has God, the establisher of the world, saying to the heavenly gods: "Make things increase by giving food and take back once more the things that suffered loss". |
| Deinde cum dicit: caelum autem etc., manifestat in speciali quod dixerat: | 292. Then at [216] he explains in detail what he had said: |
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et primo quantum ad sempiternitatem caeli; secundo quantum ad qualitatem motus eius, ibi: adhuc autem sine labore et cetera. |
First as to the eternity of the heaven; Secondly, as to the quality of its motion, at 294. |
| Quod autem caelum sit sempiternum, manifestat dupliciter. Primo quidem secundum dicta antiquorum. Et dicit quod antiqui ipsis diis attribuebant caelum et locum qui est sursum, tanquam caelum sit immortale, ut convenienter possit esse locus immortalium, sicut etiam supra dictum est in primo. Vocat autem locum sursum ipsum caelum propter communem opinionem sic loquentium; et quia locus quo feruntur levia, qui proprie dicitur locus sursum, propinquissimus est caelesti corpori. | That the heaven is eternal he shows in two ways. First from the sayings of the ancients. He says that they assigned to the gods the heaven and the place which is above, taking the heaven as immortal and suitable as a place for immortal beings, as was also stated above in Book I. And he gives to the place above the name "heaven" in keeping with the common opinion of those so speaking and also because the place whither light things are borne, and which is properly called an upward place, is nearest to the heavenly body. |
| Secundo ibi: nunc autem testificatur etc., manifestat idem per rationem supra positam, qua ostendebatur quod caelum sit ingenerabile et incorruptibile, ex hoc scilicet, quod caret contrario. Ibidem etiam est ostensum quod caelum est impassibile passione quae inducit difficultatem corruptionis, ut ibidem ostensum est. Sunt tamen corpora caelestia passibilia passione perfectionis, sicut quod luna illuminatur et recipit virtutem a sole: et haec etiam supra dicta sunt. | 293. Secondly, [217] he explains it with a reason previously cited, which showed the heaven to be ungenerable and indestructible from the fact that it has no contrary. It was also shown there that the heaven is impassible, with the passion that produces difficulty of corruption. Heavenly bodies are, however, passible with a perfective passion, as in the case where the moon is illuminated and receives virtue from the sun. These things, too, were previously mentioned. |
| Deinde cum dicit: adhuc autem sine labore etc., manifestat qualitatem motus caeli, et quod movetur sine labore. Et hoc probat quia non est ponere quod per aliquam necessitatem violentam detineatur, quae prohibeat ipsum aliter moveri, scilicet secundum suam naturam. Omne enim quod cum labore movetur, movetur contra motum naturalem sui corporis (propter quod motus animalis sursum est laboriosus): quae autem contra suam naturam moventur, si debeat eorum motus continuari, oportet quod hoc sit per aliquod violentum movens, quod imponat eis necessitatem coactionis; nam necessitas naturalis non est nisi ad ea quae sunt secundum naturam. Omne autem quod est tale, quod scilicet movetur aliquo motu contra suam naturam, tanto magis laboriosum est, quanto motus eius est magis continuus et sempiternus, et quanto magis est expers optimae dispositionis, ut scilicet sit secundum suam naturam. Hoc autem non potest attribui corpori caelesti, quod est nobilissimum corporum: unde relinquitur quod motus caeli non sit laboriosus. | 294. Then [218] he shows the quality of the heaven's motion, namely, that it is moved without labor. This he proves on the ground that there can be posited no violent necessity that would keep it from being moved otherwise, i.e., according to its nature. For whatever is moved with labor is being moved against the natural motion of its body — for which reason it is laborious for an animal to move upwards. Now in the case of things moved against their nature, if such a motion is to continue, it must be maintained by some violent mover imposing on them a motion of coercion — for natural necessity leads only to what is according to nature. Everything such, i.e., which is subject to a motion contrary to its nature, must be in more and more labor accordingly as the motion is more continuous and eternal, and as it is more alien to its best disposition, i.e., that which is according to its nature. But such a thing cannot happen to the heavenly body, which is the noblest of bodies. Consequently the motion of the heaven is not laborious. |
| Deinde cum dicit: propter quod quidem etc., excludit opiniones contrarias. | 295. Then at [219] he excludes contrary opinions. |
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Et primo excludit errores; secundo concludit veritatem intentam, ibi: si itaque quemadmodum et cetera. |
First he dismisses certain errors; Secondly, he concludes to the truth intended, at 299. |
| Circa primum excludit tres opiniones. Quarum prima est fabularis. Et dicit quod, quia motus caeli non est laboriosus nec contra naturam, non est nec leviter suspicandum quod se habeat sempiternitas caeli et motus eius secundum antiquam fabulam Homeri et aliorum poetarum, qui dicebant quod caelum, ad hoc quod conservetur in suo situ, indiget quodam gigante, quem vocabant Atlantem, stantem super duas columnas et sustentantem humeris caelum. Illi enim qui istum sermonem fabularem composuerunt, videntur eandem opinionem habuisse de corporibus caelestibus, quam habuerunt quidam posteriores, scilicet ut essent gravia et terrea, ut sic indigeret sursum contra suam naturam detineri per aliquam virtutem animatam, vel alicuius rei viventis, puta Dei vel cuiuscumque substantiae separatae. Et si quidem hoc dicant caelo esse necessarium propter hoc quod caelum habeat gravitatem, fabula est omnino reprobanda: si autem intelligant quod caelum habeat naturam talis situs et motus, et tamen natura est ei ab alio causante et conservante, sic fabula aliquid divinum continet. | With respect to the first he dismisses three opinions, the first of which is a fable. And he says [219] that because the motion of the heaven is neither laborious nor contrary to nature, no one should even slightly suspect that the eternity of the heaven and of its motion are as the ancient fables of Homer and other poets describe them. They said that the heaven, to be kept in its position, requires a giant they named Atlas, who stands upon two pillars and supports the world on his shoulders. Now the ones who originated that fable seem to have held the same opinion about celestial bodies as some later teachers, namely, that they were heavy and earthy, and as such had to be held up against their nature by animate power, or that of some living things, such as God or a separated substance of some kind. And if they maintain that this is necessary on the ground that the heaven has weight, the fable is wholly to be rejected. However, if they mean that the heaven has by nature such-and-such a position and motion, but that its nature was produced and is conserved by another, then the fable contains something divine. |
| Secundo ibi: neque propter circumgyrationem etc., excludit opinionem Empedoclis, qui ponebat quod caelum in tali situ conservatur ne cadat, propter velocitatem sui motus, quae excedit inclinationem propriae naturae ad cadendum; sicut accidit in aqua, quae non effunditur si vas aquae velocius gyretur quam sit motus aquae deorsum. Et hoc etiam dicuntur posuisse Democritus et Anaxagoras. | 296. Secondly, at [220] he rejects the opinion of Empedocles who posited that the heaven is kept in its position that prevents it from falling by the rapidity of its motion which overcomes its natural inclination to fall — as occurs with water, which will not spill if the vessel of water is rotated more rapidly than the motion of the water downward. Democritus and Anaxagoras are also said to have held this. |
| Sed hoc quidem forte esset possibile accidere in aliquo brevi tempore: sed quod per talem velocitatem motus conservetur situs caeli in tanto tempore, scilicet perpetuo et infinito, hoc est valde improbabile. Cum enim id quod est violentum sit quaedam exorbitatio ab eo quod est secundum naturam, non videtur quod possit esse maius tempus eius quod est violentum, quam eius quod est secundum naturam: quia id quod est secundum naturam est quasi semper aut sicut frequenter. Arguuntur etiam isti, sicut et primi, quia videntur putasse corpora caelestia esse gravia, sed propter velocitatem motus deorsum non cadere. | Now this could perhaps happen for a short time, but that through such a speed of motion the heaven should keep its position for so great a time, namely, an infinite and perpetual time, is most unprovable. For since that which is violent is a certain exorbitation [departure] from what is according to nature, it does not seem that what is by violence could last longer than what is according to nature — since what is according to nature occurs, as it were, always, or for the most part. These latter, like the first, seem also to base their argument on the supposition that heavenly bodies have weight but are prevented from falling downward by the rapidity of their motion. |
| Tertio ibi: sed adhuc neque ab anima etc., excludit tertiam opinionem, quae est Platonis, qui posuit in Timaeo quod in medio mundi anima eius, ad extremum caelum omniquaque complexa, incoepit incessabilem et prudentem vitam ad omne tempus. | 297. Thirdly, at [221] he rejects a third opinion, that of Plato, who says in the Timaeus that in the center of the world, its soul, reaching to the extremity of the heaven and everywhere, began an imperishable and wise life for all time. |
| Et primo ex parte ipsius corporis. Unde dicit quod non est rationabile dicere quod caelum et motus eius in sempiternum maneat propter coactionem animae rationalis, quia nullum coactum potest esse sempiternum: cum enim violentum sit contra naturam, sequeretur id quod est secundum naturam nunquam esse. | First he rejects this opinion on the part of the body. Hence he says that it is not reasonable to say that the heaven and its motion remain forever on account of the compulsion of the rational soul, because nothing forced can last forever, for, since compulsion is against nature, it would follow that what is according to nature would never exist. |
| Secundo ibi: neque enim etc., ostendit idem ex parte animae, dicens quod non posset esse vita animae moventis sic corpus, sine tristitia et beata. Cum enim motus sit corporis per violentiam, et anima moveat circulariter corpus quod est aptum natum aliter moveri, et cum hoc moveat ipsum continue, necesse est quod talis anima nunquam vacet, et quod sit remota ab omni robore prudenti. | 298. Secondly, at [222] he shows the same on the part of the soul. And he says that the life of the soul so moving a body cannot be without sadness and happy. For since the motion of the body is caused by compulsion and the soul moves that body circularly, which is inclined to be moved otherwise, and in addition moves this body continually, then of necessity that soul is never free and is removed from all "prudent strength." |
| Et potest per robur prudens intelligi operatio speculativi intellectus, ad quam requiritur prudentia et robur, quasi dicat: si nullo modo vacat anima caeli a labore quem patitur movendo caelum contra suam naturam, semper impedietur a vehementi contemplatione, quam impedit continuitas laboris et tristitia consequens. | Now "prudent strength" can refer to the operation of the speculative intellect, which requires prudence and strength, as though Aristotle were saying, "If the soul of heaven can in no way find relief from the labor it undergoes in moving the heaven against its nature, it will always be kept from vehement contemplation, which its uninterrupted labor and consequent sadness prevent." |
| Vel per prudens robur intelligit conatum animae, appositum ad movendum secundum prudentiam: non enim videtur esse prudentis adhibere robur suum ad continue laborandum sine intermissione. Nam si aliquid laboriosum assumatur ad modicum tempus, tolerabile erit: caelum autem movetur motu continuo et sempiterno. Unde si anima caeli moveret caelum contra suam naturam et cum labore, sequeretur quod esset peioris conditionis quam animae mortalium animalium, quae requiescunt a motu corporis saltem in somno: sed necessarium est quod fatum, idest ordinatio alicuius superioris, detineat ipsam animam caeli sempiternam et inconteribilem, idest non deficientem a movendo, ad similitudinem cuiusdam viri qui Ixion dicebatur, de quo fabulariter dicunt quod, cum esset praepositus a Iove nuptiis Iunonis, concupivit eam, quae loco sui supposuit ei nebulam, ex qua genuit Centaurum, unde Iupiter alligavit trocho, in quo continue moveretur. | Or "prudent strength" could refer to the effort the soul applies in order to keep things moving according to prudence. For it does not seem to be in keeping with prudence to apply its strength without ceasing to some task. For if laborious work is undertaken for a short time, it will be tolerable; but the heaven is moved with a continual and eternal motion. Hence if the soul of the heaven were to move the heaven against its nature in a laborious manner, it would follow that that soul would be worse off than the souls of mortal animals, which get rest from moving the body at least during sleep. But it is necessary that fate, i.e., the decree of some superior being keep the soul of the heaven eternal and indestructible, i.e., unfailing in moving, after the manner of a certain man called Ixion, who, the fables tell us, while acting as steward at Juno's wedding, lusted after her. But she substituted for herself a cloud, from which he begot the Centaur. For this he was condemned by Jupiter to be bound to a wheel on which he continually revolves. |
| Quod quidem videtur Aristoteles dicere contra dictum Platonis, qui dixit quod ex medio mundi ad extremum caelum anima omniquaque complexa incoepit incessabilem et prudentem vitam ad omne tempus: secundum hoc enim videtur anima caeli alligata caelo sicut Ixion trocho. Et videtur quod vita talis animae non sit prudens, sed insipiens, utpote quae incoepit perpetuum laborem. Non autem reprehendit hic Aristoteles Platonem, qui posuit caelum animatum, quia et inferius hoc ipse ponit: sed de hoc quod videtur ponere quod moveat caelum in sempiternum contra suam naturam. Sed forte Plato non intellexit motum hunc esse contra naturam caeli; sed voluit exprimere quod natura secundum quam convenit ei talis motus, est ei ab alio. | This Aristotle seems to say against the statement of Plato who asserted that from the center of the world unto the outermost heaven the soul everywhere complex began an unceasing and prudent life for all time. For this would appear to be no different than being bound to the heaven as Ixion to the wheel. And it seems that the life of such a soul is not prudent but foolish, as undertaking an endless labor. However, Aristotle is not here reprehending Plato for positing an animate heaven — because later on he does the same —but for seeming to suppose that this soul is moving the heaven forever contrary to its nature. But perhaps Plato did not understand this motion as contrary to the nature of the heaven but wanted to bring out that the nature according to which this motion befits it is in it from another. |
| Deinde cum dicit: si itaque quemadmodum etc., concludit ex praemissis quod, si contingit ita se habere de primo motu locali, qui est motus caeli, sicut diximus, ut scilicet sit sine labore, non solum hoc existimare est melius quantum ad sempiternitatem ipsius caeli, sed hoc est magis conveniens existimationi quam habemus de diis (quam quidem vocat divinationem, quasi ex divina revelatione habitam): solum enim per istum modum dicemus ubique concordes sermones; non enim videtur esse consonum quod caelum moveatur a Deo, et quod motus eius sit cum labore. Sed de talibus sermonibus satis sit nunc ad praesens dictum. | 299. Then at [223] he concludes from the foregoing that if our account of the first local motion, which is the heavenly motion, is correct, namely, that it is without labor, not only is to think this better from the point of view of the eternity of the heaven, but it is also more in conformity with out estimate of the gods — which he calls "divination," as though had by divine revelation. For that is the only way to keep our teaching consistent, since it does not appear congruent to say on the one hand that the heaven is being moved by God, and to say on the other that its motion is laborious. But this is enough on such matters for the present. |
Lecture 2:
Diversity of parts of the heaven as to position. Opinion of PythagorasChapter 2 Ἐπειδὴ δέ τινές εἰσιν οἵ φασιν εἶναί τι δεξιὸν καὶ ἀριστερὸν τοῦ οὐρανοῦ, καθάπερ οἱ καλούμενοι Πυθαγόρειοι (ἐκείνων γὰρ οὗτος ὁ λόγος ἐστίν), σκεπτέον πότερον τοῦτον ἔχει τὸν τρόπον ὡς ἐκεῖνοι λέγουσιν, ἢ μᾶλλον ἑτέρως, εἴπερ δεῖ προσάπτειν τῷ τοῦ παντὸς σώματι ταύτας τὰς ἀρχάς. Εὐθὺς γὰρ πρῶτον, εἰ τὸ δεξιὸν ὑπάρχει καὶ τὸ ἀριστερόν, ἔτι πρότερον τὰς προτέρας ὑποληπτέον ὑπάρχειν ἀρχὰς ἐν αὐτῷ. 224 Since there are some who say that there is a right and a left in the heaven, with those who are known as Pythagoreans—to whom indeed the view really belongs—we must consider whether, if we are to apply these principles to the body of the universe, we should follow their statement of the matter or find a better way. At the start we may say that, if right and left are applicable, there are prior principles which must first be applied. Διώρισται μὲν οὖν περὶ τούτων ἐν τοῖς περὶ τὰς τῶν ζῴων κινήσεις διὰ τὸ τῆς φύσεως οἰκεῖα τῆς ἐκείνων εἶναι φανερῶς γὰρ ἔν γε τοῖς ζῴοις ὑπάρχοντα φαίνεται τοῖς μὲν πάντα τὰ τοιαῦτα μόρια, λέγω δ' οἷον τό τε δεξιὸν καὶ τὸ ἀριστερόν, τοῖς δ' ἔνια, τοῖς δὲ φυτοῖς τὸ ἄνω καὶ τὸ κάτω μόνον. 225 These principles have been analysed in the discussion of the movements of animals, for the reason that they are proper to animal nature. For in some animals we find all such distinctions of parts as this of right and left clearly present, and in others some; but in plants we find only above and below. Εἰ δὲ δεῖ καὶ τῷ οὐρανῷ προσάπτειν τι τῶν τοιούτων, καὶ τὸ πρῶτον, καθάπερ εἴπομεν, ἐν τοῖς ζῴοις ὑπάρχον εὔλογον ὑπάρχειν ἐν αὐτῷ τριῶν γὰρ ὄντων ἕκαστον οἷον ἀρχή τις ἐστίν. Λέγω δὲ τὰ τρία τὸ ἄνω καὶ τὸ κάτω, καὶ τὸ πρόσθιον καὶ τὸ ἀντικείμενον, καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν ταύτας γὰρ τὰς διαστάσεις εὔλογον ὑπάρχειν τοῖς σώμασι τοῖς τελείοις πάσας. 226 Now if we are to apply to the heaven such a distinction of parts, we must exect, as we have said, to find in it also the distinction which in animals is found first of them all. The distinctions are three, namely, above and below, front and its opposite, right and left—all these three oppositions we expect to find in the perfect body—and each may be called a principle. Ἔστι δὲ τὸ μὲν ἄνω τοῦ μήκους ἀρχή, τὸ δὲ δεξιὸν τοῦ πλάτους, τὸ δ' ἔμπροσθεν τοῦ βάθους. 227 Above is the principle of length, right of breadth, front of depth. Ἔτι δ' ἄλλως κατὰ τὰς κινήσεις ἀρχὰς γὰρ ταύτας λέγω ὅθεν ἄρχονται πρῶτον αἱ κινήσεις τοῖς ἔχουσιν. Ἔστι δὲ ἀπὸ μὲν τοῦ ἄνω ἡ αὔξησις, ἀπὸ δὲ τῶν δεξιῶν ἡ κατὰ τόπον, ἀπὸ δὲ τῶν ἔμπροσθεν ἡ κατὰ τὴν αἴσθησιν ἔμπροσθεν γὰρ λέγω ἐφ' ὃ αἱ αἰσθήσεις. 228 Or again we may connect them with the various movements, taking principle to mean that part, in a thing capable of movement, from which movement first begins. Growth starts from above, locomotion from the right, sensemovement from in front (for front is simply the part to which the senses are directed). Διὸ καὶ οὐκ ἐν ἅπαντι σώματι τὸ ἄνω καὶ κάτω καὶ τὸ δεξιὸν καὶ ἀριστερὸν καὶ τὸ ἔμπροσθεν καὶ ὄπισθεν ζητητέον, ἀλλ' ὅσα ἔχει κινήσεως ἀρχὴν ἐν αὑτοῖς ἔμψυχα ὄντα τῶν γὰρ ἀψύχων ἐν οὐθενὶ ὁρῶμεν ὅθεν ἡ ἀρχὴ τῆς κινήσεως. Τὰ μὲν γὰρ ὅλως οὐ κινεῖται, τὰ δὲ κινεῖται μὲν ἀλλ' οὐ πανταχόθεν ὁμοίως, οἷον τὸ πῦρ (285a.) ἄνω μόνον καὶ ἡ γῆ ἐπὶ τὸ μέσον. 229 Hence we must not look for above and below, right and left, front and back, in every kind of body, but only in those which, being animate, have a principle of movement within themselves. For in no inanimate thing do we observe a part from which movement originates. Some do not move at all, some move, but not indifferently in any direction; fire, for example, only upward, and earth only to the centre. Ἀλλ' ἐν μὲν τούτοις λέγομεν τὸ ἄνω καὶ τὸ κάτω καὶ τὸ δεξιὸν καὶ τὸ ἀριστερὸν πρὸς ἡμᾶς ἐπαναφέροντες ἢ γὰρ κατὰ τὰ ἡμέτερα δεξιά, ὥσπερ οἱ μάντεις, ἢ καθ' ὁμοιότητα τοῖς ἡμετέροις, ὥσπερ τὰ τοῦ ἀνδριάντος, ἢ τὰ ἐναντίως ἔχοντα τῇ θέσει, δεξιὸν μὲν τὸ κατὰ τὸ ἡμέτερον ἀριστερόν, ἀριστερὸν δὲ τὸ κατὰ τὸ ἡμέτερον δεξιόν, [καὶ ὄπισθεν τὸ κατὰ τὸ ἡμέτερον ἔμπροσθεν]. Ἐν αὐτοῖς δὲ τούτοις οὐδεμίαν ὁρῶμεν διαφοράν ἐὰν γὰρ ἀνάπαλιν στραφῇ, τὰ ἐναντία ἐροῦμεν δεξιὰ καὶ ἀριστερὰ καὶ ἄνω καὶ κάτω καὶ ἔμπροσθεν καὶ ὄπισθεν. 230 It is true that we speak of above and below, right and left, in these bodies relatively to ourselves. The reference may be to our own right hands, as with the diviner, or to some similarity to our own members, such as the parts of a statue possess; or we may take the contrary spatial order, calling right that which is to our left, and left that which is to our right. We observe, however, in the things themselves none of these distinctions; indeed if they are turned round we proceed to speak of the opposite parts as right and left, a boy land below, front and back. Διὸ καὶ τῶν Πυθαγορείων ἄν τις θαυμάσειεν ὅτι δύο μόνας ταύτας ἀρχὰς ἔλεγον, τὸ δεξιὸν καὶ τὸ ἀριστερόν, τὰς δὲ τέτταρας παρέλιπον οὐθὲν ἧττον κυρίας οὔσας 231 Hence it is remarkable that the Pythagoreans should have spoken of these two principles, right and left, only, to the exclusion of the other four, which have as good a title as they. οὐθὲν γὰρ ἐλάττω διαφορὰν ἔχει τὰ ἄνω πρὸς τὰ κάτω καὶ τὰ ἔμπροσθεν πρὸς τὰ ὄπισθεν ἢ τὰ δεξιὰ πρὸς τὰ ἀριστερὰ ἐν ἅπασι τοῖς ζῴοις. Τὰ μὲν γὰρ τῇ δυνάμει διαφέρει μόνον, τὰ δὲ καὶ τοῖς σχήμασι, 232 There is no less difference between above and below or front and back in animals generally than between right and left. The difference is sometimes only one of function, sometimes also one of shape; καὶ τὸ μὲν ἄνω καὶ τὸ κάτω πᾶσι τοῖς ἐμψύχοις ἐστὶν ὁμοίως ζῴοις καὶ φυτοῖς, τὸ δὲ δεξιὸν καὶ τὸ ἀριστερὸν οὐκ ἐνυπάρχει τοῖς φυτοῖς. 233 and while the distinction of above and below is characteristic of all animate things, whether plants or animals, that of right and left is not found in plants. Ἔτι δ' ὡς τὸ μῆκος τοῦ πλάτους πρότερον, εἰ τὸ μὲν ἄνω τοῦ μήκους ἀρχή, τὸ δὲ δεξιὸν τοῦ πλάτους, ἡ δὲ τοῦ προτέρου ἀρχὴ προτέρα, πρότερον ἂν εἴη τὸ ἄνω τοῦ δεξιοῦ κατὰ γένεσιν, ἐπειδὴ πολλαχῶς λέγεται τὸ πρότερον. 234 Further, inasmuch as length is prior to breadth, if above is the principle of length, right of breadth, and if the principle of that which is prior is itself prior, then above will be prior to right, or let us say, since 'prior' is ambiguous, prior in order of generation. Πρὸς δὲ τούτοις, εἰ τὸ μὲν ἄνω ἐστὶ τὸ ὅθεν ἡ κίνησις, τὸ δὲ δεξιὸν ἀφ' οὗ, τὸ δ' ἔμπροσθεν ἐφ' ὅ, κἂν οὕτως ἔχοι τινὰ δύναμιν ἀρχῆς τὸ ἄνω πρὸς τὰς ἄλλας ἰδέας. Διά τε δὴ τὸ παραλείπειν τὰς κυριωτέρας ἀρχὰς δίκαιον αὐτοῖς ἐπιτιμᾶν, καὶ διότι ταύτας ἐν ἅπασιν ὁμοίως ἐνόμιζον ὑπάρχειν. 235 If, in addition, above is the region from which movement originates, right the region in which it starts, front the region to which it is directed, then on this ground too above has a certain original character as compared with the other forms of position. On these two grounds, then, they may fairly be criticized, first, for omitting the more fundamental principles, and secondly, for thinking that the two they mentioned were attributable equally to everything.
| Postquam philosophus determinavit de perpetuitate caeli, hic determinat de diversitate partium eius. | 300. After settling the question of the perpetuity of the heavens, the Philosopher here determines the question of the variety of its parts. |
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Et primo determinat de diversitate partium caeli quae accipiuntur secundum diversitatem situs in eodem caelo; secundo de diversitate partium quae accipiuntur secundum ordinem corporum caelestium ad invicem, ibi: quoniam autem non est contrarius motus et cetera. |
First he determines the question of the diversity of parts considered from the viewpoint of their respective position in the same heaven; Secondly, as considered from the relationship of the various heavenly bodies one to the other (L. 4). |
| Circa primum duo facit: | As to the first he does two things: |
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primo determinat de diversitate situalium partium caeli secundum opinionem aliorum; secundo secundum opinionem propriam, ibi: nobis autem quoniam determinatum est et cetera. |
First he determines concerning the diversity of the positional parts of the heaven according to the opinions of others; Secondly, according to his own opinion (L. 3). |
| Circa primum duo facit: | As to the first he does two things: |
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primo proponit quod intendit; secundo manifestat propositum, ibi: determinatum est quidem igitur et cetera. |
First he states his intention; Secondly, he manifests his proposition, at 301. |
| Dicit ergo primo quod, quia quidam dicunt quandam partem caeli esse dextram et quandam sinistram, scilicet Pythagorici, qui posuerunt dextrum et sinistrum in omnibus rebus, considerandum videtur utrum hoc modo se habeat sicut illi dicunt, vel magis aliter sint caelo attribuenda quam ipsi dicant: si tamen oportet aptare haec principia, scilicet dextrum et sinistrum, corpori totius mundi, per hoc quod insunt corpori caelesti, quod continet totum mundum. | He says therefore first [224] that because some assert that one part of the heaven is on the right and another on the left, namely, the Pythagoreans, who put a right and a left in all things, it seems necessary to inquire whether things are as they assert or whether one should not rather attribute such things in a way different from theirs — if indeed it be necessary to apply these principles, i.e., right and left, to the body of the entire world by virtue of their being found in the heavenly body, which encompasses the whole world. |
| Hoc autem ideo considerandum videtur, quia statim a principio occurrit homini quod, si dextrum et sinistrum sint in caelo, quod multo magis et per prius aestimanda sint esse in caelo priora principia, scilicet sursum et deorsum, ante et retro. | The reason why this matter should be considered is that it immediately occurs to a man that if there is a right and a left in the heaven, then there is even a greater reason and a prior one for thinking the prior principles are in the heaven, namely, up and down, before and behind. |
| Deinde cum dicit: determinatum est quidem igitur etc., manifestat propositum. | 301. Then at [225] he manifests this proposition. |
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Et primo ostendit conditionem istorum principiorum secundum quod in aliis rebus inveniuntur; secundo ostendit quod non inveniuntur in omnibus corporibus, ibi: propter quod et non in omni corpore et cetera. |
First he explains the condition of these principles as found in other things; Secondly, that they are not found in all bodies, at 305. |
| Circa primum duo facit: | As to the first he does two things: |
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primo ostendit quod non omnia praedicta principia insunt omnibus; secundo ostendit quo ordine se habeant ad invicem, ibi: est autem sursum quidem et cetera. |
First he shows that not all the aforesaid principles are found in all things; Secondly, he explains in what order they are mutually related, at 303. |
| Circa primum duo facit: | As to the first he does two things: |
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primo ostendit quod huiusmodi principia non omnia omnibus insint, sed quibusdam quaedam et non omnia; secundo ostendit hoc omnino esse inconveniens, ut caelo attribuantur quaedam et non omnia, ibi: si autem oportet caelo adaptare et cetera. |
First he shows that all these principles are not found in everything, but in some things some only and not all; Secondly, that it would be entirely unfitting that some, but not all, be attributed to the heaven, at 302. |
| Dicit ergo primo quod de huiusmodi principiis, quae dicuntur differentiae positionum, determinatum est in libro de processu animalium, propter hoc quod sunt propria naturae illorum, scilicet animatorum. In animalibus enim manifeste videntur huiusmodi existere secundum determinatas partes: ita quidem quod aliquibus animalibus, scilicet perfectis, quae non solum sentiunt sed etiam moventur motu locali, insint omnes tales partes, scilicet dextrum et sinistrum, ante et retro, sursum et deorsum; quibusdam vero animalibus, scilicet imperfectis et immobilibus, insunt quaedam eorum, scilicet sursum et deorsum, ante et retro; plantis autem non insunt nisi sursum et deorsum. | He says therefore first [225] that these principles, which are called differences of position, have been dealt with in the book De Incessu Animalium, since they are peculiar to such natures, namely, those of animals. For these differences of position are clearly found in animals according to definite parts. For some animals, namely, the perfect, which not only sense but move with local motion, possess all these parts, namely, right and left, before and behind, above and below; other animals, namely, the imperfect and stationary, possess some of them, namely, above and below, before and behind; while plants have only above and below. |
| Deinde cum dicit: si autem oportet caelo adaptare etc., ostendit quod si in caelo aliquid de his ponatur, quod necesse est omnia huiusmodi in eo ponere. Et dicit quod si aliquid talium oportet attribuere caelo, scilicet vel dextrum vel sinistrum, rationabile est quod ibi primum existat id quod invenitur in animalibus perfectis: vel, rationabile est quod in eo existat id quod est primum in animalibus, quia posito posteriori, ponitur prius. Cum autem sint tres oppositiones vel dimensiones, unumquodque horum trium, scilicet sursum, ante et dextrum, est velut quoddam principium suae oppositionis vel dimensionis. | 302. Then at [226] he shows that if any of them are assigned to the heaven, then all must be. And he explains that if we must assign any to the heaven, namely, either right or left, it is reasonable to suppose that that would be found which is found first in perfect animals; or it is reasonable that the heaven should possess that which is first in animals, because if we posit what is subsequent, we must posit what is prior. Now since there are three oppositions or "dimensions," each of them, namely, above, before and right is a certain principle of its opposite or dimension. |
| Exponit autem consequenter quae dixerit esse illa tria: quorum unum est oppositio vel dimensio quae est inter sursum et deorsum, in qua quidem sursum est principium; aliud autem est inter anterius et eius oppositum, quod dicitur retro, ubi quod est ante est principium; aliud autem est inter dextrum et sinistrum, in qua dextrum est principium. Et quia perfectum est quod constat ex omnibus partibus seu principiis, rationabile est quod omnes huiusmodi oppositiones vel dimensiones inveniantur in corporibus perfectis, idest in animalibus perfectis. Unde, cum caelum sit maxime perfectum, rationabile est quod si sit capax harum partium, quod habeat omnes, et non quasdam tantum. | He subsequently expounds the three he has stated to be: one of these is the opposition or dimension between up and down, in which "up" is the principle; another is between before and its opposite, which is called "behind," where what is before is the principle; yet another is between right and left, in which "right" is the principle. Now, since the perfect is that which is composed of all its parts or principles, it is reasonable that all these oppositions or dimensions should be found in "perfect bodies," i.e., in perfect animals. Hence, since the heaven is perfect above all, it is reasonable that if it be capable of any of these parts, it should have them all and not just some. |
| Deinde cum dicit: est autem sursum quidem etc., ostendit ordinem dictorum principiorum dupliciter. Primo quidem ex parte ipsarum dimensionum. Nam sursum est principium longitudinis: nam in homine, qui est animal maxime perfectum, dicitur longitudo, quasi maxima dimensio eius, a capite, quod est sursum eius, usque ad pedes, qui sunt deorsum eius. Dextrum autem est principium latitudinis: attenditur enim latitudo hominis secundum distantiam quae est inter dextrum et sinistrum. Anterius autem est principium profunditatis: attenditur enim profunditas sive grossities hominis secundum distantiam quae est inter ante et retro. In aliis autem animalibus proportionaliter se habet. Longitudo autem est prior latitudine, et latitudo profunditate, sicut linea superficie, et superficies corpore. Ergo sursum est prius eo quod est dextrum, et dextrum est prius eo quod est ante. | 303. Then at [227] he explains in two ways the order of the aforesaid principles. First, from the viewpoint of the dimensions themselves. For "up" is the principle of length: in man who is the most perfect animal, his length, as though his greatest dimension, is said from the head, which is his "up," to the feet, which are his "down." "Right" is the principle of width, for the width of a man is reckoned according to the distance between his right and his left. "Before" is the principle of depth: for the depth or thickness of a man is reckoned according to the distance between before and behind. The same holds respectively in other animals. But length is prior to width, and width to depth, just as line is to plane, and plane to body. Therefore, "above" is prior to "right," and "right" is prior to "before." |
| Secundo ibi: adhuc autem aliter etc., probat idem ex parte motuum. Et hoc ideo, quia ea quae dicta sunt, sunt quaedam principia a quibus primo incipiunt motus in animalibus habentibus huiusmodi partes sive principia. Motus enim augmenti incipit quidem a sursum. Et hoc manifeste apparet in hominibus: nam caput, quod est sursum hominis, est etiam sursum secundum positionem mundi; a capite autem incipit motus augmenti, quia in orificio oris, quod est in capite, trahitur alimentum, quod est augmenti materia. Plantarum autem sursum est radix, quae proportionatur capiti in animalibus in sumptione alimenti: sed id quod est sursum plantae, per oppositum se habet secundum situm ad sursum mundi. In aliis autem animalibus medio modo se habet. Motus autem qui est secundum locum, incipit a dextris: naturaliter enim animalia prius movent dextram partem quam sinistram, sicut in ambulando prius movent dextrum pedem. Sed in motu alterationis ipsorum sensuum, est principium id quod est anterius: anterior enim pars animalis dicitur in qua sensus existunt. Quia igitur motus augmenti est prior motu sensitivo, qui etiam est prior motu locali in animalibus, consequens est quod sursum sit prius quam anterius, et anterius prius quam dextrum. | 304. Secondly, he proves the same thing [228] from the viewpoint of motions. He does this because the things we have been discussing are certain principles from which motion first begins in animals that possess such parts or principles. For the motion of growth begins from above. This is evident in man, for the head, which is the "up" of man, is also up according to the position of the universe. Now the motion of growth begins from the head, because food is taken into the opening of the mouth, which is in the head, and food is the matter of growth. In plants, however, it is the root which is "up," and this is parallel to the head in animals, as far as the taking in of food is concerned. However, the "up" of a plant is opposite as to position to what is "up" for the universe. The other animals are midway between man and plants. Now motion with respect to place begins from the right, for animals move the right part before the left, as in walking they move the right foot. But in the motion by which the senses are altered, "before" is the principle, for that is said to be the forepart of the animal where the senses exist. Therefore, since the motion of growth is prior to the motion of sensation, which in turn is prior to local motion in animals, it follows that "above" is prior to "before," and "before" prior to "right." |
| Deinde cum dicit: propter quod et non in omni corpore etc., ostendit quod huiusmodi principia non sunt in omnibus corporibus. | 305. Then at [229] he shows that these principles are not present in all bodies. |
| Et primo concludit ex praemissis quod proprie et per se loquendo non sunt huiusmodi principia in corporibus inanimatis; secundo ostendit per quem modum ibi esse dicuntur, ibi: sed in his quidem et cetera. | First he concludes from the foregoing that, strictly speaking, these principles do not exist in non-living bodies; Secondly, he explains how we come to speak of them as being therein, 306. |
| Dicit ergo primo quod, quia praedicta sunt principia quorundam motuum, consequens est quod sursum et deorsum, dextrum et sinistrum, anterius et posterius non sint quaerenda in omnibus corporibus, sed solum in corporibus animatis, quaecumque habent in seipsis principium motus: sed in nullo corporum inanimatorum videmus aliquod principium unde incipiat motus. | He says therefore first [229] that since the foregoing are principles of certain motions, we should not look for above and below, right and left, before and behind, in all bodies, but only in animate bodies having a principle of motion in themselves. Now we do not find in any non-living body any originative source of motion. |
| Quod quidem potest intelligi dupliciter. Uno modo quia in corporibus animatis est principium activum motus, quod est anima: in corporibus autem inanimatis non est principium motus activum, quod scilicet moveat, sed moventur ab exteriori movente, quod est generans vel removens prohibens. Interius autem habent principium motus passivum, quo scilicet nata sunt moveri, puta gravitatem vel levitatem, ut patet in VIII Physic. | This can be understood in two ways. First, in the sense that there is in living things an active principle of motion, namely, the soul, while in non-living bodies there is no such active principle of motion which could move, but such things are moved by an external mover, which is the generator or that which removes what prevents motion. Yet they do have a passive principle of motion within, by which they are apt to be moved, for example, heaviness or lightness, as is plain in Physics VIII. |
| Alio modo potest intelligi quia in corporibus animatis invenitur determinata pars corporis a qua incipit motus, sicut dictum est: quod quidem in corporibus inanimatis non invenitur. Quia, sicut subdit, inanimatorum corporum quaedam omnino non moventur, sicut illa quae sunt in propriis locis (vel potius hoc dicit propter corpora artificialia, quae non habent ex seipsis aliquem motum): quaedam autem moventur, sicut corpora naturalia existentia extra proprium suum locum, sed tamen unumquodque eorum movetur ad suum locum similiter ab omni parte; sicut ignis solum movetur sursum et terra solum movetur ad medium mundi, nulla alia differentia situs considerata vel ex parte corporis quod movetur, ut scilicet una pars eius prius incipiat moveri quam alia, vel etiam quantum ad locum, ut scilicet ex uno situ locali moveatur corpus naturale ad suum locum, et non ex alio. | Or it can mean that in living bodies there is a definite part from which the motion begins, as has been said. But such a part is not found in non-living bodies. For, as he further says, some non-living bodies are not in motion at all, for example, those that already exist in their own place (or rather he says this with respect to artificial bodies which, as such, have no motion of themselves). Others are in motion, for example, the ones that are outside their own appropriate place, yet each such body is moved to its place in a similar way for each part. For example, fire is moved only upwards and earth only to the center of the world. In these cases no other difference of position is considered, either on the part of the body which is moved, so that one part would begin to be moved before another, or even on the part of the place, so that a natural thing would be moved to its own place from one position in space and not from another. |
| Deinde cum dicit: sed in his quidem etc., ostendit quomodo praedictae positiones quandoque dicantur in corporibus inanimatis. Et dicit quod in huiusmodi corporibus dicimus sursum et deorsum, et dextrum et sinistrum, et similiter ante et retro, solum per comparationem ad nos. Et hoc tripliciter: uno modo secundum quod dicimus dextrum id quod est nobis oppositum secundum nostram dextram, sicut divinatores, puta augures, nominant avem dextram quae est nobis ad dextram, sinistram vero quae est nobis ad sinistram; alio modo per similitudinem ad partes nostras, sicut in statua dicimus dextrum quod est simile dextro hominis, et sinistrum quod est simile sinistro; tertio modo per contrariam positionem, dicendo sinistrum quod est oppositum nostro dextro, et dextrum quod est oppositum nostro sinistro, sicut patet in imagine quae resultat in speculo. Et eadem ratio est in aliis positionibus. | 306. Then at [230] he shows how these positions are sometimes said to exist in non-living bodies. And he says that in such bodies we speak of above and below, right and left, before and behind, only in comparison to ourselves. And this can take place in three ways. In one way, as we call that the right which is opposite to our right, as diviners, e.g., augurs, refer to a bird on our right, as the right bird and one on our left as the left bird. The second way is based on a likeness to our parts, as we call the right of a statue that which is similar to the right of man and the left that which is similar to our left. The third way is by a contrary position, as when we call the left what is opposite to our right, and what is opposite to our left we call right, as is plain in the case of an image in a mirror. The same explanations apply to the other positions. |
| Sed in ipsis rebus inanimatis secundum se consideratis, nulla invenitur diversitas talium partium. Et hoc patet quia, si convertantur ad nos, e contrario se habebunt quam prius: illud enim quod erat dextrum, dicetur sinistrum, et e converso; et simile est in aliis positionibus. In rebus autem animatis, qualitercumque vertantur, semper eodem modo se habent huiusmodi partes. | But in non-living things considered in themselves, there is no such variation of parts. And this is evident from the fact that if we turn them toward us, the designations will be the opposite of what they were previously: what was right is now called left and vice-versa, and the same goes for the other positions. But in living things, no matter how they are turned about, these parts remain always the same. |
| Deinde cum dicit: propter quod et Pythagoricos etc., ostendit Pythagoricos male attribuisse caelo huiusmodi differentias: et hoc tribus modis, qui ex superioribus accipi possunt; et ideo illos per modum conclusionis hic inducit. Primus autem modus est quia, cum sint sex positiones, mirabile videtur quare solum duo horum attribuebant caelo, scilicet dextrum et sinistrum, et alia quatuor reliquerunt; cum tamen rationabile sit quod omnia caelo conveniant, ut supra dictum est. | 307. Then at [230] he shows that the Pythagoreans erred in attributing these differences to the heaven, and this in three ways, which can be gathered from the above reasoning. Consequently he adduces them here as conclusions. The first way is that, whereas there are six positions, one wonders why only two of them are attributed to the heaven, namely, the right and left, and the other four are ignored — although it is reasonable that all of them belong to the heaven, as was said above. |
| Secundum modum ponit ibi: nihil minus etc.: quia scilicet, si aliqua debuerunt praetermitti ut non attribuerentur caelo, oportuit praetermitti illa quae sunt minus principalia. Quod autem illa quatuor quae praetermisit, non sint minus principalia quam illa duo quae posuit, ostendit quatuor rationibus. | 308. The second way is given at [231], namely, that if any are to be omitted and not attributed to the heaven, it is the less principal ones which ought to have been omitted. But that the ones omitted are not less principal than the two attributed he proves with four arguments. |
| Quarum primam ponit ibi: nihil enim minorem et cetera. Non enim videmus in quibuscumque animalibus quod minorem differentiam habeat pars quae est sursum ad eam quae est deorsum, et quae est anterius ad eam quae est posterius, quam dextra ad sinistram, immo maiorem. Nam pars dextra et sinistra differunt solum virtute, et conveniunt in figura (manus enim dextra est fortior quam sinistra, licet sit eiusdem figurae; et similiter humerus dexter est fortior quam sinister ad motum, quamvis sinister sit fortior ad portandum onus; et similiter pes dexter est fortior ad motum, sed pes sinister ad fixionem); manifestum est autem quod pars anterior et posterior animalis, et superior et inferior, differunt non solum in virtute, sed etiam in figura: illa autem quae magis differunt, videntur principaliorem distantiam habere. | The first argument is given at [232], namely, that in certain animals we do not observe that the difference between the part above and the part below, or between the part in front and the part to the rear, is less than the difference between the right side and the left side; rather, the difference is greater. For the right and left differ only in power but agree in figure (for the right hand is stronger than the left, although they are of the same shape; similarly, the right shoulder is stronger than the left as far as motions are concerned, although the left is stronger than the right for carrying a burden; in like manner, the right foot is better for motion, but the left is better for maintaining a fixed position). But it is plain that the front and rear of an animal, as well as the top and bottom, differ not only in power, but in shape as well. Now things that differ more appear to have a more principal distance. |
| Secundam rationem ponit ibi: et sursum et deorsum etc.: quae talis est. Sursum et deorsum inveniuntur in omnibus corporibus animatis, tam animalibus quam plantis; sed dextrum et sinistrum non existit in plantis, sed solum in animalibus perfectis; et sic sursum et deorsum sunt priora, secundum quod prius dicitur illud a quo non convertitur consequentia essendi. | 309. The second argument is at [233], namely, that top and bottom are found in all living bodies, whether animal or plant; but right and left are not in plants but only in perfect animals. Consequently, up and down are prior, where "prior" implies a non-convertible dependence in existence [on the part of the non-prior]. |
| Tertiam rationem ponit ibi: adhuc autem etc.: quae talis est. Longitudo est prior latitudine, et hoc in via generationis, quia secundum geometras linea mota facit superficiem: sursum autem est principium longitudinis, dextrum autem principium latitudinis, ut supra ostensum est. Cum igitur principium prioris sit prius, consequens est quod sursum sit prius quam dextrum, secundum scilicet quod aliquid est prius generatione (propterea quod multis modis dicitur aliquid prius, ut patet in praedicamentis et V Metaphys.). | 310. The third argument is at [234], namely, that length is prior to width in the order of generation, for, according to geometers, a line in motion makes a surface. But "up" is a principle of length, and "right" a principle of width, as was explained above. Therefore, since the source of what is prior is itself prior, the consequence is that "up" is prior to "right," in the sense of something prior in the order of generation (for there are many ways in which things are said to be prior to others, as is plain in Predicaments and in Metaphysics V. |
| Quartam rationem ponit ibi: adhuc autem si sursum quidem et cetera. Et dicit quod sursum est unde est motus, quod potest intelligi de motu augmenti; dextrum autem est a quo est motus localis; anterius autem est ad quod procedit animal, quasi oppositum suo sensui; et sic patet quod sursum habet quandam principalitatem respectu aliarum specierum positionis, sicut motus augmenti est magis essentialis et magis intrinsecus animali quam motus localis. | 311. The fourth argument, at [235] says that "up" is an originative source of motion, which may be understood of the motion of growth; "right" is the source of local motion; "before" is that toward which an animal moves, as though being opposite to its senses. From this it is clear that "up" has a certain chief role among all the types of position, just as the motion of growth is more essential and more intrinsic to an animal than is local motion. |
| Potest autem melius totum quod hic dicitur ad motum localem referri, ut dicatur quod sursum in animali quod movetur secundum locum, est principium unde motus, quia scilicet in capite, quod est sursum, viget sensus, qui est movens in animalibus, ut dicitur in III de anima; dextrum autem est a quo incipit motus localis, quia pars dextra primo movetur, ut dictum est; sed anterius est versus quod movetur animal. Principium autem movens est principalissimum in motu animalis; et secundum hoc patet quod sursum habet principalitatem inter alias species positionis. | Nevertheless, everything stated here may be better referred to local motion, by stating that "pup," in an animal which moves according to local motion, is that whence motion proceeds, since it is in the head, namely, that sense functions and sense is the moving principle in animals, as stated in De Anima IT. But "right" is that whence local motion begins, since the right part moves first, as was said, while "before" is that toward which the animal is moved. But the moving principle is that which has the primacy in the motion of an animal. In keeping with this it is evident that "up" has the primacy among the other types of position. |
| Sic igitur ex his quatuor rationibus concludit philosophus secundum modum improbandi dictum Pythagoricorum, concludens quod iustum est eos increpare, quia derelinquebant principaliora principia, non attribuentes ea caelo. | Thus does the Philosopher by means of these four arguments conclude his second way of disproving the assertion of the Pythagoreans. And he says it is just to rebuke them, since they ignored the more important principles and did not attribute them to the heaven. |
| Tertium modum ponit ibi: et quia haec etc.: dicens quod etiam sunt increpandi quia ponebant similiter dextrum et sinistrum existere in omnibus, cum tamen non sint nisi in animalibus perfectis, ut supra dictum est. | 312. He presents his third way at [2353, saying that they should be rebuked also for claiming that right and left are found similarly in all things, whereas in truth they are found only in perfect animals, as was said above. |
| Sciendum tamen quod de intentione Pythagoricorum erat omnia reducere ad bonum et malum, sicut ad duo principia. Et quia credebant omnem numerum sub denario comprehendi, posuerunt decem ex parte boni, et decem opposita ex parte mali, ut patet in I Metaphys. Per unumquodque autem illorum quae ponebant in illa enumeratione, intelligebant omnia quae sunt sui generis. Unde per dextrum et sinistrum intelligebant omnes alias positiones, intelligentes quod sicut dextrum, ita sursum et anterius referuntur ad bonum, sinistrum autem et posterius et deorsum ad malum. Ideo autem potius ponebant dextrum et sinistrum quam alias positiones, quia manifestius dextrum consuevit referri ad bonum et sinistrum ad malum: consuevimus enim bonam fortunam vocare dextram, malam autem sinistram: et ideo omnibus attribuebant dextrum et sinistrum, quibus attribuebant bonum et malum. | But it should be kept in mind that it was the Pythagoreans' intent to reduce all things to good and evil as to two principles. And because they believed that all number is encompassed by 10, they posited ten things on the side of good and ten on the side of evil, as is plain in Metaphysics I. By each thing they placed in that enumeration they understood all the things to be found in its genus. Thus by "right" and "left" they understood all other positions, understanding that just as "right" is referred to good, so also "up" and "before," while "left," "down," and "behind" referred to evil. The reason why they posited right and left, rather than the other positions, was that the right is according to custom more obviously referred to the good and the left to evil — for we are accustomed to call good fortune "right" and evil "left" [i.e., "sinister"]. Consequently, they attributed right and left to all things to which they attributed good and evil. |
| Vel ideo nominabant tantum dextrum et sinistrum, in his alia comprehendentes, quia videbant quod in quibuscumque invenitur dextrum et sinistrum, inveniuntur et alia, sed non convertitur. Forte autem specialiter caelo attribuerunt dextrum et sinistrum potius quam alia, quia in caelo est motus localis, ad quem pertinet dextrum et sinistrum, non autem augmentum, ad quod pertinet sursum et deorsum, neque etiam alteratio sensus, ad quam pertinet ante et retro. Vel quia sursum et deorsum, ante et retro diversificantur secundum figuram, non autem dextrum et sinistrum: partes enim caeli, cum sint circulares, non diversificantur secundum figuram. | Or perhaps they mentioned only right and left, as including the others in them, because they saw that whatever possessed a right and a left possessed all the others, but not vice-versa. Likewise they perchance especially applied to the heaven a right and a left and not the others, because there is in the heaven a local motion, to which right and left belong, but no growth, or sense alteration, to which up and down, before and behind belong respectively. Or perhaps it was because up and down, before and behind, are diversified with respect to shape, whereas right and left are not — for the parts of the heaven, being circular, are uniform in shape. |
Lecture 3:
How, according to the Philosopher's opinion, the differences of position befit the parts of the heavenChapter 2 cont. Ἡμῖν δ' ἐπεὶ διώρισται πρότερον ὅτι ἐν τοῖς ἔχουσιν ἀρχὴν κινήσεως αἱ τοιαῦται δυνάμεις ἐνυπάρχουσιν, ὁ δ' οὐρανὸς ἔμψυχος καὶ ἔχει κινήσεως ἀρχήν, δῆλον ὅτι ἔχει καὶ τὸ ἄνω καὶ τὸ κάτω καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν. 236 Since we have already determined that functions of this kind belong to things which possess, a principle of movement, and that the heaven is animate and possesses a principle of movement, clearly the heaven must also exhibit above and below, right and left. Οὐ δεῖ γὰρ ἀπορεῖν διὰ τὸ σφαιροειδὲς εἶναι τὸ σχῆμα τοῦ παντός, ὅπως ἔσται τούτου τὸ μὲν δεξιὸν τὸ δὲ ἀριστερὸν ὁμοίων γ' ὄντων τῶν (285b.) μορίων ἁπάντων καὶ κινουμένων τὸν ἅπαντα χρόνον, 237 We need not be troubled by the question, arising from the spherical shape of the world, how there can be a distinction of right and left within it, all parts being alike and all for ever in motion. ἀλλὰ νοεῖν ὥσπερ ἂν εἴ τις, ἐν οἷς ἔχει τὸ δεξιὸν πρὸς τὸ ἀριστερὸν διαφορὰν καὶ τοῖς σχήμασιν, εἶτα περιθείη σφαῖραν ἕξει μὲν γὰρ τὴν δύναμιν διαφέρουσαν, δόξει δ' οὔ, διὰ τὴν ὁμοιότητα τοῦ σχήματος. 238 We must think of the world as of something in which right differs from left in shape as well as in other respects, which subsequently is included in a sphere. The difference of function will persist, but will appear not to by reason of the regularity of shape. Τὸν αὐτὸν δὲ τρόπον καὶ περὶ τῆς ἀρχῆς τοῦ κινεῖσθαι καὶ γὰρ εἰ μηδέποτ' ἤρξατο, ὅμως ἔχειν ἀναγκαῖον ἀρχήν, ὅθεν ἂν ἤρξατο, εἰ ἤρχετο κινούμενον, κἂν εἰ σταίη, κινηθείη ἂν πάλιν. 239 In the same fashion must we conceive of the beginning of its movement. For even if it never began to move, yet it must possess a principle from which it would have begun to move if it had begun, and from which it would begin again if it came to a stand. Λέγω δὲ μῆκος μὲν αὐτοῦ τὸ κατὰ τοὺς πόλους διάστημα, καὶ τῶν πόλων τὸν μὲν ἄνω τὸν δὲ κάτω 240 Now by its length I mean the interval between its poles, one pole being above and the other below; διαφορὰν γὰρ ἐν τούτοις μόνοις ὁρῶμεν τῶν ἡμισφαιρίων, τῷ μὴ κινεῖσθαι τοὺς πόλους. 241 for two hemispheres are specially distinguished from all others by the immobility of the poles. Ἅμα δὲ καὶ εἰώθαμεν λέγειν τὰ πλάγια ἐν τῷ κόσμῳ οὐ τὸ ἄνω καὶ τὸ κάτω, ἀλλὰ τὸ παρὰ τοὺς πόλους, ὡς τούτου μήκους ὄντος τὸ γὰρ εἰς τὸ πλάγιόν ἐστι τὸ παρὰ τὸ ἄνω καὶ τὸ κάτω. 242 Further, by 'transverse' in the universe we commonly mean, not above and below, but a direction crossing the line of the poles, which, by implication, is length: for transverse motion is motion crossing motion up and down. Τῶν δὲ πόλων ὁ μὲν ὑπὲρ ἡμᾶς φαινόμενος τὸ κάτω μέρος ἐστίν, ὁ δ' ἡμῖν ἄδηλος τὸ ἄνω. 243 Of the poles, that which we see above us is the lower region, and that which we do not see is the upper. Δεξιὸν γὰρ ἑκάστου λέγομεν, ὅθεν ἡ ἀρχὴ τῆς κατὰ τόπον κινήσεως τοῦ δ' οὐρανοῦ ἀρχὴ τῆς περιφορᾶς, ὅθεν αἱ ἀνατολαὶ τῶν ἄστρων, ὥστε τοῦτ' ἂν εἴη δεξιόν, οὗ δ' αἱ δύσεις, ἀριστερόν. Εἰ οὖν ἄρχεται ἀπὸ τῶν δεξιῶν καὶ ἐπὶ τὰ δεξιὰ περιφέρεται, ἀνάγκη τὸ ἄνω εἶναι τὸν ἀφανῆ πόλον εἰ γὰρ ἔσται ὁ φανερός, ἐπ' ἀριστερὰ ἔσται ἡ κίνησις, ὅπερ οὔ φαμεν. Δῆλον τοίνυν ὅτι ὁ ἀφανὴς πόλος ἐστὶ τὸ ἄνω. 244 For right in anything is, as we say, the region in which locomotion originates, and the rotation of the heaven originates in the region from which the stars rise. So this will be the right, and the region where they set the left. If then they begin from the right and move round to the right, the upper must be the unseen pole. For if it is the pole we see, the movement will be leftward, which we deny to be the fact. Clearly then the invisible pole is above. Καὶ οἱ μὲν ἐκεῖ οἰκοῦντες ἐν τῷ ἄνω εἰσὶν ἡμισφαιρίῳ καὶ πρὸς τοῖς δεξιοῖς, ἡμεῖς δ' ἐν τῷ κάτω καὶ πρὸς τοῖς ἀριστεροῖς, ἐναντίως ἢ ὡς οἱ Πυθαγόρειοι λέγουσιν ἐκεῖνοι γὰρ ἡμᾶς ἄνω ποιοῦσι καὶ ἐν τῷ δεξιῷ μέρει, τοὺς δ' ἐκεῖ κάτω καὶ ἐν τῷ ἀριστερῷ. Συμβαίνει δὲ τοὐναντίον. 245 And those who live in the other hemisphere are above and to the right, while we are below and to the left. This is just the opposite of the view of the Pythagoreans, who make us above and on the right side and those in the other hemisphere below and on the left side; the fact being the exact opposite. Ἀλλὰ τῆς μὲν δευτέρας περιφορᾶς, οἷον τῆς τῶν πλανήτων, ἡμεῖς μὲν ἐν τοῖς ἄνω καὶ ἐν τοῖς δεξιοῖς ἐσμεν, ἐκεῖνοι δὲ ἐν τοῖς κάτω καὶ ἐν τοῖς ἀριστεροῖς ἀνάπαλιν γὰρ τούτοις ἡ ἀρχὴ τῆς κινήσεώς ἐστι διὰ τὸ ἐναντίας εἶναι τὰς φοράς, ὥστε συμβαίνειν ἡμᾶς μὲν εἶναι πρὸς τῇ ἀρχῇ, ἐκείνους δὲ πρὸς τῷ τέλει. 246 Relatively, however, to the secondary revolution, I mean that of the planets, we are above and on the right and they are below and on the left. For the principle of their movement has the reverse position, since the movement itself is the contrary of the other: hence it follows that we are at its beginning and they at its end. Περὶ μὲν οὖν τῶν κατὰ τὰς δια(286a.) στάσεις τῶν μορίων καὶ τῶν κατὰ τόπον ὡρισμένων τοσαῦτα εἰρήσθω. Here we may end our discussion of the distinctions of parts created by the three dimensions and of the consequent differences of position.
| Postquam philosophus determinavit de partibus situalibus caeli secundum opinionem aliorum, hic determinat de his secundum opinionem suam. Et circa hoc tria facit: | 313. After determining the question of the positional parts of the heaven according to the opinions of others, the Philosopher here discusses them according to his own opinion. As to this he does three things: |
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primo ostendit quod huiusmodi differentias oportet esse in caelo; secundo ostendit secundum quam dimensionem caeli accipiatur sursum et deorsum in ipso, ibi: dico autem longitudinem etc.; tertio ostendit quae pars in caelo sit sursum et quae deorsum, ibi: polorum autem qui quidem super nos et cetera. |
First he shows that such positional differences must be in the heaven; Secondly, he explains which dimension determines "up" and "down" in the heaven, at 320; Thirdly, he shows which part of the heaven is up, and which is down, 323. |
| Circa primum duo facit: | About the first he does two things: |
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primo ostendit propositum; secundo excludit quasdam obiectiones, ibi: non oportet enim dubitare et cetera. |
First he proves his proposition; Secondly, he excludes certain objections, at 317. |
| Circa primum ponit talem rationem. Determinatum est prius quod in habentibus principium motus, scilicet in corporibus animatis, quae habent in se principium movens, existunt tales virtutes, idest positionum differentiae, secundum determinatas virtutes partium; et non solum secundum habitudinem ad nos, sicut est in corporibus inanimatis, quae non habent in se principium activum motus, sed solum passivum, ut dicitur in VIII Physic. Caelum autem est animatum, et habet principium motus. | 314. With respect to the first he gives the following argument [236]: It has been previously determined that in things possessing a principle of motion, namely, in living bodies which possess a moving principle within themselves, there are found "such powers," i.e., differences of position according to the respective virtues in the parts, and not merely with respect to us, as in the case of non-living bodies which do not possess within themselves an active principle of motion but a passive one only, as is said in Physics VIII. But the heaven is animated and possesses a principle of motion. |
| Quod autem caelum sit animatum, supponit ex eo quod probatum est in VIII Physic., quod omnia mobilia necesse est reducere in unum primum, quod est movens seipsum, et habet in se principium motus activum, et non solum principium passivum, sicut quidam posuerunt, ut Simplicius refert qui posuerunt Aristotelem dicere caelum animatum, non quia haberet animam rationalem, sed ita quod haberet quandam vitam complantatam corpori, ita quod in eo nihil est aliud anima quam natura talis corporis. Quod manifeste ostenditur esse falsum ex hoc quod Aristoteles in XII Metaphys. dicit, quod primum movens, quod est omnino immobile, movet caelum sicut desideratum et intellectum: et sic sequitur quod secundum opinionem eius, caelum est secundum suam animam appetens et intelligens. Et secundum hoc motus caeli est et a natura et ab anima eius: sed a natura quidem sicut a principio secundario et passivo, inquantum scilicet tale corpus est aptum natum sic moveri; ab anima vero sicut a principio principali et activo motus. | That the heaven is animated he supposes from something proved in Physics VIII, namely, that all mobile beings must be reduced to one first self-mover that possesses its own active principle of motion and not merely its own passive principle, as some mentioned by Simplicius would claim. For they say that Aristotle called the heaven animate not because it had a rational soul but inasmuch as it had a kind of life implanted in its body in such a way, however, that the soul in it is nothing other than the nature of such a body. But that this is false is clearly shown by the words of Aristotle in Metaphysics XII to the effect that the first mover, which is completely immobile, moves the heaven as an object of thought and desire moves something. Consequently, it follows that, according to his opinion, the heaven is according to its soul something that desires and understands. And according to this, the motion of the heaven proceeds from its nature and from its soul: from its nature, indeed, as from a secondary and passive principle, inasmuch, namely, as such a body is apt to be moved in such a way; from its soul, however, as from a primary and active principle of motion. |
| Nec multum refert quantum ad hunc modum movendi, utrum moveatur a substantia spirituali coniuncta quae dicatur anima eius, vel tantum a substantia spirituali separata; nisi quod ponere ipsum moveri a substantia spirituali coniuncta, pertinet ad maiorem dignitatem ipsius caeli; quod attendentes Plato et Aristoteles, posuerunt caelum animatum. | 315. Now in regard to this way of causing motion, it makes little difference whether the heaven is moved by a conjoined spiritual substance called its soul, or by a separated spiritual substance, except that a greater dignity accrues to the heaven if it is considered moved by a conjoined spiritual substance. This last consideration led Plato and Aristotle to posit an animated heaven. |
| Quamvis possit aliquis e contrario dicere quod, sicut nobilius est corpus quod habet substantiam spiritualem coniunctam, ita nobilior est substantia spiritualis quae omnino est a corpore separata: unde et Plato posuit in bonum animae rationali esse quod quandoque a corpore separatur. Et secundum hoc, cum movens sit nobilius moto, et magis ab eo dependeat motus, magis videtur dicendum substantiam moventem caelum esse a corpore separatam, quam corpus caeli esse animatum, ut motus caeli sit nobilior: alioquin videretur, secundum dictum Platonis, quod anima caeli esset peioris conditionis quam anima humana. | Someone could object, however, that although it is more noble for a body to have a spiritual substance conjoined to it, yet for the spiritual substance it is nobler to be separated from a body. For this reason Plato was led to say that it is for the good of the rational soul to be separated from the body at some time. Now according to this, since the mover is nobler than the moved and since motion depends more on the former, it seems better to say that the substance moving the heaven is separated from the body than to say that the heaven is animated; for this will give greater nobility to the motion of the heaven. Otherwise it would seem, following Plato's opinion, that the soul of the heaven would be in a worse condition than the human soul. |
| Sed ad hoc responderi potest quod animae humanae quantum ad aliquid nobilius est esse extra corpus quam in corpore, scilicet quantum ad hoc quod movet corpus cum labore contra naturam eius; sed quantum ad naturale esse ipsius animae melius est ei esse in corpore, quia per hoc consequitur perfectum esse speciei. Unde si sit aliqua substantia spiritualis cuius virtus sit determinata ad motum caeli, quod movet sine labore, ut supra dictum est, nobilius est ei esse in tali corpore quam esse separatam: quia perfectior est actio quam quis agit per instrumentum coniunctum, quam per instrumentum separatum. Sed substantia separata cuius virtus non determinatur ad hunc effectum, est omnino nobilior. | But an answer to this could be that in one sense it is nobler for the human soul to exist outside the body than in the body, namely, to the extent that it moves the body with labor against its nature. But in respect to the natural existence of the soul it is better for the soul to be in the body, because through it the soul attains the perfect existence of its species. Consequently, if there be a spiritual substance whose power is determined to the motion of the heaven, which it moves without labor, as was said above, then for that substance it is nobler to be in such a body than to be separated; because the action is more perfect which is performed through a conjoined instrument than with a separated instrument. But a separated substance whose power is not determined to this effect is absolutely nobler. |
| Ex hoc autem quod caelum est animatum, concludit secundum praedicta quod habeat sursum et deorsum, dextrum et sinistrum. | Now from the fact that the heaven is animated, he concludes, in keeping with what was said, that it possesses an "up" and "down" as well as "right" and "left." |
| Sed videtur hoc non esse conveniens. Dixit enim supra quod sursum et deorsum competit corpori animato secundum augmentum, ante et retro secundum sensum, dextrum et sinistrum secundum motum localem; nullus autem ponens caelum animatum, ponit in eo motum augmenti, neque etiam motum sensus; ergo neque deberet poni in caelo sursum aut deorsum, aut ante aut retro. | 316. But this seems inappropriate. For he said previously that up and down belong to an animated body on account of growth, but front and behind on account of sense, and right and left on account of local motion. But no one who posits an animated heaven assumes for it either a motion of growth or a motion of sensation. Therefore one should not posit an up and down in the heaven, or a front and behind. |
| Sed dicendum est quod in animalibus perfectis habentibus motum localem, attenduntur praedictae differentiae non solum secundum augmentum et secundum sensum, sed etiam secundum motum localem. Unde ipse supra dixit in quadam ratione quod sursum est unde est motus, dextrum autem a quo, anterius autem ad quod. Sed in illis quae non habent motum localem, quae omnino carent dextro et sinistro, inveniuntur sursum et deorsum, ante et retro, secundum alios motus. Et sic oportet omnia ista attribui caelo secundum solum motum localem, sicut perfectissimo. | But it must be said that in perfect animals having local motion, these differences are considered not only with respect to growth and sense but also with respect to local motion. For which reason he said previously in one of his arguments that "up" is the originative source of motion, "right" is the terminus "from which," and front is the terminus "to which." But in things that lack local motion and have no right and left, their up and down, front and behind, are based on other motions. Consequently all these dimensions ought to be attributed to the heaven solely on the ground of local motion, as to a thing which is most perfect. |
| Deinde cum dicit: non oportet enim dubitare etc., excludit duas obiectiones: et primo ponit eas. Quarum prima talis est. Caelum enim est sphaericae figurae, et ita omnes partes eius sunt similes; praedictae autem differentiae positionum requirunt dissimilitudinem partium, vel in virtute solum, sicut dextrum et sinistrum, vel etiam in figura, sicut sursum et deorsum, ante et retro, ut supra dictum est; non ergo videtur quod huiusmodi positionum differentiae possint caelo attribui. | 317. Then at [237] he excludes two objections, the first of which is this: The heaven is spherical in shape; consequently all its parts are similar. But the aforesaid differences of position require dissimilarity of parts either in respect to power alone, as in the case of right and left, or in respect to shape as well, as in the case of up and down, front and behind, as was said above. Therefore it does not seem that these differences of position can be attributed to the heaven. |
| Secunda obiectio est, quia in animalibus, quibus huiusmodi positionum species attribuuntur, una pars movetur ante alteram; sed hoc non potest esse in caelo, sed partes eius omni tempore moventur, ut ipse dicit in VIII Physic.; unde videtur quod huiusmodi positiones non sint ponendae in caelo. | The second objection is that in animals where these various kinds of position are found, one part is moved before the other. But this cannot occur in the heaven, for its parts are always being moved, as he says in Physics VIII. Hence it seems that such positions are not to be attributed to the heaven. |
| Secundo ibi: sed intelligere etc., solvit praedictas obiectiones. Et primo primam, dicens quod non oportet propter hoc dubitare, sed hoc modo oportet hoc intelligere in caelo, sicut si aliquam habeat differentiam dextri et sinistri etiam secundum figuras partium, et postea circumponat aliquis ei sphaeram, non quidem exterius sicut vestimentum, sed sicut corpus coniunctum naturaliter contegens exterius: sic enim quod huiusmodi est haberet virtutem differentem dextri et sinistri, sed videretur non habere propter similitudinem figurae quae exterius apparet. Et similiter ab anima caeli sunt diversae virtutes in diversis partibus eius, quamvis similibus secundum figuram, propter quas praedictae positiones caelo attribuuntur. | 318. Then at [238] he answers these objections, and first the first. He says that this argument should not cause us to doubt our conclusion, but one should rather understand the case with the heaven as though it had a difference between right and left even according to a difference of shape in the parts, but later one should put a sphere around it, not exteriorly as a garment but as a body joined to it naturally and covering it exteriorly. Then what would be thus would in reality possess one power on the right and a different one on the left, although it would not appear to be so differentiated, on account of the similarity of shape which would outwardly appear. In like manner, from the soul of the heaven there are different powers in its several parts, although they are alike in shape. It is on account of this variety of powers that the aforesaid positions are attributed to the heaven. |
| Secundam solvit ibi: eodem autem modo et cetera. Et dicit quod eodem modo non est dubitandum propter hoc quod animalia, in quibus sunt huiusmodi differentiae, habent principium eius quod est moveri. Etsi enim caelum nunquam incoepit moveri, tamen quia motus eius est ordinatus, necesse est in motu eius accipere aliquod principium unde motus eius incoeperit, si incoepit moveri, et unde etiam iterum moveri inciperet, si contingeret ipsum stare. | 319. Then at [239] he answers the second objection and says that doubt should not arise from the fact that animals, in which these differences exist, possess a principle [or starting-point] of their motion. For even though the heaven never begins to be moved, yet, because its motion is orderly, it is necessary to consider something in its motion as a starting-point whence its motion would begin if it did begin, or whence its motion would resume, if it should happen to stop. |
| Deinde cum dicit: dico autem longitudinem etc., ostendit secundum quam dimensionem caeli attendatur sursum et deorsum. Et primo proponit quod intendit: et dicit quod longitudo caeli est distantia quae est inter polos ipsius, Arcticum scilicet ad Antarcticum, ita quod unus polorum sit sursum et alius deorsum. | 320. Then at [240] he explains which dimensions of the heaven are considered as up and down. First he proposes what he intends, and says that the length of the heaven is the distance between its poles, namely, the arctic and antarctic, in such a way that one of these poles is up, and the other down. |
| Secundo ibi: differentiam enim etc., probat propositum dupliciter. Primo quidem per rationem. Manifestum est enim quod in quolibet corpore longitudo attenditur secundum maximam dimensionem ipsius. Maxima autem dimensio corporis sphaerici est secundum diametrum eius. Diameter autem in caelo determinatur solum qui est inter duos polos, qui sunt duo puncta sphaerae immobilia et semper eodem modo se habentia; quaecumque autem alia puncta in sphaera accipiantur, sunt mobilia; unde et diametri inter quaecumque alia duo puncta protrahantur, indeterminate se habent. Et propter hoc, secundum lineam quae est inter duos polos, maxime attenditur longitudo caeli: quia in his solis punctis caeli videmus determinatam differentiam hemisphaeriorum, per hoc quod huiusmodi Poli non moventur. | 321. Secondly at [241] he proves this proposition in two ways. First by reasoning. For it is plain that the length of any body is measured along its greatest dimension. Now the greatest dimension of a spherical body is diametric. But the diameter of the heaven is solely the one between the two poles, which are two immovable points of a sphere that never vary, whereas all other points taken are subject to motion. Consequently diameters drawn between any other two points are indeterminate. For this reason it is with respect to the line joining the two poles that the length of the heaven is considered, for inasmuch as these poles are not in motion, they allow us to see a definite difference of hemispheres. |
| Secundo ibi: simul autem etc., probat idem per communem modum loquendi. Consuevimus enim dicere quod latera in mundo non sunt ipsi Poli, quos dicimus sursum et deorsum, sed id quod est iuxta polos, ex utraque scilicet parte eorum, ut scilicet oriens sit unum latus mundi et occidens sit aliud, tanquam distantia polorum sit ipsa longitudo caeli: hoc enim dicimus laterale quod est iuxta sursum et deorsum ex utraque parte eius, sicut patet in homine. | 322. Secondly, at [242] he proves the same thing from the way people generally speak. For when we refer to the asides" of the world, we do not mean the poles, which we call "up" and "down," but we mean something beside the poles, so that "east" is one side of the world, and "west" another, while the distance between the poles is the length of the heaven. For we call "side" what is adjoining "up" and "down" on either side, as is evident in man. |
| Est autem attendendum quod, secundum astrologos considerantes non dimensiones caeli, sed magis dimensiones nostrae habitabilis, attenditur longitudo secundum differentiam orientis et occidentis, latitudo autem secundum distantiam meridiei et Septentrionis: quia quantitas nostrae habitabilis est maior plus quam in duplo ab oriente in occidentem quam a polo versus aequinoctialem, quia nec hoc totum habitatur. | But it should be noted that for astronomers, who consider, not the dimensions of the heaven, but more the dimensions of the habitable earth, length is considered with respect to east and west, and width according to the distance from south to north — their reason being that the quantity of habitable earth from east to west is more than double that from pole to 'equator, since this is not fully inhabited. |
| Deinde cum dicit: polorum autem qui quidem super nos etc., ostendit quis polorum sit sursum et quis deorsum. | 323. Then at [243] he shows which of the poles is up and which down. |
|
Et primo ostendit hoc quantum ad motum primum; secundo quantum ad motum planetarum, ibi: sed secundae quidem et cetera. |
First he shows this with respect to the first motion; Secondly, with respect to the motion of the planets, at 329. |
| Circa primum tria facit: | As to the first he does three things: |
|
primo proponit quod intendit; secundo probat quod dixerat, ibi: dextrum enim etc.; tertio infert conclusionem ex dictis, ibi: et ibi quidem habitantes et cetera. |
First he proposes what he intends; Secondly, he proves what he has said, at 324; Thirdly, he draws a conclusion from this, at 328. |
| Dicit ergo primo quod inter polos ille qui semper apparet super nos, est pars caeli quae est deorsum, scilicet polus Arcticus: ille autem qui semper nobis est immanifestus, qui dicitur Antarcticus propter hoc quod est ei oppositus, est pars caeli quae est sursum. | He says therefore first [243] that the pole which seems always to be over us is the downward part of the heaven, namely, the arctic pole; but the pole which is always hidden from us and called the antarctic is the part of the heaven referred to as up. |
| Deinde cum dicit: dextrum enim etc., probat quod dixerat. Manifestum est enim quod in unoquoque animali dextrum dicimus unde est principium motus localis eius (et propter hoc pars dextra animalis est calidior, ut sit magis apta ad motum); principium autem circularis motus caeli est ex illa parte unde astra oriuntur, quae vocatur oriens; unde oriens dicitur dextrum caeli, et per consequens occasus erit sinistrum eius. Si ergo motus caeli incipit a dextris et circumfertur ad dextram, tanquam ab eodem in idem, necesse est quod polus immanifestus, scilicet Antarcticus, sit sursum caeli: si enim polus Arcticus, qui semper est nobis manifestus, esset sursum, sequeretur quod motus caeli esset a sinistra et ad sinistram, quod nos non dicimus. | 324. Then at [244] he proves what he has said. Now it is manifest in the case of every animal that we call the "right" that which is the originative source of its local motion (on which account the right side of an animal is warmer, in order to be more apt for motion); but the circular motion of the heaven originates from that part whence the stars rise and which is called "east"; consequently the west will be its left. If, therefore, the motion of the heaven begins at the right and circulates back to the right, as though going from the same to the same, then necessarily the pole hidden from us, namely, the antarctic, is referred to as the upper part of the heavens, for if the arctic pole, which is never hidden from us, were the upper side, it would follow that the motion of the heaven would be from left to left. But this is not the way we speak of it. |
| Et hoc sic apparet. Imaginemur enim hominem cuius caput sit in polo Arctico et pedes in polo Antarctico: manus eius dextra erit in occidente et manus sinistra in oriente; si tamen facies eius sit versus hemisphaerium superius, quod est nobis apparens. Cum ergo motus caeli sit ab oriente in occidentem, sequetur quod sit a sinistro in dextrum. Sed si ponamus e converso quod caput hominis sit in polo Antarctico et pedes in polo Arctico, eadem dispositione faciei manente, manus dextra erit in oriente et sinistra in occidente: et sic motus incipiet a dextra, secundum quod convenit. Et ita manifestum est quod sursum caeli est polus immanifestus. | This will be easier to understand if we imagine a man with his head in the arctic and his feet in the antarctic poles of the heaven. His right hand will be in the west and his left in the east, provided his face is toward the upper hemisphere, i.e., the one visible to us on earth. Therefore, since the motion of the heaven is from east to west, it will follow that it is from the left to the right. On the other hand, if we place his head in the antarctic and his feet in the arctic pole, with his face as before, his right hand will be in the east and his left in the west. Then the motion would begin from the right, as it should. Thus it is clear that the heaven's "up" is the pole which is hidden from us. |
| Sed primo contra hoc obiicitur, quod Aristoteles praetermittit determinare quid sit anterius et posterius caeli. Sed dicendum est quod hoc praetermittit tanquam manifestum ex his quae determinantur. Motus enim animalis, a dextris incipiens, procedit in ante, et non retrorsum: unde cum caelum moveatur ab oriente versus superius hemisphaerium, quod apparet per elevationem stellarum orientium, consequens est quod anterius caeli sit superius hemisphaerium, posterius autem caeli sit hemisphaerium inferius. | 325. But there are three objections to this. First it is objected that Aristotle fails to determine what is "front" and what is "behind" in the heaven. But it should be answered that he passed over this as clear from what he has already determined. For an animal's motion, beginning from its right, proceeds forward and not backward. Hence, since the heaven is moved from east to west toward the upper hemisphere (which is evident from the fact that the stars seem to climb after they rise), the consequence is that "front" in the heaven is the upper hemisphere and "behind" the lower hemisphere. |
| Secundo obiicitur quia, cum in animalibus sit semper eadem pars dextra et eadem pars sinistra, hoc in caelo observari non videtur: nam eadem pars caeli, quae prius est in oriente, posterius est in occidente; et sic, si dextrum est oriens et sinistrum occidens, eadem pars caeli quandoque erit dextra, quandoque sinistra. | 326. In the second place it is objected that, although it is always the same part of the animal that is its right and another same part which is always its left, this does not seem to be observed in the heaven: for the same part of the heaven that was in the east comes to be in the west; consequently, if the east is the right side and the left the west, the same part of the heaven will be the right at one time and the left at another time. |
| Sed hoc solvitur per hoc quod philosophus dicit in VIII Physic., quod principium movens caelum non movetur secundum accidens, sicut principium movens animalia inferiora. Huiusmodi autem virtutes, secundum quas attribuuntur praedictae positiones animalibus, dependent ex principio motivo: et ideo in animalibus quae sunt hic, virtus dextra movetur per accidens, moto corpore animalis; sed in caelo virtus illa intelligitur quasi immobiliter stans, etiam partibus caelestis corporis motis. Et ideo semper dextrum caeli est in oriente, quamcumque partem singularem caeli contingat ibi esse. Et eadem ratio est de aliis virtutibus. | But this is answered by something that Aristotle states in Physics VIII, namely, that the principle which moves the heaven is not moved per accidens as it is in animals. For these powers, according to which the aforesaid positions are attributed to animals, depend on the motive principle. Hence in animals that exist here the "right" power is moved per accidens when the body of the animal is moved. But in the heaven that power is understood to be immovably rigid, even though the parts of the heavenly body are moved. Therefore the "right" of the heaven is always in the east, no matter which single part of the heaven happens to be there. And the same holds for the other powers. |
| Tertio obiicitur quia oriens et occidens non videtur esse determinata pars caeli, sed diversificari secundum horizontem uniuscuiusque regionis. Sic igitur si dextrum et sinistrum attribuitur ortui et occasui, dextrum et sinistrum non erunt determinata in caelo secundum se, sicut in corporibus animatis, sed relatione ad nos, sicuti in corporibus inanimatis. | 327. In the third place it is objected that east and west seem not to be definite parts of the heaven but to vary according to the horizon in each region. Consequently, if right and left are attributed respectively to the regions of rising and setting, right and left will not be determinate in the heavens according to themselves, as they are in the bodies of animals, but only in relation to us, as is the case with inanimate bodies. |
| Sed dicendum est quod, propter immobilitatem polorum, sursum et deorsum dicit esse determinata in caelo: dextrum autem et sinistrum lateraliter se habent ad sursum et deorsum. Accipit ergo hic Aristoteles ortum et occasum, non per comparationem ad aspectum nostrum, sed per comparationem ad polos immobiles mundi. | But it should be answered that, due to the immobility of the poles, up and down are said by him to be determinate in the heaven, while right and left are sides in relation to up and down. Therefore Aristotle is here taking rising and setting not in relation to our outlook but in relation to the immobile poles of the world. |
| Deinde cum dicit: et ibi quidem habitantes etc., concludit secundum praedicta differentiam habitationis terrae: dicens quod ex quo polus immanifestus est sursum, illi qui habitant sub illo polo sunt in hemisphaerio superiori et apud dextram caeli; nos autem qui in hac parte terrae habitamus, sumus in inferiori hemisphaerio et in sinistra. Et hoc est e contrario ei quod Pythagorici dixerunt, qui posuerunt nos habitare sursum et in dextra parte, illos autem deorsum et in sinistra parte; cum tamen contrarium accidat secundum praedicta. | 328. Then at [245] he concludes in the light of the foregoing to a difference as to the habitation of the earth. He says that since the hidden pole is up, those who live under that pole live in the upper hemisphere and on the right side of the heaven; but we who live on the other side of the earth are in the lower hemisphere and in the left side of the heaven. And this is contrary to the Pythagoreans, who held that we live in the upper direction and in the right side and the others in the downward direction and in the left side, while according to the foregoing the contrary happens. |
| Hemisphaerium autem hic videtur accipere secundum quod dividitur caelum per circulum aequinoctialem aeque distantem ab utroque polo. Et ex hoc patet Aristotelem hic dicere quod etiam ex alia parte aequinoctialis aliqui homines habitant vel habitare possunt, in parte opposita nobis. Si qui autem habitant vel habitarent in duabus quartis terrae quae distinguuntur a nobis per circulum qui intelligitur secare aequinoctialem ad rectos angulos, transeuntem per polos aequinoctiales, illi distinguerentur a nobis utrisque, qui scilicet habitamus sursum et deorsum, tanquam habitantes in posteriori parte caeli ab habitantibus in anteriori, inquantum motus caeli posterius ad eos pervenit, utpote stellis eis orientibus cum nobis occidunt, et redeuntibus ad principium motus, quod est dextrum, in occasu stellarum. Sed cum dextrum et sinistrum aequaliter distent et lateraliter ab eo quod est sursum et deorsum, videtur inconvenienter dicere quod nos qui sumus sub polo Arctico, habitemus in inferiori parte et sinistra, alii autem in superiori et dextra. | Aristotle here seems to take "hemisphere's as that which results from dividing the heaven through the equinoxial circle [i.e., the equator] in a plane equidistant from the poles. From this it is plain that Aristotle is here saying that some men live or can live on the other side of the equator in a direction opposite to us. Now, if people are living or should live on the two quarters of earth that are distinguished from us by a circle intersecting the equator at right angles, passing through the equatorial poles, those people would be distinct from both of us, namely, who live above and below the equator, as people living on the rear of the heaven are distinct from the inhabitants of the fore part of the heaven, inasmuch as the motion of the heaven reaches them later, so that stars setting for us are rising for them and returning to the principle of motion, which is the right, when they are setting for them. But since the right and left are equally distant on the side from the up and down, it seems improper to say that we who live under the arctic pole inhabit the nether and left side, while the others inhabit the upper and right side. |
| Et ad hoc potest dici quod Aristoteles locutus est secundum Graeciam, in qua habitabat, quae quidem est ad sinistram inquantum est versus occidentem, est autem deorsum inquantum est sub polo Arctico. Sed quia Aristoteles hic loqui videtur communiter pro habitantibus omnibus in nostra habitabili, melius respondetur quod ipse loquitur more Pythagoricorum, qui ad idem referebant dextrum, sursum et ante, et opposita etiam ad idem: Pythagoras autem secundum hoc aestimavit nos esse in parte superiori et dextra; vel secundum aspectum, quia polus Arcticus supereminet nobis; vel magis, aspiciens ad motus planetarum, ut immediate patebit. | To this it can be said that Aristotle spoke with respect to Greece in which he lived. Greece is indeed to the left inasmuch as it faces west and it is nether inasmuch as it is under the arctic pole. But since Aristotle seems here to speak in general for all the inhabitants in our habitat, it is better to say that he is speaking after the manner of Pythagoreans who referred right, up, and front, to the same thing, and the opposites to the same thing. According to this, Pythagoras considered that we live in the upper and right part. Or this could be according to perspective, because the arctic pole is directly above us, or better, looking to motions of the planets, as will be immediately evident.. |
| Deinde cum dicit: sed secundae quidem etc., ostendit quomodo istae positiones distinguantur secundum motus planetarum. Et dicit quod quantum ad secundum motum circularem, qui est planetarum, nos e converso sumus sursum et in dextra, illi autem deorsum et in sinistra: quia principium huius motus e contrario se habet (incipiunt enim moveri ab occidente); et hoc ideo, quia isti duo motus sunt contrarii, idest diversi (nam contrarietas proprie non est in motibus circularibus, ut in primo ostensum est). Et secundum hoc accidit nos esse in principio, et illos in fine motus planetarum. Et ideo illi videntur esse potiores quantum ad permanentiam, quae est in primo motu; nos autem quantum ad diversitatem generationis et corruptionis, quae dependet ex secundo motu, ut infra dicetur. | 329. Then at [246] he shows how these positions are distinguished according to the motions of the planets. And he says that with respect to the second circular motion, namely, that of the planets, we conversely, are up and to the right, while the people on the other side of the earth are down and to the left. For the principle of planetary motion is contrary (for they begin to be moved from the west). The reason for this difference is that the two motions are "contrary," i.e., diverse, since contrariety, strictly speaking, is not found in a circular motion, as was explained in Book I. According to this, then, we live where the planet's motion begins and they live where it ends. Therefore those people seem to be stronger according to permanency, which is in the first motion; but we according to diversity of generation and corruption, which depend on the second motion, as will be explained later. |
| Ultimo autem epilogat, dicens quod tanta dicta sunt de partibus caeli, quae determinantur secundum dimensiones caeli et secundum locum, non autem secundum materiales partes caeli, ut dictum est. | Finally, at [247] he summarizes and says that we have said this much about the parts of the heaven, which are determined according to the dimensions of the heaven and according to place, but not according to the material parts of the heaven, as was said above. |
Lecture 4:
The reason why there are in the heaven, several spheres moved with a circular motionChapter 3 3 3 Ἐπεὶ δ' οὐκ ἔστιν ἐναντία κίνησις ἡ κύκλῳ τῇ κύκλῳ, σκεπτέον διὰ τί πλείους εἰσὶ φοραί, 248 Since circular motion is not the contrary of the reverse circular motion, we must consider why there is more than one motion, καίπερ πόρρωθεν πειρωμένοις ποιεῖσθαι τὴν ζήτησιν, πόρρω δ' οὐχ οὕτω τῷ τόπῳ, πολὺ δὲ μᾶλλον τῷ τῶν συμβεβηκότων αὐτοῖς περὶ πάμπαν ὀλίγων ἔχειν αἴσθησιν. Ὅμως δὲ λέγωμεν. 249 though we have to pursue our inquiries at a distance—a distance created not so much by our spatial position as by the fact that our senses enable us to perceive very few of the attributes of the heavenly bodies. But let not that deter us. Ἡ δ' αἰτία περὶ αὐτῶν ἐνθένδε ληπτέα. Ἕκαστόν ἐστιν, ὧν ἐστιν ἔργον, ἕνεκα τοῦ ἔργου. Θεοῦ δ' ἐνέργεια ἀθανασία τοῦτο δ' ἐστὶ ζωὴ ἀΐδιος. ὥστ' ἀνάγκη τῷ θεῷ κίνησιν ἀΐδιον ὑπάρχειν. Ἐπεὶ δ' ὁ οὐρανὸς τοιοῦτος (σῶμα γάρ τι θεῖον), διὰ τοῦτο ἔχει τὸ ἐγκύκλιον σῶμα, ὃ φύσει κινεῖται κύκλῳ ἀεί. 250 The reason must be sought in the following facts. Everything which has a function exists for its function. The activity of God is immortality, i.e. eternal life. Therefore the movement of that which is divine must be eternal. But such is the heaven, viz. a divine body, and for that reason to it is given the circular body whose nature it is to move always in a circle. Διὰ τί οὖν οὐχ ὅλον τὸ σῶμα τοῦ οὐρανοῦ τοιοῦτον; ὅτι ἀνάγκη μένειν τι τοῦ σώματος τοῦ φερομένου κύκλῳ, τὸ ἐπὶ τοῦ μέσου, τούτου δ' οὐθὲν οἷόν τε μένειν μόριον, οὔθ' ὅλως οὔτ' ἐπὶ τοῦ μέσου. Καὶ γὰρ ἂν ἡ κατὰ φύσιν κίνησις ἦν αὐτοῦ ἐπὶ τὸ μέσον φύσει δὲ κύκλῳ κινεῖται οὐ γὰρ ἂν ἦν ἀΐδιος ἡ κίνησις οὐθὲν γὰρ παρὰ φύσιν ἀΐδιον. Ὕστερον δὲ τὸ παρὰ φύσιν τοῦ κατὰ φύσιν, καὶ ἔκστασίς τίς ἐστιν ἐν τῇ γενέσει τὸ παρὰ φύσιν τοῦ κατὰ φύσιν. Ἀνάγκη τοίνυν γῆν εἶναι τοῦτο γὰρ ἠρεμεῖ ἐπὶ τοῦ μέσου. Νῦν μὲν οὖν ὑποκείσθω τοῦτο, ὕστερον δὲ δειχθήσεται περὶ αὐτοῦ. 251 Why, then, is not the whole body of the heaven of the same character as that part? Because there must be something at rest at the centre of the revolving body; and of that body no part can be at rest, either elsewhere or at the centre. It could do so only if the body's natural movement were towards the centre. But the circular movement is natural, since otherwise it could not be eternal: for nothing unnatural is eternal. The unnatural is subsequent to the natural, being a derangement of the natural which occurs in the course of its generation. Earth then has to exist; for it is earth which is at rest at the centre. (At present we may take this for granted: it shall be explained later.) Ἀλλὰ μὴν εἰ γῆν, ἀνάγκη καὶ πῦρ εἶναι 252 But if earth must exist, so must fire. τῶν γὰρ ἐναντίων εἰ θάτερον φύσει, ἀνάγκη καὶ θάτερον εἶναι φύσει, ἐάν περ ᾖ ἐναντίον, καὶ εἶναί τινα αὐτοῦ φύσιν ἡ γὰρ αὐτὴ ὕλη τῶν ἐναντίων, 253 For, if one of a pair of contraries naturally exists, the other, if it is really contrary, exists also naturally. In some form it must be present, since the matter of contraries is the same. καὶ τῆς στερήσεως πρότερον ἡ κατάφασις (λέγω δ' οἷον τὸ θερμὸν τοῦ ψυχροῦ), ἡ δ' ἠρεμία καὶ τὸ βαρὺ λέγεται κατὰ στέρησιν κουφότητος καὶ κινήσεως. 254 Also, the positive is prior to its privation (warm, for instance, to cold), and rest and heaviness stand for the privation of lightness and movement. Ἀλλὰ μὴν εἴπερ ἔστι πῦρ καὶ γῆ, ἀνάγκη καὶ τὰ μεταξὺ αὐτῶν εἶναι σώματα ἐναντίωσιν γὰρ ἔχει ἕκαστον τῶν στοιχείσων πρὸς ἕκαστον. Ὑποκείσθω δὲ καὶ τοῦτο νῦν, ὕστερον δὲ πειρατέον δεῖξαι. 255 But further, if fire and earth exist, the intermediate bodies must exist also: each element stands in a contrary relation to every other. (This, again, we will here take for granted and try later to explain.) Τούτων δ' ὑπαρχόντων φανερὸν ὅτι ἀνάγκη γένεσιν εἶναι διὰ τὸ μηδὲν οἷόν τ' αὐτῶν εἶναι ἀΐδιον πάσχει γὰρ καὶ ποιεῖ τἀναντία ὑπ' ἀλλήλων, καὶ φθαρτικὰ ἀλλήλων ἐστίν. 256 [Since this is so, in] these four elements generation clearly is involved, since none of them can be eternal: for contraries interact with one another and destroy one another. Ἔτι δ' οὐκ εὔλογον εἶναί τι κινητὸν ἀΐδιον, οὗ μὴ ἐνδέχεται εἶναι κατὰ φύσιν τὴν κίνησιν ἀΐδιον (286b.) τούτων δ' ἔστι κίνησις. Ὅτι μὲν τοίνυν ἀναγκαῖον εἶναι γένεσιν, ἐκ τούτων δῆλον. 257 Further, it is inconceivable that a movable body should be eternal, if its movement cannot be regarded as naturally eternal: and these bodies we know to possess movement. Thus we see that generation is necessarily involved. Εἰ δὲ γένεσιν, ἀναγκαῖον καὶ ἄλλην εἶναι φοράν, ἢ μίαν ἢ πλείους κατὰ γὰρ τὴν τοῦ ὅλου ὡσαύτως ἀναγκαῖον ἔχειν τὰ στοιχεῖα τῶν σωμάτων πρὸς ἄλληλα. Λεχθήσεται δὲ καὶ περὶ τούτου ἐν τοῖς ἑπομένοις σαφέστερον. 258 But if so, there must be at least one other circular motion: for a single movement of the whole heaven would necessitate an identical relation of the elements of bodies to one another. This matter also shall be cleared up in what follows: Νῦν δὲ τοσοῦτόν ἐστι δῆλον, διὰ τίνα αἰτίαν πλείω τὰ ἐγκύκλιά ἐστι σώματα, ὅτι ἀνάγκη γένεσιν εἶναι, γένεσιν δ', εἴπερ καὶ πῦρ, τοῦτο δὲ καὶ τἆλλα, εἴπερ καὶ γῆν ταύτην δ' ὅτι ἀνάγκη μένειν τι ἀεί, εἴπερ καὶ κινεῖσθαί τι ἀεί. 259 But for the present so much is clear, that the reason why there is more than one circular body is the necessity of generation, which follows on the presence of fire, which, with that of the other bodies, follows on that of earth; and earth is required because eternal movement in one body necessitates eternal rest in another.
| Postquam philosophus determinavit de diversitate partium situalium caeli, hic determinat de diversitate partium quantum ad ordinem sphaerarum, ostendens videlicet causam quare in caelo non est una sphaera tantum circulariter mota, sed sunt plures sphaerae quae circulariter moventur. Et circa hoc tria facit: | 330. After discussing the diversity of positional parts of the heaven, the Philosopher here settles the question of the diversity of parts based on the order of the spheres, and explains why there is not just one circularly-moved sphere in the heaven but several of them. Concerning this he does three things: |
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primo ponit dubitationem; secundo ostendit difficultatem solutionis, ibi: et quidem a longe tentantibus etc.; tertio incipit solvere, ibi: unumquodque est quorum est opus et cetera. |
First he states the problem; Secondly, he explains why this problem is difficult to solve, at 332; Thirdly, he begins to solve it, at 333. |
| Circa primum considerandum est quod, si contingeret motus circulares esse contrarios, non esset difficile videre quare in caelo non est tantum unus motus circularis, sed plures. Cum enim contraria differant specie, eo quod contrarietas est differentia secundum formam, ut dicitur X Metaphys., non esset universum perfectum in suis speciebus, si esset unus motus contrarius et non alius, puta si esset motus deorsum et non esset motus sursum. Quia ergo, ut supra probatum est, unus motus circularis non est contrarius alteri, oportet diligenter considerare quae est necessitas quod in caelo essent multi et diversi motus circulares. Et quaestio satis congrue sequitur ad praemissa, in quibus dictum est quod sursum et deorsum et alia huiusmodi aliter considerantur in caelo quantum ad primum motum, et aliter quantum ad secundum. | 331. In regard to the first it should be kept in mind that if circular motions were contrary, it would not be difficult to see why there are many circular motions in the heaven and not just one. For since contraries differ specifically, inasmuch as contrariety is a difference with respect to form, as is said in Metaphysics X, the universe would not be perfect in its species if there were one contrary motion and not another, for example, if there were downward motion and not upward motion. Since, therefore, it has been previously proved that one circular motion is not contrary to another, we should inquire diligently as to the necessity of having many and diverse circular motions in the heaven. This question quite logically follows our previous discussion where it was said that up and down, and other such are assigned to the heaven in one way with respect to the first motion, and in another way with respect to the second. |
| Deinde cum dicit: et quidem a longe tentantibus etc., ostendit difficultatem solvendae quaestionis. Hoc enim dicit esse considerandum hominibus qui tentant facere quaestionem a longe, idest de corporibus caelestibus longe a nobis existentibus; cum tamen de his quae sunt elongata a nobis, non possimus habere certum iudicium. Corpora autem caelestia non ita sunt longe a nobis tanto, idest secundum quantitatem localis distantiae; sed multo magis eo quod pauca accidentium eorum cadant sub sensum nostrum; cum tamen connaturale sit nobis quod ex accidentibus, idest sensibilibus, deveniamus ad cognoscendam naturam alicuius rei. Hanc autem elongationem dicit multo maiorem esse quam localem: quia si consideremus localem distantiam, aliqua proportio est distantiae qua distat a nobis corpus caeleste, ad distantiam qua distat a nobis aliquod inferiorum corporum, puta lapis aut lignum, et utraque distantia est unius generis; sed accidentia caelestium corporum sunt alterius rationis, et omnino improportionata accidentibus inferiorum corporum. Et tamen, quamvis sit difficile, dicamus propter quid est talis diversitas motus in caelo. Et huius diversitatis causa est accipienda ex his quae nunc dicentur. | 332. Then at [249] he points out the difficulty of solving this question. For that is difficult for men to consider when the question is "from afar," i.e., concerning the heavenly bodies far removed from us, since concerning things distant from us we cannot have a certain judgment. However, heavenly bodies are not only removed "by so much," i.e., according to the quantity of local distance, but much more by the fact that few of their accidents fall on our sense observation, whereas it is connatural for us to pass from the knowledge of "accidents," i.e., sensible things, to an understanding of a thing's nature. He states this distance to be much more than the local distance. For if we should consider the local distance, there is some proportion between the distance separating us from a heavenly body and that separating us from various lower bodies, e.g., a stone or some wood, and both distances are in one genus, but the accidents of heavenly bodies have a different notion and are wholly improportionate to the accidents of lower bodies. Yet, in spite of the difficulty, let us inquire into the "why" of the variety of heavenly motions. And the cause of this variety will be derived from what we are about to say. |
| Deinde cum dicit: unumquodque est quorum est opus etc., assignat causam praedictorum. | 333. Then at [250] he assigns the cause of the aforesaid. |
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Et primo assignat eam per viam compositionis, procedendo a primo ad ultimum quod quaeritur; secundo per viam resolutionis, procedendo ab ultimo quod quaeritur usque ad primum, ibi: nunc autem tantum manifestum est et cetera. |
First he assigns it by the method of composition [synthesis], going from what is first to what is last in the order of inquiry; Secondly, by that of resolution [analysis], proceeding from what is last sought to what is first, at 343. |
| Circa primum ponit talem rationem. Si caelum est quoddam corpus divinum, necesse est motum eius esse sempiternum et circularem; si motus eius est sempiternus et circularis, necesse est terram esse; si terra est, necesse est ignem esse; si ignis est et terra, est necesse etiam aliqua corpora intermedia esse; si autem sunt huiusmodi corpora, necesse est generationem esse; si autem generatio est, necesse est plures motus esse in caelo. Ergo, si caelum est corpus perpetuum et divinum, necesse est plures motus esse in caelo, et per consequens plura corpora mobilia. | With respect to the first [250] he gives the following argument: If the heaven is a certain divine body, its motion must be eternal and circular; if its motion is eternal and circular, earth must exist; if earth exists, fire must exist; if fire and earth exist, there must be intermediate bodies; if such bodies exist, there must be generation; if there is generation there must be several motions in the heaven. Therefore, if the heaven is a perpetual and divine body, there must be a number of motions in the heaven, and consequently a number of mobile bodies. |
| Singula igitur per ordinem manifestat: et primo primum. Circa quod considerandum est quod Platonici ponebant unum Deum summum, qui est ipsa essentia bonitatis et unitatis, sub quo ponebant ordinem superiorum intellectuum separatorum, qui apud nos consueverunt intelligentiae vocari; et sub hoc ordine ponebant ordinem animarum, sub quo ordine ponebant ordinem corporum. Dicebant ergo quod inter intellectus separatos, superiores et primi dicuntur intellectus divini, propter similitudinem et propinquitatem ad Deum; alii vero non sunt divini, propter distantiam ad Deum; sicut etiam animarum supremae sunt intellectivae, infimae autem non intellectivae, sed irrationales. Corporum autem suprema et nobiliora dicebant esse animata, alia vero inanimata. Rursus dicebant quod supremae animae propter hoc quod dependent ex intelligentiis divinis, sunt animae divinae; et iterum corpora suprema, propter hoc quod sunt coniuncta animabus divinis, sunt corpora divina. | 334. Then he explains each of these conditionals in order: and first of all the first one. With respect to this it must be remembered that the Platonists posited one supreme God Who is the very essence of goodness and unity, under Whom they put a superior order of separated intellects, which we are accustomed to call "intelligences"; under this order they placed the order of souls, and under this the order of bodies. They said, therefore, that among the separated intellects the first and superior ones are called "divine" intellects on account of their likeness and nearness to God; but the others are not 'divine, because of their distance from God. Similarly, among souls the supreme are intellective, while the lowest are not intellectual but irrational. The supreme and nobler bodies were said to be animate; the others inanimate. Furthermore, they said that the supreme souls, because they depend on the divine intelligences, were divine souls; and the supreme bodies, because united to divine souls, divine bodies. |
| Hoc igitur modo etiam Aristoteles hic loquitur, dicens quod unumquodque quod habet propriam operationem, est propter suam operationem: quaelibet enim res appetit suam perfectionem sicut suum finem, operatio autem est ultima rei perfectio (vel saltem ipsum operatum, in his in quibus est aliquod opus praeter operationem, ut dicitur in I Ethic.); dictum est enim in II de anima quod forma est actus primus, operatio autem est actus secundus, tanquam perfectio et finis operantis. Et hoc est verum tam in corporalibus quam in spiritualibus, puta in habitibus animae; et tam in naturalibus quam in artificialibus. Dicit tamen quorum opus est, propter ea quae sunt contra naturam, sicut sunt monstra; quorum non est aliquod opus inquantum huiusmodi, sed patiuntur defectum operativae virtutis, ut patet in his qui nascuntur claudi vel caeci; non enim claudicatio est finis intentus a natura, propter quem faciat nasci animal claudum, sed hoc accidit praeter intentionem naturae ex defectu naturalium principiorum. | Now, Aristotle uses this manner of speaking here. He says that anything which possesses its on operation exists for its operation, for everything seeks its perfection as its end; but operation is the ultimate perfection of a thing (or at least the product of the operation is, in the case of those things in which there is some product beyond the operation, as is said in Ethics I). For it is said in On the Soul II that form is first act, and operation second act as the perfection and end of the thing acting. And this is true both in material and in spiritual things (such as habits existing in the soul), and in natural as well as artificial things. And he adds the expression, "which produce a work" to take care of things contrary to nature, such as monstrosities, which produce no work as such, but suffer a defect in their operational power, as is plain in those born lame or blind. For lameness is not an end intended by nature, for the sake of which it makes an animal to be born lame; such a thing happens outside the intent of nature, by reason of a defect in the natural principles. |
| Subdit autem quod operatio Dei est immortalitas. Nominat autem hic Deum, non solum primam causam omnium rerum, sed, more Platonicorum et aliorum gentilium, omnia quae dicuntur divina, secundum morem praedictum. | He adds further that "God's operation is immortality," where "God" refers not only to the first cause of all things but to all things called "divine" according to the custom of the Platonists and other gentiles. |
| Sed videtur quod immortalitas non sit operatio, sed potius differentia vel impassibilitas, sicut mortale est differentia vel passio. Dicendum est ergo quod immortalitas signat vitam indeficientem: vivere autem non solum nominat ipsum esse viventis, sed etiam operationem vitae, sicut intelligere est quoddam vivere, et sentire et alia huiusmodi, ut patet in II de anima et in IX Ethic. Et ad hoc exprimendum subiungit, haec autem, scilicet immortalitas, est vita sempiterna: propter quod etiam non dicit quod Dei operatio sit incorruptibilitas, quae importat solum sempiternitatem ipsius esse, sed dicit immortalitas, ut includat sempiternitatem operationis. Unde concludit quod, si aliquid mobilium dicatur Deus secundum modum praedictum, quod motus eius sit sempiternus; sicut et si qua substantia immobilis Deus dicitur, eius operatio est sempiterna absque motu; alioquin frustra esset talis res sempiterna non habens operationem sempiternam, propter quam unaquaeque res est. | But immortality appears not to be an operation but rather a difference or an impassibility. To this it must be answered that immortality designates unfailing life. Now life refers not only to the existence of the living being, but to its operation as well, as understanding is a certain living and as are sensing and other such, as is plain from On the Soul II and Ethics IX. This point is brought out when he says further that "phis," namely, immortality, "is eternal life" — for which reason he does not say that God's operation is indestructibility, which refers only to the eternity of His existence but he says it is "immortality," in order to include eternity of action. Hence he concludes that if any mobile being is called "God" in this sense, its motion is eternal; just as, if some immobile substance is called "God," its operation is eternal without motion. If this were not so, then such a thing, eternal in existence but lacking an eternal operation (since things exist in order to act) would exist without a purpose. |
| Quia ergo caelum est tale quod secundum antiquos Deus dicebatur, non quia sit ipse summus Deus, sed quia corpus eius est quoddam divinum, propter hoc quod est ingenitum et incorruptibile, ut supra ostensum est; inde est quod habet corpus circulare, ad hoc quod possit semper et circulariter moveri. Ostensum est enim in VIII Physic. quod solus motus circularis potest esse perpetuus: nam super lineam rectam infinitam nullus est motus, ut etiam in primo probatum est; super lineam autem rectam finitam non potest esse motus infinitus nisi per reflexionem, quae quidem non potest esse sine interpolatione quietis, ut probatur in VIII Physic. | Therefore, since the heaven is such as to have been called "God" by the ancients, not indeed because it is the supreme God, but because its body is something divine by virtue of being ungenerated and indestructible, as was previously explained; consequently it possesses a circular body in order that it may be moved forever and in a circular way. For it has been shown in Physics VIII that only circular motion can be eternal, since there is no motion over an infinite straight line, as was also proved in Book I, and motion over a finite straight line cannot be infinite except by reflexion, which involves interposing states of rest, as was proved in Physics VIII. |
| Et est attendendum quod Aristoteles hic probat sempiternitatem motus caeli ex sempiternitate corporis eius; qua via non fuit usus in VIII Physic., quia nondum probaverat sempiternitatem caeli. Sed quia ad motum caeli se habet ipsum corpus caeleste ut materia et subiectum, primum autem movens, scilicet Deus, sicut agens quod facit ipsum esse in actu; ex parte caeli probari potest quod sit potens semper moveri, ex parte autem voluntatis divinae dependet quod moveatur in actu vel semper vel non semper. | It should be noted that Aristotle here proves the eternity of the motion of the heaven from the eternity of its body; but in Physics VIII he did not use this way, because he had not yet proved the eternity of the heaven. But because the heavenly body is related to the motion of the heaven as its matter and subject, whereas the first mover, namely, God, is the agent making it actually exist, then from the side of the heaven it can be preyed able to be moved forever, but on the part of the divine will depends whether it is to be actually moved forever or not forever. |
| Deinde cum dicit: propter quid igitur etc., ostendit secundam conditionalem, scilicet quod si caelum movetur sempiterno et circulari motu, quod necesse sit esse terram. Dicit ergo: si ita est quod caelum est corpus divinum sempiterne et circulariter motum, propter quid ergo non est tale corpus totius caeli, idest totius mundi, ut scilicet quaelibet pars mundi esset de natura caelestis corporis? Et ad hoc respondet quod necesse est esse aliquid manens et quietum in medio corporis quod circulariter fertur: manifestum est enim quod omnis motus circularis est circa aliquod medium quiescens. Et hoc oportet esse aliquod corpus: nam hoc quod dico medium, non est aliquid subsistens, sed accidens alicui rei corporeae, si sit medium corporis. Non est autem possibile quod tale aliquid sit aliqua pars huius, idest aliqua pars caelestis corporis, quod supra dixerat corpus divinum, licet oporteat quod sit pars totius mundi. | 335. Then at [251] he proves the second conditional, namely, that if the heaven is moved with an eternal and circular motion, earth must exist. He says, therefore: If it is true that the heaven is a divine body which is eternally and circularly moved, why then does not the entire heaven, i.e., the entire world, have such a body, i.e., why does not each part of the world have the nature of heavenly body? To this he answers that there has to be something permanent and at rest in the middle [center] of the body which is in circular motion — for it is plain that every circular motion goes around something at rest. And this something must be a body: for the thing I am calling the middle [center] is not something subsistent, but an accident of a bodily thing, if it is the center of a body. Now such a thing cannot be a part of this, i.e., of the heavenly body, which has already been described as divine, although it must be a part of the whole world. |
| Et hoc probat dupliciter. Primo quia nulla pars caelestis corporis universaliter potest quiescere ubicumque, cum corpori caelesti conveniat sempiternus motus, ut ostensum est: medium autem circa quod est motus circularis, oportet esse quietum. Secundo quia specialiter non potest esse quod quiescat in medio. Quia si secundum naturam in medio quiesceret, naturaliter moveretur ad medium (unumquodque enim naturaliter movetur ad locum in quo quiescit, ut in primo habitum est): nulla autem pars corporis caeli naturaliter movetur ad medium, quia naturalis eius motus est quod moveatur circulariter, et, sicut in primo habitum est, unius simplicis corporis non possunt esse duo motus naturales. Unde relinquitur quod quies partis illius caelestis corporis in medio esset ei contra naturam. | This he proves in two ways. First, because no part of a heavenly body generally can be at rest everywhere, since to the heavenly body belongs eternal motion, as was shown. But the center about which there is circular motion must be stationary. Secondly, because taken specifically it cannot rest in the center. For if it rested there naturally, it would be naturally moved to the center (for each thing is naturally moved to the place in which it rests naturally, as was explained in Book I). But no part of the heavenly body is naturally moved to the center, because its natural motion is for it to be moved circularly, and, as was explained in Book I, no simple body can possess two natural motions. Hence it remains that the rest of a part of the heavenly body in the center would be against its nature. |
| Et ex hoc sequitur quod motus caeli non possit esse sempiternus: quia non potest esse nisi sit aliquid quietum in medio, et si quies eius quod est in medio esset violenta, sequeretur quod non posset esse sempiterna; et per consequens nec motus eius sempiternus. Nihil enim quod est praeter naturam, est sempiternum: quia illud quod est praeter naturam, est posterius eo quod est secundum naturam: quod quidem patet ex hoc quod in generatione cuiuslibet rei, id quod est praeter naturam est excessus quidam, idest corruptio et defectus, eius quod est secundum naturam (sicut videmus quod monstra sunt quaedam corruptiones et defectus rei naturalis); corruptio autem et defectus est naturaliter posterior, sicut privatio quam habitus. Non autem est possibile id quod est naturaliter prius, nunquam esse, et id quod est naturaliter posterius, esse semper. Unde patet quod non est possibile id quod est violentum esse sempiternum. Id autem quod in medio quiescit, sempiterne quiescit, sicut et caelum sempiterne movetur. Relinquitur ergo quod oporteat esse aliquid quod naturaliter quiescat in medio, si motus caeli est circularis et sempiternus. Hoc autem quod naturaliter quiescit in medio, est terra, ut infra ostendetur. Ergo, si caelum movetur circulariter et sempiterne, necesse est terram esse, quod fuit propositum. | From this it follows that the motion of the heaven could not be eternal: because it cannot take place unless there is something at rest in the center, and if the state of rest of that of it which was in the center were violent, it would follow that it [the rest] could not be eternal, and consequently neither could the heaven's motion be eternal. For nothing contrary to nature is eternal — since what is contrary to nature is subsequent to what is according to nature. This is plain from the fact that in the generation of anything, whatever is outside nature is a kind of "excess," i.e., a corruption and defect of that which is according to nature (for example, monstrosities are certain corruptions and defects of a natural thing). But corruptions and defect are naturally posterior, just as privation is subsequent to possession. Now it is not possible that something naturally prior should never exist, and that what is naturally apt to be later, should always exist. Consequently, it is plain that what is violent cannot be eternal. But that which is at rest in the center, is eternally at rest, just as the heaven is eternally in motion. What is left, therefore, is that there must be something naturally at rest in the center, if the motion of the heaven is circular and eternal. But it is the earth that is naturally at rest in the center, as will be proved later. Therefore, if the heaven is moved circularly and eternally, then earth must exist. And this is what was proposed to be proved. |
| Deinde cum dicit: sed adhuc si terram etc., ostendit tertiam conditionalem, scilicet quod si est terra, quod sit ignis. | 336. Then at [252] he proves the third conditional, namely, if there is earth, there is fire. |
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Et primo proponit quod intendit, dicens quod adhuc, si necesse est terram esse, necesse est et ignem esse. Secundo ibi: contrariorum enim etc., probat hoc duabus rationibus. |
First he proposes what he intends, and says that it is also true that if earth must exist, then fire must exist. Secondly, he proves this with two arguments. |
| Quarum prima talis est. Si unum contrariorum est in natura, necesse est etiam quod alterum sit in natura. Et hoc quidem probat sic: quia si sit aliquod contrariorum, necesse est quod sit aliqua natura ei subiecta, ut patet ex I Physic.; est autem eadem materia contrariorum, ut ibidem ostenditur, et sic oportet quod materia unius contrarii habeat potentiam ad aliud contrarium; quae quidem potentia esset frustra, si illud contrarium non posset esse in natura. Unde, cum nihil sit frustra in natura, necesse est quod si unum contrariorum est, quod et reliquum sit. Ignis autem et terra sunt contraria: quia maxime distant secundum contrarietatem situs, de qua nunc loquimur, inquantum unum est gravissimum et aliud levissimum (quantum autem ad alias qualitates, ignis maxime contrariatur aquae, sicut calidissimum frigidissimo: sed nunc loquitur de istis corporibus secundum eorum situm; sic enim sunt partes totius universi). Relinquitur ergo quod si est terra, necesse est etiam ignem esse. | The first is this. If one contrary exists in nature, the other also must exist in nature. He proves this as follows: If there be any contrary, there must be a matter subject to it, as is plain from Physics I; but the matter of contraries is the same, as is shown in the same place. Consequently, the matter of one contrary must be in potency to the other. Now this potency would be in vain if that other contrary could not exist in nature. But since nothing is in vain in nature, then, if one contrary exists, so must the other. Now fire and earth are contraries, for they are the maximum distance apart, so far as contrariety of position is concerned, inasmuch as one is the heaviest of all things and the other the lightest (although in respect of other qualities, fire is especially contrary to water, as the hottest to the coldest — however, we are now speaking of bodies from the viewpoint of position, from which aspect they are parts of the whole universe). Consequently, if there is earth, there must also be fire. |
| Secundam rationem ponit ibi: et privatione et cetera. Circa quam considerandum est quod semper contraria se habent secundum peius et melius, ut dicitur in I Physic.; ita scilicet quod unum est privatio et defectus respectu alterius, sicut frigidum respectu calidi, et nigrum respectu albi. Manifestum est autem quod affirmatio, idest omne quod positive dicitur ut aliquid completum, est prius eo quod dicitur per privationem et defectum, sicut calidum est prius frigido. Quies autem et gravitas, quae attribuuntur terrae, dicuntur per privationem levitatis et motus, quae attribuuntur igni: ergo ignis naturaliter est prior terra. Posito autem posteriori, ponitur prius. Ergo necesse est quod si est terra, quod sit ignis. | 337. The second argument is at [254]. With respect to it, it should be considered that contraries are always related according to "worse" and "better," as is said in Physics I, in such a way, namely, that one of them is a privation and a defect in comparison to the other, as are, for example, cold in relation to hot, and black in relation to white. Now it is evident that "affirmation," i.e., whatever is said positively as something complete, is prior to what is described in terms of privation and defect, as hot is prior to cold. But rest and heaviness, which are attributed to earth, are stated in terms of the privation of lightness and of motion, which are attributed to fire. Therefore, fire is naturally prior to earth. For if the subsequent is posited, so must be the prior. Consequently, if earth exists, fire too must exist. |
| Et est considerandum quod Plato in Timaeo probavit esse terram et ignem, per hoc quod necesse est corpora esse visibilia propter ignem, et palpabilia propter terram. | One should also note that Plato in the Timaeus proved that earth and fire exist on the ground that bodies have to be visible by virtue of fire and palpable by virtue of earth. |
| Deinde cum dicit: sed adhuc si quidem etc., ponit quartam conditionalem, scilicet quod si est ignis et terra, quod sint media elementa. Quia unumquodque elementorum habet aliqualiter contrarietatem ad unumquodque aliorum trium; sicut terra contrariatur igni secundum contrarietatem gravis et levis, et calidi et frigidi, aeri autem secundum contrarietatem calidi et frigidi, humidi et sicci: et hoc quidem dicit esse inferius manifestandum, praecipue in II de generatione. Unde relinquitur, si sunt duo elementa, quod necesse est esse alia duo, ex hoc quod probatum est quod si necesse est esse unum contrariorum, necesse est esse alterum. | 338. Then at [255] he proves the fourth conditional, namely, that if fire and earth exist, so do the intermediate elements. For each of the elements is in some respect contrary to each of the other three, as earth is contrary to fire on the basis of heavy and light and cold and hot, and is contrary to air according to a contrariety of hot and cold as well as of wet and dry. And he says that this is to be made clear below, especially in On Generation II. Hence it remains that if two of the elements exist, the other two must also exist, it having been proved that if one contrary exists, the other must. |
| Plato autem probavit ex extremis elementis quod necesse est esse media, per proportiones numerales: quia inter duos cubicos numeros necesse est esse duos alios numeros secundum continuam proportionalitatem; sicut cubicus binarii est octonarius, cubicus autem ternarii sunt viginti septem, inter quos cadunt media in proportione duodeviginti et duodecim, quae omnia se habent secundum sesquialteram proportionem. | Plato, however, used proportional numbers to prove that if there are extreme elements there must be intermediate elements. For between two numbers that are cubes there must be two other numbers according to a continuous proportion: for example, the cube of 2 is 8 and the cube of 3 is 27 and between these cubes the numbers 18 and 12 fall as proportional means, so that all can be arranged to form a ratio of 3 to 2. |
| Deinde cum dicit: his autem existentibus etc., probat quintam conditionalem, scilicet quod si sint huiusmodi corpora, necesse est esse generationem et corruptionem. Quod quidem probat duplici ratione. Quarum prima est quia contraria agunt et patiuntur ab invicem, et se invicem corrumpunt, ut probabitur in libro de generatione; sed praedicta corpora sunt contraria ad invicem, ut dictum est; ergo se invicem corrumpunt. Et ita necesse est esse generationem et corruptionem. | 339. Then at [256] he proves the fifth conditional, namely, that if such bodies exist, there must be generation and corruption. This he proves with two arguments. The first of these is that contraries act upon one another and are acted upon by one another, and corrupt each other, as will be proved in the book On Generation. But the aforesaid bodies are contrary to one another, as has been said. Therefore they mutually corrupt one another. Consequently, generation and corruption must exist. |
| Secundam rationem ponit ibi: adhuc autem etc.: quae talis est. Non est rationabile quod sit aliquod corpus sempiternum, cuius motus non potest esse sempiternus: quia motus est operatio corporis mobilis, et omnis res est propter suam operationem, ut dictum est. Sed praedicta corpora, scilicet elementa, habent motus rectos, qui non possunt esse sempiterni, ut in VIII Physic. probatur. Ergo ipsa non possunt esse sempiterna, sed necesse est quod sint generabilia et corruptibilia. Et ita necesse est quod generatio et corruptio fiat. | 340. The second argument is at [257] and is as follows: It is unreasonable to assume that there exists an eternal body whose motion cannot be eternal, because motion is the operation of a mobile body and each thing is for the sake of its operation, as has been said. But the above-mentioned bodies, namely, the elements, have straight motions which cannot be eternal, as was proved in Physics VIII. Therefore they can not be eternal but have to be generable and corruptible. Consequently, it is necessary that generation and corruption exist. |
| Deinde cum dicit: si autem etc., probat sextam conditionalem, scilicet quod si sit generatio, quod necesse est esse alium motum circularem praeter primum, aut unum aut plures. Quia, cum primus motus circularis, qui est supremae sphaerae revolventis totum caelum ab oriente in occidentem, sit uniformis, non causaret diversam dispositionem in corporibus inferioribus; et ita elementa corporum et alia corpora similiter se haberent ad invicem; unde non esset generatio et corruptio. Et hoc manifestabitur magis in sequentibus, scilicet in II de generatione. Unde necesse est esse alium motum, qui est per obliquum circulum, qui proprie causet generationem et corruptionem per elongationem et appropinquationem planetarum ad nos, sicut primus motus causat permanentiam et sempiternitatem in rebus. | 341. Then at [258] he proves the sixth conditional, namely, that, if there is generation, there has to be besides the first circular motion some other circular motion, either one or several. For since the first circular motion (which is that of the supreme sphere revolving the whole heaven from east to west) is uniform, it would not cause a diversity of dispositions in lower bodies. Consequently, the elements of bodies and other bodies would always retain the same disposition toward each other and there would be no generation and corruption. This will be explained more in detail later, namely, in On Generation II. Hence there must exist another motion, through the oblique [i.e., zodiacal] circle, to act as the proper cause of generation and corruption through the distance of the planets from us or their nearness to us, just as the first motion causes permanence and eternity in things. |
| Quaerit autem Alexander, si cessante motu caeli elementa contraria remanerent, utrum se invicem corrumperent. Et dicit quod sic, propter contrarietatem ipsorum: non tanquam esset generatio et corruptio ordinata secundum quandam reciprocationem, ut scilicet nunc ex calidis generarentur frigida, nunc e converso; sed contingeret, sicut Heraclitus posuit, quod quandoque omnia fierent ignis; nam ordinatio reciprocae conversionis invicem est etiam per virtutem caeli. | 342. Here Alexander asks if, supposing the motion of the heaven to cease, but the contrary elements to remain, they would corrupt one another? And, on the ground of their contrariety, he answers affirmatively; but not as though there would be reciprocal generation and corruption as now occurs when cold things are generated from hot and vice versa. That would happen would be what was posited by Heraclitus who said that at some time everything would become fire. For the present orderly mutual interplay of generation and corruption is traceable to the virtue of the heavens. |
| Sed melius est dicere quod, cessante motu caeli, omnis motus corporum inferiorum cessaret, ut Simplicius dicit: quia virtutes inferiorum corporum sunt sicut materiales et instrumentales respectu caelestium virtutum, ita quod non movent nisi motae. | But it is better to say that if the motion of the heavens were to cease, so too would the motion of all lower bodies, as Simplicius said. For the powers of the lower bodies are as matter and instruments in relation to the heavenly powers, and hence do not move unless moved. |
| Deinde cum dicit: nunc autem tantum manifestum est etc., recolligit eandem rationem ordine resolutorio. Et dicit quod hoc nunc manifestum est, propter quam causam oportet esse plura corpora circulariter mota: quia scilicet necesse est esse generationem; generationem autem necesse est esse, si est ignis et alia corpora; ignem autem et alia huiusmodi corpora necesse est esse, si sit terra; quam quidem necesse est esse, quia necesse est esse aliquid sempiterne quiescens in medio, si est aliquid circulariter motum. | 343. Then at [259] he summarizes the same argument in the resolutary [i.e., analytic] order. And he says that the reason why there must be several circularly moved bodies is now plain, namely, because there must be generation. But generation must exist, if fire and other bodies exist; these must exist" if earth exists; earth must exist, because there has to be something eternally at rest in the center, if something undergoing circular motion exists. |
Lecture 5:
Spherical shape of the heaven shown from fact that it is the first of figuresChapter 4 Σχῆμα δ' ἀνάγκη σφαιροειδὲς ἔχειν τὸν οὐρανόν τοῦτο γὰρ οἰκειότατόν τε τῇ οὐσίᾳ καὶ τῇ φύσει πρῶτον. 260 The shape of the heaven is of necessity spherical; for that is the shape most appropriate to its substance and also by nature primary. Εἴπωμεν δὲ καθόλου περὶ τῶν σχημάτων, τὸ ποῖόν ἐστι πρῶτον, καὶ ἐν ἐπιπέδοις καὶ ἐν στερεοῖς. 261 First, let us consider generally which shape is primary among planes and solids alike. Ἅπαν δὴ σχῆμα ἐπίπεδον ἢ εὐθύγραμμόν ἐστιν ἢ περιφερόγραμμον. Καὶ τὸ μὲν εὐθύγραμμον ὑπὸ πλειόνων περιέχεται γραμμῶν, τὸ δὲ περιφερόγραμμον ὑπὸ μιᾶς. Ἐπεὶ δὲ πρότερον [τῇ φύσει] ἐν ἑκάστῳ γένει τὸ ἓν τῶν πολλῶν καὶ τὸ ἁπλοῦν τῶν συνθέτων, πρῶτον ἂν εἴη τῶν ἐπιπέδων σχημάτων ὁ κύκλος. 262 Every plane figure must be either rectilinear or curvilinear. Now the rectilinear is bounded by more than one line, the curvilinear by one only. But since in any kind the one is naturally prior to the many and the simple to the complex, the circle will be the first of plane figures. Ἔτι δὲ εἴπερ τέλειόν ἐστιν οὗ μηδὲν ἔξω τῶν αὐτοῦ λαβεῖν δυνατόν, ὥσπερ ὥρισται πρότερον, καὶ τῇ μὲν εὐθείᾳ πρόσθεσίς ἐστιν ἀεί, τῇ δὲ τοῦ κύκλου οὐδέποτε, φανερὸν ὅτι τέλειος ἂν εἴη ἡ περιέχουσα τὸν κύκλον ὥστ' εἰ τὸ τέλειον πρότερον τοῦ ἀτελοῦς, καὶ διὰ ταῦτα πρότερον ἂν εἴη τῶν σχημάτων ὁ κύκλος. 263 Again, if by complete, as previously defined, we mean a thing outside which no part of itself can be found, and if addition is always possible to the straight line but never to the circular, clearly the line which embraces the circle is complete. If then the complete is prior to the incomplete, it follows on this ground also that the circle is primary among figures. Ὡσαύτως δὲ καὶ ἡ σφαῖρα τῶν στερεῶν μόνη γὰρ περιέχεται μιᾷ ἐπιφανείᾳ, τὰ δ' εὐθύγραμμα πλείοσιν ὡς γὰρ ἔχει ὁ κύκλος ἐν τοῖς ἐπιπέδοις, οὕτως ἡ σφαῖρα ἐν τοῖς στερεοῖς. 264 And the sphere holds the same position among solids. For it alone is embraced by a single surface, while rectilinear solids have several. The sphere is among solids what the circle is among plane figures. Ἔτι δὲ καὶ οἱ διαιροῦντες εἰς ἐπίπεδα καὶ ἐξ ἐπιπέδων τὰ σώματα γεννῶντες μεμαρτυρηκέναι φαίνονται τούτοις μόνην γὰρ τῶν στερεῶν οὐ διαιροῦσι τὴν σφαῖραν ὡς οὐκ ἔχουσαν πλείους ἐπιφανείας ἢ μίαν ἡ γὰρ εἰς τὰ ἐπίπεδα διαίρεσις οὐχ ὡς ἂν τέμνων τις εἰς τὰ μέρη διέλοι τὸ ὅλον, τοῦτον διαιρεῖται τὸν τρόπον, ἀλλ' ὡς εἰς ἕτερα τῷ εἴδει. Ὅτι μὲν οὖν πρῶτόν ἐστιν ἡ σφαῖρα τῶν στερεῶν σχημάτων, δῆλον. 265 Further, those who divide bodies into planes and generate them out of planes seem to bear witness to the truth of this. Alone among solids they leave the sphere undivided, as not possessing more than one surface: for the division into surfaces is not just dividing a whole by cutting it into its parts, but division of another fashion into parts different in form. It is clear, then, that the sphere is first of solid figures. Ἔστι δὲ καὶ κατὰ τὸν ἀριθμὸν τὴν τάξιν ἀποδιδοῦσιν οὕτω τιθεμένοις εὐλογώτατον, τὸν μὲν κύκλον κατὰ τὸ ἕν, τὸ δὲ τρίγωνον (287a.) κατὰ τὴν δυάδα, ἐπειδὴ ὀρθαὶ δύο. Ἐὰν δὲ τὸ ἓν κατὰ τὸ τρίγωνον, ὁ κύκλος οὐκέτι ἔσται σχῆμα. 266 If, again, one orders figures according to their numbers, it is most natural to arrange them in this way. The circle corresponds to the number one, the triangle, being the sum of two right angles, to the number two. But if one is assigned to the triangle, the circle will not be a figure at all. Ἐπεὶ δὲ τὸ μὲν πρῶτον σχῆμα τοῦ πρώτου σώματος, πρῶτον δὲ σῶμα τὸ ἐν τῇ ἐσχάτῃ περιφορᾷ, σφαιροειδὲς ἂν εἴη τὸ τὴν κύκλῳ περιφερόμενον φοράν. Καὶ τὸ συνεχὲς ἄρα ἐκείνῳ τὸ γὰρ τῷ σφαιροειδεῖ συνεχὲς σφαιροειδές. 267 Now the first figure belongs to the first body, and the first body is that at the farthest circumference. It follows that the body which revolves with a circular movement must be spherical. Ὡσαύτως δὲ καὶ τὰ πρὸς τὸ μέσον τούτων τὰ γὰρ ὑπὸ τοῦ σφαιροειδοῦς περιεχόμενα καὶ ἁπτόμενα ὅλα σφαιροειδῆ ἀνάγκη εἶναι τὰ δὲ κάτω τῆς τῶν πλανήτων ἅπτεται τῆς ἐπάνω σφαίρας. Ὥστε σφαιροειδὴς ἂν εἴη πᾶσα πάντα γὰρ ἅπτεται καὶ συνεχῆ ἐστι ταῖς σφαίραις. 268 The same then will be true of the body continuous with it: for that which is continuous with the spherical is spherical. The same again holds of the bodies between these and the centre. Bodies which are bounded by the spherical and in contact with it must be, as wholes, spherical; and the bodies below the sphere of the planets are contiguous with the sphere above them. The sphere then will be spherical throughout; for every body within it is contiguous and continuous with spheres.
| Postquam philosophus determinavit de perpetuitate caeli et diversitate partium eius, hic determinat de figura ipsius. | 344. Having discussed the eternity of the heaven and the diversity of its parts, the Philosopher here determines the question of the figure of the heaven. |
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Et primo ostendit caelum esse sphaericae figurae; secundo ostendit quod haec figura perfecte in ipso existit, ibi: quod quidem igitur sphaericus est et cetera. |
First he shows that the heaven is spherical in shape; Secondly, that this shape exists in it perfectly (L. 6). |
| Circa primum duo facit: | Concerning the first he does two things: |
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primo ostendit caelum esse sphaericae figurae, rationibus sumptis ex parte ipsius caeli; secundo ratione sumpta ex parte inferiorum corporum, ibi: sumet autem utique quis et cetera. |
First he proves with arguments based on the heaven itself that it is spherical in shape; Secondly, with an argument based on the lower bodies (L. 6). |
| Circa primum duo facit. | About the first he does two things: |
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Primo proponit quod intendit: et dicit quod necesse est caelum habere sphaericam figuram, tum quia ista figura est maxime propria, idest conveniens, corpori caelesti; tum etiam quia est prima figurarum, et naturaliter, sicut perfectum est prius imperfecto, et substantia, idest secundum rationem, sicut unum est prius multis. Secundo ibi: dicamus autem universaliter etc., probat propositum. |
First he proposes what he intends [260] and says that the heaven has to be spherical in shape both because such a shape is most "proper," i.e., appropriate, to the heavenly body, and because it is the first of all figures not only "by nature," as the perfect is naturally prior to the imperfect, but "by substance," i.e., according to its notion, as one is prior to many. Secondly, he proves his proposition. |
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Et primo ostendit caelum esse sphaericae figurae, ex hoc quod haec figura est prima figurarum; secundo ex hoc quod est convenientissima caelo, ibi: adhuc autem quoniam videtur et cetera. |
First he shows that the heaven is spherical in shape because this figure is the first of figures; Secondly, because it is most appropriate to the heaven (L. 6). |
| Circa primum duo facit: | Regarding the first he does two things: |
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primo ostendit quod supremum caelum est sphaericae figurae; secundo ostendit quod etiam alia caelestia corpora inferiora sunt sphaericae figurae, ibi: et continuum igitur illi et cetera. |
First he shows that the supreme heaven has a spherical shape; Secondly, that the other heavenly bodies also are spherical in shape, at 352. |
| Circa primum ponit talem rationem. Prima figura debetur corpori primo; sed inter figuras corporales sphaerica figura est prima; ergo caelum, quod est corpus primum, est sphaericae figurae. | 345. With respect to the first he gives the following argument: The first figure should belong to the first body. But among bodily figures, the spherical is first. Therefore the heaven which is the first body is spherical in shape. |
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Huius autem rationis primo probat minorem; secundo, posita maiori, infert conclusionem, ibi: quoniam autem prima quidem et cetera. |
In regard to this argument he first proves the minor premis;
Secondly, the major having been laid down, he draws the conclusion, at 351. |
| Circa primum duo facit: | As to the first he does two things: |
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primo probat figuram sphaericam esse primam corporalium figurarum, per rationes; secundo per opiniones aliorum, ibi: adhuc autem dividentes et cetera. |
First he proves with arguments that the spherical shape is the first of all bodily shapes; Secondly, by appealing to the opinions of others, at 349. |
| Circa primum duo facit. Primo proponit quod intendit: et dicit quod universaliter est dicendum de figuris quae sit prima earum, tam in figuris planis, idest in superficialibus, quam in solidis, idest in corporalibus figuris. Dicitur autem superficialis figura, qua figuratur superficies; corporalis autem figura, qua figuratur corpus. | Regarding the first he does two things: First he proposes what he intends [261] and says that we must determine universally which is the first of all figures both in the realm of plane figures, i.e., surfaces, and in the realm of solid, i.e., bodily, figures. A plane figure is the shape of a plane and a bodily figure is the shape of a body. |
| Secundo ibi: omnis itaque etc., probat propositum: |
346. Secondly, he proves his proposition.
|
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et primo quantum ad figuras superficiales; secundo quantum ad corporales, ibi: similiter autem et sphaera et cetera. |
First with respect to plane figures;
Secondly, with respect to bodily figures, at 348. |
| Circa primum ponit duas rationes: quarum prima talis est. Omnis figura plana, idest superficialis, aut est rectilinea, sicut triangulus et quadratum, aut est circularis, sicut ipse circulus. Omnis autem rectilinea figura continetur a pluribus lineis et non ab una sola (una enim sola linea recta non porrigitur nisi ad unam partem, de ratione autem figurae est quod sit terminata ex omni parte): sed circularis figura comprehenditur ab una sola linea, quae undique porrigitur. In unoquoque autem genere unum est prius multitudine, et simplex est prius compositis. Unde relinquitur quod inter superficiales figuras circularis est prima. | With respect to the first he gives two arguments, the first of which [262] is this: Every plane figure is either rectilinear, as in the case of a triangle or square, or it is curved, as in the case of a circle. But every rectilinear figure is enclosed by a plurality of lines and not by just one (for a single straight line can be extended only in one direction, whereas the nature of a plane figure is that it be entirely closed in every direction). On the other hand, a circular figure is enclosed by but one single line extended in all directions. Now, in every genus, unity is prior to multiplicity, and simplicity to composition. Hence it remains that in the realm of plane figures, the circular is first. |
| Secundam rationem ponit ibi: adhuc autem si quidem et cetera. Perfectum dicitur esse illud extra quod nihil est accipere eorum quae possunt ipsi convenire, sicut homo dicitur esse perfectus cui non deest aliquid eorum quae ad hominem pertinent: et hoc determinatum est prius, tam in III Physic. quam in principio huius libri. Videmus autem quod rectae lineae semper potest fieri appositio quantum est ex natura ipsius lineae, licet forte ex aliqua alia causa non posset ei aliquid aliud apponi, sicut diametro totius mundi. Et hoc manifestum est si linea recta sit finita: unde omnis linea recta finita est imperfecta. De infinita autem manifestum est quod sit imperfecta: caret enim fine, quem nata est habere. Lineae vero circulari non potest fieri additio, quia finis eius coniungitur principio: unde manifestum est quod linea continens circulum est perfecta. | 347. The second argument is given at [263], namely, that the perfect is by definition that outside of which there exists nothing that could befit it; for example, a man is said to be perfect, if he lacks nothing that pertains to man. And this has been settled previously both in Physics III and in the beginning of this book. Now, we observe that, so far as the nature of a straight line is concerned, addition can always be made to it — although for some other reason it might be impossible to do so, as, for example, to add anything to the diameter of the world. And this is plain if the straight line is finite. Accordingly, every finite straight line is imperfect. But it is plain that an infinite line, too, is imperfect, for it lacks an end, which it should have. On the other hand, no addition can be made to a circular line, because its end meets its beginning. Consequently, the line encompassing a circular body is perfect. |
| Perfectum autem est prius imperfecto: simpliciter quidem natura et tempore; in uno autem et eodem perfectum prius est natura, sed imperfectum est prius tempore, sicut aliquis homo prius tempore est puer quam vir perfectus; tamen vir perfectus est prius natura, quia hoc est quod natura intendit; simpliciter autem etiam tempore perfectum est prius, nam puer ab aliquo viro generatur. Sic igitur patet quod propter hanc rationem etiam circulus est prima superficialium figurarum. | Now the perfect is prior to the imperfect, absolutely speaking, both by nature and in point of time. But in one and the same thing, the perfect is prior by nature but the imperfect is prior in point of time — for example, a man in point of time is a boy prior to being a perfect man; yet the perfect man is prior by nature, because this is what nature intends. Absolutely speaking, even in point of time the perfect is prior to the imperfect, because a boy is generated by some man. From this it is plain that the circle, too, is the first among plane figures. |
| Deinde cum dicit: similiter autem et sphaera etc., ostendit quae sit prima figurarum corporalium. Et dicit quod similiter sphaera est prima inter figuras solidas, idest corporeas: quia sola sphaerica figura continetur una sola superficie, quae undique ambit corpus sphaericum; figurae autem rectilineae corporales continentur pluribus superficiebus, sicut corpus cubicum sex superficiebus, et pyramis triangularis quatuor: sicut enim se habet circulus in superficiebus, ita se habet sphaera in solidis, idest in corporibus. | 348. Then at [264] he shows which is the first shape among bodily figures. And he says that in like manner the sphere is the first among solid, i.e., bodily, figures, since the spherical figure alone is bounded by just one surface which everywhere surrounds the spherical body. Rectilinear bodily figures, on the other hand, are bounded by several planes — as a cubic body by six, and a triangular pyramid by four. Therefore, as the circle is to planes, so the sphere is to solids, i.e., bodies. |
| Deinde cum dicit: adhuc autem dividentes etc., ostendit propositum per opiniones aliorum. Et ponit duas opiniones. Quarum prima est eorum qui resolvunt corpora in superficies, et ex superficiebus generant corpora. Quia solam sphaericam figuram inter figuras solidas non resolvunt in plures superficies, eo quod continetur una sola superficie: alias vero figuras resolvunt in plures superficies, sicut pyramidem in quatuor superficies triangulares. Talis autem divisio corporum in superficies non est per illum modum quo corpus aliquod dividitur in suas partes corporeas; sic enim et sphaera dividitur in suas partes: sed haec est divisio quasi in ea quae differunt specie ab eo quod dividitur. Sic igitur concludit planum esse quod sphaera sit prima solidarum figurarum. | 349. Then at [265] he shows his proposition by appealing to the opinions of others. And he gives two such opinions. The first is held by those who resolve bodies into surfaces, and produce bodies from surfaces. For the only body that does not resolve into a number of surfaces is the sphere, because it is bounded by just one surface, while other figures are resolved into many surfaces, as, for example, a pyramid is into four triangular surfaces. However, such a division of bodies into surfaces is not according to the manner by which a body is divided into its bodily parts; for a sphere also is thus divided into its parts. But the division under discussion is one that, so to speak, separates into things that are different in kind from the whole that is divided. He concludes, therefore, that it is clear that the sphere is the first among solid figures. |
| Secundam opinionem ponit ibi: est autem et secundum numerum et cetera. Et dicit quod quidam assignaverunt ordinem figurarum secundum species numerorum, adaptando figuras numeris. Et secundum hoc dicit rationabilissimum esse quod circulus adaptetur unitati, propter hoc quod est prima et simplicissima figurarum; triangulus autem adaptetur dualitati, propter hoc quod anguli trianguli adaequantur duobus rectis. Si autem acciperetur unitas secundum triangulum, sequeretur quod circulus, qui est naturaliter prior triangulo, esset extra genus figurae, si triangulus esset prima figurarum. | 350. The second opinion is given at [266]. And he says that some have assigned the order of figures according to the species of numbers, by adapting the figures to numbers. And he says that, according to this, it is most reasonable for the circle to be adapted to unity, on the ground that it is the first and simplest of shapes; but that triangle be adapted to 2, because its angles equal two right angles. Now, if unity were aligned with triangle, it would follow that the circle, which is naturally prior to the triangle, would be outside the genus of figures, supposing triangle to be the first of shapes. |
| Deinde cum dicit: quoniam autem prima quidem etc., probata minori, syllogizat ad propositum. Et dicit quod, quia prima figura debetur primo corpori, cum primum corpus sit id quod est in extrema circumferentia totius mundi, consequens est quod tale corpus, quod circulariter fertur, etiam ipsum in seipso sit sphaericum. | 351. Then at [267], having proved the minor premis, he syllogises to his proposition. And he says that, since the first figure is due to the first body, and the first body is that which is on the outer periphery of the whole world, it follows that such a body, which is moved circularly, will in itself be spherical. |
| Deinde cum dicit: et continuum igitur illi etc., ostendit quod etiam inferiora caelestia corpora sunt sphaerica. Et dicit quod ex quo primum corpus est sphaericum, consequens est quod et corpus consequens continuum illi, idest immediate coniunctum ad ipsum, sit sphaericum: illud enim corpus quod est continuum, idest immediate coniunctum, sphaerico, oportet quod etiam sit sphaericum. Et hoc est verum si corpus primum sit sphaericum non solum secundum suum convexum, sed etiam secundum suum concavum: cum enim eadem natura sit primi corporis in concavo et convexo, oportet quod utrobique habeat eandem figuram. | 352. Then at [268] he shows that even the lower heavenly bodies are spherical. And he says that from the fact that the first body is spherical, it follows that the next body "continuous" to it, i.e., immediately joined to it, is spherical: for that body which is "continuous" to, i.e., immediately joined to, the spherical body, must itself be spherical. Now this is true if the first body is spherical not only on its convex, but also on its concave, side. Since the very same nature of first body is in both these sides, it must have the same figure on both sides. |
| Et eadem ratio est de corporibus aliis quae sunt in medio horum contenta ab istis, quod oportet ea sphaerica esse. Illa enim corpora quae continentur et continguntur a corpore sphaerico secundum suum convexum, necesse est esse sphaerica secundum suum convexum; et per consequens secundum concavum, si sunt unius naturae. Cum igitur sphaerae planetarum inferiorum contingant sphaeram superiorem, sequitur quod tota latio, idest totum corpus quod circulariter fertur, habeat sphaericam figuram: quia omnia illa corpora caelestium sphaerarum se invicem tangunt, et sunt continua, idest immediate sibi invicem coniuncta. Nec est aliquod corpus intermedium quod suppleat vacuitates sphaerarum, ut quidam ponunt: sequeretur enim illa corpora esse otiosa, cum non haberent motum circularem. | The same argument holds for the other bodies which are in the center of these and contained by them, namely, they too have to be spherical. For those bodies that are contained and touched by the body that is spherical according to its convex side must also be spherical on their convex side, and consequently spherical according to their concave side, if they are of one nature. Since, therefore, the spheres of the lower planets touch the higher sphere, it follows that the whole of "what is carried," i.e., the whole body which is circularly moved, has a spherical shape, for all those bodies of the heavenly spheres mutually touch and are "continuous," i.e., in immediate contact one with the other. And there is no intermediate body that fills up voids between spheres, as some say — for it would follow that those bodies would be idle, since they would not have a circular motion. |
Lecture 6:
The heavens must be spherical, because this shape is most fittingChapter 4 cont. Ἔτι δὲ ἐπεὶ φαίνεται καὶ ὑπόκειται κύκλῳ περιφέρεσθαι τὸ πᾶν, δέδεικται δ' ὅτι τῆς ἐσχάτης περιφορᾶς οὔτε κενόν ἐστιν ἔξωθεν οὔτε τόπος, ἀνάγκη καὶ διὰ ταῦτα σφαιροειδῆ εἶναι αὐτόν. Εἰ γὰρ ἔσται εὐθύγραμμος, συμβήσεται καὶ τόπον εἶναι ἔξω καὶ σῶμα καὶ κενόν. Κύκλῳ γὰρ στρεφόμενον τὸ εὐθέγραμμον οὐδέποτε τὴν αὐτὴν ἐφέξει χώραν, ἀλλ' ὅπου πρότερον ἦν σῶμα, νῦν οὐκ ἔσται, καὶ οὗ νῦν οὐκ ἔστι, πάλιν ἔσται, διὰ τὴν παράλλαξιν τῶν γωνιῶν. Ὁμοίως δὲ κἂν εἴ τι ἄλλο σχῆμα γένοιτο μὴ ἴσας ἔχον τὰς ἐκ τοῦ μέσου γραμμάς, οἷον φακοειδὲς ἢ ᾠοειδές ἐν ἅπασι γὰρ συμβήσεται καὶ τόπον ἔξω καὶ κενὸν εἶναι τῆς φορᾶς, διὰ τὸ μὴ τὴν αὐτὴν χώραν κατέχειν τὸ ὅλον. 269 Again, since the whole revolves, palpably and by assumption, in a circle, and since it has been shown that outside the farthest circumference there is neither void nor place, from these grounds also it will follow necessarily that the heaven is spherical. For if it is to be rectilinear in shape, it will follow that there is place and body and void without it. For a rectilinear figure as it revolves never continues in the same room, but where formerly was body, is now none, and where now is none, body will be in a moment because of the projection at the corners. Similarly, if the world had some other figure with unequal radii, if, for instance, it were lentiform, or oviform, in every case we should have to admit space and void outside the moving body, because the whole body would not always occupy the same room. Ἔτι δ' εἰ τῶν μὲν κινήσεων τὸ μέτρον ἡ τοῦ οὐρανοῦ φορὰ διὰ τὸ εἶναι μόνη συνεχὴς καὶ ὁμαλὴς καὶ ἀΐδιος, ἐν ἑκάστῳ δὲ μέτρον τὸ ἐλάχιστον, ἐλαχίστη δὲ κίνησις ἡ ταχίστη, δῆλον ὅτι ταχίστη ἂν εἴη πασῶν τῶν κινήσεων ἡ τοῦ οὐρανοῦ κίνησις. Ἀλλὰ μὴν τῶν ἀφ' αὑτοῦ ἐφ' αὑτὸ ἐλαχίστη ἐστὶν ἡ τοῦ κύκλου γραμμή κατὰ δὲ τὴν ἐλαχίστην ταχίστη ἡ κίνησις ὥστ' εἰ ὁ οὐρανὸς κύκλῳ τε φέρεται καὶ τάχιστα κινεῖται, σφαιροειδῆ αὐτὸν ἀνάγκη εἶναι. 270 Again, if the motion of the heaven is the measure of all movements whatever in virtue of being alone continuous and regular and eternal, and if, in each kind, the measure is the minimum, and the minimum movement is the swiftest, then, clearly, the movement of the heaven must be the swiftest of all movements. Now of lines which return upon themselves the line which bounds the circle is the shortest; and that movement is the swiftest which follows the shortest line. Therefore, if the heaven moves in a circle and moves more swiftly than anything else, it must necessarily be spherical. Λάβοι δ' ἄν τις καὶ ἐκ τῶν περὶ τὸ μέσον ἱδρυμένων σωμάτων ταύτην τὴν πίστιν. Εἰ γὰρ τὸ μὲν ὕδωρ ἐστὶ περὶ τὴν γῆν, ὁ δ' ἀὴρ περὶ τὸ ὕδωρ, τὸ δὲ πῦρ περὶ τὸν ἀέρα, καὶ τὰ ἄνω σώματα κατὰ τὸν αὐτὸν λόγον (συνεχῆ μὲν γὰρ οὐκ ἔστιν, ἅπτεται δὲ (287b.) τούτων), ἡ δὲ τοῦ ὕδατος ἐπιφάνεια σφαιροειδής ἐστιν, τὸ δὲ τῷ σφαιροειδεῖ συνεχὲς ἢ κείμενον περὶ τὸ σφαιροειδὲς καὶ αὐτὸ τοιοῦτον ἀναγκαῖον εἶναι ὥστε κἂν διὰ τοῦτο φανερὸν εἴη ὅτι σφαιροειδής ἐστιν ὁ οὐρανός. 271 Corroborative evidence may be drawn from the bodies whose position is about the centre. If earth is enclosed by water, water by air, air by fire, and these similarly by the upper bodies—which while not continuous are yet contiguous with them—and if the surface of water is spherical, and that which is continuous with or embraces the spherical must itself be spherical, then on these grounds also it is clear that the heavens are spherical. Ἀλλὰ μὴν ὅτι γε ἡ τοῦ ὕδατος ἐπιφάνεια τοιαύτη φανερόν, ὑπόθεσιν λαμβάνουσιν ὅτι πέφυκεν ἀεὶ συρρεῖν τὸ ὕδωρ εἰς τὸ κοιλότερον κοιλότερον δέ ἐστι τὸ τοῦ κέντρου ἐγγύτερον. Ἤχθωσαν οὖν ἐκ τοῦ κέντρου ἡ ΑΒ καὶ ἡ ΑΓ, καὶ ἐπεζεύχθω ἐφ' ἧς ΒΓ. Ἡ οὖν ἀχθεῖσα ἐπὶ τὴν βάσιν, ἐφ' ἧς ΑΔ, ἐλάττων ἐστὶ τῶν ἐκ τοῦ κέντρου κοιλότερος ἄρα ὁ τόπος. Ὥστε περιρρεύσεται τὸ ὕδωρ, ἕως ἂν ἰσασθῇ. Ἴση δὲ ταῖς ἐκ τοῦ κέντρου ἡ ΑΕ. Ὥστ' ἀνάγκη πρὸς ταῖς ἐκ τοῦ κέντρου εἶναι τὸ ὕδωρ τότε γὰρ ἠρεμήσει. Ἡ δὲ τῶν ἐκ τοῦ κέντρου ἁπτομένη περιφερής σφαιροειδὴς ἄρα ἡ τοῦ ὕδατος ἐπιφάνεια, ἐφ' ἧς ΒΕΓ. 272 But the surface of water is seen to be spherical if we take as our starting-point the fact that water naturally tends to collect in a hollow place—'hollow' meaning 'nearer the centre'. Draw from the centre the lines AB, AC, and let their extremities be joined by the straight line BC. The line AD, drawn to the base of the triangle, will be shorter than either of the radii. Therefore the place in which it terminates will be a hollow place. The water then will collect there until equality is established, that is until the line AE is equal to the two radii. Thus water forces its way to the ends of the radii, and there only will it rest: but the line which connects the extremities of the radii is circular: therefore the surface of the water BEC is spherical. Ὅτι μὲν οὖν σφαιροειδής ἐστιν ὁ κόσμος, δῆλον ἐκ τούτων, καὶ ὅτι κατ' ἀκρίβειαν ἔντορνος οὕτως ὥστε μηθὲν μήτε χειρόκμητον ἔχειν παραπλησίως μήτ' ἄλλο μηθὲν τῶν ἡμῖν ἐν ὀφθαλμοῖς φαινομένων. Ἐξ ὧν γὰρ τὴν σύστασιν εἴληφεν, οὐδὲν οὕτω δυνατὸν ὁμαλότητα δέξασθαι καὶ ἀκρίβειαν ὡς ἡ τοῦ πέριξ σώματος φύσις δῆλον γὰρ ὡς ἀνάλογον ἔχει, καθάπερ ὕδωρ πρὸς γῆν, καὶ τὰ πλεῖον ἀεὶ ἀπέχοντα τῶν συστοίχων. 273 It is plain from the foregoing that the universe is spherical. It is plain, further, that it is turned (so to speak) with a finish which no manufactured thing nor anything else within the range of our observation can even approach. For the matter of which these are composed does not admit of anything like the same regularity and finish as the substance of the enveloping body; since with each step away from earth the matter manifestly becomes finer in the same proportion as water is finer than earth.
| Postquam philosophus ostendit quod caelum est sphaericae figurae, ex eo quod haec figura est prima figurarum, hic ostendit idem ex eo quod haec figura est convenientissima caelo. | 353. After showing that the heaven has a spherical shape on the ground that such a shape is the first of all figures, the Philosopher shows the same thing on the ground that this shape is most suitable to the heaven. |
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Et primo ex eo quod est propria caelo quantum ad hoc quod est universaliter continens omnia corpora; secundo quantum ad hoc quod motus eius est universalis mensura omnium motuum, ibi: adhuc autem si quidem et cetera. |
First from the fact that it is suitable to the heaven on account of its being the universal container of all bodies; Secondly, on account of its motion being the universal measure of all motions, at 356. |
| Circa primum praemittit duas suppositiones in superioribus manifestatas. Quarum prima est quod caelum movetur circulariter: hoc enim et ad sensum videtur, et supponitur ex probationibus primi libri. Secunda suppositio est ex eo quod ostensum est in primo libro, in capitulo de unitate mundi, scilicet quod extra extremam circulationem supremae sphaerae non est nec vacuum nec locus. | 354. With respect to the first [269] he puts forward two suppositions previously made clear. The first is that the heaven is moved circularly —which is both evident to sense and is supposed from the proofs in Book I. The second supposition is taken from what was proved in Book I, in the chapter on the unity of the world, namely, that beyond the final circulation of the outermost sphere there is neither place nor void. |
| Et ex his suppositionibus ex necessitate concludit quod corpus caeli sit sphaericum. Si enim non sit sphaericum, oportet quod aut habeat figuram rectilineam totaliter, aut oportet quod habeat quantum ad aliquam partem circularem figuram, quae tamen non perveniat ad perfectionem sphaerae. Si vero corpus caeli sit vere rectilineum, puta cubicum vel pyramidale, sequetur quod extra caelum sit aliquis locus, et aliquod corpus, et aliquod vacuum. | From these suppositions he necessarily concludes that the body of the heaven is spherical. For if it were not it would have to be either entirely rectilinear, or only partially circular without being a perfect sphere. But if the body of the heaven should be truly rectilinear — for example, a cube or a pyramid — it follows that beyond the heaven there would exist a place and a body and a void. |
| Quam quidem consequentiam ex hoc probat, quod corpus rectilineum, si circulariter vertatur, non permanebit in eodem loco secundum omnes partes suas: immo sequetur quod ubi primo erat aliqua pars eius, nunc nulla pars eius est, et quod iterum ubi nunc non est aliqua pars eius, iterum erit aliqua pars eius; et hoc propter permutationem angulorum. Cuiuslibet enim corporis rectilineae figurae oportet esse aliquos angulos corporales praeeminentes ceteris partibus, quia linea ducta a medio talis corporis est maior linea ducta ad aliquod punctum designatum in superficie plana eius: et sic quando, secundum versionem corporis, linea terminata ad angulum pervenerit ad locum in quo erat linea ducta ad aliud punctum quod est inter angulos, accipiet plus de loco, et ita erit corpus ubi prius non erat; et subsequens linea quae pertinget ad locum anguli, non poterit occupare totum locum qui occupabatur ab angulo, et ideo ubi nunc non est corpus, prius erat. Sic ergo extra illum locum in quo nunc est caelum, potest esse aliquod corpus, idest aliqua pars eiusdem caeli; et per consequens est ibi locus, qui est corporis receptaculum; et consequenter est ibi vacuum, quod nihil aliud est quam locus non plenus corpore cuius est capax. | That this consequence follows he shows on the ground that a rectilinear body in circular motion will not remain in the same place with respect to all its parts. As a matter of fact it will follow that where one part of it first was, no part of it now is; and again where no part of it now is, a part of it will later be. This is true on account of the interchange of corners. For in any body rectilinear in shape there must be certain bodily corners which extend beyond the other parts of the body, since a line drawn from the center of such a body [to a corner] is greater than a line drawn to some point on the plane surface of the body. Accordingly as the body turns, the line ending at the corner will reach the place previously occupied by the line drawn to a point between the corners and will occupy more space, and thus there will be a body where one was not before. The subsequent line [i.e., the line to the plane surface], arriving at the place formerly occupied by the corner will not be able to occupy the whole place formerly occupied by the corner, so that where there is now no body, there previously was body. Thus, therefore, outside the place in which the heaven now is, there can be existing a body, i.e., some part of the same heaven. Consequently there is a place there, i.e., the receptacle of a body. Likewise there is a void, which is nothing more than a place not filled with the body of which it is capable. |
| Sed quia etiam sunt quaedam figurae non habentes angulos, quae tamen non sunt sphaericae, ideo idem ostendit consequenter de huiusmodi figuris. Et dicit quod simile inconveniens sequitur si attribuatur caelo aliqua alia figura, a cuius medio non omnes lineae protractae sint aequales, quod est proprium sphaerae. Et has figuras dicit esse duas, lenticularem scilicet et ovalem. In figura enim ovali, linea quae designat longitudinem, est maior ea quae designat profunditatem: est enim figura ovalis quasi ex duabus pyramidalibus rotundis coniunctis in basi. | 355. But because there are certain figures that have no angles and yet are not spheres, he subsequently shows the same thing for these figures. And he says that a similar impossibility follows if we should attribute to the heaven some other shape, such that not all the lines from its center would be equal, as is proper to a sphere. And he says that there are two such figures, namely, lentil-shaped and oval-shaped. Now in an oval figure the line designating the length is greater than that designating the depth; indeed, an oval figure can be conceived as the result of two round pyramids joined at their bases. |
| Figura autem lenticularis est quasi facta ad modum rotae, cuius latitudo est maior quam grossities. In omnibus enim huiusmodi figuris accidit secundum aliquem modum quod extra ultimum motum supremae sphaerae est locus et vacuum, propter hoc quod totum secundum omnes partes suas non semper retinet eundem locum. Et hoc quidem accidit, si Poli super quos revolvitur corpus ovalis figurae, accipiantur ex parte minoris diametri ipsius: tunc enim oportet quod maiores diametri circumvolvantur, et sic occupabit unum caput ovi motum aliquem locum, in quo prius nulla pars ovi erat. Si vero longitudo ovi acciperetur in motu ipsius sicut axis immobilis, fieret revolutio semper secundum partes circulares, ita quod una pars succederet alteri. Et similiter est etiam imaginandum in figura lenticulari: et ita etiam est de figura columnari, et de quacumque alia huiusmodi. | But the shape of a lentil is as though made in the fashion of a wheel whose width is greater than its thickness. Now in all such figures, it comes about in some way that beyond the ultimate motion of the outermost sphere a place and a void will exist, because of the fact that the whole is not always retaining the same place according to all its parts. This happens if one takes the poles about which the oval-shaped body is revolved on the part of its lesser diameter; for then the greater diameters must describe a circular motion and consequently one head of the moved oval will occupy a place in which previously no part of it was. But if, however, the length of the oval should be taken in its motion as the fixed axis, the revolutions would always take place according to circular parts, so that one part would succeed another. The same thing is also to be imagined with respect to the lentil-shaped figure; and likewise for a cylindrical figure and for any other such figure. |
| Unde patet quod sola sphaerica figura est quae, a quacumque parte moveatur, non occupat de novo aliquem locum secundum aliquam sui partem, sed semper una pars eius succedit alteri. Unde talis figura est convenientissima caelo. | Hence it is plain that only a spherical shape is such that, no matter how it be moved, no part will occupy some new place [not previously occupied by some other part]; rather one part of it always succeeds another part of it. Hence such a shape is most suitable to the heaven. |
| Deinde cum dicit: adhuc autem si quidem etc., probat idem per aliam rationem, quae sumitur ex mensuratione motuum. Et primo ponit hanc suppositionem, quod motus caeli sit mensura omnium motuum, ut habitum est in IV Physic. Et huius rationem assignat, quia solus motus caeli est continuus et regularis et sempiternus: aliter enim per ipsum motum caeli non posset certificari quantitas aliorum motuum, quod est mensurare ipsos. Si enim non esset motus caeli continuus, sed interpolatus, non esset aequalitas temporis inter motum mensurantem et mensuratum; si autem non esset regularis, sed quandoque velocior quandoque tardior, non haberet in se certitudinem determinatam, per quam posset certificari quantitas aliorum motuum; si autem non esset sempiternus, non mensurarentur secundum ipsum motus qui fuerunt ante et qui erunt post, secundum opinionem ponentium motum secundum suum genus esse aeternum. | 356. Then at [270] he proves the same with another argument, based on the measurement of motions. First he lays down the supposition that the motion of the heaven is the measure of all motions, as was maintained in Physics IV. And he gives the reason for this, namely, that only the motion of the heaven is continuous and regular and eternal; for in no other way could the quantity of other motions be certified through the motion of the heaven — and this is to measure them. For if the motion of the heaven were not continuous, but interrupted, there would not be equality of time between the measuring motion and the measured motion. If the motion were not regular, but now faster and now slower, it would not have within itself a determined certitude by which the quantity of other motions could be certified. If it were not eternal, there could not be measured through it motions that existed before and which will exist later, following the opinion of those who hold motion to be eternal by nature. |
| His autem suppositis, argumentatur ad propositum sic. Manifestum est quod id quod est minimum in unoquoque genere, est mensura illius generis, ut habetur in X Metaphys., sicut in melodia tonus, et in ponderibus uncia, et in numeris unitas; manifestum est autem quod minimus motus est qui est velocissimus, qui scilicet habet minimum de tempore, quod est mensura motus; omnium ergo motuum velocissimus est motus caeli. Et accipitur hic motus velocissimus, qui citius peragit cursum suum ex parte brevitatis temporis, licet non supponatur aequalitas ex parte magnitudinis super quam transit motus, sicut supponitur in VI Physic., ubi dicitur quod velocius est quod pertransit in minori tempore aequale spatium vel etiam maius. Unde hic subdit quod velocissimus motus attenditur secundum minimam magnitudinem. Inter omnes autem lineas quae ab eodem in idem redeunt, minima est circularis: quia in figuris rectilineis sunt anguli, ad quos lineae protractae a medio sunt maiores, et sic anguli illarum figurarum excedunt lineam circularem. Et ideo oportet quod caelum, quod movetur circulariter quasi ab eodem in idem, et velocissimo motu, quod motus eius sit super lineam circularem. Et ita oportet quod ipsum sit sphaericum. | With these suppositions in mind, he argues to his point in the following manner: It is plain that whatever is the least in each genus is the measure of that genus, as is had in Metaphysics X, as a tone in melody, and the ounce among weights, and unity among numbers. It is also plain that the least motion is the one which is most rapid, i.e., the one having the least time, which is the measure of motion. Therefore the swiftest of all motions is the motion of the heaven. Here the swiftest of motions means the one which goes through its course sooner as to shortness of time, although there is not supposed equality on the part of the magnitude traversed by the motion, as is supposed in Physics IV, where it is stated that the swifter is that which in a lesser time traverse an equal, or even greater, distance. That is why he now adds here that the swiftest motion is considered with respect to the least magnitude. Now among all lines that return to their beginning the circle is the smallest — since in rectilinear figures there are angles such that lines drawn to them from the center are greater and consequently the corners of such figures jut out farther than a circular line. Accordingly, the motion of the heaven, which moves circularly, as though from the same to the same, and with the swiftest motion, traverses a circle in its motion. Therefore the heaven must be spherical. |
| Deinde cum dicit: sumet autem utique quis etc., ostendit quod caelum sit sphaericae figurae, ratione sumpta ex corporibus inferioribus. | 357. Then at [271] he shows that the heaven has a spherical shape by using an argument taken from the lower bodies. |
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Et primo ponit rationem; secundo probat quod supposuerat, ibi: sed et quod aquae superficies et cetera. |
First he presents his argument; Secondly, he proves what he had supposed, at 359. |
| Dicit ergo primo quod aliquis potest sumere fidem ad ostendendum caelum esse sphaericum, ex corporibus inferioribus, quae sunt collocata circa medium mundi. Aqua enim est circa terram, licet non ex omni parte cooperiat terram (quod est propter necessitatem generationis et conservationis vitae, maxime animalium et plantarum), aer autem circumdat aquam, ignis autem circumdat aerem; et secundum eandem rationem superiora corpora circumdant inferiora usque ad supremum caelum. Huiusmodi enim corpora non sunt continua, ut sit totum unum corpus, quia sic non esset quodlibet ipsorum sphaericum, sed totum (pars enim corporis continui non est actu figurata); sed haec corpora tangunt se invicem absque aliqua interpolatione alterius corporis, vel etiam vacui, ut Democritus posuit; et hoc supra nominavit continuum. Superficies autem unius horum inferiorum corporum est sphaerica: illud autem quod continuatur, idest sine interpolatione coniungitur, corpori sphaerico continenti, aut etiam quod movetur circa corpus sphaericum contentum, necesse est esse sphaericum. | He says therefore first [271] that someone can Unde ab inferiori probari potest ascendendo usque ad supremum caelum, quod caelum sit sphaericum. come to hold that the heaven is spherical by considering the lower bodies that are located about the center of the heaven. For water is about the earth, although it does not entirely cover the earth (because of the need for the generation and preservation of life, specially that of animals and plants) and air surrounds the water, and fire surrounds the air. And according to the same procedure the upper bodies surround the lower bodies up to the outermost heaven. Now such bodies are not continuous as though forming one body, for then each of them would not be spherical in shape but rather the whole (for a part of a continuous body is not shaped in act). But these bodies touch one another without any other body existing between them, and without any empty space between them as Democritus laid down. Now, the surface of one of these lower bodies being spherical, consequently the body "continuous" to it, i.e., conjoined without interpolation to the spherical containing [contained?] body, or which moves around the spherical contained body, must be spherical. Hence beginning with the lower body, it can be proved, by ascending to the outermost heaven, that the heaven is spherical. |
| Sed videtur quod haec probatio non habeat necessitatem. Si enim detur quod aqua sit sphaericae figurae, ex hoc manifeste habebitur quod aer sit sphaericae figurae quantum ad eius concavum; non autem oportet, ut videtur, quod quantum ad convexum. | 358. But it seems that this proof lacks necessity. For if it is assumed that water has a spherical shape, it will clearly follow that air on the concave side will be spherical, but this does not necessarily seem to follow for its convex side. |
| Ad hoc igitur Alexander respondet, quod ex hac demonstratione probatur corpora mundi esse sphaerica quantum ad concavum, sicut ex priori, qua procedebat a supremo caelo procedendo, probabatur quod haec corpora essent sphaerica quantum ad suum convexum: et secundum hoc neutra demonstrationum est sufficiens sine alia, sed ex duabus una demonstratio conficitur. | To this Alexander responds that from this demonstration it is proved that the bodies of the world are spherical as to their concave side, just as from the previous argument, which proceeded from the outermost heaven proceeding downward, it was proved that these bodies are spherical on their convex side. Hence according to this, neither of these arguments is complete without the other, but from the two arguments one demonstration results. |
| Quod videtur esse contra intentionem Aristotelis, qui utramque demonstrationem divisim inducit, quasi utraque sit per se sufficiens. Et ideo dicendum est, sicut Simplicius dicit, quod per hanc demonstrationem sufficienter probatur corpora mundi esse sphaerica, non solum quantum ad concavum, sed etiam quantum ad convexum. Quod enim superficies concava aeris sit sphaerica, patet ex hoc, quod superficies convexa aquae est sphaerica. Quod autem superficies aeris convexa sit sphaerica, patet eodem modo sicut de aqua, quia scilicet omnes partes eius aequaliter concurrunt ad suum locum. Et sic patet quod etiam superficies concava ignis sit sphaerica. Quod autem superficies ignis convexa sit sphaerica, patere potest tum ex eo quod continuatur cum sphaera lunae (unde et simul revolvitur cum ea, ut manifeste apparet ex motu stellae comatae, quae movetur ab oriente in occidentem secundum motum caeli); tum etiam ex hoc quod partes ignis moventur undique aequaliter ad suum ubi. | But this seems to be contrary to Aristotle's intention, who presents each as a separate argument, as though each was complete in itself. And therefore it should be said, as Simplicius asserts, that this demonstration sufficiently proves that the bodies of the world are spherical both with respect to their concave and their convex. For since the convex surface of water is spherical, it is plain that the concave side of air is spherical. That the convex side of air is spherical is plain in the same way that it is plain for the water, namely, because all its parts equally concur to the same place. Accordingly it is also plain that the concave side of fire is also spherical. But that the convex surface of fire is spherical can be plain both from the fact that it is continuous with the sphere of the moon (for which reason it revolves together with it, as is clearly plain from the movement of a comet which moves from east to west in accordance with the motion of the heaven), as well as from the fact that the parts of fire are from all directions moved equally to their proper place. |
| Deinde cum dicit: sed et quod aquae superficies etc., probat quod supposuerat, scilicet quod superficies convexa aquae sit sphaerica: nam de terra inferius ostendet. Ad hoc autem ostendendum praemittit duas suppositiones. Quarum prima est quod, quia aqua naturaliter est gravis, semper naturaliter fluit ad id quod est magis concavum, vel magis infimum. Alia autem suppositio est, quod illud est magis concavum et magis infimum, quod est propinquius centro mundi. | 359. Then at [272] he proves what he had supposed, namely, that the convex side of water is spherical; for later on he will prove it for earth. In order to show this, he premises two suppositions. The first of these is that, since water is naturally heavy, it always naturally flows to a place that is more concave, or lower. The other supposition is that a thing is more concave and lower according as it is nearer to the center of the world. |
| His igitur suppositis, sit centrum mundi a, et signentur in superficie aquae duo puncta b et g, aequaliter distantia a centro, et producantur duae lineae quae sunt ab et ag. Deinde coniungantur duo puncta b et g per lineam bg; quae quidem linea est recta, si suprema superficies aquae sit plana. Signetur igitur in linea bg, quae est basis trianguli, punctum d, et ducatur a centro linea quae est ad. Hanc lineam necesse est esse minorem utraque duarum linearum a centro procedentium: si enim esset aequalis, tunc omnes tres lineae essent aequales ab eodem puncto procedentes, et ita linea bdg, transiens per summitates earum, esset circularis, ut patet ex III Euclidis; quod est contra positum, quo posuimus lineam bg esse lineam rectam. Supposito ergo quod linea ad sit minor, sequetur quod punctum d minus distabit a centro; et ita locus ille erit profundior, vel magis infimus. Unde sequetur, secundum suppositionem praemissam, quod aqua quae est in puncto g et in puncto b, circumfluet ad punctum d, donec adaequetur locus medius aliis duobus extremis; et sit linea tota adaequata duobus extremis ex concursu aquae, linea ae. Oportet igitur quod aqua sit apud omnes lineas egredientes a centro aequales: tunc enim solum aqua quiescit, quando omnes lineae sunt aequales. Sed linea quae tangit tres lineas egredientes a centro aequales, est circularis, ut probatur in III Euclidis. Sequitur ergo quod superficies aquae, in qua describitur linea beg, sit superficies sphaerica; et hoc est quod demonstrare intendit. | On these suppositions let A be the center of the world, and B and G two designated points on the surface of the water that are equidistant from the center, and let there be drawn two lines AB and AG. Join the two points B and G so as to form the line BG, which will be a straight line, if the water's surface is flat. Let there be marked a point D in the line BG, which is the base of a triangle, and draw the line AD from the center. This line must be less than either of the other two lines AB and AG drawn from the center. For if it were equal, then all three lines proceeding from the same point would be equal, and thus the line BDG, passing through their extremities, would be circular, as is plain from Euclid III. But this would be against our assumption that the line BG is a straight line. Therefore, supposing that the line AD is shorter than the others, it will follow that the point D will be less distant from the center, and consequently its place will be deeper or lower. Hence, it will follow according to the foregoing supposition that the water in point G and in point B will flow to point D until the middle place is equated with the other two extremes. Let AE be the whole line equated to the two extremes from the meeting of the waters. Therefore the water must be along all the equal lines coming from the center; for water rests only when all the lines are equal. But the line which touches three equal lines proceeding from the center is circular, as is proved in Euclid III. It follows therefore that the surface of the water, on which the line BEG is described, is a spherical surface — and this is what he intended to demonstrate. |
| Deinde cum dicit: quod quidem igitur sphaericus est etc., concludit ex praemissis manifestum esse quod mundus sit sphaericus, tum propter corpus primum quod continet totum mundum, tum etiam propter alia corpora ab eo contenta. Sunt autem apud nos quaedam corpora sphaerica, quae tamen non perfecte habent sphaericam figuram; sicut ipsum corpus terrae dicitur esse sphaericum, cum tamen habeat magnas elevationes montium et concavitates vallium. In corporibus etiam artificialibus quae sunt apud nos sphaerica, inveniuntur aliquae tumorositates vel depressiones, quibus non obstantibus huiusmodi artificiata dicuntur esse sphaericae figurae, quia huiusmodi additiones vel subtractiones secundum sensum quasi non apparent. | 360. Then at [237] he concludes from the foregoing that the world is manifestly spherical both on account of the first body which contains the entire world and also on account of the other bodies contained by it. But among us there are spherical bodies which nevertheless do not have a perfectly spherical shape; for example, the very body of the earth is said to be spherical, even though it has the great elevations of mountains and the depressions of valleys. Likewise, in our artificial bodies that are spherical, we find bumps and depressions, in spite of which such artifacts are said to be spherical in shape, since such additions or subtractions are reckoned as though nothing according to sense. |
| Ne igitur credatur hoc etiam accidere in corpore caelesti, addit quod est secundum diligentiam tornatus, idest carens omni tumorositate et concavitate, sicut corpora quae diligenter tornantur; in tantum quod nihil, neque chirocmeton, idest manu elaboratum, se habeat similiter ad corpus caeleste quantum ad hoc quod dictum est, neque etiam quodcumque corpus aliud naturale quod nostris oculis appareat: quia illa ex quibus huiusmodi corpora constituuntur, non possunt illam regularitatem, idest uniformitatem, suscipere per actionem artis vel naturae inferioris, et illam diligentiam quantum ad perfectionem sphaericae figurae, quam habet corpus caeleste, quod est naturaliter sphaericae figurae. | Therefore lest anyone believe that the same thing happens in the heavenly body, Aristotle adds that it is "turned with diligence," i.e., lacks all bumps and hollows, as do bodies carefully turned on a lathe, so much so that nothing chirocmeton, i.e., made by hand, is comparable to a heavenly body in this respect, nor any other natural body that our eyes behold. For the things from which such bodies are constituted cannot obtain, through the action of art or lower nature, that regularity, i.e., uniformity, and diligence for perfect spherical shape which a heavenly body possesses in virtue of its natural spherical shape. |
| Et hoc probat per proportionem partium mundi ad invicem. Manifestum est enim quod secundum eandem proportionem qua aqua excedit terram, semper elementa continentia distant a corporibus contentis, et etiam adhuc plus. Aqua autem, quae continet terram, non habet huiusmodi tumorositates et concavitates in superficie quas habet terra, sed magis est regularis quam superficies terrae. Similiter oportet quod superficies aeris sit magis regularis quam superficies aquae. Unde sequitur quod superficies supremi corporis caelestis sit maxime regularis, ita quod in eo omnino nihil sit, nec minimum, superadditum vel subtractum. | This he proves through the proportion of the parts of the world to one another. For it is plain that according to the same proportion by which water exceeds earth,. the containing elements always exceed the bodies contained — or even in greater proportion. But water, which contains the earth, does not have the swellings and depressions on its surface that earth has; rather its surface is more regular than the earth's surface. Similarly, the air's surface must be more regular than water s. Hence it follows that the surface of the outermost heavenly body is supremely regular, so that in it there is not even the slightest addition or subtraction. |
Lecture 7:
Why the circular motion of the heaven is in one direction rather than anotherChapter 5 Ἐπεὶ δ' ἔστι διχῶς ἐπὶ τοῦ κύκλου κινηθῆναι, οἷον ἀπὸ τοῦ Α τὴν μὲν ἐπὶ τὸ Β τὴν δ' ἐπὶ τὸ Γ, ὅτι μὲν οὖν οὐκ εἰσὶν ἐναντίαι αὗται, πρότερον εἴρηται. 274 Now there are two ways of moving along a circle, from A to B or from A to C, and we have already explained that these movements are not contrary to one another. Ἀλλ' εἰ μηδὲν ὡς ἔτυχε μηδ' ἀπὸ ταὐτομάτου ἐνδέχεται ἐν τοῖς ἀϊδίοις εἶναι, ὁ δ' οὐρανὸς ἀΐδιος καὶ ἡ κύκλῳ φορά, διὰ τίνα ποτ' αἰτίαν ἐπὶ θάτερα φέρεται, ἀλλ' οὐκ ἐπὶ θάτερα; 275 But nothing which concerns the eternal can be a matter of chance or spontaneity, and the heaven and its circular motion are eternal. We must therefore ask why this motion takes one direction and not the other. ἀνάγκη γὰρ καὶ τοῦτο ἢ ἀρχὴν εἶναι ἢ εἶναι αὐτοῦ ἀρχήν. 276 Either this is itself an ultimate fact or there is an ultimate fact behind it. Ἴσως μὲν οὖν τὸ περὶ ἐνίων ἀποφαίνεσθαί τι πειρᾶσθαι καὶ τὸ περὶ πάντων καὶ τὸ παριέναι μηθὲν τάχ' ἂν δόξειεν εἶναι σημεῖον ἢ πολλῆς εὐηθείας ἢ πολλῆς προθυμίας. Οὐ μὴν δίκαιόν γε πᾶσιν ὁμοίως ἐπιτιμᾶν, ἀλλ' ὁρᾶν δεῖ τὴν αἰτίαν τοῦ λέγειν τίς ἐστιν, ἔτι δὲ πῶς ἔχων τῷ πιστεύειν, πότερον ἀνθρωπίνως ἢ καρτερώτερον. Τὰς μὲν οὖν ἀκριβεστέρας ἀνάγκας, ὅταν (288a.) τις ἐπιτύχῃ, τότε χάριν ἔχειν δεῖ τοῖς εὑρίσκουσι, νῦν δὲ τὸ φαινόμενον ῥητέον. 277 It may seem evidence of excessive folly or excessive zeal to try to provide an explanation of some things, or of everything, admitting no exception. The criticism, however, is not always just: one should first consider what reason there is for speaking, and also what kind of certainty is looked for, whether human merely or of a more cogent kind. When any one shall succeed in finding proofs of greater precision, gratitude will be due to him for the discovery, but at present we must be content with a probable solution. Εἰ γὰρ ἡ φύσις ἀεὶ ποιεῖ τῶν ἐνδεχομένων τὸ βέλτιστον, ἔστι δὲ καθάπερ τῶν ἐπὶ τῆς εὐθείας φορῶν ἡ πρὸς τὸν ἄνω τόπον τιμιωτέρα (θειότερος γὰρ τόπος ὁ ἄνω τοῦ κάτω), τὸν αὐτὸν τρόπον καὶ ἡ εἰς τὸ πρόσθεν τῆς εἰς τοὔπισθεν, ἔχει, εἴπερ καὶ τὸ δεξιὸν καὶ τὸ ἀριστερόν, καθάπερ ἐλέχθη πρότερον, (καὶ μαρτυρεῖ δ' ἡ ῥηθεῖσα ἀπορία ὅτι ἔχει) τὸ πρότερον καὶ ὕστερον αὕτη γὰρ ἡ αἰτία λύει τὴν ἀπορίαν. Εἰ γὰρ ἔχει ὡς ἐνδέχεται βέλτιστα, αὕτη ἂν εἴη αἰτία καὶ τοῦ εἰρημένου βέλτιστον γὰρ κινεῖσθαι ἁπλῆν τε κίνησιν καὶ ἄπαυστον, καὶ ταύτην ἐπὶ τὸ τιμιώτερον. 278 If nature always follows the best course possible, and, just as upward movement is the superior form of rectilinear movement, since the upper region is more divine than the lower, so forward movement is superior to backward, then front and back exhibits, like right and left, as we said before and as the difficulty just stated itself suggests, the distinction of prior and posterior, which provides a reason and so solves our difficulty. Supposing that nature is ordered in the best way possible, this may stand as the reason of the fact mentioned. For it is best to move with a movement simple and unceasing, and, further, in the superior of two possible directions.
| Postquam philosophus determinavit de partibus caeli et de figura ipsius, hic determinat de motu eius. | 361. After determining as to the parts of the heaven and its shape, the Philosopher here decides the question of its motion. |
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Et primo determinat de modo motus; secundo determinat de uniformitate motus caelestis, ibi: de motu autem ipsius et cetera. |
First he discusses the manner of its motion; Secondly, the uniformity of its motion (L. 8). |
| Circa primum tria facit: | Regarding the first he does three things: |
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primo ponit quaestionem; secundo ostendit difficultatem quaestionis, ibi: forte quidem igitur etc.; tertio proponit solutionem, ibi: nunc autem quod videtur et cetera. |
First he raises the question; Secondly, he shows the difficulty of the question, at 364; Thirdly, he proposes a solution, at 365. |
| Circa primum tria facit. | About the first he does three things: |
| Primo proponit quaedam ex quibus oritur dubitatio. Quorum unum est, quod dupliciter contingit per aliquem circulum aliquid moveri. Signetur enim punctum a in aliquo circulo, et ab eo ducatur diameter, et in superiori semicirculo signetur punctum b, in inferiori autem signetur punctum g. Dupliciter ergo potest aliquid moveri per hunc circulum: uno modo quod moveatur ab a versus b, alio modo quod moveatur ab a versus g. | First he mentions certain things that give rise to the question. One of these is that there are two ways in which a thing could be moved through a circle. For if we let A be a point on a circle and draw a diameter from A, and let B be a point on the upper semicircle, and G a point on the lower, there will then be two possible ways for something to move over this circle: in one way, something could go from A to B; in another, from A to G. |
| Aliud autem quod proponit est, quod isti duo motus non sunt contrarii: ostensum est enim in primo quod duo motus circulares non sunt contrarii. Si enim isti motus essent contrarii, oporteret quod competerent naturis contrariorum mobilium, ita quod unus eorum attribueretur uni mobili, et alius contrario: quia sicut supra dictum est, si unum contrariorum est in natura, necesse est alterum esse. | Another thing he mentions is that those two motions are not contrary, for it has been shown in Book I that two circular motions are not contrary. For if they were contrary, they would have to belong to the natures of contrary mobile things, so that one motion would be attributed to one mobile and the other to the contrary mobile — because, as has been said, if one of two contraries exists in nature, so must the other. |
| Secundo ibi: sed si nihil etc., movet dubitationem. Manifestum est enim ex praemissis quod in sempiternis nihil accidit contingenter aut casualiter: quia ea quae sunt a casu, non sunt semper, neque etiam ut frequenter. Dictum est autem supra quod caelum est sempiternum, et etiam circularis motus eius. Unde rationabiliter quaeritur propter quam causam caelum movetur versus unam partem et non versus aliam, puta ab oriente versus superius hemisphaerium, et non versus inferius. | 362. Secondly, at [275] he raises the question. For it is plain from the foregoing that in things that are eternal nothing happens contingently or fortuitously, because happenings due to chance do not occur always or even nearly always.. But it has been said above that the heaven is eternal and also its circular motion. Hence it is reasonable to ask why it is that the heaven is moved in one direction rather than in the other; for example, from the east in the direction of the upper hemisphere and not of the lower. |
| Tertio ibi: necesse enim etc., ostendit qualiter sit huiusmodi causa assignanda. In praecedentibus enim dupliciter assignavit causam caelestium accidentium. Primo enim ostendit quod oportet esse diversos motus in caelo, ad hoc quod sit principium generationis et corruptionis: secundo ostendit quod oportet figuram caeli esse rotundam, ex aliquo principio priori supposito, quia scilicet corpori primo debetur figura prima; et sic primitas corporis est principium primae figurae. Et ideo hic dicit quod, si debeat assignari ratio quare caelum sic moveatur et non aliter, necesse est huiusmodi rationem assignari, aut secundum hoc quod talis modus motionis sit principium alicuius effectus, aut potius quod iste modus motionis dependeat ex aliquo priori principio. | 363. Thirdly, at [276] he shows how such a cause must be assigned. For in the previous accounts he assigned a cause of celestial events in two ways. First, he showed that there have to be various motions in the heaven in order that generation and corruption be possible; secondly, he showed that the figure of the heaven has to be round by assuming a prior principle, namely, that the first shape is appropriate to the first body. Thus the primacy of the body is the reason why it has the first shape. And therefore he says here that if we must assign the reason why the heaven is moved as it is and not in some other way, that reason must be assigned either on the ground that such a type of motion is the principle of some effect, or rather that this type of motion depends on some prior principle. |
| Potest autem et aliter intelligi. Dixerat enim quod sempiterna non possunt esse a casu: nec tamen omnia sempiterna habent causam, sed aliquod sempiternum est quod causam non habet, sed ipsum est prima causa aliorum. Quia igitur ex sempiternitate caeli et motus eius concluserat quaestionem, qua quaeritur propter quam causam motus caeli est versus unam partem et non versus aliam; ne videatur quaestio irrationabilis seu inutilis, subiungit quod necesse est hoc ipsum quod est caelum sic moveri, aut esse primum principium omnium (quod est impossibile, cum omnis motus habeat causam moventem); aut oportet dicere quod eius sit quoddam aliud principium. Et sic rationabiliter quaesitum est de causa quare movetur ad hanc partem et non ad aliam. | This can also be understood in another way. For he had said that eternal things cannot be due to chance. Yet not all eternal things have a cause, for there is an eternal thing which has no cause but is itself the first cause of other things. Since, therefore, on the grounds of the eternity of the heaven and of its motion, he had arrived at the question concerning the cause why the motion of the heaven is in one direction rather than another, lest the question appear foolish or useless, he adds that it is necessary that the manner of the heaven's movement be either the first principle of all motions (which is impossible, because all motion has a movent cause) or else there must be said to be some other principle of its motion. Consequently it is reasonable to ask why it is that the heaven is moved in this direction rather than some other. |
| Deinde cum dicit: forte quidem igitur etc., ostendit difficultatem huius quaestionis. Et dicit quod hoc quod aliquis de quibusdam difficilibus et occultis velit attente enuntiare, assignando causam eorum, et quod de omnibus velit inquirere et nihil praetermittere, forte videbitur esse signum vel multae stultitiae, ex qua provenit quod nescit discernere inter facilia et difficilia; aut est signum multae promptitudinis, idest magnae praesumptionis, ex qua contingit quod homo non cognoscit mensuram suae facultatis circa inquisitionem veritatis. Et quamvis quidam super hoc sint increpandi, non tamen iustum est quod omnes similiter reprehendantur, sed ad duo oportet attendere. | 364. Then at [277] he shows the difficulty of this question. And he says that the very desire to attentively set forth difficult and occult things and give their cause, and to inquire into all the aspects, without omitting anything, will perhaps be seen as a sign either of a deep-rooted stupidity, causing one to be unable to distinguish between what is easy and what is difficult, or else as a sign of "great promptitude," i.e., of great presumption, causing one not to know the measure of his ability with respect to the search for truth. And although some deserve rebuke on this point, it is not a just thing to condemn all investigators indiscriminately. Rather we should first have regard to two things. |
| Primo quidem ad causam quae movet hominem ad loquendum de talibus: utrum scilicet hoc faciat ex amore veritatis, an ad ostentationem sapientiae. Secundo oportet considerare quomodo se habeat aliquis in credendo ea quae asserit: utrum scilicet habeat de eis debilem certitudinem, secundum communem hominum modum, aut etiam firmius ea cognoscat, scilicet supra communem modum hominum. Quando igitur aliquis potest attingere ad hoc quod cognoscat necessarias causas certius quam secundum communem hominum modum, tunc oportet reddere gratias his qui tales necessitates inveniunt, magis quam eos increpare. | First we must look for the motive which induces a man to speak of such things: Is he doing it out of love for the truth or in order to show off his wisdom? Secondly, we must consider how one is in assenting to the things he asserts: Does he have a weak certitude about them like the common run of mankind, or does he know them more firmly, i.e., above the general run? When, therefore, a person can attain to a knowledge of necessary causes with greater certitude than the general run of man, he who finds such necessary reasons deserves our thanks rather than a rebuke. |
| Deinde cum dicit: nunc autem quod videtur etc., solvit praemissam quaestionem. Et dicit quod, si gratiae sint agendae his qui certiores necessitates inveniunt, nunc autem in hac quaestione sufficit dicere illud quod nobis videtur, etsi non sit adeo certum. Dicit ergo quod inter ea quae contingit fieri, natura semper facit id quod est optimum, tanquam mota et directa a primo principio, quod est ipsa essentia bonitatis. Videmus autem quod tanto aliquis motus localis est dignior, quanto versus digniorem partem procedit; motus enim accipit speciem a termino; sicut in motibus localibus rectis, motus localis qui est ad superiorem locum, est honorabilior et nobilioris corporis quam motus localis qui est ad inferiorem locum, eo quod locus qui est sursum est dignior loco qui est deorsum. | 365. Then at [278] he solves the question he raised. And he says that if thanks should be rendered to those who discover more certain necessary things, as to the present question it is enough to say how the matter seems to us, even though it is not so certain. He says, therefore, that among things that come to be produced, nature always does what is best, as moved and directed by the first principle, which is the essence of goodness, Now, we observe that a local motion is more noble to the extent that it tends toward a nobler direction — for the species of a motion is determined by its terminus. Thus with regard to straight local motions, a local motion toward a higher place is more honorable and more noble than one to a nether place, since the place which is above is of more worth than one which is down. |
| Et hoc quidem manifestum est in homine: nam caput, quod est sursum, est nobilius pedibus, qui sunt deorsum. Et similiter pars anterior dignior est posteriori, sicut etiam et dextrum est dignius quam sinistrum, sicut supra dictum est, et sicut patet in animalibus. idest versus superius hemisphaerium; non autem versus inferius, quod est caeli posterius. | This fact is also plain with regard to man: for the head, which is above, is nobler than the feet, which are down. Likewise, the front of a man is nobler than the back, and the right than the left, as we have said above, and as is plain also with respect to animals. |
| Dicta ergo dubitatio quam nunc movimus, testificatur quod in caelo sit prius et posterius, idest ante et retro, de quibus supra nullam mentionem fecit. Haec enim causa, scilicet distinctio anterioris et posterioris in caelo, solvit praedictam dubitationem. Si enim motus caeli se habet optime quantum contingit, sicut dictum est, haec erit causa dictae dubitationis: quia optimum est quod caelum moveatur motu simplici, idest semper versus eandem partem, et incessabili, idest sine interpolatione quietis, quam necesse esset intervenire, si quandoque moveretur versus unam partem, quandoque versus aliam; et ulterius optimum est quod moveatur versus honorabiliorem partem, est autem anterior pars nobilior. Et ideo caelum movetur ab oriente versus suum anterius, | Therefore the question under discussion testifies to the fact that in the heaven there is a before and an after, i.e., a front and a back, which things he did not mention previously. Now it is this, namely, the distinction between front and back in the heaven, that solves the question at hand. For if the motion of the heaven is the best possible, as has been maintained, then the cause in the aforesaid question is this: It is best for the heaven to be moved with a "simple" motion, i.e., always toward the same direction and one "without any interruption," i.e., without the interpolation of rest (which would have to occur if the heaven were now moving in this direction and now in that direction); furthermore, it is best that it be moved toward the nobler part of the direction, and the front part is the more noble. And that is why the heaven is moved from the east toward its "front," i.e., toward the upper hemisphere and not toward the lower, which is the "back" of the heaven. |
| Sed videtur quod inconvenienter hanc rationem assignet. Supra enim assignavit distinctionem harum partium in caelo ex principio motus, quia scilicet motus caeli videtur incipere ab una parte et non ab alia; hic autem assignat rationem quare caelum sic moveatur et non aliter, ex distinctione partium caeli; et ita videtur processus eius esse circularis. | 366. But this argument does not seem appropriate. For above he had explained the distinction of these parts in the heaven from the beginning of motion, namely, from the fact that the motion of the heaven seems to begin from one direction and not from another. But here he assigns the reason why the heaven is moved the way it is and not some other way, from the distinction of the parts of the heaven. Consequently, he seems to be arguing in a circle. |
| Ad quod dicendum est quod distinctio partium caeli est causa quod motus caeli incipiat ab hac parte et non ab alia, et non e converso: sed motum incipere ab hac parte caeli et non ab alia, est signum distinctionis partium caeli. Causa autem distinctionis harum partium est virtus animae moventis caelum, vel cuiuscumque intellectualis substantiae, diversimode attributa diversis partibus caeli. Nihil autem prohibet, cum quaeritur an aliquid sit, probare illud per signum; cum tamen quaeritur de causa alicuius propter quam est, oportebit signum ad causam reducere; sicut si probemus cor moveri per motum venae pulsatilis, si tamen quaeratur quae sit causa motus venae pulsatilis, dicetur quod hoc est propter motum cordis. Et similiter Aristoteles probavit esse talem distinctionem partium in caelo, per inchoationem motus a determinata parte, sicut per signum; et tamen inchoationem motus reducit in differentiam partium caeli, sicut in causam. | To this it should be answered that the distinction among the parts of the heaven is the reason why the motion of the heaven begins whence it does and not elsewhere; and not conversely. But the fact that the motion does begin whence it does and not somewhere else is a sign of the distinction of the parts of the heaven. Now the cause of the distinction of these parts is the power of the soul moving the heaven, or of some intellectual substance differently applied to the different parts of the heaven. There is nothing wrong, when asking "Whether something is," should one prove with a sign; but when one is dealing with the "reason why something is," the sign must be reduced to the cause. For example, we might prove that the heart is moved by the motion of the pulsating vein; but if we should ask what is the cause of the motion of the pulsating vein, it will be said that it is because of the heart's movement. In like manner, Aristotle, from the fact that the motion of the heaven begins at a certain part, proved, as though from a sign, that there is such-and-such a distinction of parts in the heaven. Nevertheless he reduces the beginning of the motion to the difference in the parts of the heaven, as to the cause. |
| Distinguitur autem pars anterior et posterior in caelo, non naturaliter, scilicet secundum determinatam partem corporis caelestis, quia una et eadem pars caelestis corporis quae nunc est in superiori hemisphaerio, postea erit in hemisphaerio inferiori; sed secundum situm, sicut etiam supra dictum est de differentia dextri et sinistri. | Now the front and rear of the heaven are distinguished, not naturally, namely, in terms of some specific part of the heavenly body (since one and the same part of the heavenly body which is now in the upper hemisphere will later be in the lower), but in terms of position, just as was stated above concerning the difference between the right and left [sides of the heaven]. |
Lecture 8:
The regularity, or uniform velocity, of the heaven's motion shown a two argumentsChapter 6 Περὶ δὲ τῆς κινήσεως αὐτοῦ, ὅτι ὁμαλής ἐστι καὶ οὐκ ἀνώμαλος, ἐφεξῆς ἂν εἴη τῶν εἰρημένων διελθεῖν. 279 We have next to show that the movement of the heaven is regular and not irregular. Λέγω δὲ τοῦτο περὶ τοῦ πρώτου οὐρανοῦ καὶ περὶ τῆς πρώτης φορᾶς ἐν γὰρ τοῖς ὑποκάτω πλείους ἤδη αἱ φοραὶ συνεληλύθασιν εἰς ἕν. 280 This applies only to the first heaven and the first movement; for the lower spheres exhibit a composition of several movements into one. Εἰ γὰρ ἀνωμάλως κινήσεται, δῆλον ὅτι ἐπίτασις ἔσται καὶ ἀκμὴ καὶ ἄνεσις τῆς φορᾶς ἅπασα γὰρ ἡ ἀνώμαλος φορὰ καὶ ἄνεσιν ἔχει καὶ ἐπίτασιν καὶ ἀκμήν. Ἀκμὴ δ' ἐστὶν ἢ ὅθεν φέρεται ἢ οἷ ἢ ἀνὰ μέσον, οἷον ἴσως τοῖς μὲν κατὰ φύσιν οἷ φέρονται, τοῖς δὲ παρὰ φύσιν ὅθεν, τοῖς δὲ ῥιπτουμένοις ἀνὰ μέσον. Τῆς δὲ κύκλῳ φορᾶς οὐκ ἔστιν οὔτε ὅθεν οὔτε οἷ οὔτε μέσον οὔτε γὰρ ἀρχὴ οὔτε πέρας οὔτε μέσον ἐστὶν αὐτῆς ἁπλῶς τῷ τε γὰρ χρόνῳ ἀΐδιος καὶ τῷ μήκει συνηγμένη καὶ ἄκλαστος ὥστ' εἰ μή ἐστιν ἀκμὴ αὐτοῦ τῆς φορᾶς, οὐδ' ἂν ἀνωμαλία εἴη ἡ γὰρ ἀνωμαλία γίγνεται διὰ τὴν ἄνεσιν καὶ ἐπίτασιν. 281 If the movement is uneven, clearly there will be acceleration, maximum speed, and retardation, since these appear in all irregular motions. The maximum may occur either at the starting-point or at the goal or between the two; and we expect natural motion to reach its maximum at the goal, unnatural motion at the starting-point, and missiles midway between the two. But circular movement, having no beginning or limit or middle in the direct sense of the words, has neither whence nor whither nor middle: for in time it is eternal, and in length it returns upon itself without a break. If then its movement has no maximum, it can have no irregularity, since irregularity is produced by retardation and acceleration. Ἔτι δ' ἐπεὶ πᾶν τὸ κινούμενον ὑπό τινος κινεῖται, ἀνάγκη τὴν ἀνωμαλίαν γίγνεσθαι τῆς κινήσεως ἢ διὰ τὸ κινοῦν ἢ διὰ τὸ κινούμενον ἢ δι' ἄμφω εἴτε γὰρ τὸ κινοῦν μὴ τῇ αὐτῇ δυνάμει κινοῖ, εἴτε τὸ κινούμενον ἀλλοιοῖτο καὶ μὴ διαμένοι τὸ αὐτό, εἴτε ἄμφω μεταβάλλοι, οὐθὲν κωλύει ἀνωμάλως κινεῖσθαι τὸ κινούμενον. Οὐθὲν δὲ τούτων δυνατὸν περὶ τὸν οὐρανὸν γενέσθαι τὸ μὲν γὰρ κινούμενον δέδεικται ὅτι πρῶτον καὶ ἁπλοῦν καὶ (288b.) ἀγένητον καὶ ἄφθαρτον καὶ ὅλως ἀμετάβλητον, τὸ δὲ κινοῦν πολὺ μᾶλλον εὔλογον εἶναι τοιοῦτον τὸ γὰρ πρῶτον τοῦ πρώτου καὶ τὸ ἁπλοῦν τοῦ ἁπλοῦ καὶ τὸ ἄφθαρτον καὶ ἀγένητον τοῦ ἀφθάρτου καὶ ἀγενήτου κινητικόν. Ἐπεὶ οὖν τὸ κινούμενον οὐ μεταβάλλει σῶμα ὄν, οὐδ' ἂν τὸ κινοῦν μεταβάλλοι ἀσώματον ὄν. Ὥστε καὶ τὴν φορὰν ἀδύνατον ἀνώμαλον εἶναι. 282 Further, since everything that is moved is moved by something, the cause of the irregularity of movement must lie either in the mover or in the moved or both. For if the mover moved not always with the same force, or if the moved were altered and did not remain the same, or if both were to change, the result might well be an irregular movement in the moved. But none of these possibilities can be conceived as actual in the case of the heavens. As to that which is moved, we have shown that it is primary and simple and ungenerated and indestructible and generally unchanging; and the mover has an even better right to these attributes. It is the primary that moves the primary, the simple the simple, the indestructible and ungenerated that which is indestructible and ungenerated. Since then that which is moved, being a body, is nevertheless unchanging, how should the mover, which is incorporeal, be changed? It follows then, further, that the motion cannot be irregular.
| Postquam philosophus assignavit causam quare caelum movetur versus unam partem et non versus aliam, hic determinat de uniformitate motus caeli. | 367. After assigning the reason why the heaven is moved toward one direction rather than the other, the Philosopher here discusses the uniformity of the heaven's motion. |
|
Et primo proponit quod intendit; secundo probat propositum, ibi: si enim irregulariter movebitur et cetera. |
First he proposes what he intends; Secondly, he proves his proposition, at 369. |
| Circa primum duo facit. | About the first he does two things: |
| Primo proponit quod intendit: et dicit quod post praedicta consequenter est pertranseundum, idest breviter dicendum, de motu caeli, ostendendo quod est regularis, idest semper uniformem velocitatem habens, et nunquam irregularis, ut quandoque scilicet velocius quandoque tardius moveatur. Et hoc rationabiliter: nam iste motus est regula et mensura omnium aliorum motuum; unde nulla irregularitas vel inaequalitas in eo debet apparere. | First he proposes what he intends [279], and says that after the fore-going we must "cover," i.e., say something briefly about, the motion of the heaven and show that it is "regular," i.e., that it always has a uniform velocity, and is never irregular so as to be at one time slower and at another swifter. And this is reasonable: for this motion is the rule and measure of all other motions. Hence no irregularity or inequality should appear in it. |
| Secundo ibi: dico autem hoc etc., exponit quod dixerat. Et dicit quod hic intendit dicere de primo caelo, idest de suprema sphaera, et de prima latione, idest de motu diurno quo totum caelum revolvitur, per motum primi mobilis, ab oriente usque in occidentem. Ideo autem de hoc motu specialiter loquitur, quia in hoc motu neque est aliqua irregularitas secundum rei veritatem, neque secundum apparentiam. Sed in his quae de subtus, idest in motu planetarum, iam plures motus conveniunt ad movendum unum corpus; vel secundum diversas sphaeras volventes et revolventes, sicut dicebant astrologi qui fuerunt tempore Aristotelis, ut patet in XII Metaphys.; vel secundum motus eccentricorum et epicyclorum, secundum modernos astrologos. Et ex hac diversitate motuum causatur irregularitas quae apparet circa planetas, secundum quam quandoque videntur directi motus, quandoque retrogradi, quandoque stationarii; quamvis secundum rei veritatem nullus motus in caelo sit irregularis. Rationes enim quas hic inducet, habent locum non solum in motu primi caeli, qui est simplex, et ex hoc nulla apparet in eo irregularitas; sed etiam in motibus planetarum, in quibus apparet irregularitas propter concursum multorum motuum. | 368. Secondly, at [280] he explains what he had said. And he says that he intends here to speak of the "first heaven," i.e., the outermost sphere and of the "first carrying," i.e., of the diurnal motion by which the whole heaven is revolved, though the motion of the first mobile, from east to west. Now he speaks of this motion in particular because there is in it no irregularity either in fact or in appearance. But "in those things below," i.e., in the motion of the planets, several motions concur to move one body, either according to different shifting and revolving spheres, as the astronomers of Aristotle's time said, as is plain in Metaphysics XII, or according to the motions of eccentrics and epicycles according to modern astronomers. From this variety of motions is caused the irregularity which appears as to the planets, according to which they seem at one time to be moved with a forward motion, at another with a retrograde, and at still another to be at rest — although in fact no motion of the heaven is irregular. Now, the arguments which he will here adduce apply not only to the motion of the first heaven which is simple and hence gives no appearance of irregularity, but also to the motions of the planets, in which there is apparent irregularity due to the concurrence of many motions. |
| Deinde cum dicit: si enim irregulariter movebitur etc., probat propositum quatuor rationibus. Quarum prima sumitur ex ipsa forma motus circularis, et procedit sic. Si primum caelum irregulariter moveretur, manifeste oporteret quod in eo esset intensio, idest augmentum velocitatis, et virtus, idest summum velocitatis, et remissio, idest deminutio velocitatis. Omnis enim motus irregularis habet ista tria; non ita quod in quolibet motu irregulari vel inaequali sint ista tria, sed quia in quolibet motu sunt duo horum; idest virtus et intensio, sicut in motu naturali corporum gravium et levium est intensio et virtus, quia talis motus semper augetur in velocitate usque ad finem, in quo est velocissimus; motus autem horum corporum qui est contra naturam, habet virtutem et remissionem, quia in principio est velocissimus, et semper deminuitur velocitas, quousque tandem totus motus consumatur. Et sic ly omnis accipitur quasi collective, ut intelligatur quod in omnibus motibus irregularibus ista tria inveniuntur, non autem in unoquoque eorum. | 369. Then at [281] he proves his proposition with four arguments. The first is taken from the very form of circular motion, and proceeds thus: If the first heaven were moved in an irregular manner there would obviously have to be "intension," i.e., an increase of velocity, and "power," i.e., a maximum velocity, and "remission," i.e., a decrease of velocity. For every irregular motion possesses all three. This is not in the sense that these three are found in each and every irregular or unequal motion, but in the sense that in any motion two of them are found. Thus "power" [a maximum] and "intension" [an increase] are found, as they are found in the natural motion of heavy and light bodies, since such motion is always increasing in velocity up to the end, when it is at its swiftest; on the other hand, when such bodies are subjected to a motion contrary to their nature, there is "power" [a maximum] and "remission" [a decrease], because in the beginning such a motion is swiftest but its velocity is continually decreased until at last the whole motion is exhausted. Thus the word "every" is taken collectively in the sense that these three things are found in all motions that are irregular but not all in each one. |
| Deinde ostendit in qua parte motus irregularis inveniatur maxima velocitas. Et dicit quod virtus motus, idest maxima eius velocitas, invenitur aut unde fertur, idest versus terminum a quo, aut quo fertur, idest versus terminum ad quem, aut circa medium; sicut in his quae naturaliter moventur motu recto, invenitur maxima velocitas versus terminum ad quem feruntur, quia motus naturalis intenditur in fine, ut in primo habitum est; in his autem quae moventur contra naturam, invenitur maxima velocitas unde, idest versus terminum a quo, quia motus violentus intenditur in principio et remittitur in fine, ut in primo libro habitum est; sed in proiectis maxima velocitas motus invenitur circa medium. | 370. Then he shows where the maximum speed is found in an irregular motion. And he says that the "power" of a motion, i.e.., its maximum speed, is found either "whence it is brought forth," at the terminus a am, or "whither it is borne," i.e., at the terminus ad quem, or near the middle. Thus, in things that are being naturally moved with a straight motion the greatest velocity is toward the terminus toward which they are borne, since a natural motion is intensified at the end, as was had in Book I; while in things that are moved contrary to nature, the greatest velocity is found "whence," i.e., toward the terminus a quo, since a violent motion is intense in the beginning and slackens at the end, as was had in Book I. But in things projected, the maximum velocity is found near the middle. |
| Dubitatur autem quae philosophus vocet hic proiecta. Nam quaecumque proiiciuntur, aut moventur secundum motum naturalem, sicut cum lapis deorsum iacitur, et sic videtur quod motus intendatur in fine; vel moventur violenter, sicut cum lapis iacitur sursum, et sic motus eius debet esse intensissimus in principio, non autem in medio. | 371. Now there is a question about what the Philosopher here calls "things projected." For things that are projected are moved either according to a natural motion, as when a stone is thrown downward, in which case it is seen that the motion is increased at the end, or they are moved with compulsion, as when a stone is thrown upward, in which case its motion must be most intense at the beginning, and not in the middle. |
| Dicit autem Simplicius quod proiecta hic philosophus vocat corpora animalium, quae moventur ab anima non in sursum directe, neque directe in deorsum, sed quasi in latus, ad modum sagittae et aliorum proiectorum; propter quod et Aristoteles hic ea proiecta vocat. Manifestum est autem quod in motibus animalium maxima velocitas non invenitur neque a principio, quando quodammodo paulatim membra sua animalia expediunt ad motum; neque etiam circa finem, quando iam membra eorum sunt lassata; sed circa medium, quando sunt in ipso impetu motus. | But Simplicius says that by "things projected" the Philosopher here means the bodies of animals, whose soul does not move them directly upward or downward but, as it were, laterally, after the manner of an arrow and other projectiles, and that is why Aristotle here calls them things projected. Now it is plain [Simplicius continues], that in the case of the motions of animals, the maximum velocity is found neither in the beginning, when animals in a sense gradually depute their members to motion, or at the end, when their members are now tired, but near the middle, when they are in the very onrush of their motion. |
| Sed haec expositio videtur esse extorta. Unde Alexander dicit quod medium hic est accipiendum secundum locum, et non secundum tempus. Motus enim sagittae et aliorum sic proiectorum, non est neque in sursum neque in deorsum, sed in intermedio utriusque; et in hoc intermedio maxima velocitas horum motuum invenitur. | However, this seems to be a forced explanation. For this reason, Alexander says that "middle" here should refer to the place, and not to the time. For the motion of an arrow and of other things similarly projected is neither upward nor downward, but in what is intermediate to both these, and it is in this intermediate area that the maximum velocity of these motions is reached. |
| Possumus autem dicere quod etiam in his secundum tempus accipiendo medium, talia proiecta circa medium velocius moventur. Causatur enim motus talium proiectorum ex impulsu medii deferentis, quod facilius recipit impressionem moventis quam ipsum corpus grave quod proiicitur, ut patet in VIII Physic.; et ideo, quando multum de aere fuerit commotum, velocior est motus proiectionis in medio quam in principio, quando adhuc parum de aere commovetur, vel etiam quam in fine, quando iam incipit debilitari impressio proiicientis. Et huius signum est, quia huiusmodi proiecta non tantum impulsum faciunt in eo quod est omnino propinquum, vel in eo quod est multum remotum, sicut in eo quod mediocriter distat. | But we cay say that even if we take "middle" as referring to time, such projectiles still move more swiftly near the middle. For the motion of such projectiles is caused from the impulsion of the deferent medium which more easily receives the impression of the mover than does the heavy body that is projected, as is plain in Physics VIII. Consequently, after much air has now been set in motion, the motion of projection is swifter in the middle than at the beginning, when still only little air was being set in motion, or at the end, when the impulsion of the one projecting has already begun to fade. And a sign of this is that such projectiles do not strike with as much force an object which is entirely near or which is very remote as they do one which is at a mediate distance. |
| Sic igitur manifestum est quod maxima velocitas cuiuslibet motus irregularis, vel est in principio, vel in medio, vel in fine. Sed haec tria non est accipere in motu circulari caelestis corporis, neque quantum ad tempus, cum sit sempiternus, secundum eius opinionem; neque etiam quantum ad longitudinem, idest quantum ad figuram loci, quae est secundum lineam circularem, quae quidem est conducta, quasi circulariter in seipsam rediens, et est infrangibilis, non divisa in actu, ut possit ibi actu designari principium et finis. Et ita in circulatione caeli non invenitur secundum aliquam eius partem virtus, idest maxima eius velocitas; et per consequens neque irregularitas, quae fit propter intensionem et remissionem. | 372. Thus it is plain, therefore, that the maximum velocity of any irregular motion is either at the beginning, or in the middle, or at the end. But these three are not to be found in the circular movement of the heavenly body — neither with respect to time (since it is eternal according to his opinion) nor with respect to "length," i.e., with respect to the shape of the place, which is along a circular line "drawn around," i.e., as though always returning circularly to itself, and "unbreakable," i.e., not divided in act so as to allow an actual beginning and an end to be designated in it. Therefore in the revolution of the heaven there is no "power," i.e., maximum velocity, discernible at any part, and, as a consequence, no irregularity, which is due increase and remission. |
| Secundam rationem ponit ibi: adhuc quoniam omne etc.; quae accipitur simul ex parte moventis et mobilis. Ostensum est enim in VII et in VIII Physic. quod omne quod movetur, ab aliquo movente movetur. Unde necesse est, si in aliquo motu sit irregularitas, quod aut hoc fiat propter movens, aut propter id quod movetur, aut propter utrumque. Si enim movens non semper et aequali virtute moveat, sed quandoque maiori quandoque minori, fiet motus quandoque quidem velocior quandoque autem tardior: quia velocitas motus contingit ex hoc quod virtus moventis, propter suam magnitudinem, multum dominatur mobili. Et similiter si corpus quod movetur, per aliquam alterationem non permaneat in eadem dispositione, non erit aequaliter subiectum virtuti moventis, et ita non erit aequa velocitas motus. Et similiter si fiat transmutatio circa utrumque, scilicet moventem et mobile, poterit esse motus irregularis. | 373. He gives at [282] the second argument which is taken at once on the part of the mover and mobile. For it has been shown in Physics VII and VIII that whatever is moved is moved by some movent. Consequently, if there is irregularity in a motion, it must be due either to the movent, or to the thing moved, or to both. For if the movent does not move always and with equal power, but sometimes with more and sometimes with less, the motion will be sometimes slower, sometimes swifter. For the velocity of a motion results from the fact that the power of the movent, on account of its size, greatly dominates the mobile. And similarly, if the body being subjected to motion, by virtue of some alteration, does not maintain the same state, it will not be at all times equally subject to the power of the movent, and so there will not be an equal speed of motion. Finally, if both are modified, namely, the movent and the mobile, the motion could be irregular. |
| Sed nihil horum potest accidere circa caelum. De ipso enim corpore mobili ostensum est supra quod est primum et simplex, quia movetur primo et simplici motu; et quod est ingenitum et incorruptibile et totaliter intransmutabile (transmutatione scilicet variante substantiam et virtutem eius). Motor autem eius multo magis rationabile est quod sit talis conditionis. Cum enim movens sit potius moto, si corpus quod movetur est primum et simplex, et ingenitum et incorruptibile, multo magis motivum eius erit tale. Ostensum est etiam in VIII Physic. quod motor caeli est incorporeus, nullam habens magnitudinem: si igitur ipsum caelum, quod est corpus, non immutetur a dispositione suae substantiae et virtutis, multo magis non transmutabitur motor eius, qui est incorporeus. Ex quo patet quod impossibile est motum caeli esse irregularem. | But none of these possibilities can be verified with regard to the heaven. For it has been shown above that the mobile body here involved is first and simple, since it is moved by a first and simple motion; moreover, that it is ungenerated, indestructible and utterly unchangeable {i.e., with a change causing a variance in substance or strength). Now there is all the more reason for the mover of such a body to be of such a condition. For since the mover is more powerful than the moved, if the body which is moved is a primary and simple body and subject neither to generation nor corruption, so much the more so will its mover be. It was also shown in Physics VIII that the mover of the heaven is incorporeal and without any magnitude. If then the heaven, which is a body, is not changed in the state of its substance and strength, much less will its mover, which is incorporeal, be changed. From this it is plain that it is impossible for the motion of the heaven to be irregular. |
Lecture 9:
Two other arguments, proving no irregularity in the motion of the heavenChapter 6 cont. Καὶ γὰρ εἰ γίνεται ἀνώμαλος, ἤτοι ὅλη μεταβάλλει καὶ ὁτὲ μὲν γίνεται θάττων ὁτὲ δὲ βραδυτέρα πάλιν, ἢ τὰ μέρη αὐτῆς. Τὰ μὲν οὖν μέρη ὅτι οὐκ ἔστιν ἀνώμαλα, φανερόν ἤδη γὰρ ἂν ἐγεγόνει διάστασις τῶν ἄστρων ἐν τῷ ἀπείρῳ χρόνῳ, τοῦ μὲν θᾶττον κινουμένου τοῦ δὲ βραδύτερον. Οὐ φαίνεται δ' οὐθὲν ἄλλως ἔχον τοῖς διαστήμασιν. Ἀλλὰ μὴν οὐδὲ τὴν ὅλην ἐγχωρεῖ μεταβάλλειν ἡ γὰρ ἄνεσις ἑκάστου γίνεται δι' ἀδυναμίαν, ἡ δ' ἀδυναμία παρὰ φύσιν καὶ γὰρ αἱ ἐν τοῖς ζῴοις ἀδυναμίαι πᾶσαι παρὰ φύσιν εἰσίν, οἷον γῆρας καὶ φθίσις. Ὅλη γὰρ ἴσως ἡ σύστασις τῶν ζῴων ἐκ τοιούτων συνέστηκεν ἃ διαφέρει τοῖς οἰκείοις τόποις οὐθὲν γὰρ τῶν μερῶν ἔχει τὴν αὑτοῦ χώραν. Εἰ οὖν ἐν τοῖς πρώτοις μή ἐστι τὸ παρὰ φύσιν (ἁπλᾶ γὰρ καὶ ἄμικτα καὶ ἐν τῇ οἰκείᾳ χώρᾳ, καὶ οὐθὲν αὐτοῖς ἐναντίον), οὐδ' ἂν ἀδυναμία εἴη, ὥστ' οὐδ' ἄνεσις οὐδ' ἐπίτασις εἰ γὰρ ἐπίτασις, καὶ ἄνεσις. 283 For if irregularity occurs, there must be change either in the movement as a whole, from fast to slow and slow to fast, or in its parts. That there is no irregularity in the parts is obvious, since, if there were, some divergence of the stars would have taken place before now in the infinity of time, as one moved slower and another faster: but no alteration of their intervals is ever observed. Nor again is a change in the movement as a whole admissible. Retardation is always due to incapacity, and incapacity is unnatural. The incapacities of animals, age, decay, and the like, are all unnatural, due, it seems, to the fact that the whole animal complex is made up of materials which differ in respect of their proper places, and no single part occupies its own place. If therefore that which is primary contains nothing unnatural, being simple and unmixed and in its proper place and having no contrary, then it has no place for incapacity, nor, consequently, for retardation or (since acceleration involves retardation) for acceleration. Ἔτι δὲ καὶ ἄλογον ἄπειρον χρόνον ἀδύνατον εἶναι τὸ κινοῦν, καὶ πάλιν ἄλλον ἄπειρον δυνατόν οὐθὲν γὰρ φαίνεται ὂν ἄπειρον χρόνον παρὰ φύσιν (ἡ δ' ἀδυναμία παρὰ φύσιν), οὐδὲ τὸν ἴσον χρόνον παρὰ φύσιν καὶ κατὰ φύσιν, οὐδ' ὅλως δυνατὸν καὶ ἀδύνατον ἀνάγκη δ', εἰ ἀνίησιν ἡ κίνησις, ἄπειρον ἀνιέναι χρόνον. 284 Again, it is inconceivable that the mover should first show incapacity for an infinite time, and capacity afterwards for another infinity. For clearly nothing which, like incapacity, unnatural ever continues for an infinity of time; nor does the unnatural endure as long as the natural, or any form of incapacity as long as the capacity. But if the movement is retarded it must necessarily be retarded for an infinite time. Ἀλλὰ μὴν οὐδ' ἐπιτείνειν ἀεὶ ἢ πάλιν ἀνίενται δυνατόν ἄπειρος γὰρ ἂν εἴη καὶ ἀόριστος ἡ κίνησις, ἅπασαν δέ φαμεν ἔκ τινος εἴς τι εἶναι καὶ ὡρισμένην. 285 Equally impossible is perpetual acceleration or perpetual retardation. For such movement would be infinite and indefinite, but every movement, in our view, proceeds from one point to another and is definite in character. Ἔτι δ' εἴ τις λάβοι εἶναί τινα χρόνον ἐλάχιστον, οὗ οὐκ ἐνδέχεται ἐν ἐλάττονι κινηθῆναι τὸν οὐρανόν (ὥσπερ γὰρ οὐδὲ κιθαρίσαι οὐδὲ βαδίσαι ἐν ὁτῳοῦν χρόνῳ δυνατόν, ἀλλ' ἔστιν ἑκάστης πράξεως ὡρισμένος ὁ ἐλάχιστος χρόνος κατὰ τὸ μὴ ὑπερβάλλειν, οὕτως οὐδὲ κινηθῆναι τὸν οὐρανὸν (289a.) ἐν ὁτῳοῦν χρόνῳ δυνατόν) εἰ οὖν τοῦτ' ἀληθές, οὐκ ἂν εἴη ἀεὶ ἐπίτασις τῆς φορᾶς (εἰ δὲ μὴ ἐπίτασις, οὐδ' ἄνεσις ὁμοίως γὰρ ἄμφω καὶ θάτερον), εἴπερ τῷ αὐτῷ τε ἐπιτείνει τάχει ἢ μείζονι, καὶ ἄπειρον χρόνον. 286 Again, suppose one assumes a minimum time in less than which the heaven could not complete its movement. For, as a given walk or a given exercise on the harp cannot take any and every time, but every performance has its definite minimum time which is unsurpassable, so, one might suppose, the movement of the heaven could not be completed in any and every time. But in that case perpetual acceleration is impossible (and, equally, perpetual retardation: for the argument holds of both and each), if we may take acceleration to proceed by identical or increasing additions of speed and for an infinite time. Λείπεται δὴ λέγειν ἐναλλὰξ εἶναι τῇ κινήσει τὸ θᾶττον καὶ τὸ βραδύτερον τοῦτο δὲ παντελῶς ἄλογον καὶ πλάσματι ὅμοιον. Ἔτι δὲ καὶ τὸ μὴ λανθάνειν ἐπὶ τούτων εὐλογώτερον εὐαισθητότερα γὰρ τὰ παρ' ἄλληλα τιθέμενα. 287 The remaining alternative is to say that the movement exhibits an alternation of slower and faster: but this is a mere fiction and quite inconceivable. Further, irregularity of this kind would be particularly unlikely to pass unobserved, since contrast makes observation easy. Ὅτι μὲν οὖν εἷς τε μόνος ἐστὶν ὁ οὐρανός, καὶ οὗτος ἀγένητος καὶ ἀΐδιος, ἔτι δὲ κινούμενος ὁμαλῶς, ἐπὶ τοσοῦτον ἡμῖν εἰρήσθω. 288 That there is one heaven, then, only, and that it is ungenerated and eternal, and further that its movement is regular, has now been sufficiently explained.
| Hic ponit tertiam rationem, quae sumitur solum ex parte mobilis. Et dicit quod si motus caeli irregulariter peragatur, aut hoc erit ita quod tota caeli mutatio transmutetur, ita quod quandoque sit velocior quandoque tardior, aut partes eius: et intelligitur tota mutatio motus totius sphaerae supremae, partes autem mutationis intelliguntur motus partium caeli. | 374. Here the Philosopher gives the third argument which is taken solely from the viewpoint of the mobile [283]. And he says that if the motion of the heaven were executed irregularly this would be either in such a way that the entire change of the heaven would vary in such a way as to be now slower, now swifter, or else parts of it would vary. The phrase "entire change" refers to the motion of the whole highest sphere, while "parts" of the change refers to the motions of the parts of the heaven. |
| Quod autem partes supremae sphaerae non moveantur irregulariter, ita scilicet quod una pars caeli quandoque citius quandoque tardius moveatur, ostendit supponendo quod sphaera stellarum fixarum sit suprema sphaera: nondum enim suo tempore deprehensum erat quod stellae fixae haberent proprium motum praeter motum diurnum; et ideo attribuit primum motum, scilicet diurnum, sphaerae stellarum fixarum, quasi proprium ei; cum tamen posteriores astrologi dicant quod sphaera stellarum fixarum habeat quendam proprium motum, supra quem ponunt aliam sphaeram, cui attribuunt primum motum. | But that the parts of the supreme sphere are not moved irregularly so that one part of the heaven moves now swifter and now slower, he shows on the supposition that the sphere of the fixed stars is the supreme sphere. For in his [Aristotle's] time it had not yet been discovered that the fixed stars, in addition to the diurnal motion of the heaven, had a motion of their own [the precession of the equinox]. And therefore he attributes the first motion, namely, the diurnal motion, to the sphere of the fixed stars, as though proper to it. Later astronomers, however, assert the sphere of the fixed stars to have a certain proper motion, above which they place another sphere to which they attribute the first motion. |
| Supposito ergo quod sphaera stellarum fixarum sit suprema sphaera, probat quod partes eius non moveantur irregulariter. Quia si singulae partes eius quandoque citius quandoque tardius moverentur, iam a longinquo tempore stellae fixae in alia distantia se haberent ad invicem quam prius, una earum velocius et alia tardius mota. Sed huius contrarium apparet: quia inveniuntur eandem figuram conservare, et eodem modo ab invicem elongari in hoc tempore, sicut etiam invenerunt antiquissimi observatores. Non ergo est irregularitas in motu primi caeli quantum ad partes eius. | On the supposition, therefore, that the sphere of the fixed stars is the supreme [outermost] sphere, he proves that its parts are not moved irregularly. For if its individual parts were moved now slower, now faster, then over a long period of time the fixed stars would have come to have different distances between themselves than previously as a result of one star moving faster and another slower. But the contrary of this appears. For they are found to retain the same configuration, and to be at the same distance from one another, now as when these were established by the earliest observers. Therefore there is no irregularity in the motion of the first heaven so far as its parts are concerned. |
| Sed neque etiam tota transmutatio primi caeli transmutatur de velocitate in remissionem velocitatis. Manifestum est enim quod remissio velocitatis motus cuiuscumque mobilis sit propter impotentiam; sicut videmus quod quando corpora animalium lassantur, remittitur eorum motus. Omnis autem impotentia et defectus est praeter naturam, sicut patet in animalibus, in quibus senectus et decrementum et alia huiusmodi sunt praeter naturam. | 375. But if we pass from the parts to the whole "change" of the first heaven, there is no variation in velocity to a remission of velocity either. For it is plain that the slowing down of a mobile's motion is due to lack of power, just as, when the bodies of animals become tired, their motion slows down. But all impotency and defect is against nature, as is plain in animals, in which old age and decrease and other things of the sort are against nature. |
| Quod est intelligendum quantum ad naturam particularem, quae est conservativa uniuscuiusque individui quantum potest: unde praeter intentionem eius est quod deficiat in conservando. Non autem est praeter naturam universalem, ex qua causatur non solum generatio, sed etiam corruptio, et per consequens alii defectus ad corruptionem tendentes, in his inferioribus: dicitur autem natura universalis virtus activa in causa universali, puta in corpore caelesti. | This of course is to be understood with respect to the particular nature, which preserves the individual as far as it can; hence it is against its intent that it be deficient in conserving. But it is not against universal nature, which is the cause not only of generation but also of corruption and, consequently, of the other defects that lead to corruption in the lower bodies. By universal nature is meant the active power present in a universal cause, for example, in the heavenly body. |
| Ideo autem defectus praeter naturam particularem in animalibus accidere possunt, quia tota substantia animalis consistit ex talibus corporibus quae distant a propriis locis: componitur enim corpus animalis ex quatuor elementis, quorum nullum tenet proprium locum. Et quia ea quae sunt praeter naturam non possunt esse sempiterna, ut patet ex his quae supra dicta sunt, necesse est quod quandoque animalibus accidat corruptio et defectus. Sed in primis corporibus, scilicet caelestibus, nihil potest accidere praeter naturam: quia sunt simplicia, non autem mixta ex diversis, et in proprio loco existunt, et nihil contrarium est eis, ut patet ex his quae in primo libro dicta sunt. Et ita in eis non potest esse aliqua impotentia. Et ideo in eis non potest esse aliqua remissio, idest deminutio velocitatis: et per consequens neque intensio, idest velocitatis augmentum, quia ista duo se invicem consequuntur; sicut enim quando intenditur motus, proceditur a remisso ad intensum, ita quando remittitur, proceditur ab intenso ad remissum. | Now the reason why defects beyond the particular nature can occur in animals is that the whole substance of an animal is a resultant of bodies that are outside their appropriate places. For the body of an animal is composed of the four elements, none of which is in its own proper place. And because those things which are "outside nature" cannot last forever, as is evident from what has been stated above, necessarily corruption and defect will occur at some time to animals. But in the first bodies, namely, the heavenly bodies, nothing "outside nature" can happen, for they are simple things and not mixtures of various elements; moreover, they are in their appropriate place and there is nothing contrary to them, as is plain from what was said in Book I. Hence no impotency can be found in them. Therefore, too, there cannot be in them any "remission," i.e., decrease of velocity, and consequently any "intension," i.e., increase of velocity, because these two follow upon each other — for just as a motion, when it is intensified, proceeds from "remiss" to "intense," so when it diminishes, it goes from "intense" to "remiss." |
| Quartam rationem ponit ibi: adhuc autem et irrationabile etc.; quae sumitur ex parte moventis, et procedit ex quadam divisione. Si enim in motu caeli sit intensio et remissio, hoc non potest esse nisi tribus modis: uno modo ut semper intendatur vel semper remittatur; alio modo ut quandoque intendatur et quandoque remittatur, et hoc dupliciter: uno modo ut tota intensio et tota remissio sit simul, ad quod quidem, supposito quod caelum moveatur tempore infinito, secundum eius opinionem, sequitur quod infinito tempore prius intendatur motus eius et postea remittatur, aut e converso; alio modo ut vicissim quandoque remittatur et quandoque intendatur. Sed quodlibet istorum est impossibile. Ergo impossibile est quod in motu caeli sit remissio et intensio. | 376. The fourth argument, at [2843 is considered from the standpoint of the mover, and proceeds from a certain division. For if there is intensity and remission in the motion of the heaven, this can take place in only three ways: In one way, it might be always growing in intensity or always becoming remiss; in another way, it could at one time be getting intense and at another time be getting remiss, and this in two ways — in one way, such that the whole intensity and the whole remission would occur at once, on which follows (supposing, according to his opinion, that the heaven is moved for infinite time), that for an infinite time its motion first becomes intense and later becomes remiss, or conversely; in another way so that it alternates between successive states of intensity and remission. But each one of these is impossible. Therefore, it is impossible for remission and intensity to occur in the motion of the heaven. |
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Primo ergo ostendit impossibile esse quod infinito tempore intendatur prius, et postea infinito tempore remittatur, vel e converso; secundo ostendit impossibile esse quod semper intendatur vel semper remittatur, ibi: sed adhuc neque etc.; tertio ostendit impossibile esse quod vicissim intendatur et remittatur, ibi: relinquitur itaque et cetera. |
First, therefore he shows that it is impossible for that motion to become intense for an infinite time and later become remiss for an infinite time, or conversely; Secondly, he shows that it is impossible for it to be always becoming intense or always becoming remiss, at 378; Thirdly, he shows that it cannot be alternately becoming intense and remiss, at 381. |
| Dicit ergo primo quod irrationabile est quod motor caeli infinito tempore sit potens et velociter moveat, et rursus alio infinito tempore sit impotens et tarde moveat (nam remissio motus causatur ex impotentia, intensio autem ex potentia). | 377. He says therefore first [2843 that it is unreasonable to suppose that the mover of the heaven for an infinite time is in power and moves swiftly, and then for another infinite time is weak and moves slowly (for remission of motion is due to lack of power, whereas intensity is due to power). |
| Et hoc idem esse irrationabile, ostendit duobus mediis. Primo quidem quia nihil praeter naturam videtur existere tempore infinito: ea enim quae sunt secundum naturam, sunt semper vel in maiori parte. Impotentia autem est praeter naturam, ut habitum est: ergo impossibile est quod aliquid infinito tempore sit impotens. | The same conclusion that this is unreasonable, he now proves through two middles. First, because nothing contrary to nature is seen to exist for an infinite time — for things according to nature exist always or for the most part. Now lack of power is contrary to nature, as was had. Therefore, it is impossible for anything to be deficient in power for an infinite time. |
| Secundo quia non est aequale tempus eius quod est secundum naturam, et eius quod est praeter naturam: quia id quod est praeter naturam est in paucioribus, id autem quod est secundum naturam est ut in pluribus vel semper. Sed potentia rei est secundum naturam, impotentia autem est praeter naturam. Ergo impossibile est quod aliquid tempore aequali, scilicet tempore infinito, sit potens et impotens: et per consequens impossibile est quod infinito tempore intendatur motus, et iterum infinito tempore remittatur. Sed si remittitur motus caeli secundum modum qui dictus est, necesse est quod infinito tempore remittatur. | Secondly, because the time is not equal in the case of that which is according to nature and in the case of that which is not according to nature —for that which is not according to nature occurs in a few cases only, whereas what is according to nature happens for the most part or always. But the power. of a thing is according to nature, whereas defeat of strength is "outside" nature.. Therefore, it is impossible for anything for an equal period of time, namely, for an infinite time, to be in power and powerless. Consequently, it is also impossible for motion to become intense for an infinite time and then to become remiss for an infinite time. But if the motion of the heaven becomes remiss in the manner described, it must become so for an infinite time. |
| Quidam tamen, non intelligentes intentionem Aristotelis, accipiunt hoc quasi simpliciter et absolute dictum, eo quod non est ratio quare magis uno tempore remittatur quam alio. Sed hoc est praeter intentionem philosophi. | Now some, not understanding Aristotle's intention, take this as stated absolutely on the ground that there is no reason why it should become remiss at one time rather than another. But this is not according to his intention. |
| Deinde cum dicit: sed adhuc neque etc., ostendit quod impossibile sit motum caeli vel semper intendi, vel semper remitti; et hoc duabus rationibus. Quarum prima est, quia intensio et remissio cuiuslibet motus irregularis deficit circa aliquem terminum ipsius motus; sicut motus naturalis intenditur usque ad aliquem terminum, et similiter motus violentus remittitur usque ad aliquem terminum. Si ergo intensio vel remissio motus caeli nunquam terminetur, sed in infinitum procedat, sequitur quod motus caeli sit infinitus et indeterminatus. Quod patet esse falsum: probatum est enim in VI Physic. quod, quia omnis motus est ex aliquo in aliquid, necesse est quod sit determinatus. Unde etiam una circulatio caeli est determinata: sed motus caeli dicitur infinitus secundum diversas circulationes sibi succedentes. | 378. Then a [285] he shows that it is impossible for the motion of the heaven to become always more intense or to become always more remiss. He shows this with two arguments. The first of these is that the intensity and remission of any irregular motion cease near some terminus of the motion, just as a natural motion becomes intense up to a certain terminal point and as a violent motion becomes remiss up to a certain terminal point. If, therefore, the intensity or remission of the motion of the heaven should be never terminated but proceed ad infinitum, it would follow that the motion of the heaven would be infinite and undeterminate, Now this is plainly false, for it has been proved in Physics VI that, since every motion proceeds from something to something, it must necessarily be determinate. For this reason even a single revolution of the heaven is determinate. It is only according to the various revolutions that succeed one another that the motion of the heaven is said to be infinite. |
| Secundam rationem ponit ibi: adhuc autem si quis et cetera. Et dicit quod hoc etiam esse impossibile est manifestum, si quis concedat esse aliquod tempus minimum, ita quod in minori non contingat moveri caelum. Quilibet enim motus vel actio habet determinatum tempus, quod non transcendit: quamvis enim tempus sit divisibile in infinitum, non tamen est possibile citharizare vel ambulare in quocumque tempore; sed quilibet actus habet determinatum minimum tempus, quod non excedit velocitate, ut scilicet in minori tempore perficiatur. Unde nec caelum possibile est moveri in quocumque tempore, sed habet aliquod minimum tempus determinatum. Ex quo patet quod non semper intenditur velocitas motus eius, quia sic velocitas eius excederet quodlibet minimum tempus. Si vero non semper potest intendi motus caeli, pari ratione neque semper potest remitti, quia eadem ratio est de uno et de altero: sicut enim est minimum tempus alicuius actionis, ita et maximum in quo peragitur. | 379. The second argument on this point he gives at [286]. And he says, that this is impossible is also evident if you grant that there is a minimum time, in less than which the heaven cannot be moved. For every motion or action involves a determinate time that it cannot ignore. Thus, although time is divisible ad infinitum, yet it is not possible to play the harp or walk in just any time whatever; rather, every action requires a minimum of time which it cannot exceed by speed, in such a way as for it to be performed in less time. For this reason it is not possible for the heaven to be moved in just any period of time, but rather it has some definite minimum time. From this it is clear that the speed of its motion is not forever being increased, because then its speed would exceed any minimum time whatever, Now if the speed of the heavenly motion cannot be always increasing, then for the same reason it cannot be always decreasing, because the same argument applies to both — for just as there is a minimum time required for an action, so too there is a maximum in which it takes place. |
| Posset autem aliquis praedictae rationi obviare, dicendo quod semper intenditur velocitas motus caeli, et tamen nunquam transcenditur quoddam minimum tempus datum, si quidem fiat appositio velocitatis non aequalis aut maior, sed semper minor et minor; sicut dicitur in III Physic. quod, si linea dividatur secundum eandem proportionem, puta ut subtrahatur a tota linea tertia pars, et iterum a residuo tertia pars, et a residuo iterum tertia pars, hoc poterit in infinitum procedere; et si eorum quae subtrahuntur posterius addatur priori, fiet in infinitum additio, nec tamen pervenietur unquam ad quantitatem totius lineae, quia semper erit aliquid residuum de linea quae dividebatur. Si tamen semper subtraheretur pars aequalis quantitatis vel maioris, et adderetur ad id quod prius acceptum est, oporteret transcendere omnem quantitatem determinatam. | 380. But someone could object to this argument and say that the velocity of the heavenly motion can be always increasing, without, nevertheless, some minimum given time ever being transgressed, so long as any addition of speed is not equal or greater but is always smaller and smaller. For it is said in Physics III that if a line be divided according to the same proportion, for example, by taking 1/3 from the whole line and then 1/3 from the remainder, and again 1/3 from that remainder, the process could go on ad infinitum; and if the segments removed subsequently be added to what was removed earlier, the process of adding will continue forever without ever arriving at the quantity of the whole line, because there will always be some part left of the line which is being divided. However, if one always takes a part of equal or greater quantity, and it is added to what was taken previously, one will necessarily exceed any predetermined quantity. |
| Et similiter dicit hic intelligendum esse quod transcendetur omne minimum tempus datum, quod est transcendere omnem magnitudinem velocitatis, si semper per infinitum tempus addatur aequalis velocitas vel etiam maior. Si vero prius adderetur magna velocitas, et postea minor, et sic inde, sicut dictum est in divisione et additione lineae, non transcenderetur omnis velocitas, nec omne minimum tempus; cum non esset pura intensio, sed intensio remissioni adiuncta, quia movens non posset semper aequaliter addere ad velocitatem. | And he says that we should understand this case similarly in the sense of every minimum given time's being surpassed, which is to exceed every greatness of velocity, by the addition, over an infinite time, of equal or greater speed. For if a great velocity were first added, and then a lesser one, and so on, as was said in the division and addition of a line, not every velocity or every minimum time would be transcended, since there would not be a pure intensification, but an intensification combined with remission, because the mover would not be able always to make equal additions to the velocity. |
| Deinde cum dicit: relinquitur itaque etc., ostendit impossibile esse quod vicissim intendatur et remittatur motus caeli; et hoc dupliciter. Primo quidem quia hoc videtur penitus esse irrationabile, et simile fictioni: nulla enim ratio assignari potest huius vicissitudinis. Secundo quia talis diversitas in motu caeli non lateret; opposita enim iuxta se posita magis sentiuntur: et tamen nihil tale percipimus. Unde relinquitur quod in motu caeli nulla sit irregularitas. | 381. Then at [287] he shows that it is impossible for the motion of the heaven to be alternately intensified and remitted, and this for two reasons. First, such a thing is seen to be utterly unreasonable, and like something imaginary — since no reason for this alternation can be assigned. Secondly, such diversity in the motion of the heaven would not escape observation — for when two opposites are juxtaposed, their differences become more striking. Yet we perceive no such variations. Hence it remains that there is no irregularity in the motion of the heaven. |
| Ultimo autem, quia hic finit suam considerationem de toto caelo, epilogat intantum dictum esse quod sit unum tantum caelum, et quod sit ingenitum et sempiternum, et quod regulariter moveatur. | Finally, at [288], because he here puts an end to his consideration of the whole heaven, he states in summary that so far it has been said that there is one single heaven, and that it is ungenerated and eternal, and it is moved with a regular motion. |
Lecture 10:
On the nature of the starsChapter 7 Περὶ δὲ τῶν καλουμένων ἄστρων ἑπόμενον ἂν εἴη λέγειν, ἐκ τίνων τε συνεστᾶσι καὶ ἐν ποίοις σχήμασι καὶ τίνες αἱ κινήσεις αὐτῶν. 289 We have next to speak of the stars, as they are called, of their composition, shape, and movements. Εὐλογώτατον δὴ καὶ τοῖς εἰρημένοις ἑπόμενον ἡμῖν τὸ ἕκαστον τῶν ἄστρων ποιεῖν ἐκ τούτου τοῦ σώματος ἐν ᾧ τυγχάνει τὴν φορὰν ἔχον, ἐπειδὴ ἔφαμέν τι εἶναι ὃ κύκλῳ φέρεσθαι πέφυκεν 290 It would be most natural and consequent upon what has been said that each of the stars should be composed of that substance in which their path lies, since, as we said, there is an element whose natural movement is circular. ὥσπερ γὰρ οἱ πύρινα φάσκοντες εἶναι διὰ τοῦτο λέγουσιν, ὅτι τὸ ἄνω σῶμα πῦρ εἶναί φασιν, ὡς εὔλογον ὂν ἕκαστον συνεστάναι ἐκ τούτων ἐν οἷς ἕκαστόν ἐστιν, ὁμοίως καὶ ἡμεῖς λέγομεν. 291 In so saying we are only following the same line of thought as those who say that the stars are fiery because they believe the upper body to be fire, the presumption being that a thing is composed of the same stuff as that in which it is situated. Ἡ δὲ θερμότης ἀπ' αὐτῶν καὶ τὸ φῶς γίνεται παρεκτριβομένου τοῦ ἀέρος ὑπὸ τῆς ἐκείνων φορᾶς. Πέφυκε γὰρ ἡ κίνησις ἐκπυροῦν καὶ ξύλα καὶ λίθους καὶ σίδηρον εὐλογώτερον οὖν τὸ ἐγγύτερον τοῦ πυρός, ἐγγύτερον δὲ ὁ ἀήρ οἷον καὶ ἐπὶ τῶν φερομένων βελῶν ταῦτα γὰρ αὐτὰ ἐκπυροῦται οὕτως ὥστε τήκεσθαι τὰς μολυβδίδας, καὶ ἐπείπερ αὐτὰ ἐκπυροῦται, ἀνάγκη καὶ τὸν κύκλῳ αὐτῶν ἀέρα τὸ αὐτὸ τοῦτο πάσχειν. 292 The warmth and light which proceed from them are caused by the friction set up in the air by their motion. Movement tends to create fire in wood, stone, and iron; and with even more reason should it have that effect on air, a substance which is closer to fire than these. An example is that of missiles, which as they move are themselves fired so strongly that leaden balls are melted; and if they are fired the surrounding air must be similarly affected. Ταῦτα μὲν οὖν αὐτὰ ἐκθερμαίνεται διὰ τὸ ἐν ἀέρι φέρεσθαι, ὃς διὰ τὴν πληγὴν τῇ κινήσει γίγνεται πῦρ. Τῶν δὲ ἄνω ἕκαστον ἐν τῇ σφαίρᾳ φέρεται, ὥστ' αὐτὰ μὲν μὴ ἐκπυροῦσθαι, τοῦ δ' ἀέρος ὑπὸ τὴν τοῦ κυκλικοῦ σώματος σφαῖραν ὄντος ἀνάγκη φερομένης ἐκείνης ἐκθερμαίνεσθαι, 293 Now while the missiles are heated by reason of their motion in air, which is turned into fire by the agitation produced by their movement, the upper bodies are carried on a moving sphere, so that, though they are not themselves fired, yet the air underneath the sphere of the revolving body is necessarily heated by its motion, καὶ ταύτῃ μάλιστα ᾗ ὁ ἥλιος τετύχηκεν ἐνδεδεμένος διὸ δὴ πλησιάζοντός τε αὐτοῦ καὶ ἀνίσχοντος καὶ ὑπὲρ ἡμῶν ὄντος γίγνεται ἡ θερμότης. 294 and particularly in that part where the sun is attached to it. Hence warmth increases as the sun gets nearer or higher or overhead. Ὅτι μὲν οὖν οὔτε πύρινά ἐστιν οὔτ' ἐν πυρὶ φέρεται, ταῦθ' ἡμῖν εἰρήσθω περὶ αὐτῶν. 295 Of the fact, then, that the stars are neither fiery nor move in fire, enough has been said.
| Postquam philosophus determinavit de caelo, hic determinat de stellis. | 382. After settling the question of the heaven, the Philosopher now treats of the stars. |
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Et primo determinat veritatem; secundo movet quasdam dubitationes et solvit, ibi: duabus autem dubitationibus et cetera. |
First he determines the truth; Secondly, he raises and settles some doubts (L. 17). |
| Circa primum quatuor facit: | As to the first he does four things: |
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primo determinat de natura stellarum; secundo de motu earum, ibi: quoniam autem videntur etc.; tertio de ordine earum, ibi: de ordine autem ipsorum etc.; quarto de figura earum, ibi: figuram autem uniuscuiusque et cetera. |
First he determines the nature of the stars; Secondly, their motion (L. 11); Thirdly, their order (L. 15); Fourthly, their shape (L. 16). |
| Circa primum tria facit: | With respect to the first he does three things: |
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primo dicit de quo est intentio; secundo manifestat veritatem, ibi: rationabilissimum autem etc.; tertio excludit obiectionem, ibi: calor autem ab ipsis et cetera. |
First he states his intention; Secondly, he manifests the truth at 383; Thirdly, he excludes an objection, at 387. |
| Dicit ergo primo quod, postquam determinatum est de toto caelo, consequens est ut dicamus de his quae vocantur astra, ex quibus constant, idest ex qua natura sint, et quam figuram habeant, et quales sint motus eorum. | He says therefore first [289] that, after having determined the question of the whole heaven, we should next consider those things called "stars" and determine "what they are made out of," i.e., of what nature they are, and what shape they have, and of what sort are their motions. |
| Deinde cum dicit: rationabilissimum autem etc., ostendit ex qua natura sint corpora stellarum. Et primo proponit quod intendit, dicens quod ponere unamquamque stellam esse de natura corporis sphaerici in quo movetur, est in se consideratum valde rationabile, eo quod loca consequuntur naturas corporum; unde rationabile est quod stellae pertineant ad naturam sphaerae in qua situantur. Consequitur etiam hoc ex necessitate ad ea quae supra diximus. Dictum est enim quod caelum habet naturam aliam praeter naturam quatuor elementorum, propter hoc quod habet alium motum naturalem a motibus elementorum, scilicet motum circularem; unde, cum stellae moveantur circulariter sicut sphaerae caelestes, consequens est quod habeant eandem naturam cum sphaeris caelestibus, et differant a natura quatuor elementorum. | 383. Then at [290] he shows of what nature the stars are. First he proposes what he intends, and says that the assumption that each star is of the nature of the spherical body in which it is moved is of itself most reasonable, since places follow upon the natures of bodies. Hence it is reasonable that the stars pertain to the nature of the sphere in which they are situated. Moreover, this follows of necessity from what we have said above. For it was said that the heaven has a nature other than the nature of the four elements, since it has a motion distinct from the motions of the [four] elements, namely, a circular motion. Hence, since the stars are moved circularly as the heavenly spheres are, the consequence is that they have a nature in common with the heavenly spheres and differ from the nature of the four elements. |
| Sed circa hoc videtur esse duplex dubitatio. Prima quidem dubitatio est quia corpora stellarum videntur habere differentiam ad corpora sphaerarum caelestium, ex eo quod sunt lucida et videntur spissiora; et ita videtur in corporibus caelestibus esse aliqua contrarietas. Contrarietas autem est causa corruptionis. Videtur ergo quod corpora caelestia sint corruptibilia secundum suam naturam; quod est contra ea quae in primo libro determinata sunt. | 384. But there seems to be a twofold doubt on this matter. The first one arises from the fact that the bodies of the stars appear to differ from the bodies of the heavenly spheres, since they shine and seem to be more compact; consequently, there seems to be contrariety in the heavenly bodies. Now contrariety is the cause of corruption. It seems, therefore, that heavenly bodies are according to their nature corruptible, which is against what has been determined in Book I. |
| Et ad hoc dicendum est quod non omnis diversitas, proprie loquendo, habet rationem contrarietatis; sed ad hoc quod aliqua diversa sint contraria, duo requiruntur. Quorum unum est quod sint nata aliqualiter esse in eodem subiecto, vel proximo vel saltem remoto: calor enim contrariatur frigori, quod tamen non est natum esse in igne, sed est natum esse in materia ignis, quae est primum subiectum. Secundo requiritur quod diversa quae sunt contraria, non possint esse simul, sed mutuo se expellant. Unde album et nigrum, secundum quod sunt in materia, sunt contraria mutuo se expellentia; secundum tamen quod sunt in intellectu, non habent contrarietatem, sed sunt simul; quinimmo unum eorum cognoscitur per aliud. | The answer to this is that not every diversity, strictly speaking, has the notion of contrariety. Rather, in order that things be contrary, two things are required: One of these is that they be apt to exist in some way in the same subject, whether proximate, or at least remote — thus heat is contrary to cold, which latter, however, is not apt to exist in fire, but is apt to exist in the matter of fire, which is the first subject. Secondly, it is required that the diverse things that are contrary not be able to exist together, but mutually expel one another. Hence, white and black, as existing in matter, are contraries mutually expelling one another. But as existing in the intellect they have no contrariety but can exist together; as a matter of fact, one of them is known through the other. |
| Formae autem vel qualitates diversae quae videntur esse in corporibus caelestibus, nullo modo sunt natae esse in eodem, nec sicut in proximo, nec sicut in primo subiecto: non enim corpus stellae est natum reduci ad dispositionem ceterarum partium sphaerae caelestis, sed nec e converso. | Now the differing forms or qualities that seem to be in the heavenly bodies are in no sense apt to exist in the same subject, whether it be a proximate subject or a first subject — for the body of a star is not apt to be reduced to the disposition of the other parts of the heavenly spheres, or vice versa. |
| Similiter etiam oportet dicere formas seu qualitates contrarias quae sunt in inferioribus corporibus, esse aliqualiter in corporibus caelestibus, non quidem univoce, sed sicut in causis universalibus, per quandam similitudinem, ad modum quo formae quae sunt particulariter in materia sensibili, sunt universaliter in intellectu. Et ideo, sicut nec in intellectu, ita nec in corporibus caelestibus sunt sub ratione contrarietatis. Unde et Plato dixit quod in corporibus caelestibus sunt excellentiae seu sublimitates elementorum, quasi primordialia eorum activa principia: comparantur enim corpora caelestia ad elementaria, sicut activa ad passiva. Et ideo e contrario accidit in corporibus caelestibus et elementaribus. Nam corpora elementaria, quanto magis congregantur per inspissationem, tanto sunt magis materialia et passiva, et minus habentia de luce, sicut patet in terra, quae etiam dominatur in corporibus mixtis: sed in corporibus caelestibus, quanto est maior congregatio per modum inspissationis, tanto magis multiplicatur luminositas et virtus activa, sicut patet in ipsis corporibus stellarum. | Similarly, it is also necessary to say that the contrary forms or qualities found in the lower bodies exist in some sense in heavenly bodies, not, indeed, in a univocal way, but as in universal causes, in a certain likeness to the manner in which forms that exist individually in sensible matter, exist universally in the intellect. Hence, just as in the intellect they do not exist under the notion of contrariety, so neither do they in the heavenly bodies. Hence Plato said that in the heavenly bodies are found the excellences or sublimations of the elements, the former being, as it were, their primordial active principles — for the heavenly bodies are related to elementary bodies as are active principles to passive. Therefore the opposite happens in heavenly bodies and in elementary bodies. For elementary bodies, the more compact they are made as a result of thickening, the more material, and passive, and less light-endowed they are. This is evident with respect to earth, which is the dominant factor in mixed bodies. On the other hand, in the heavenly bodies, the more compact they are as a result of thickening, the greater their luminosity and active power, as is plain in the bodies of the stars. |
| Sic igitur patet quod talis diversitas quae in corporibus caelestibus apparet, non videtur habere rationem contrarietatis. Unde non sequitur quod sint susceptiva corruptionis. Sequeretur autem hoc si ibi esset vera contrarietas, sicut in primo Aristoteles ostendit. | Consequently, it is plain that such diversity as is apparent in the heavenly bodies is not seen to possess the nature of contrariety. Therefore, it does not follow that they are susceptible to corruption. But that would follow if there were true contrariety, as Aristotle showed in Book I. |
| Secunda dubitatio est quia, cum in corpore caelesti appareat diversitas inter stellas et reliquas partes sphaerarum, videtur quod non sint simplicia corpora. Sed dicendum est quod intantum dicuntur corpora simplicia, inquantum non sunt composita ex contrariis naturis. Est tamen in eis aliqua diversitas secundum naturam speciei, licet conveniant in natura generis; sicut conveniunt in communi ratione motus, quia omnia circulariter moventur. | 385. The second doubt is to the effect that, since diversity appears between the stars and the remaining parts of the spheres, it seems that they are not simple bodies. But the answer to this is that these bodies are called simple to the extent that they are not composed of contrary natures. Yet there is in them some diversity with respect to the nature of their species, although they agree in the nature of their genus — thus they agree in the common aspect of their motion, because all are moved circularly. |
| Secundo ibi: sicut enim ignea etc., ostendit hoc etiam esse consonum aliqualiter dictis aliorum: dicens quod, sicut illi qui dicunt stellas esse igneas, propterea hoc dicunt quia caeleste corpus existimant ignem esse, quasi rationabile sit quod unumquodque astrum constet ex natura illarum sphaerarum in quibus est; ita etiam et nos dicimus quod stellae sunt de natura alia a natura quatuor elementorum, propter hoc quod supra probavimus caelos tales esse. | 386. Secondly, at [291] he shows that this is in a way in agreement with the statements of others. For he says that, just as those who assert that the stars are fiery, concluded this because they believe the heavenly body is fire, as though it were reasonable for each of the stars to consist of the nature of those spheres in which it exists; so, too, we assert that the stars are of a nature different from the nature of the four elements, because we have previously proved the heavens to be such. |
| Deinde cum dicit: calor autem ab ipsis etc., excludit obiectionem: quia quidam opinabantur stellas esse de natura ignis, sic argumentantes. Esse calidum et luminosum videtur esse proprium ignis; sed stellae calefaciunt et illuminant; ergo videtur quod sint de natura ignis. | 387. Then at [292] he excludes an objection; for some believed the stars to be of the nature of fire and argued in the following manner: To be hot and luminous is seen to be proper to fire. But the stars heat and give light. Therefore, it seems that they are of the nature of fire. |
| Et circa hoc tria facit: | Regarding this he does three things: |
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primo solvit hanc obiectionem per quoddam exemplum; secundo ostendit differentiam exempli ad propositum, ibi: hae quidem ipsae etc.; tertio respondet tacitae quaestioni, ibi: et hac maxime et cetera. |
First he resolves this objection with an example; Secondly, he shows how the example differs from his proposition, at 388; Thirdly, he replies to a tacit question, at 389. |
| Dicit ergo primo quod calor et lumen generatur a stellis per quandam contritionem sive confricationem aeris ex motu eorum, non propter hoc quod sunt ignea. Videmus enim quod motus natus est ignire et ligna et lapides et ferrum: unde multo magis rationabile est quod per motum possit igniri corpus quod est propinquius igni quam praedicta corpora; quia eorum quae sunt sibi propinquiora, facilior est transmutatio in invicem. Aer autem propinquius se habet ad ignem quam corpora praedicta: unde magis aer potest igniri ex motu quam praedicta corpora. Et ponit exemplum de sagittis, quae cum sint plumbeae quantum ad aliquam sui partem, ex vehementia motus sic calefiunt, ut quandoque liquescat plumbum. Et quia ipsae sagittae igniuntur ex motu, necesse est quod multo magis aer qui est in circuitu sagittarum igniatur. Nec hoc est intelligendum quod calefactio sagittarum sit causa calefactionis aeris, sicut Simplicius intellexit; sed magis est intelligendum quod calefactio aeris per motum sit causa calefactionis sagittarum, ut exposuit Alexander. Aristoteles enim vult probare per locum a minori, quod si sagittae calefiunt, necesse est quod aer circumstans calefiat, qui est propinquior igni, ut supra dixit: non autem per locum a causa, ut intellexit Simplicius. | He says therefore first [292] that heat and light are generated by the stars by a certain stroking of, or friction with, air and not because they are of a fiery nature. For we observe that motion is apt to ignite wood and stones and iron; hence it is all the more reasonable that a body which is more like fire than the bodies mentioned should be ignited by motion, because when two things are more alike, it is easier for them to change into each other. But air is more like fire than the above mentioned bodies are. Hence air can be more easily ignited by motion than those bodies. And he gives the example of arrows. Part of them being of lead, they are so heated by the violence of their motion that sometimes the lead melts. Since arrows can be ignited as a result of motion, there is all the more reason why the air surrounding the arrows should become ignited. This does not mean that the heated arrow causes the air to become heated, as Simplicius understood. Rather, it is to be understood that the heat produced in the air through motion causes the heating of the arrows, as Alexander explained it. For Aristotle wishes to prove from a lesser case that if arrows are heated, the surrounding air must be heated, it being closer to fire, as he said above. He is not taking the case [of the heated arrow] as a cause, as Simplicius understood. |
| Deinde cum dicit: hae quidem ipsae etc., ostendit differentiam exempli inducti ad propositum. Et dicit quod ipsae sagittae calefiunt propter hoc quod feruntur per aerem; qui quidem aer ignitur ex motu propter plagam, idest propter percussionem et divisionem quam patitur a sagitta; unde ex contactu aeris calefacti sagittae calefiunt. Sed hoc non accidit in stellis: quia unaquaeque stellarum non fertur per aerem, sed in propria sphaera separata ab aere. Et ideo ipsae stellae non igniuntur nec calefiunt: tum quia sunt longe ab aere, qui ignitur per motum; tum etiam quia non sunt susceptivae peregrinae impressionis. Sed aer qui existit sub sphaera corporis circularis, necesse est quod incalescat per motum sphaerae caelestis: quia scilicet ex ipso motu sphaerae caelestis movetur non solum ignis, sed etiam aer (usque scilicet ad istum aerem qui infra montes continetur), ut apparet ex motu comatarum stellarum, ut dicitur in I Meteor. | 388. Then at [293] he shows the difference between this example and his proposition. And he says that those arrows become hot because they are being moved through air, and the air becomes ignited by the "blow," i.e., as a result of its being struck and divided by the arrow; hence it is from contact with heated air that the arrows become hot. But this is not what happens in the stars, since each star is not being moved through air but in its own sphere insulated from air. Therefore, the stars are neither ignited nor made hot, first of all because they are far from air, which is ignited by motion, and, secondly, because they are not receptive to a transitory impression. But it is the air which exists under the sphere of the heavenly body that must become hot as a result of the motion of the heavenly sphere, since the motion of the heavenly sphere agitates not only the fire but the air as well (namely, as far as the air contained below the mountains), as is apparent from the motion of comets, as stated in Meteorology I. |
| Deinde cum dicit: et hac maxime etc., respondet tacitae obiectioni. Si enim per motum sphaerae caelestis aer inferior ignitur, cum sphaera caelestis continue moveatur, videtur esse consequens quod semper debeat esse aequalis calor in aere, scilicet aestate et hieme, nocte et die; cuius contrarium videmus. | 389. Then at [294] he responds to a tacit objection. For if the lower air is ignited by the motion of the heavenly sphere, then, since the heavenly sphere is in continuous motion, it seems that there should always be an equal amount of heat in the air at all times, i.e., in winter and in summer, during the day and during the night. But we observe that it is the contrary that happens. |
| Sed ad hoc ipse respondet quod maxime aer ignitur per motum illius sphaerae cui sol est infixus; et ideo generatur calor propter propinquitatem solis ad nos. Et hoc dupliciter: uno modo secundum quod per suum ortum ascendit ad nostrum hemisphaerium superius; alio modo inquantum accedit ad summitatem capitum nostrorum; sicut enim est maior calor in die quam in nocte, ita etiam est maior calor in meridie quam in mane. | To this he responds that air is mainly ignited by the motion of the particular sphere in which the sun is fixed. Therefore heat is generated on account of the sun's nearness to us. And this happens in two ways: First, insofar as by its rising, the sun ascends to our upper hemisphere; secondly, insofar as it reaches a point directly overhead — for just as there is more heat during day than during night, so too there is more at noon than at dawn. |
| Ultimo autem concludit epilogando tantum dictum esse de stellis, quod neque ipsae sunt igneae naturae, neque etiam feruntur in corpore igneo, sed supra sphaeram ignis in sphaeris caelestibus. | Lastly, he concludes [295) by way of summary that so far we have said that the stars are not fiery in nature, and are not moved in a fiery body, but above the sphere of fire, in the heavenly spheres. |
| Est autem hic primo dubium: cum Aristoteles proponat quod ex motu stellarum generetur calor et lumen, videtur insufficienter hoc manifestare, cum non manifestet de lumine, sed solum de calore. | 390. But a first doubt arises: Since Aristotle asserts that the motion of the stars generates heat and light, his proof seems insufficient, since he gives no evidence for light, but only for heat. |
| Et ad hoc respondet Alexander quod illud quod pertinet ad lumen, reservat ad determinandum ad librum de anima, in cuius secundo dicit quod lumen non est proprium ignis, sed est aliquid commune sibi et supremo corpori. | To this Alexander responds that he reserves his treatment of light for settling in his book, On the Soul, in the second part of which he states that light is not a peculiarity of fire but something common to it and to the supreme body. |
| Sed cum Aristoteles hic dicat quod utrumque eorum generatur ex contritione aeris, melius est ut dicamus quod utrumque Aristoteles hic manifestat, per hoc quod ostendit ex motu stellarum igniri inferiora corpora; in igne autem invenitur calor et lumen. | However, since Aristotle says that both are generated from the striking of the air, it is better to say that Aristotle has taken care of both right here by showing that as a result of the stars' motion the lower bodies are set afire — for in fire are found both heat and light. |
| Sed adhuc dubium est, ex qua natura contingat quod motus habeat virtutem igniendi sive calefaciendi. | 391. But a doubt still remains, namely, the doubt as to that nature whence motion has the power to ignite or heat things. |
| Ad quod respondet Averroes in suo commento quod proprium est calidi esse mobile; et ideo cum aliquid actu movetur, fit etiam actu calidum. | To this Averroes responds in his Commentary that it is proper to the hot to be mobile; consequently, when something is being moved in act, it also becomes hot in act. |
| Sed hoc non videtur verum. Primo quidem quia moveri non est proprium calidi, sed cuiuslibet corporis naturalis: nam ea quae moventur motu recto, in suis locis quiescunt, moventur autem existentia extra sua loca; corpora autem caelestia moventur circulariter in suis locis, quae neque sunt calida neque frigida. Secundo quia posterius non est causa prioris: si ergo moveri sit proprium calidi, magis calor erit causa motus, quam e converso. | But this is not seen to be true. First of all, because to be moved is not peculiar to the hot but is common to every natural body — for things moved with a straight motion rest when they are in their appropriate places, but are moved when they are outside their places; heavenly bodies are moved circularly in their places, which are neither hot nor cold. In the second place, the subsequent is not the cause of the prior — hence, if motion were proper to what is hot, heat would be the cause of motion rather than motion the cause of heat. |
| Et ideo dicendum est quod, sicut probatur in VIII Physic., motus localis est primus motuum. In quolibet autem genere id quod est primum est causa eorum quae sunt post in eodem genere: unde motus localis est causa alterationis, quae est prima inter alios motus; et praecipue est causa primae alterationis, quae est calefactio. Alteratio enim secundum omnes alias qualitates, causatur ex alteratione primarum quatuor qualitatum; inter quas duae activae, scilicet calidum et frigidum, sunt priores passivis, scilicet humido et sicco; calidum autem est prius frigido, sicut forma privatione, ut patet ex supra dictis. Unde motus localis proprie est causa calefactionis. Habet autem hoc omnis motus localis ex virtute motus caelestis, qui est primus localium motuum. | Therefore, it must be said that, as is proved in Physics VIII, local motion is the first of motions. Now in every genus, whatever is first is the cause of the things that are subsequent in that genus. Hence, local motion is the cause of alteration, which is the first motion among the other motions, and in particular the cause of the first alteration which is heating. For alteration in all the other qualities is caused by alteration in the first four qualities, among which the two active, namely, hot and cold, are prior to the passive, namely, moist and dry. But hot is prior to cold, as form is prior to privation, as is clear from what was said previously. Hence local motion is properly the cause of heat. However, every local motion possesses this from the power of the heavenly motion, which is the first of local motions. |
| Dubitatur autem ulterius, cum sol immediate non tangat neque aerem neque ignem, quomodo ex motu solis causatur calor in aere et in igne: non enim media corpora caelestia, scilicet sphaerae Veneris, Mercurii et lunae, ex motu solis calefiunt. Ad quod respondet Alexander quod nihil prohibet ab aliquo agente aliquid alterari per medium, ita tamen quod illud medium non alteretur; sicut piscis qui dicitur stupor, stupefacit manus piscatoris mediante reti, quod tamen non stupescit. Recipit tamen aliqualiter impressionem piscis secundum suum modum, alio tamen modo quam manus. Ita etiam sol imprimit aliquid in corpora caelestia media, non tamen calefactionem; sed impressio solis pervenit ad corpora inferiora per modum calefactionis, secundum eorum conditionem. | 392. Another doubt now arises: Since the sun immediately touches neither the air nor the fire, how is heat caused in the air and in fire from the motion of the sun? For the intermediate heavenly bodies, namely, the spheres of Venus, Mercury and the moon, are not heated from the motion of the sun. To this Alexander responds that there is nothing preventing a thing from being altered by an agent acting through a medium, without the medium itself being altered. For example, the fish called stupor shocks the fisherman's hand through the net, although the net does not shock. Yet the net does receive in some way the impression from the fish, but in a manner different from the way the hand does. So, too, the sun imprints something on the intermediate heavenly bodies, even though it is not heating; but the effect of the sun reaches the lower bodies after the manner of heat, in keeping with their condition. |
| Sed contra hanc responsionem videtur esse, quod Aristoteles dicit quod calor causatur in aere trito vel compresso per motum stellarum; hoc autem non est possibile, quod contritio vel compressio a motu solis perveniat ad aerem, nisi media corpora caelestia conterantur; quod est impossibile. | But against this answer appears to be the fact that Aristotle asserts that heat is caused in air that has been struck or compressed by the motion of the stars. But it is not possible for this striking or compressing effect from the motion of the sun to reach the air without the intermediate heavenly bodies also being struck, which is impossible. |
| Et ideo Averroes in commento dicit quod totum corpus caeleste movetur motu diurno quasi unum corpus, vel quasi unum animal totum; motus autem planetarum proprii sunt quasi motus partium animalis. Causatur autem calor in aere praecipue ex motu totius caeli, qui est motus diurnus: unde et Aristoteles dicit quod approximante sole, et oriente et super nos existente, generatur calor; quod quidem fit per motum diurnum. Manifestum est autem quod corpus alterans non alterat solum secundum extremam superficiem, qua tangit corpus alteratum, sed secundum suam totam profunditatem vel grossitiem: et huius signum est, quia corpus tenue non est ita efficax ad alterandum sicut corpus habens profunditatem vel grossitiem, supposita identitate naturae. Et ita totum caelum calefacit non solum secundum infimam sphaeram, sed secundum totam grossitiem caeli, quasi una alteratione. Et ideo alteratio sequitur in istis inferioribus non solum secundum orbem lunae, qui immediate contingit inferiora corpora; sed etiam secundum virtutem stellarum, in quibus est magis adunata et quasi commassata virtus activa caelestis corporis; et praecipue secundum virtutem solis, qui excedit alia corpora virtute et magnitudine. Quia igitur totum caelum agit ut unum corpus secundum motum diurnum, non est intelligendum quod seorsum una sphaera imprimat in aliam; sed quod totum caelum una impressione alteret inferiorem aerem virtute solis et aliarum stellarum, quando nobis appropinquant. | Therefore Averroes in his Commentary says that the entire heavenly body is moved with the diurnal motion as though it were one body, or one whole animal, whereas the particular motions of the planets are as motions of the parts of an animal. Now heat in the air is caused mainly by the motion of the whole heaven, i.e., by the diurnal motion. For this reason Aristotle says that heat is caused by the nearness of the sun when it rises and is overhead, all of which is due to the diurnal motion. Now, it is plain that when one body alters another it does not do so only according to its outermost surface where it touches the body altered, but does this according to its whole depth or mass — and a sign of this is that a thin body is not as well suited for causing alteration as a body having thickness or mass, supposing that both bodies possess the same nature. Thus the whole heaven causes heat, not only in virtue of the lowest sphere, but in virtue of the whole mass of the heaven, as though by a single alteration. Therefore alteration takes place in those lower bodies not only in virtue of the moon's orb, which is in immediate contact with the lower bodies, but also according to the virtue of the stars, in which the active power of the heavenly body is more unified and as though massed together. This is particularly true of the sun, which exceeds the other bodies in power and size. Since, therefore, the whole heaven acts as one body according to its diurnal motion, we should not suppose that one sphere acts separately upon another, but that the whole heaven, with one imprint, alters the lower air by means of the power in the sun and other stars as they draw near to us. |
| Sed etiam haec ratio non videtur esse sufficiens, ut Simplicius dicit. Primo quidem quia, si secundum contritionem vel compressionem aeris ex motu caelestis corporis, praesente sole, causaretur calor aeris, primo quidem sequeretur quod loca quae sunt inferiora, minus calefierent, tanquam magis remota a motu calefaciente: nunc autem videmus contrarium, nam in planitie est maior calor quam in montibus. Secundo quia, cum sphaera terrae fere se habeat per modum puncti ad sphaeram solis, sol supra terram existens videtur ex omni parte quasi aequaliter esse nobis propinquus; et ita non deberet esse tanta differentia calefactionis ex sole, quanta apparet inter mane et meridiem, et inter hiemem et aestatem. Tertio quia nulla ratio esset quare minor esset calor in locis umbrosis, quam in locis in quibus radii solis percutiunt. | But, as Simplicius says, even this explanation does not seem to be sufficient. First, because if heat were produced in the air on account of its being struck or compressed by the motion of the heavenly body when the sun is present, it would follow first of all that lower places would become less heated, since they are farther from the heating motion. But just the opposite is seen, for there is more heat on the plains than on the mountains. Secondly, since the sphere of the earth is almost like a point in relation to the sphere of the sun, when the sun is over the earth it seems to be more or less equally near to every part of the earth; consequently, there should not be such a great variation of heat from the sun as there is between dawn and noon, or winter and summer. Thirdly, because there would be no reason for finding less heat in shaded places than in places where the rays of the sun strike. |
| Et eisdem rationibus probatur quod sol non calefacit quasi igneae naturae existens. | The same reasons prove that the sun does not cause heat as though it were of the nature of fire. |
| Et ideo Simplicius dicit quod a solis corpore egrediuntur radii, quos dicit esse corporales; et quod per caelestia corpora quae sunt infra solem, quae sunt immaterialia, sine prohibitione penetrare possunt; per aerem autem penetrant propter aeris poros; sed a corporibus solidis, scilicet terra et aqua, reflectuntur ad aequales angulos (quia, ut probant perspectivi, omnis reflexio fit ad aequales angulos). Quando ergo radius solaris percutit terram diametraliter, radius reflectitur in seipsum, et sic fit maxima inspissatio, quae causat maximum calorem: et hoc contingit quando sol est directe super summitatem capitum nostrorum. Quanto autem sol magis recedit a summitate capitum nostrorum, tanto reflexio radii fit ad magis distans, et ideo generatur minor calor: et inde est quod in hieme, et apud ortum solis vel occasum, fit minor calor in aere, quia radii solares percutiunt terram secundum angulos magis obtusos, unde radii reflexi magis distant a radiis primo obiectis. Et propter hoc Aristoteles signanter non simpliciter dixit quod sole magis appropinquante generatur maior calor, sed addidit et oriente et super nos existente; ut intelligatur approximatio per respectum ad summitatem capitum nostrorum, non autem secundum quantitatem linearum a sole ad nos ductarum, quia fere ex omni parte sunt aequales. | And therefore Simplicius says that there emerge from the body of the sun rays he says to be corporeal, and that they can without hindrance penetrate those heavenly bodies below the sun that are immaterial, and air they penetrate on account of its pores. But they are reflected by solid bodies, namely, earth and water, at equal angles (because, as perspective proves, all reflection occurs at equal angles). When, therefore, a solar ray strikes the earth diametrically, it is reflected back upon itself and thus there is produced a maximum thickening, which causes maximum heat; and this happens when the sun is directly overhead. But as the sun declines from its overhead position, the distance between the reflection of its rays increases more and more, and consequently less heat is generated. This is the reason why in the winter, and at sunrise and sunset, there is less heat in the air, namely, because the solar rays strike the earth at angles which are more obtuse, with the result that the distance between the rays first striking and the reflected rays is increased. And it is for this reason that Aristotle purposely did not say unqualifiedly that as the sun gets nearer more heat is generated, but was careful to add, "as rising and when it is overhead," in order to give us to understand that the nearness is in reference to its nearness overhead and not in reference to the linear distance from the sun to us, because those distances to any part of the earth are almost equal. |
| Et si quidem intelligat Simplicius in his verbis radios esse corpora confricantia aerem et inspissantia, et per hunc modum calefacientia, expresse falsum dicit: probat enim Aristoteles in II de anima quod radius neque est corpus neque defluxus corporis alicuius. Si vero dicat radios esse corporales, quia ad modum corporum se habent, inquantum directe proiiciuntur, et reflectuntur a corpore spisso quod radii penetrare non possunt, sic verum dicit: tales enim reflexiones per contra-resistentiam corporum, non solum competunt corporibus, sed etiam qualitatibus; nam et calor reflectitur cum invenit obstaculum, et similiter alia huiusmodi. | Now if Simplicius means with these words that the rays are bodies which strike and thicken the air and thus produce heat, his statement is expressly false, for Aristotle in On the Soul II proves that a ray is neither a body nor an emanation from a body. But if, in saying that the rays are corporeal, he means that they act after the manner of bodies, in the sense that they are directly projected and are reflected from any dense body they cannot penetrate, then he speaks the truth — for such reflections, being caused by the counter-resistance of bodies, belong not only to bodies but also to qualities, since heat, too, is reflected when it meets an obstacle, as do other things of the same sort. |
| Si quis autem diligenter consideret, omnia quae dicta sunt aliqualiter vera sunt. Dicit enim Aristoteles quod a stellis generatur et calor et lumen, trito aere ab illorum latione. Quod non videtur sic intelligendum quasi calor et lumen generentur per aeris contritionem ex motu caelestium corporum: non enim agitur hic de lumine ignis generati ex motu, ut prius dicebatur, sed de lumine quod causatur ab ipsis stellis, inquantum sunt entia lucida in actu. Duplex est ergo causa caloris ex corporibus caelestibus in his inferioribus generati: una quidem causa est motus, alia causa est lumen. Quare autem motus causa sit calefactionis, supra dictum est. Non est autem intelligendum quod mutua contritio vel confricatio corporis caelestis et aeris sit causa caloris; sed solum motus aeris ex superiori motu caelestis corporis causatus. Movetur autem aer superior, et similiter ignis, secundum motum diurnum caeli totius, secundum virtutem solis et omnium stellarum, ut Averroes dicit. | 393. However, if one examines them diligently, all the things said on this point are true in some sense. For Aristotle says that "heat and light are generated by the stars as a result of the air being struck by their motion." Now it seems that this is not to be understood as meaning that heat and light are generated by the striking of the air caused by the motion of the heavenly bodies: for it is not a question here of the light of fire generated from motion, as previously stated, but of the light caused by the stars themselves insofar as they are light-giving things in act. Therefore, the cause of heat generated in lower bodies by the heavenly bodies is twofold: One cause is motion, and the other is light. Why motion is the cause of heating has been explained above. But we must not suppose that a mutual stroking or rubbing of a heavenly body and of air is the cause of heat; rather it is solely the motion produced in the air by the higher motion of the heavenly body. The higher air, and likewise fire, are moved by the diurnal motion of the entire heaven according to the power of the sun and all the stars, as Averroes says. |
| Secunda autem causa calefactionis corporum inferiorum ab astris, et praecipue a sole, est lumen. Quod quidem habet virtutem calefaciendi inquantum est qualitas activa primi alterantis, scilicet caeli; unde directe causat qualitatem primam inferiorum corporum, quae est calor. Et quia haec qualitas, scilicet lumen, magis abundat in sole, inde est quod est maxime potens ad calefaciendum. Reliqua autem caelestium corporum, inquantum participant de lumine, quae est universalis virtus activa caelestium corporum, habent virtutem calefaciendi; intantum quod etiam lumen lunae est calefactivum, secundum id quod philosophus dicit in libro de partibus animalium, quod noctes plenilunii sunt calidiores, unde quidam pisces moventur ad superficiem aquae. | The second cause of the heating of lower bodies by the stars and especially the sun is light. It indeed has the power to heat insofar as it is an active quality of the first thing altering, namely, the heaven. Hence, it directly causes the first quality found in inferior bodies, namely, heat. And since this quality, namely, light, abounds more in the sun, the sun is especially capable of heating. But the rest of the heavenly bodies, insofar as they partake of light (which is the universal active power of heavenly bodies), have the power to produce heat. This extends even to the light of the moon, according to what the Philosopher says in his book, On the Parts of Animals, namely, that the nights of full moon are warmer, for which reason certain fish come to the surface of the water. |
| Quod autem quaedam astra dicantur infrigidare vel humectare, Averroes in commento dicit hoc non esse per se, sed inquantum agunt calorem proportionatum unicuique corpori: unde reprehendit Avicennam, qui dicit quod stellae faciunt et infrigidationem et calefactionem. | As to the statement that some stars cause things to be cool or moist, Averroes says in his Commentary that they do not do this per se but only insofar as producing a heat proportionate to each body; on which account he scolds Avicenna, who says that the stars cause both cooling and heating. |
| Sed in hoc non recte dicit Averroes. Illud enim videtur esse per accidens, quod non per se producitur ab agente. Corpora autem caelestia sunt agentia eorum quae sunt hic. Si igitur non per se agerent frigiditatem et humiditatem et alia huiusmodi, sequeretur quod ista essent per accidens in universo. Item, cum omnes formae substantiales inferiorum corporum sint ex virtute caelestium corporum, consequens est quod ex eorum virtute sint etiam qualitates consequentes species seu formas elementorum, quae sunt calidum, frigidum, humidum et siccum, et alia huiusmodi. | But Averroes does not speak correctly in this matter. For a thing is seen to be per accidens when it is not produced by the agent per se. But the heavenly bodies are the agent causes of the things that are here. If, therefore, they did not per se cause cooling and moisture and so on, it would follow that such things would be per accidens in the universe. Moreover, since all the substantial forms of the lower bodies come to be from the power of the heavenly bodies, it follows that from their power are also the qualities consequent upon the species or forms of the elements, namely, hot, cold, wet and dry, and so on. |
| Dicendum est ergo quod omnia corpora caelestia, secundum communem virtutem luminis, habent calefacere; sed secundum alias proprias virtutes singulis corporibus attributas, habent non solum calefacere et infrigidare, sed etiam omnes alios effectus corporales efficere in istis inferioribus. Et secundum influentiam luminis et harum virtutum, verum est quod Alexander dixit, media corpora caelestia recipere impressionem solis alio modo quam corpora inferiora. | Accordingly, it must be said that all the heavenly bodies, in keeping with their common power of light, have the property of heating, but according to other peculiar powers attributed to specific bodies, they not only heat and cool, but also produce other corporeal effects in lower bodies. And in the matter of the influence of light and these powers, what Alexander says is true, namely, that the intermediate heavenly bodies receive an impression from the sun in a way different from the way the lower bodies do. |
| Est igitur considerandum quod, secundum quod calor causatur in inferioribus corporibus ex motu astrorum et totius caeli, corpora propinquiora caelo, scilicet ignis et superior aeris pars, quae circumferuntur secundum motum caeli, sunt calidiora: secundum autem quod ex lumine stellarum causatur calor, sunt calidiora ea quae sunt infima, quia in superioribus reflexiones radiorum magis disperguntur. Et inde est etiam quod circa terram plures species rerum generantur ex virtute radiorum solis et stellarum, quae per reflexionem circa terram multiplicantur. | One should consider, therefore, that accordingly as heat is caused in lower bodies by the motion of the stars and of the whole heaven, the bodies nearer to the heaven, namely, fire and the upper region of the air, which are carried around according to the motion of the heaven, are hotter. But accordingly as heat is caused from the light of the stars, the lowest things are hotter, because in the upper regions the reflections of the rays are dispersed more. This also explains why many species of things on the earth are generated by the power of solar and stellar rays which are multiplied about the earth as a result of reflexion. |
| Movet autem hic quaestionem Alexander: si corpora caelestia suo motu conterunt aerem, videtur sequi quod sint tangibilia; et ita videtur sequi quod sint calida et frigida; haec enim sunt primae tangibiles qualitates, ut dicitur in II de Generat. | 394. But Alexander raises a question here: If the heavenly bodies strike the air in their motion, it seems to follow that they can be touched and, consequently, that they are hot and cold — for those are the first tangible qualities, as is said in On Generation II. |
| Sed ad hoc de facili patet responsio per id quod philosophus dicit in I de Generat., quod illa quae sunt nata agere et pati ad invicem, tangunt se ad invicem; et talium qualitates sunt calidum et frigidum. Corpora autem caelestia agunt et non patiuntur: unde tangunt et non tanguntur. Unde in corporibus caelestibus non sunt qualitates tangibiles per modum quo sunt in inferioribus corporibus, sed per modum eminentiorem, sicut in causa activa. Non est enim ibi calidum vel frigidum, humidum vel siccum, sed virtus quae est horum causativa. Similiter non est ibi grave et leve; sed loco horum est ibi aptitudo ad motum circularem. Rarum autem et densum invenitur in corporibus caelestibus, secundum quod astra sunt spissiora et magis commassata quam sphaerae eorum: non tamen secundum differentiam contrarietatis, sed solum secundum additionem et deminutionem virtutis, secundum maiorem et minorem congregationem partium. | But the answer to this is easily evident from what Aristotle says in On Generation I, namely, that things apt to act and be acted upon touch each other mutually, and that the qualities of such things are heat and cold. The heavenly bodies, however, act but are not acted upon. Hence, they touch without being touched. Hence, too, the tangible qualities in heavenly bodies are not there in the way they are in lower bodies; rather, they are present in a more eminent way, i.e., as existing in their active cause. For hot and cold, moist and dry, are not present therein, but the power that causes them is present therein. Similarly, neither do heavy and light exist there; but in place of these is an aptitude to circular motion. Finally, rare and dense are present in heavenly bodies, accordingly as the stars are thicker and more massive than their spheres; nevertheless this is not according to the difference of contrariety, but only according to increase or decrease of power proportionate to a greater or lesser aggregation of parts. |
Lecture 11:
Proof that the stars move, not of themselves, but as carried by the motion of the spheres, from a comparison with their, circlesChapter 8 (289b.) Ἐπεὶ δὲ φαίνεται καὶ τὰ ἄστρα μεθιστάμενα καὶ ὅλος ὁ οὐρανός, ἀναγκαῖον ἤτοι ἠρεμούντων ἀμφοτέρων γίγνεσθαι τὴν μεταβολήν, ἢ κινουμένων, ἢ τοῦ μὲν ἠρεμοῦντος τοῦ δὲ κινουμένου. 296 Since changes evidently occur not only in the position of the stars but also in that of the whole heaven, there are three possibilities. Either (1) both are at rest, or (2) both are in motion, or (3) the one is at rest and the other in motion. Ἀμφότερα μὲν τοίνυν ἠρεμεῖν ἀδύνατον ἠρεμούσης γε τῆς γῆς οὐ γὰρ ἂν ἐγίγνετο τὰ φαινόμενα. Τὴν δὲ γῆν ὑποκείσθω ἠρεμεῖν. Λείπεται δὴ ἀμφότερα κινεῖσθαι, ἢ τὸ μὲν κινεῖσθαι τὸ δ' ἠρεμεῖν. 297 (1) That both should be at rest is impossible; for, if the earth is at rest, the hypothesis does not account for the observations; and we take it as granted that the earth is at rest. It remains either that both are moved, or that the one is moved and the other at rest. Εἰ μὲν οὖν ἀμφότερα κινήσεται, ἄλογον τὸ ταὐτὰ τάχη τῶν ἄστρων εἶναι καὶ τῶν κύκλων ἕκαστον γὰρ δὴ ὁμοταχὲς ἔσται τῷ κύκλῳ καθ' ὃν φέρεται. Φαίνεται γὰρ ἅμα τοῖς κύκλοις καθιστάμενα πάλιν εἰς τὸ αὐτό. Συμβαίνει οὖν ἅμα τό τε ἄστρον διεληλυθέναι τὸν κύκλον καὶ τὸν κύκλον ἐνηνέχθαι τὴν αὑτοῦ φοράν, διεληλυθότα τὴν περιφέρειαν. 298 (2) On the view, first, that both are in motion, we have the absurdity that the stars and the circles move with the same speed, i.e. that the ace of every star is that of the circle in it moves. For star and circle are seen to come back to the same place at the same moment; from which it follows that the star has traversed the circle and the circle has completed its own movement, i.e. traversed its own circumference, at one and the same moment. Οὐκ ἔστι δ' εὔλογον τὸ τὸν αὐτὸν λόγον ἔχειν τὰ τάχη τῶν ἄστρων καὶ τὰ μεγέθη τῶν κύκλων. Τοὺς μὲν γὰρ κύκλους οὐθὲν ἄτοπον ἀλλ' ἀναγκαῖον ἀνάλογον ἔχειν τὰ τάχη τοῖς μεγέθεσι, τῶν δ' ἄστρων ἕκαστον τῶν ἐν τούτοις οὐθαμῶς εὔλογον εἴτε γὰρ ἐξ ἀνάγκης τὸ τὸν μείζω κύκλον φερόμενον θᾶττον ἔσται, δῆλον ὅτι κἂν μετατεθῇ τὰ ἄστρα εἰς τοὺς ἀλλήλων κύκλους, τὸ μὲν ἔσται θᾶττον τὸ δὲ βραδύτερον (οὕτω δ' οὐκ ἂν ἔχοιεν οἰκείαν κίνησιν, ἀλλὰ φέροιντ' ἂν ὑπὸ τῶν κύκλων), εἴτε ἀπὸ ταὐτομάτου συνέπεσεν, οὐδ' οὕτως εὔλογον ὥστ' ἐν ἅπασιν ἅμα τόν τε κύκλον εἶναι μείζω καὶ τὴν φορὰν θάττω τοῦ ἐν αὐτῷ ἄστρου τὸ μὲν γὰρ ἓν ἢ δύο τοῦτον τὸν τρόπον ἔχειν οὐθὲν ἄτοπον, τὸ δὲ πάνθ' ὁμοίως πλάσματι ἔοικεν. Ἅμα δὲ καὶ οὐκ ἔστιν ἐν τοῖς φύσει τὸ ὡς ἔτυχεν, οὐδὲ τὸ πανταχοῦ καὶ πᾶσιν ὑπάρχον τὸ ἀπὸ τύχης. 299 But it is difficult to conceive that the pace of each star should be exactly proportioned to the size of its circle. That the pace of each circle should be proportionate to its size is not absurd but inevitable: but that the same should be true of the movement of the stars contained in the circles is quite incredible. For if, on the one and, we suppose that the star which moves on the greater circle is necessarily swifter, clearly we also admit that if stars shifted their position so as to exchange circles, the slower would become swifter and the swifter slower. But this would show that their movement was not their own, but due to the circles. If, on the other hand, the arrangement was a chance combination, the coincidence in every case of a greater circle with a swifter movement of the star contained in it is too much to believe. In one or two cases it might not inconceivably fall out so, but to imagine it in every case alike is a mere fiction. Besides, chance has no place in that which is natural, and what happens everywhere and in every case is no matter of chance. Ἀλλὰ μὴν πάλιν εἰ οἱ μὲν κύκλοι μένουσιν, αὐτὰ δὲ τὰ ἄστρα κινεῖται, τὰ αὐτὰ καὶ ὁμοίως ἔσται ἄλογα συμβήσεται γὰρ θᾶττον κινεῖσθαι τὰ ἔξω, καὶ τὰ τάχη εἶναι κατὰ τὰ μεγέθη τῶν κύκλων. 300 (3) The same absurdity is equally plain if it is supposed that the circles stand still and that it is the stars themselves which move. For it will follow that the outer stars are the swifter, and that the pace of the stars corresponds to the size of their circles. Ἐπεὶ τοίνυν οὔτ' ἀμφότερα κινεῖσθαι εὔλογον οὔτε τὸ ἕτερον μόνον, λείπεται τοὺς μὲν κύκλους κινεῖσθαι, τὰ δὲ ἄστρα ἠρεμεῖν καὶ ἐνδεδεμένα τοῖς κύκλοις φέρεσθαι μόνως γὰρ οὕτως οὐθὲν ἄλογον συμβαίνει τό τε γὰρ θᾶττον εἶναι τοῦ μείζονος κύκλου τὸ τάχος εὔλογον περὶ τὸ αὐτὸ κέντρον ἐνδεδεμένων (290a.) (ὥσπερ γὰρ ἐν τοῖς ἄλλοις τὸ μεῖζον σῶμα θᾶττον φέρεται τὴν οἰκείαν φοράν, οὕτως καὶ ἐν τοῖς ἐγκυκλίοις μεῖζον γὰρ τῶν ἀφαιρουμένων ὑπὸ τῶν ἐκ τοῦ κέντρου τὸ τοῦ μείζονος κύκλου τμῆμα, ὥστ' εὐλόγως ἐν τῷ ἴσῳ χρόνῳ ὁ μείζων περιοισθήσεται κύκλος), τό τε μὴ διασπᾶσθαι τὸν οὐρανὸν διά τε τοῦτο συμβήσεται καὶ ὅτι δέδεικται συνεχὲς ὂν τὸ ὅλον. 301 Since, then, we cannot reasonably suppose either that both are in motion or that the star alone moves, the remaining alternative is that the circles should move, while the stars are at rest and move with the circles to which they are attached. Only on this supposition are we involved in no absurd consequence. For, in the first place, the quicker movement of the larger circle is natural when all the circles are attached to the same centre. Whenever bodies are moving with their proper motion, the larger moves quicker. It is the same here with the revolving bodies: for the are intercepted by two radii will be larger in the larger circle, and hence it is not surprising that the revolution of the larger circle should take the same time as that of the smaller. And secondly, the fact that the heavens do not break in pieces follows not only from this but also from the proof already given of the continuity of the whole.
| Postquam philosophus ostendit qualis sit natura stellarum, hic determinat de motu earum. | 395. After showing what the nature of the stars is, the Philosopher here determines their motion. |
|
Et primo ostendit qualiter stellae moveantur; secundo ostendit utrum ex eorum motu sonus causetur, ibi: manifestum autem ex his et cetera. |
First he shows how the stars are moved; Secondly, he shows whether a sound is produced as a result of their motion (L. 14). |
| Circa primum, ostendit stellas non per se moveri, sed deferri eas motu orbium, tribus rationibus. Quarum prima sumitur per comparationem stellarum ad orbes. | With respect to the first he shows, by three arguments, that the stars do not move of themselves but are carried along by the motion of their orbs. The first of these arguments rests on comparing the stars to the orbs [or spheres]. |
| In qua quidem ratione unum praesupponit ex eo quod apparet secundum sensum: videmus enim et stellas et totum caelum moveri. Necesse est autem hoc contingere tribus modis: uno quidem modo ita quod utrumque quiescat, scilicet et stella et orbis; alio quidem modo ita quod utrumque moveatur; tertio vero modo ita quod unum eorum quiescat et alterum moveatur. Hac autem divisione posita, prosequitur tria membra praedicta. | In this argument he presupposes a fact which is sensibly evident: we see the stars and the whole heaven moving. Now there are three ways in which this must happen: In one way, so that both the star and its orb are at rest; in another, so that both are in motion; in a third, so that one of them is at rest and the other in motion. Then having presented this division, he considers each one. |
| Et primo prosequitur primum, cum dicit: utraque quidem igitur et cetera. Circa quod dicit quod impossibile est dicere quod utrumque quiescat, scilicet stella et orbis, si supponatur quod etiam terra quiescat: non enim posset salvari apparens motus stellarum, si et stellae quae videntur moveri quiescerent, et homines qui vident. Quod enim motus appareat, causatur vel ex motu visibilis vel ex motu videntis. Et ideo quidam, ponentes stellas et totum caelum quiescere, posuerunt terram in qua nos habitamus, moveri ab occidente in orientem circa polos aequinoctiales qualibet die semel; et ita per motum nostrum videtur nobis quod stellae in contrarium moveantur; quod quidem dicitur posuisse Heraclitus Ponticus et Aristarchus. Supponit autem Aristoteles ad praesens quod terra quiescat, quod postmodum probabit. Unde relinquitur, remoto primo membro, quo ponebatur caelum et stellas quiescere, alterum duorum membrorum verificari: scilicet, vel quod utrumque moveatur, scilicet stella et orbis; vel quod unum eorum moveatur et alterum quiescat. | 396. First he considers the first one [297], and says that it is impossible that both, i.e., the star and its orb, be at rest if we assume that the earth is also at rest. For the apparent motion of the stars cannot be saved if both the stars which appear to be in motion are at rest, and the men who see them. For, that motion should appear, this must be caused either by the motion of the thing seen or of the one seeing. For this reason, some, positing the stars and the whole heaven to be at rest, posited the earth on which we live to be moved from west to east around the equinoxial poles [i.e., its axis] once a day. According to this, it is due to our own motion that the stars seem to move in a contrary direction. This is said to have been the opinion of Heraclitus of Pontus and Aristarchus. However, Aristotle is supposing for the present that the earth is at rest — which fact he will later prove. Hence it remains, the first member, in which the.heaven and the stars were assumed to be at rest, having been set aside, to verify one of the two others — namely, that stating that both, i.e., the star and the orb, are in motion, or that stating one to be in motion and the other at rest. |
| Deinde cum dicit: si quidem igitur ambo movebuntur etc., destruit alterum membrum, scilicet quod tam stella quam orbis moveatur. Et dicit quod si ambo moventur, videtur sequi quiddam quod est irrationabile, scilicet quod sit eadem velocitas stellae et circuli deferentis ipsam. Si enim utrumque movetur, oportet dicere quod velocitas uniuscuiusque stellae sit aequalis velocitati circuli in quo fertur: apparent enim stellae simul cum circulis redeuntes iterum in idem a quo incoeperant moveri. | 397. Then at [298] he destroys one member, namely, that holding both the star and the orb as being in motion. And he says that if both are being moved, something unreasonable is seen to follow, namely, that there is the same velocity for the star and the circle carrying it. For if both are being moved, then we must say that the velocity of each star is equal to that of the circle in which it is being carried — for the stars appear along with their circles, returning to the same spot whence they had begun to be moved. |
| Et hoc quidem manifeste apparet, si loquatur de stellis fixis, quae sunt in sphaera octava. Nam omnes huiusmodi stellae simul cum tota sphaera videntur uno motu moveri; ita quod stella quae est in circulo aequinoctiali, qui est circulus maximus dividens sphaeram per medium, in eodem tempore circuit totum circulum suum magnum, in quo tempore alia stella quae est in minori circulo versus alterum polorum, circuit circulum suum parvum. Et sic, cum illud sit velocius quod in aequali tempore movetur per maius spatium, ut patet in VI Physic., sequitur quod stella, quanto est in maiori circulo, tanto sit velocioris motus. Et similiter quanto circulus erit maior, tanto motus eius erit velocior. | This is indeed very plain if we speak of the fixed stars which exist in the eighth sphere. For all such stars are seen to move together with the whole sphere with one motion, in such a way that a star in the equinoxial circle [i.e., the equator],'which is the largest circle dividing the sphere through its center, completes its whole great circle in the same time that another star, in a smaller circle located toward one of the poles, completes its small circle. Consequently, since a thing is swifter if it covers a greater distance in equal time, as is plain from Physics VI, it follows that the larger the circle in which a star exists, the swifter its motion. Similarly, the larger the circle itself is, the swifter its motion. |
| Potest etiam hoc intelligi, ut Alexander dicit, adaptando ad circulos planetarum. Nam secundum quod moventur motu diurno, simul revolvuntur cum suprema sphaera, nisi inquantum per motus proprios planetae in suis circulis per aliquod spatium retrocedunt. Et quia circulus superioris planetae est maior, sequetur quod superior planeta sit velocior, quantum ad motum diurnum: quia in eodem tempore per maiorem circulum revolvitur. | This explanation can also be understood, as Alexander says, in adaptation to the circles of the planets. For to the extent that the planets are moved by the diurnal motion, they are revolved along with the supreme sphere, except insofar as the planets through their own motions retrogress somewhat in their own circles. And since the circle of the superior planet is larger, that planet will be swifter as to its diurnal motion — for in the same time it is being revolved through a larger circle. |
| Sic igitur tam in stellis fixis quam in planetis, aliqualiter accidit quod simul stella pertransivit totum circulum, et quod circulus est motus proprio motu, pertranseundo propriam peripheriam, idest circumferentiam. Quod quidem intelligitur inquantum aliquod punctum signatum in circulo redit ad pristinum statum. | Thus, therefore, it happens to some extent, both to the fixed stars and the planets, that the star is at once completing a complete circle while that circle itself is moved by a motion of its own as it traverses its own "periphery," i.e., circumference. This is to be understood in the sense that some designated point in the circle returns to its original place. |
| Sic igitur ostenso quod accidat ex dicta positione easdem esse velocitates astrorum et circulorum, ostendit hoc esse irrationabile, ut supposuerat, cum dicit: non est autem et cetera. | 398. Therefore, having shown what happens from the assumption of equal velocities for the stars and for their circles, he shows that this is unreasonable, as he had supposed, at [2993. |
| Et primo quidem proponit quod non est rationabile quod sit eadem proportio velocitatis astrorum et magnitudinis circulorum, ut scilicet tanto aliquod astrum sit velocius, quanto movetur in maiori circulo. | First of all he proposes that it is not reasonable that there should be a same proportion between the velocity of the stars and the size of their circles, so that by so much is a star swifter as it is moved in a larger circle. |
| Secundo autem ostendit non esse inconveniens hoc dicere circa ipsos circulos. Immo magis videtur necessarium esse quod eorum velocitates analogice, idest proportionaliter, se habeant ad eorum magnitudines: quia ita videmus in omnibus corporibus naturalibus, quod quanto aliquid fuerit maius, tanto velocius movetur motu proprio. Et sic, si non est rationabile quod velocitas stellarum proportionetur magnitudini circulorum; est autem rationabile quod velocitas circulorum proportionetur magnitudini propriae; consequens est irrationabile esse aequales esse velocitates astrorum et circulorum. | Secondly, he shows that it is not unreasonable to say this of the circles themselves. Indeed, it seems to be necessary that their velocities be "analogous," i.e., proportionate, to their sizes — since that is what we see in all natural bodies; namely, that so much the greater something is, so much the swifter does it move by its proper motion. Consequently, if it is not reasonable for the velocity of the stars to be proportionate to the size of their circles, it is nevertheless reasonable for the velocity of the circles to be proportionate to their own size. From this it follows that it is unreasonable for the velocity of the stars and of the circles to be equal. |
| Quod autem non sit rationabile quod motus cuiuslibet stellae proportionetur in velocitate magnitudini sui circuli, sic ostendit. Quia aut hoc contingeret ex necessitate naturali, aut a casu. Si autem contingat ex naturali necessitate quod stella sit velocior quae movetur in maiori circulo, sequetur quod si transponantur stellae in alios circulos, ut scilicet stella quae prius erat in maiori circulo, postea ponatur in minori, sequetur quod stella quae prius erat tardior, sit velocior; et e converso. Et ita videbitur quod stellae non habebunt proprium motum, sed movebuntur a circulis; ex quo stella non conservat velocitatem aliquam propriam in suo motu, sed velocitas eius consequitur solam magnitudinem circuli. | That it is not reasonable for the motion of each star to be proportionate in velocity to the size of its circle he shows in the following way: Such a thing would happen either from necessity of nature or from chance. But if it should occur from natural necessity that a star be swifter on account of being moved in a larger circle, it follows that if stars were transposed into other circles, so that a star previously in a larger circle should be placed in a smaller circle, then the star that previously was slower would be faster, and vice versa. So, it will appear that the stars do not possess a motion of their own but are moved by the circles — from the fact that a star does not preserve some proper velocity in its own motion but its velocity depends on the sole size of the circle. |
| Si autem dicatur quod hoc contingit a casu, quod stella quae est in maiori circulo velocius moveatur, hoc improbat dupliciter. | But if it be maintained that chance is the explanation why a star in a larger circle is moved more swiftly, he disproves this in two ways. |
| Primo quidem quia si hoc esset a casu, non esset rationabile in omnibus circulis et stellis hoc inveniri, simul esse maiorem circuli magnitudinem et maiorem velocitatem motus stellae. Quod enim hoc contingeret in uno vel in duobus, non videretur esse inconveniens; sed quod hoc contingat in omnibus et a casu, videtur esse quoddam fictitium; ea enim quae sunt a casu, non eodem modo se habent in omnibus aut in pluribus, sed in paucioribus. | First of all, because, if this were due to chance, it would not be reasonable to find this in the case of all circles and stars, namely, that a greater size of the circle goes hand in hand with a greater velocity of a star's motion. For that this should happen in one or two cases would not seem impossible, but that it happen in all cases, and be a result of chance is seen to be a fiction — for things that are due to chance do not occur in the same way in all cases, or in the majority of cases, but only in a lesser number. |
| Secundo ostendit quod hoc non possit esse a casu, per hoc quod casus non contingit in his quae sunt a natura, sed ea quae casualiter fiunt, sunt praeter naturae ordinem: unde ea quae a casu vel fortuna fiunt, non similiter se habent in omnibus, sicut ea quae sunt a natura. Cum igitur in motibus caelestium corporum nihil sit praeter naturam, ut supra habitum est, non potest esse quod hoc quod dictum est, a casu accidat. Et ita patet non esse verum quod simul circulus et stella moveantur, et aequali velocitate. | Secondly, he shows that this cannot be due to chance, on the ground that chance has no place in things that are due to nature; rather, things that happen fortuitously are outside the order of nature. That is why things produced by chance or fortune do not occur in the same way in all cases, as do things due to nature. Therefore, since there is nothing outside nature in the motions of the heavenly bodies, as was had above, it cannot be that the case under discussion is due to chance. Thus it is plainly not true that the circle and the star are moved together, and with equal velocity. |
| Potest etiam ad hoc improbandum alia ratio induci: quia, ut Alexander dicit, sequeretur quod alter motuum esset superfluus; quod non contingit in his quae sunt a natura. | It is possible to offer yet another reason to disprove this assertion: for, as Alexander says, it would follow that one or other of the motions would be superfluous, which does not occur in things from nature. |
| Deinde cum dicit: sed adhuc iterum etc., inquirit de tertio membro. | 399. Then at [300] he investigates the third possibility. |
| Et primo ostendit quod non est possibile quod stella moveatur et circulus quiescat. Et dicit quod si dicatur circulos manere in eodem situ et stellas moveri, sequentur eadem irrationabilia quae et prius. Accidet enim quod stella velocius moveatur quae est extra. Et si hoc referamus ad stellas fixas, dicetur illa stella esse extra, quae est extra polos, propinquior aequinoctiali; si autem referamus ad planetas, dicetur esse extra stella illa quae est in circulo continenti (contentum enim est infra continens); utroque enim modo circulus qui est extra, est maior. Et ita sequetur quod velocitates stellarum sint proportionales magnitudini circulorum; quod prius improbatum est. | First he shows that it is not possible for the star to be moved and the circle to be at rest, and says that, if one should hold the circles to remain in the same position and the stars to move, the same unreasonable things as before will follow. For it will turn out that the star which is "outside" is moved more swiftly. And if this refers to the fixed stars, a star will be said to be "outside" if it is outside the poles and nearer the equinoxial circle [the equator]; if it refers to planets, a star will be said to be "outside" if it is in a containing circle (for the contained is within the container). In either case, the circle which is outside is greater. Consequently, it will follow that the velocities of the stars will be proportioned to the size of the circles — which has already been disproved. |
| Secundo cum dicit: quoniam quidem igitur etc., verificat ultimum membrum divisionis: dicens quod, quia neque rationabile est quod utrumque, scilicet tam stella quam circulus, moveatur; neque etiam rationabile est quod solum stella moveatur; relinquitur quod circuli, idest sphaerae, moveantur, sed astra secundum se quidem quiescant, quasi non per se motae, sed moventur ad motum sphaerarum quibus sunt infixae; non sicut alterius naturae existentes, sicut clavus ferreus infigitur rotae ligneae, sed sicut eiusdem naturae existentes; ac si stella sit nobilior pars sphaerae, in qua congregatur lumen et virtus activa. | 400. Secondly, at [301], he verifies the last member of the division and says that, since it is not reasonable for both, i.e., the star and the circle, to be moved or for the star alone to be moved, what remains is that the "circles," i.e., the spheres, are moved, and the stars are at rest with respect to themselves, in the sense of not being moved per se, but with the motion of the spheres in which they are fixed. They will be moved together not as two things with different natures (as happens in the case of a nail embedded in a wooden wheel) but as two things of the same nature. It is as though the stars were the more noble part of the sphere, in which light and active power are concentrated. |
| Et hoc quidem rationabile est dicere, quia hoc posito nihil irrationabile sequitur. | Now this is a reasonable supposition, since, one it is assumed, nothing unreasonable follows. |
| Primo enim non est irrationabile quod sit maior velocitas maioris circuli: inter circulos tamen collocatos circa idem centrum. | For in the first place it is not unreasonable for the greater circle to have a greater velocity, so long as the circles in question are related to the same center. |
| Et si quidem centrum hic proprie accipiatur, oportet hoc referri ad diversos circulos planetarum, qui secundum intentionem Aristotelis, omnes sunt circa idem centrum, quod est terra: non enim astrologi sui temporis ponebant excentricos neque epicyclos. Non autem poterit hoc referri ad diversos circulos quos describunt stellae fixae in suo motu: non enim omnium illorum circulorum est idem centrum. Sed si ad stellas fixas referre velimus, oportet quod hic nomine centri polus significetur; eo quod sicut se habet centrum ad circulum in superficie plana, ita se habet aliqualiter polus ad circulum in superficie sphaerica. | If "center" be here taken in its proper sense, this must be referred to the various circles of the planets, which, according to Aristotle, are all about the same center, namely, the earth — for the astronomers of his time did not posit eccentrics, nor epicycles. But this could not be applied to the various circles described by the fixed stars in their motion, for not all those circles have the same center. However, if we desire to apply it to the fixed stars, then we must take the word "center" as meaning the "pole" [i.e., axis] since, just as the center is to a circle on a plane surface, so is the pole [axis] in a way to a circle on a spherical surface. |
| Cum autem in eadem sphaera designantur diversi circuli circa eosdem polos, tanto aliquis circulus est minor et tardioris motus, quanto est polo propinquior; sicut et inter circulos sub invicem positos, tanto aliquis circulus est minor et tardior, quanto est propinquior centro. Unde centrum et polus sunt indivisibilia et penitus immobilia. | Now since various circles can be designated on the same sphere with respect to the same poles, a circle is smaller and its motion slower according to its nearness to the pole, just as, among circles set one under the other, that circle is less and slower which is nearer the center. Hence the center and the pole are indivisible and completely immovable. |
| Ideo autem hoc dixit esse rationabile, quia etiam in aliis corporibus, quae moventur motu recto, quanto aliquod corpus est maius, tanto velocius movetur proprio motu naturali, sicut maior pars terrae velocius movetur deorsum (e contrario autem se habet in motu violento, in quo corpus quanto est maius, tanto tardius movetur). Unde et in corporibus quae moventur motu circulari, cum motus eorum sit naturalis, rationabile est quod quanto circulus fuerit maior, tanto velocius moveatur. | The reason why he says this is reasonable is that, in other bodies also, which are moved with rectilinear motion, the greater the body, the more rapidly is it moved by its own natural motion — as a larger portion of earth is moved downward with greater speed (while the contrary happens in compulsory motion, in which the motion is slower according as the body is larger). Hence, too, in bodies that are moved with a circular motion, since their motion is natural, it is reasonable that the larger the circle, the more rapidly it be moved. |
| Et quod motus maioris circuli sit velocior, patet ex hoc quod, si a centro ducantur duae lineae rectae per omnes circulos usque ad supremum, portio illa quae abscinditur ab his duabus lineis, erit maior in circulo maiori, et minor in minori. Et eadem ratio est si ducantur duae lineae circulares a polo per omnes circulos usque ad maximum eorum. Cum ergo una dictarum linearum circularium tota simul perveniat ad locum in quo erat alia, manifestum est quod in maiori circulo pertransibit maiorem portionem in eodem tempore: et hoc est velocius moveri, sicut dicitur in VI Physic., scilicet pertransire maius spatium in aequali tempore. Sic ergo rationabile erit quod maior circulus pertransibit maius spatium in aequali tempore; et ita motus erit velocior. | That the motion of a larger circle is swifter is plain from the fact that, if two lines be drawn from the center through all the circles to the last, the portion cut off [i.e., the arc] by those two lines will be greater in a larger circle and less in a smaller. And the same holds if two circular [longitudinal] lines be drawn from the pole through all the circles to the largest of them [at the equator]. When, therefore, one of the said circular lines shall as a whole reach the place previously occupied by the other, it is plain that in the greater circle it will traverse a greater distance in the same time, which is to be moved more rapidly, as is said in Physics VI, namely, to traverse a greater distance in equal time. It will thus be reasonable, therefore, that a greater circle will traverse a greater distance in an equal amount of time, and that thus its motion will be swifter. |
| Secundo autem non accidet hoc inconveniens, quod caelum divellatur, idest scindatur; quod oportebit dicere si stellae moventur et orbes quiescunt; et praecipue quia ostensum est quod totum caelum est continuum, ita quod inferior sphaera tangit superiorem secundum totum. Si igitur orbes quiescerent et stellae moverentur, si quidem stellae essent profundatae in corporibus sphaerarum, sequeretur quod suo motu divellerent sive dirumperent ipsam sphaerarum substantiam. Si autem moverentur in superficie sphaerae superioris, oporteret quod vel inferior sphaera scinderetur a motu stellae, vel quod esset aliquod spatium medium inter duas sphaeras, secundum quantitatem stellae: et hoc spatium oporteret vel esse vacuum, vel esse plenum aliquo corpore passibili, quod dirumperetur ad modum aeris vel aquae, per motum corporis transeuntis; utrumque autem horum est impossibile. | 401. Secondly, there does not occur the unacceptable consequence that the heaven would be "torn apart," i.e., rent, which we would have to say if the stars are moved and their orbs are at rest — especially since it has been shown that the entire heaven is continuous, in such a way that the lower sphere is wholly in contact with the higher. If, then, the orbs should be at rest and the stars in motion, and assuming that the stars are embedded in the bodies of the spheres, it would follow that the stars by their motion would split or shatter the very substance of the spheres. But if they were moved on the surface of the higher sphere, either the lower sphere would have to be split by the motion of the star, or else there would have to be an intermediate space between the two spheres, depending on the size of the star. Now this space would have to be either empty, or full of some passible body that would be rent, after the manner of air or water, by the passage of the moving body. But both these alternatives are impossible. |
| Sed haec omnia inconvenientia evitantur, si ponamus stellas non moveri per se, sed solum per motum orbium. | All these unacceptable situations are avoided, however, if we suppose the stars not to be moved per se but only by the motion of the orbs. |
| Haec autem expositio quae dicta est, convenit tam quantum ad stellas fixas, quam etiam quantum ad planetas. Potest autem aliter exponi, secundum quod refertur solum ad stellas fixas. Quia enim probaverat quod motus maioris circuli est velocior, per quantitatem portionum intersectarum a duabus lineis procedentibus a centro vel a polo, probat hoc iterum alia ratione: quia nisi maior circulus in sphaera stellarum fixarum velocius moveretur, sequeretur quod sphaera stellarum non esset tota continua, sed divelleretur per partes; cum stella quae est in minori circulo, si haberet motum aeque velocem, oporteret quod in minori tempore suum circulum perageret; hoc enim est de ratione aeque velocis, quod in minori tempore minus spatium pertranseat. | This explanation which has been given fits both the fixed stars and the planets. It can, however, be applied in another way referring to the fixed stars only. Since he had proved that the motion of the larger circle is more rapid on the basis of the portions cut off by the two lines drawn from the center or from the pole, he proves this [i.e., that the stars are carried in their spheres] once more with another argument: Unless the greater circle in the sphere of fixed stars were not in more rapid motion, it would follow that the sphere of the stars would not be a continuous whole, but would be separated into parts — since a star in a smaller circle, if it had a motion equally as swift, would necessarily complete its circuit in less time, for the notion of the equally rapid is that in a lesser time it traverses a lesser distance. |
Lecture 12:
That the stars do not move themselves concluded from the motions proper to the spherical shapeChapter 8 cont. Ἔτι δ' ἐπεὶ σφαιροειδῆ τὰ ἄστρα, καθάπερ οἵ τ' ἄλλοι φασὶ καὶ ἡμῖν ὁμολογούμενον εἰπεῖν, ἐξ ἐκείνου γε τοῦ σώματος γεννῶσιν, τοῦ δὲ σφαιροειδοῦς δύο κινήσεις εἰσὶ καθ' αὑτό, κύλισις καὶ δίνησις, εἴπερ οὖν κινεῖται τὰ ἄστρα δι' αὑτῶν, τὴν ἑτέραν ἂν κινοῖτο τούτων ἀλλ' οὐδετέραν φαίνεται. Δινούμενα μὲν γὰρ ἂν ἔμενεν ἐν ταὐτῷ καὶ οὐ μετέβαλλε τὸν τόπον, ὅπερ φαίνεταί τε καὶ πάντες φασίν. Ἔτι δὲ πάντα μὲν εὔλογον τὴν αὐτὴν κίνησιν κινεῖσθαι, μόνος δὲ δοκεῖ τῶν ἄστρων ὁ ἥλιος τοῦτο δρᾶν ἀνατέλλων καὶ δύνων, καὶ οὗτος οὐ δι' αὑτὸν ἀλλὰ διὰ τὴν ἀπόστασιν τῆς ἡμετέρας ὄψεως ἡ γὰρ ὄψις ἀποτεινομένη μακρὰν ἑλίσσεται διὰ τὴν ἀσθένειαν. Ὅπερ αἴτιον ἴσως καὶ τοῦ στίλβειν φαίνεσθαι τοὺς ἀστέρας τοὺς ἐνδεδεμένους, τοὺς δὲ πλάνητας μὴ στίλβειν οἱ μὲν γὰρ πλάνητες ἐγγύς εἰσιν, ὥστ' ἐγκρατὴς οὖσα πρὸς αὐτοὺς ἀφικνεῖται ἡ ὄψις πρὸς δὲ τοὺς μένοντας κραδαίνεται διὰ τὸ μῆκος, ἀποτεινομένη πόρρω λίαν. Ὁ δὲ τρόμος αὐτῆς ποιεῖ τοῦ ἄστρου δοκεῖν εἶναι τὴν κίνησιν οὐθὲν γὰρ διαφέρει κινεῖν τὴν ὄψιν ἢ τὸ ὁρώμενον. Ἀλλὰ μὴν ὅτι οὐδὲ κυλίεται τὰ ἄστρα, φανερόν τὸ μὲν γὰρ κυλιόμενον στρέφεσθαι ἀνάγκη, τῆς δὲ σελήνης ἀεὶ δῆλόν ἐστι τὸ καλούμενον πρόσωπον. Ὥστ' ἐπεὶ κινούμενα μὲν δι' αὑτῶν τὰς οἰκείας κινεῖσθαι κινήσεις εὔλογον, ταύτας δ' οὐ φαίνεται κινούμενα, δῆλον ὅτι οὐκ ἂν κινοῖτο δι' αὑτῶν. 302 Again, since the stars are spherical, as our opponents assert and we may consistently admit, inasmuch as we construct them out of the spherical body, and since the spherical body has two movements proper to itself, namely rolling and spinning, it follows that if the stars have a movement of their own, it will be one of these. But neither is observed. (1) Suppose them to spin. They would then stay where they were, and not change their place, as, by observation and general consent, they do. Further, one would expect them all to exhibit the same movement: but the only star which appears to possess this movement is the sun, at sunrise or sunset, and this appearance is due not to the sun itself but to the distance from which we observe it. The visual ray being excessively prolonged becomes weak and wavering. The same reason probably accounts for the apparent twinkling of the fixed stars and the absence of twinkling in the planets. The planets are near, so that the visual ray reaches them in its full vigour, but when it comes to the fixed stars it is quivering because of the distance and its excessive extension; and its tremor produces an appearance of movement in the star: for it makes no difference whether movement is set up in the ray or in the object of vision. (2) On the other hand, it is also clear that the stars do not roll. For rolling involves rotation: but the 'face', as it is called, of the moon is always seen. Therefore, since any movement of their own which the stars possessed would presumably be one proper to themselves, and no such movement is observed in them, clearly they have no movement of their own.
| Praemissa prima ratione ad ostendendum quod astra moventur per motum circulorum, quae sumebatur ex comparatione stellarum ad circulos seu orbes, hic ponit rationem secundam, quae sumitur ex figura stellarum: quae talis est. Stellae sunt sphaericae figurae; unde si moverentur, oporteret eas moveri motu qui est proprius corpori sphaerico, qui est duplex, scilicet volutatio et circumgyratio; neutro autem horum motuum stellae moventur; ergo non moventur secundum seipsas, sed hoc quod apparet de motu earum, est quia moventur secundum motum circulorum. | 402. Having presented the first argument to show that the stars are moved by the motion of their circles, which argument was based on a comparison of the stars with their circles or orbs, the Philosopher here presents a second argument based on the shape of the stars [302]. The argument is this: The stars are spherical in shape; hence, if they were to be moved, they would have to be moved with a motion that is proper to a spherical body, which is twofold, namely, "volutation" and "circumgyration." But the stars are moved with neither of these motions. Therefore, they are not moved according to themselves but what appears of their motion is due to their being moved according to the motion of the circles. |
| Primo ergo proponit stellas esse sphaericae figurae: quod quidem manifestat dupliciter. Uno modo quia omnes alii ita dicunt, scilicet stellas esse sphaericas; et ita hoc est tanquam probabile accipiendum. Alio modo secundum rationem quae sumitur ex praedeterminatis. Dictum est enim quod stellae sunt factae ex natura caelestium corporum: unde oportet confiteri quod habeant eandem figuram quam habet caelum. Ostensum est autem supra caelum esse sphaericae figurae: unde oportet stellas sphaericae figurae esse. | 403. First, therefore, he proposes that the stars are spherical in shape and this he manifests in two ways. In one way, because everyone else speaks thus, namely, to the effect that the stars are spherical: for which reason it should be accepted as probable. In another way, from an argument taken from what has already been determined. For it has been said that the stars are made out of the nature of the heavenly bodies. Hence we must profess that they have the same shape as the heaven. But it has been shown above that the heaven is spherical in shape. Hence the stars must be spherical in shape. |
| Deinde ostendit differentiam motuum circularium, qui sunt proprii sphaerici corporis. Et dicit quod duo sunt motus sphaerici corporis qui conveniunt ei per se, idest secundum rationem propriae figurae, scilicet volutatio et circumgyratio. Differunt autem hi duo motus secundum diversitatem axis et polorum, super quos intelligitur corpus sphaericum moveri; et hoc per comparationem ad nos. Si enim intelligatur corpus stellae moveri super duos polos, quorum unus sit in superficie quae est versus nos, et alius in superficie opposita, ita quod intelligamus axem esse lineam transeuntem per profunditatem stellae; sic stella movetur motu circumgyrationis, conservans eandem superficiem versus nos, ad modum quo movetur mola molendini. Si vero intelligatur corpus stellae moveri super duos polos, quorum uterque accipitur in quacumque parte qua coniungitur corpori sphaerae, sic in suo motu non semper servabit eandem superficiem versus nos; et erit motus volutationis. Quia igitur isti duo motus sunt proprii corporis sphaerici, oportet, si stellae moventur per seipsas, quod altero horum motuum moveantur. | 404. Then he shows the difference between the circular motions proper to spherical bodies. And he says that there are two motions that belong ear se to a spherical body, i.e., in virtue of its spherical shape, namely, "volutation" and "circumgyration." Now these two motions differ according as the axis and poles upon which the spherical body is understood to be moving are diverse — and these differences are reckoned in relation to us. For if the stellar body is reckoned to be in motion upon two poles, one of which is in the surface facing us and the other in the surface opposite, in such a way that we take the axis as a line passing through the star's depth, then the star is being moved with a motion of "circumgyration." In this motion the stars keep the same face toward us after the manner in which a millstone is moved. But if the stellar body is understood to be in motion upon two poles, both of which are taken at some point where it joins the body of its sphere, then the star in its motion will not always keep the same face toward us. In this case the motion will be "volutation." Therefore, because these are the two motions proper to a spherical body, if the stars are moved with motions of their own, they should be moved with one or the other of these. |
| Deinde ostendit quod neutro horum motuum causetur motus qui in eis videtur. Et primo ostendit quod motus qui in stellis videtur, non sit motus circumgyrationis: et hoc quidem probat dupliciter. Primo quidem quia, si corpus stellarum moveretur motu circumgyrationis, oporteret quod, licet partes stellae mutarent locum subiecto, tamen tota stella maneret in eodem loco secundum subiectum, diversificato solum secundum rationem, sicut patet ex his quae probantur in VI Physic.: talis enim est dispositio motus sphaerici, eo quod est circa centrum et polos, quae non moventur. Sed hoc non possumus dicere in stellis, quia contrarium huius apparet sensu: videmus enim quandoque stellas in oriente, quandoque in occidente. Similiter etiam hoc ab omnibus dicitur, quod stellae non semper manent in eodem loco, sed de uno loco transferuntur in alium. Non ergo motus qui apparet in eis, est motus circumgyrationis. | 405. Then he shows that the motion seen in the stars is due to neither of these two motions. First he shows that the motion seen in the stars is not one of circumgyration; and he proves this in two ways. First, because if the stellar bodies were being moved with the motion of circumgyration, then, even though the parts of the star exchanged places as to subject, the star as a whole would have to remain in the same place as to subject, the place being varied only according to notion, as is clear from what was proved in Physics Vi. For that is the way things turn out for a spherical motion due to its relation to a center and to poles that are stationary. But we cannot admit such a situation in the stars, since the contrary is evident to sense — for we see stars sometimes in the east and sometimes in the west. Likewise, everyone says that the stars do not remain always in the same place but are transferred from one place to another. Therefore, the motion that appears to be in the stars is not one of circumgyration. |
| Alio modo ostendit idem quia, si motus circumgyrationis conveniret stellis, rationabile esset quod omnes tali motu moverentur; eo quod omnes sunt unius naturae, scilicet de natura caelestis corporis, ut supra ostensum est. Sed talis motus non apparet in omnibus stellis, sed solum in sole; nec etiam in quacumque parte caeli sit, sed solum quando oritur et quando occidit. Et hoc ipsum non accidit propter ipsum solem, quia circumgyretur, sed propter elongationem visus nostri a sole: visus enim noster, quia longe distat a sole, nutat, idest tremit, propter infirmitatem suam, inquantum supervincitur a superexcellenti claritate solis. | He shows the same thing another way, from the fact that if the motion of circumgyration should befit the stars, it would be reasonable for all to be moved with that kind of motion, since they are all of one nature, namely, the nature of heavenly body as was shown above. But such a motion is not seen in all stars but in the sun alone, and not when it is in just any part of the heaven, but only when it rises and sets. And these appearances are due not to the fact that the sun is circumgyrated but to the increased distance between the sun and our vision — for our vision, since it is so far from the sun, "wavers," i.e., quivers, on account of its feebleness, insofar as it is overwhelmed by the sun's exceeding brightness. |
| Et ista etiam forte est causa quod stellae fixae videntur scintillare, propter maximam distantiam earum a nobis, eo quod sunt in sphaera octava. Planetae autem non videntur scintillare, propter hoc quod sunt propinquiores nobis; et ideo visus noster potens est in suo vigore pertingere ad ipsos. Sed respiciens ad stellas manentes, idest fixas, visus noster tremit, quasi porrectus valde in longinquum, propter elongationem illarum stellarum a nobis. Tremor autem qui accidit in visu nostro, facit videri quod astrum moveatur, vel secundum scintillationem, sicut stella fixa, vel etiam secundum circumgyrationem, sicut sol; eo quod nihil differt quantum ad hoc quod aliquid videatur moveri, utrum moveatur visus vel res quae videtur; sicut patet de illis qui navigant circa littora, quod, quia ipsi sunt in motu, videtur eis quod montes et terra moveantur. | And this may also be why the stars seem to twinkle, namely, because of their being at the greatest distance from us, since they are in the eighth sphere. On the other hand, the planets are not seen to twinkle, because being nearer to us, our vision is powerful enough to reach them in full strength. But when looking at the "stationary," i.e., fixed, stars, our vision quivers as though from being extended to something very far off, due to the distance separating those stars from us. Now it is the quivering that occurs in our vision that makes the stars seem to be in motion, either according to twinkling, as in the case of a fixed star, or according to circumgyration in the case of the sun. For in order that something appear to be in motion, it makes no difference whether it is our vision, or the thing observed, that is in motion. This is plain in the case of those sailing along the coast, where, because they are in motion, it seems to them that the mountains and the land are in motion. |
| Est autem circa ea quae hic dicuntur considerandum, quod philosophus dicit hic quod visus noster tremit porrectus longe valde, respiciens ad stellas fixas, non quia visus fiat extra mittendo, quod improbat in libro de sensu et sensato; sed quia in huiusmodi eadem ratio est, sive visus fiat extra mittendo sive intus suscipiendo. Conatur enim visus ad videndum rem a remotis, non solum si oporteat eum radium visualem emittere usque ad corpus distans; sed etiam si oporteat eum suscipere speciem a corpore distante provenientem; quia corporis distantis debilior est impressio, et ideo difficilius est eam sentire. Utitur autem modo loquendi ac si visus fiat extra mittendo, quia mathematici ita utuntur in suis demonstrationibus, et plures homines ita loquuntur; nominibus autem utendum est ut plures, sicut ipse dicit in II Topic. | 406. With respect to what is said here, one should consider that the Philosopher says here that our vision quivers as greatly extended, when looking at the fixed stars, not because seeing takes place by means of something sent out from the sight — for he disproves this theory in De Sensu et Sensato —but because in such a situation it makes no difference whether vision takes place because sight sends something out or because it receives something within it. For our vision strains to see things afar, not only if it should have to emit a visual ray to the distant body, but also if it has to receive a species travelling from the distant body, for the impression from a distant body is weaker and is, accordingly, more difficult to sense. However, Aristotle uses a manner of speaking in this instance as though sight took place by sending something out, because mathematicians so use it in their proofs, and many people speak in such terms. Now, as he himself says in II, words are to be used as most people use them. |
| Item considerandum est quod stellas quasdam vocat fixas vel manentes, non quia omnino non moveantur secundum motum suae sphaerae, sicut et planetae, qui dicuntur erratici; sed quia semper a se invicem conservant eandem distantiam et configurationem, quod de planetis non accidit. | 407. It should also be noted that he calls certain stars "fixed" or "stationary," not because they are not moved at all when their sphere is moved, as are the planets, which are called "wandering," but because, unlike the planets, they always maintain the same relative position to one another and present the same configurations. |
| Item quod dicit planetas non scintillare, sicut Simplicius dicit, intelligendum est ut in pluribus: nam Mercurius scintillat, unde et in Graeco nominatur Stilbon, a scintillando. Sol etiam et scintillat et circumgyrari videtur. Sed scintillatio quidem videtur ex eo quod visus non potest perfecte apprehendere rem visam: quod quidem in stellis fixis accidit propter earum distantiam, in sole autem propter excellentiam claritatis. Circumgyratio autem videtur ex eo quod res visa potens est ad immutandum visum intantum quod, circumvoluto spiritu visibili, videatur ipse sol circumvolvi. Et inde est quod maxime videtur sol circumgyrari in ortu et occasu, quando visus noster magis potest defigi in ipsum, quia non tanta virtus est claritatis eius, propter vapores terrenos: cum autem elevatus fuerit, propter excellentiam claritatis, non potest oculus intantum defigi in ipsum quod sufficiat ad apparentiam circumvolutionis, sed eum videt scintillantem. | Likewise his assertion that the planets do not twinkle, must, as Simplicius says, be understood as applying to the majority of planets — for Mercury twinkles, and hence in Greek it is called Stilbon, from "twinkling." The sun, too, seems to twinkle and even circumgyrate. But the twinkling appears due to the fact that our sight cannot properly apprehend the things seen: in the case of the fixed stars this occurs on account of their distance; in the case of the sun on account of its exceeding brilliance. The circumgyration on the other hand is seen due to the fact that the seen object is able to transmute the sight in such a way that, the visual spirit having been turned about, the sun itself seems to turn about. Hence it is that the sun especially seems to rotate more when it rises and sets, for then our vision can fix itself more on it because its brilliance is not as powerful, on account of earthly vapors. But when it has risen, because of the excess of its brightness the eye cannot fix itself on it long enough to make it appear to rotate, but sees it scintillate. |
| Alexander autem dicit quod ideo sol in ortu et occasu videtur circumgyrari, quia sentitur duplex motus eius, scilicet diurnus et motus proprius, ex comparatione ad quietem terrae. Sed hoc non est credibile, quod motus solis, praecipue quo movetur motu proprio, possit in tam brevi spatio percipi, cum vix etiam in multis diebus sentiatur. Aristoteles etiam dicit in littera quod ista circumgyratio apparet non propter ipsum solem, sed propter elongationem visus nostri. | But Alexander says that the reason why the sun appears to rotate at sunrise and sunset is because one senses its twofold motion, namely, the diurnal and its own proper motion, in comparison to the motionlessness of the earth. But this is not believable, namely, that the motion of the sun, especially that by which it is moved with its own proper motion, should be perceived in so short a space — when it is hardly felt even over many days. Aristotle says also, in the letter of the text, that this rotation appears, not from the sun, but from the distance of our vision. |
| Et est sciendum quod Plato posuit stellas, praeter hoc quod moventur motu orbium, moveri motu circumgyrationis. Quod quidem Simplicius nititur ostendere esse verum multipliciter. Primo quia, cum stellae sint corpora naturalia, oportet quod habeant aliquem motum naturalem; et quia sunt de natura caeli, oportet quod secundum seipsas moveantur motu circulari, qui est circumgyratio. Secundo quia stellae, secundum plures, sunt corpora animata, et ita oportet quod per se moveantur: et quamvis sint quodammodo partes orbium, habent tamen secundum seipsas propriam integritatem et circumgyrationem. Tertio quia, cum figura sphaerica sit aptissima ad motum circularem, sicut est ineptissima ad alios motus, videtur quod stellae moveantur circulariter motu circumgyrationis secundum seipsas. Et secundum hoc Plato posuit quod stellae fixae moventur duobus motibus, scilicet motu circumgyrationis secundum seipsas, et motu orbis (quia videntur moveri ab oriente in occidentem). Stellae autem erraticae moventur secundum ipsum tribus motibus, scilicet motu circumgyrationis, et motu proprii orbis, et motu supremi orbis, qui est motus diurnus | 408. One should know that Plato supposed that the stars are subject to a motion of circumgyration in addition to the motion they undergo in virtue of their orbs. Simplicius tries in various ways to show that this is so. First, because, since the stars are natural bodies, they must have some natural motion; and since they share in the nature of the heaven, they must of themselves be moved with a circular motion, which is circumgyration. Secondly, because the stars, in the opinion of many, are animated bodies and therefore must have self-movement: although they are in some sense parts of their orbs, since they have in themselves their own integrity and their own circumgyration. Thirdly, because, since a spherical figure is most suitable for circular motions and most unsuitable for other motions, it seems that stars are of themselves moved circularly with their own motion of circumgyration. In line with this, Plato proposed that the fixed stars are moved with two motions, namely, with a motion of circumgyration according to themselves, and with the motion of the orb (because they are seen to be moved from east to west). But the wandering stars are, according to him, moved with three motions: namely, with a motion of circumgyration, and with the motion of their own orb, and with the motion of the outermost orb, which is diurnal motion. |
| Dicit etiam Simplicius quod Aristoteles hanc positionem non intendit nunc improbare. Non enim ostendit quod stellae nullo modo circumgyrentur, sed quod iste motus qui sensibiliter apparet in stellis, non est circumgyratio; quia circumgyrata manent in eodem loco secundum totum, stellae autem, secundum motum qui in eis videtur, non manent in eodem loco. Et quia circumgyratio videtur in sole apertius in ortu et occasu, propter hoc ostendit quod id quod in eo videtur de huiusmodi motu, non est propter seipsum, sed propter passionem visus nostri. | Simplicius also says that Aristotle is not here concerned with disproving this position. For he does not show that the stars are not circumgyrated at all, but rather that the motion which is manifest to sense in the stars is not one of circumgyration, since circumgyrated things remain in their entirety in the same place, whereas the stars, so far as the motion observed in them is concerned, do not remain in the same place. And because circumgyration is more clearly apparent in the sun at sunrise and sunset, he therefore shows that what is seen in it of such a motion, is not because of it, but because of a transmutation of our vision. |
| Sed quia propositum Aristotelis fuit non recedere ab eis quae ad sensum apparent, quia talis circumgyratio non sensibiliter apparet in stellis, ideo non asseruit hunc motum in stellis esse, licet non directe improbaverit. Simul etiam quia motus caelestium corporum causant motus inferiorum corporum, inquantum appropinquant vel elongantur a nobis; secundum autem huiusmodi stellarum circumgyrationem, nullus effectus deprehenditur in istis inferioribus, nec secundum hunc motum stellae appropinquant vel elongantur a nobis. Et ideo Aristoteles non curavit hunc motum attribuere stellis. | But since it was Aristotle's intent not to get away from sensible appearances, consequently, since such a circumgyration does not sensibly appear in the stars, he therefore did not assert this motion to exist in the stars, even though he did not directly disprove it. Likewise, he also did not do so because the movements of the heavenly bodies cause the motions of the lower bodies according as the former approach or recede from us — yet there is no effect noticed in lower bodies according to such a circumgyration of the stars, nor do the stars approach or recede from us according to this motion. For this reason, Aristotle is not concerned with attributing this motion to the stars. |
| Deinde ostendit quod stellae non moventur motu volutationis. Illud enim quod revolvitur, necesse est quod volvatur, ita scilicet quod non semper eadem superficies eius appareat. Sed videmus quod in aliquo astrorum, scilicet in luna, semper eadem superficies nobis apparet, scilicet illa superficies quae vocatur facies, eo quod apparet in ea quaedam distinctio, sicut in facie hominis quaedam distinctio secundum quandam lineationem videtur. Et sic patet quod luna non movetur motu volutationis. Et eadem ratione nec stellae aliae: quoniam, cum sit eadem natura omnium stellarum, eadem ratio videtur esse de una et de aliis. Et ita concludit quod, quia stellae, si per se moverentur, rationabile esset eas moveri propriis motibus, qui sunt regyratio et volutatio; his autem motibus non moventur, ut ostensum est; consequens est quod stellae per seipsas non moveantur. | 409. Then he shows that the stars are not moved with a motion of "volutation." For whatever is revolved must be so turned that the same face is not always turn to the observer. But we see that in one of the stars, namely, in the moon, the same surface always appears to us, namely, that surface which is called the "face," because there appear in it certain distinguishing marks, just as there is in the face of a man a certain distinguishing according to lineament. From this it is clear that the moon is not moved with a motion of volutation. For the same reason no other stars are, because, since the same nature is in all the stars, the same reason is seen to hold for one and for the others. Thus he concludes: Since it would be reasonable for the stars, if they were moved on their own, to be moved with proper motions, namely, "regyration" and "volutation," and yet, as has been shown, they are not moved with these motions, therefore they are not moved of themselves. |
| Considerandum est autem quod causa illius diversitatis quae in superficie lunae apparet, a diversis diversimode assignatur. Quidam enim dicunt quod causa illius diversitatis est aliquod corpus interpositum inter nos et lunam, quod prohibet nos ne videamus totaliter claritatem lunae; unde ex illa parte qua inter visum nostrum et lunam interponuntur huiusmodi corpora, videtur esse quaedam obscuritas, ex eo quod claritatem lunae in illa parte non videmus. Sed hoc non potest esse: quia illud corpus interpositum inter nos et lunam, non eodem modo interponeretur inter lunam et visum hominis in quacumque parte mundi; et ita non videretur similis dispositio in luna ex omni parte mundi; sicut non videtur similis dispositio eclipsis solaris ex omnibus partibus mundi, ex interpositione lunae inter solem et visum nostrum. Quod circa praedictam diversitatem lunae non accidit: nam similiter videtur ex omnibus partibus terrae, sive Orientalibus sive Occidentalibus, sive Australibus sive borealibus. | 410. It should be noted that the diversity which appears on the surface of the moon is variously explained by different ones. For some say that the cause of this diversity is the interposition of some body between us and the moon, thus preventing us from seeing its full brightness. Hence, in that portion where such bodies are interposed between us and the moon, it appears to be dark because we do not see the brightness of the moon in that part. However, this cannot be, for such an interposed body would not be interposed in the same way between the moon and the sight of a man in any part of the world whatever. Consequently a like disposition would not be observed in the moon from everywhere in the world, just as there is not seen a similar view of a solar eclipse from everywhere in the world, when the moon gets between the sun and the earth. But this does not occur in connection with the aforesaid diversity in the moon — for it is seen in a similar way from all parts of the earth, whether east, west, south, or north. |
| Alii vero dicunt quod huiusmodi obscuritas apparens in luna, est quaedam similitudo alicuius corporis, puta terrae aut maris aut montium, quae resultat in luna ad modum quo resultat forma in speculo. | Others hold that this darkness appearing in the moon is a certain likeness of some body, such as the earth, or the sea, or mountains, which results in the moon after the manner in which a form results in a mirror. |
| Et hoc etiam tollitur per eandem rationem. Quia si huiusmodi formae in speculo viderentur ex quadam reflexione visualium radiorum, vel etiam formarum visualium, non ex omni parte terrae similis diversitas appareret in luna, sicut nec forma in speculo apparet secundum eandem dispositionem undique aspicienti: quia reflexio fit ad loca determinata, secundum proportionem corporum ad quae fit reflexio. Et praeterea secundum hoc ratio Aristotelis non valeret: quia posset dici quod semper talis diversitas apparet nobis in luna, non quia semper eadem eius superficies sit ad nos conversa, sed quia quaelibet eius superficies ex praedictis causis recipit in se huiusmodi apparentiam, quando ad nos convertitur. | But this too is voided for the same reason. Because if such forms of this sort were mirrored by a reflection of visual rays or visual forms, there would not appear a similar variation from everywhere on earth, any more than a form in a mirror appears according to a same disposition no matter from what angle one looks at it. The reason for this is that an image is reflected back at determined places according to the position of the bodies reflected. Moreover, the proposed explanation would nullify Aristotle's argument, because it could be said that the reason why the same diversity always appears to us in the moon is not because the same surface is always turned toward us, but because whatever the surface, it receives from the aforesaid causes such an appearance when it is turned toward us. |
| Et ideo alii dicunt, et melius, quod talis diversitas videtur in luna propter dispositionem suae substantiae, non autem propter interpositionem alicuius corporis, vel quamcumque reflexionem. Et horum est duplex opinio. Quidam enim dixerunt quod formae effectuum sunt quodammodo in suis causis, ita tamen quod quanto aliqua causa est superior, tanto diversae formae effectuum sunt in ea magis uniformiter; quanto vero est inferior, tanto formae effectuum sunt in ea magis distincte. Corpora autem caelestia sunt causa inferiorum corporum; inter corpora caelestia infimum est luna; et ideo in luna, secundum inferiorem eius superficiem, continetur quasi exemplaris diversitas corporum generabilium. Et ista fuit sententia Iamblichi. | And therefore other say — and this is a better explanation — that such a diversity [on the surface of the moon] is seen in the moon because of the disposition of its substance, and not because of the interposition of some body or because of some reflection. There is a twofold opinion among them. For some say that the forms of effects are in a certain sense in their causes, in such a way, however, that, the higher the cause, the more uniformly the various forms of its effects are in it, whereas the lower the cause, the more distinctly are the forms of its effects in it. Now the heavenly bodies are the cause of the lower bodies, and among the heavenly bodies, the moon has the lowest rank. Therefore, in the moon, according to its lower surface there is contained, so to speak, the diversity of generable bodies as in an exemplar. This was Iamblichus' opinion. |
| Alii vero dicunt quod, licet corpora caelestia sint alterius naturae a quatuor elementis, praeexistunt tamen in corporibus caelestibus, sicut in causis, proprietates elementorum; non tamen eodem modo sicut in elementis, sed quodam excellentiori modo. Inter elementa autem supremum est ignis, qui plurimum habet de luce; infimum autem terra, quae minimum habet de luce. Et ideo luna, quae est infima inter corpora caelestia, proportionatur terrae, et assimilatur quodammodo naturae ipsius; et ideo non totaliter est illustrabilis a sole. Unde ex illa parte qua non perfecte illustratur ab eo, videtur in ea esse quaedam obscuritas. Quae quidem obscuritas semper apparet secundum eandem dispositionem in luna: quod non esset si luna revolveretur, quia paulatim immutaretur aspectus talis obscuritatis. | But others say that, although the heavenly bodies are of another nature than the four elements, yet the properties of the elements pre-exist in the heavenly bodies as in their causes — not in the same way as in the elements however, but in a certain more excellent manner. Now among the elements the top rank is held by fire, which has the greatest light, while the lowest in rank is held by earth which has a minimum of light. Consequently, the moon, which is the lowest of the heavenly bodies, is proportionate to earth and is in some sense similar to it in nature — for which reason it cannot be totally lit up by the sun. Hence, in that portion where it is not perfectly lit up by the sun, there is seen to be a certain darkness. And this darkness always appears according to the same disposition in the moon — something that would not be if the moon were revolving, for then the look of that obscurity would gradually change. |
Lecture 13:
From their shape the stars shown, not to move themselves. No sense power in the heavenly, bodiesChapter 8 cont. Πρὸς δὲ τούτοις ἄλογον τὸ μηθὲν ὄργανον αὐτοῖς ἀποδοῦναι τὴν φύσιν πρὸς τὴν κίνησιν (οὐθὲν γὰρ ὡς ἔτυχε ποιεῖ ἡ φύσις), οὐδὲ τῶν μὲν ζῴων φροντίσαι, τῶν δ' οὕτω τιμίων ὑπεριδεῖν, ἀλλ' ἔοικεν ὥσπερ ἐπίτηδες ἀφελεῖν πάντα δι' ὧν ἐνεδέχετο προϊέναι καθ' αὑτά, καὶ ὅτι πλεῖστον ἀποστῆσαι τῶν ἐχόντων ὄργανα πρὸς κίνησιν. Διὸ καὶ εὐλόγως ἂν δόξειεν ὅ τε (290b.) ὅλος οὐρανὸς σφαιροειδὴς εἶναι καὶ ἕκαστον τῶν ἄστρων. Πρὸς μὲν γὰρ τὴν ἐν ἑαυτῷ κίνησιν ἡ σφαῖρα τῶν σχημάτων χρησιμώτατον (οὕτω γὰρ ἂν καὶ τάχιστα κινοῖτο καὶ μάλιστα κατέχοι τὸν αὐτὸν τόπον), πρὸς δὲ τὴν εἰς τὸ πρόσθεν ἀχρηστότατον ἥκιστα γὰρ ὅμοιον τοῖς δι' αὑτῶν κινητικοῖς οὐδὲν γὰρ ἀπηρτημένον ἔχει οὐδὲ προέχον, ὥσπερ τὸ εὐθύγραμμον, ἀλλὰ πλεῖστον ἀφέστηκε τῷ σχήματι τῶν πορευτικῶν σωμάτων. Ἐπεὶ οὖν δεῖ τὸν μὲν οὐρανὸν κινεῖσθαι τὴν ἐν ἑαυτῷ κίνησιν, τὰ δ' ἄλλα [ἄστρα] μὴ προϊέναι δι' αὑτῶν, εὐλόγως ἂν ἑκάτερον εἴη σφαιροειδές οὕτω γὰρ μάλιστα τὸ μὲν κινήσεται τὸ δ' ἠρεμήσει. 303 There is, further, the absurdity that nature has bestowed upon them no organ appropriate to such movement. For nature leaves nothing to chance, and would not, while caring for animals, overlook things so precious. Indeed, nature seems deliberately to have stripped them of everything which makes selforiginated progression possible, and to have removed them as far as possible from things which have organs of movement. This is just why it seems proper that the whole heaven and every star should be spherical. For while of all shapes the sphere is the most convenient for movement in one place, making possible, as it does, the swiftest and most selfcontained motion, for forward movement it is the most unsuitable, least of all resembling shapes which are self-moved, in that it has no dependent or projecting part, as a rectilinear figure has, and is in fact as far as possible removed in shape from ambulatory bodies. Since, therefore, the heavens have to move in one lace, and the stars are not required to move themselves forward, it is natural that both should be spherical—a shape which best suits the movement of the one and the immobility of the other.
| Praemissis duabus rationibus ad ostendendum quod corpora stellarum non moventur secundum seipsa, sed feruntur per motum circulorum sive sphaerarum, hic ponit ad idem tertiam rationem, quae sumitur ex figura stellarum. | 411. Having presented two arguments to show that the stellar bodies are not moved with a motion of their own but are carried along by the motion of their circles or spheres, the Philosopher now proves the same thing with a third argument [303], which is based on the shape of the stars. |
| Et dicit quod si stellae moverentur motu progressivo, quasi circulos suos perambulantes, irrationabile videretur quod natura non dedisset eis instrumenta convenientia ad motum localem. Natura enim non facit suos effectus qualitercumque contingit: et hoc praecipue observat in nobilioribus effectibus. Et ideo non est rationabile quod natura curaverit de animalibus terrestribus, attribuens eis instrumenta convenientia motui progressivo, et quod despexerit sic pretiosa corpora, scilicet stellas, ut non dederit eis instrumenta apta ad motum progressivum. Sed videtur quasi studiose factum a natura quod non moveantur stellae per seipsas, ex hoc quod abstulit eis omnia instrumenta, quibus possent progressivo motu moveri secundum seipsas: et etiam, quod plus est, quia stellae maxime distant a figura animalium habentium instrumenta ad motum progressivum apta. Nam huiusmodi animalia, quanto sunt perfectiora, tanto habent maiorem diversitatem in partibus: stellae autem habent maximam uniformitatem undique, eo quod sunt sphaericae figurae. | And he says that if the stars were moved with a forward motion, as though walking through their circles, it would seem unreasonable that nature should not equip them with instruments suitable for local motion. For nature does not produce its effects haphazardly especially when it comes to its more noble products. Consequently, it is not unreasonable to suppose that nature would have care for terrestrial animals by equipping them with organs suitable for progressive motion and would neglect bodies as precious as the stars and not equip them with organs suitable for progressive motion. Rather it seems that nature deliberately did not intend the stars to be moved on their own, from the fact that it deprived them of all instruments by which they might move of themselves with progressive movement, and furthermore, because the stars are most removed from the shape of animals having instruments suitable to progressive motion. For animals of this sort, the more perfect they are, the greater variety do they exhibit in their parts — but the stars have everywhere the greatest degree of uniformity, since they are spherical in shape. |
| Et ideo rationabiliter videtur esse factum quod et totum caelum sit sphaericum, et unaquaeque stella. Nam sphaerica figura videtur esse maxime utilis ad motum circularem, quo sphaericum corpus movetur in seipso, idest non mutans locum secundum totum nisi secundum rationem, sed solum secundum partes, ut probatur in VI Physic. Per hoc enim quod corpus circulariter motum est sphaericum, velocissime movetur: tum quia linea circularis est minima inter omnes figuras continentes aequale spatium; tum etiam quia corpora rectilinea non habent uniformem motum ex omni parte, quia magis figuntur ex illa parte qua habent superficiem planam, quam ex parte angulorum. Unde cum sphaerica figura ex nulla parte habeat planitiem, sed ex omni parte stet in uno puncto, idest in angulo, constat corpus sphaericum velocissime moveri motu circulari. Similiter etiam maxime retinebit proprium locum: quia scilicet nulla pars eius incipiet esse nisi ubi alia fuit; quod in corporibus rectilineis non contingit, propter praeeminentias angulorum. | 412. On this account it seems reasonable for the entire heaven, and for each star, to be spherical. For a spherical shape seems uniquely suitable to circular motion, i.e., a motion in which a spherical body is moved "in itself," i.e., not changing its place as a whole except as to notion, but only as to its parts, as is proved in Physics VI. The fact that a body circularly moved is spherical allows it to be moved with the greatest speed, not only because a circular line is the smallest of all the figures that can contain an equal area but also because rectilinear bodies do not have a uniform motion in every part, since they are more fixed wherever they have a flat surface than where they have corners. Hence, since a sphere is nowhere flat but everywhere constitutes a point, i.e., a corner, it is plain that a spherical body moves swiftest with a circular motion. Likewise, it will most perfectly retain its own place, since no part of it ever begins to be except where another was, whereas this does not happen with rectilinear bodies, whose corners jut out further than their surfaces. |
| Sed figura sphaerica est maxime inepta ad motum quo proceditur in anterius. In nullo enim similatur corporibus animalium, quae moventur per seipsa. In corpore enim sphaerico nihil est depressum vel supereminens, sicut invenitur in corpore rectilineo: sed figura sphaerica plurimum distat a figura corporum animalium, quae moventur motu progressivo secundum quandam elevationem et depressionem; unde et membra animalium in suis iuncturis sunt flexibilia, ut sint apta ad motum progressivum. | However, a spherical shape is least suited for forward motion. Sphericity has nothing in common with the bodies of animals that are capable of self-movement. For there are not depressions or eminences in a sphere as there are in a rectilinear body. But sphericity is most unlike the shape of the bodies of animals which move forward by a certain raising and lowering, for which reason the members of animals are flexible at their joints in order to be suitable for progressive movements. |
| Quia ergo oportebat quod totum caelum, idest ipsa sphaera, moveretur motu circulari; et quod stellae non moverentur motu progressivo; rationabiliter factum fuit quod utrumque esset sphaericum, scilicet et sphaera et stella. Quia per hoc quod caelum est sphaericum, est aptum ad motum circularem: per hoc autem quod stellae sunt sphaericae, sunt ineptae ad motum progressivum. Unde non moventur in circulis, sed manent, delatae per motum circulorum. | Since, therefore, it was necessary for the whole heaven, i.e., the sphere thereof, to be moved with circular motion, whereas the stars were not to be moved with a forward motion, it was reasonable for each to be made spherical, namely, both the sphere and the star. For the heaven being spherical makes it suitable for circular motion, and the stars' being spherical makes them unsuited for progressive motion. Consequently, the latter are not moved within the circles, but, while remaining stationary in themselves, are carried along by the motion of the circles. |
| Potest autem hic esse dubitatio, cum corpora sphaerarum non percipiantur visu, eo quod sunt diaphana, et possit dici quod stellae moveantur quasi in aere, quare hoc Aristoteles praetermisit inquirere. | 413. Now, a difficulty can arise here: namely, since the bodies of the spheres are not visible, being transparent, and it could be said that the stars are moved, as it were, in air, why did Aristotle omit to make inquiry on this point? |
| Sed dicendum est quod multipliciter apparet ex his quae Aristoteles docet, esse in caelo non solum corpora stellarum distincta, sed etiam sphaerarum. | But it should be said that it is abundantly clear from Aristotle's teachings that in the heaven are not only distinct stellar bodies but also distinct bodily spheres. |
| Primo quidem ex hoc ipso quod ostendit stellas non per se moveri hoc motu qui in eis apparet. | First, from the fact that he shows the stars are not being moved on their own by the motion which appears in them. |
| Secundo ex ratione quam supra praemisit, quia nulla esset ratio quare stella quae peragit maiorem circulum, velocius moveretur: quod tamen habet rationem supposito motu circulorum, quia maior circulus rationabiliter proprio motu velocius movetur. | Secondly, it is clear from an argument he previously gave, namely, that there would be no reason why a star which traverses a greater circle should be moved more swiftly, whereas there is a reason if a motion of the circles is assumed, since it is reasonable for a greater circle by its own motion to be moved more swiftly. |
| Tertio quia Aristoteles in principio huius libri probavit esse aliquod corpus quod circulariter movetur: motus autem stellae, si per se moveretur absque orbe, esset processivus et non circularis, quia non moveretur in eodem loco. | Thirdly, because Aristotle in the beginning of this book proved that there is a body which is moved circularly, while the movement of a star, if it were moved on its own, without its orb, would be progressive and not circular, because it would not be moved while remaining in the same place. |
| Quarto apparet quia illud spatium in quo stellae moventur, non potest esse vacuum, eo quod impossibile est esse vacuum in natura, ut in IV Physic. probatum est. Si vero sit plenum aliquo alio corpore, quod non pertineat ad naturam stellarum, puta igne vel aere, hoc manifeste est inconveniens duplici ratione: primo quidem quia non esset conveniens ut idem esset locus corporum generabilium et corruptibilium, scilicet ignis et aeris, et corporum incorruptibilium, scilicet stellarum, cum diversa corpora habeant diversa loca, naturis eorum proportionata; secundo quia non est rationabile quod corpora inferiora sint continua, et corpora caelestia sint ad invicem discontinuata. Relinquitur ergo quod totum illud spatium in quo stellae videntur moveri, est plenum caelesti corpore, quod pertinet ad ipsam substantiam sphaerarum. | Fourthly, because that space in which the stars would be moved cannot be void, since it is impossible for a void to exist in nature, as was proved in Physics IV. But if it were filled with some other body that had nothing in common with the nature of the stars, for example, fire or air, this would be clearly unacceptable for two reasons. First, because it is not fitting for one and the same place to act as a place for generable-corruptible bodies such as fire and air, and for uncorruptible bodies, namely, the stars, since diverse bodies have places that are diverse, each being suited to the natures involved. Secondly, because it is not reasonable that the lower bodies be continuous and the heavenly bodies mutually discontinuous. What remains therefore is that the entire space in which the stars are seen to be moved is filled with a heavenly body which pertains to the very substance of the spheres. |
| Quinto etiam apparet ex hoc quod sol et luna moventur super circulos se invicem intersecantes: quod apparet ex hoc quod luna quandoque est Australior, quandoque borealior, respectu circuli in quo sol movetur. Manifestum est autem quod intersectiones duorum circulorum, qui dicuntur nodi, sive caput et cauda, non semper sunt in iisdem punctis: alioquin semper in eisdem punctis fierent eclipses solis et lunae, quae non possunt contingere nisi luna in coniunctione vel oppositione existente circa aliquem nodorum praedictorum. Si autem haec diversitas accideret solummodo per motum lunae, sequeretur quod luna non moveretur circulariter, sed secundum elicam figuram: quod est contra naturam caelestium corporum. Sic ergo patet quod ipse circulus lunae habet suum motum. Et eadem ratione circulus solis et aliarum stellarum. | Fifthly, it is clear from the fact that the sun and moon are moved upon circles that mutually intersect. This is plain from the fact that the moon is now north and now south of the circle in which the sun is moved. But it is evident that the intersections of two circles which are called "nodes," or "head and tail," do not occur always in the same points, since they cannot happen unless the moon is in conjunction or in opposition to the sun with respect to one of these nodular points. But if this variation were due solely to the motion of the moon, it would follow that the moon would not be moved circularly but spirally, which is contrary to the nature of the heavenly bodies. Therefore, it is plain that the circle of the moon has a motion of its own. For the same reason, so do the circle of the sun and those of the other stars. |
| Est autem considerandum quod, cum Aristoteles dicit non esse rationabile quod natura curaverit de animalibus, et quod corpora sic pretiosa reliquerit, stellas non vocat animalia. Quia, ut Alexander dicit, sensitivum constituit animal; in caelestibus autem corporibus, si sunt animata, non est virtus animae sensitiva, sicut etiam neque nutritiva; unde non dicuntur animalia nisi aequivoce, ex eo scilicet quod habent animam intellectivam. | 414. Now it should be kept in mind that when Aristotle states it is not reasonable that nature would be solicitous for the animals and neglect so precious bodies, he is not calling stars animals. Because, as Alexander says, it is sensitivity that makes up the animal nature; but in the heavenly bodies, if they are animate, there is not the sensitive power of the souls nor likewise the nutritive. Wherefore, it is only in an equivocal sense that they are called animals, namely, because they have an intellective soul. |
| Sed hoc Simplicius in commento suo nititur improbare: quia omne quod est honorabile, magis est attribuendum caelestibus corporibus quam terrenis; cum ergo sentire pertineat ad dignitatem corporis, videtur quod multo magis caelestia corpora sentiant quam terrena. Praeterea, cum corpora caelestia se invicem tangant, inconveniens videtur quod etiam se invicem non sentiant. Concedit igitur quod in corporibus caelestibus sunt tres sensus, scilicet visus, auditus et tactus: excludit autem ab eis duos alios sensus materialiores, scilicet olfactum et gustum. | However, in his commentary, Simplicius endeavors to refute this on the ground that if anything honorable is attributed to terrestrial bodies, then with more reason to heavenly bodies. But since sensitivity pertains to the excellence of a body, there seems to be much more reason for heavenly bodies to possess it than terrestrial bodies. Morover, since heavenly bodies touch one another, it seems unfitting that they should not sense one another. Therefore, he concedes the existence of three senses in heavenly bodies, namely, sight, hearing and touch, but excludes from them the other two more material senses, namely, smell and taste. |
| Est igitur videndum quid horum sit secundum sententiam Aristotelis. Qui videtur sentire quod in corporibus caelestibus non sit alia de partibus animae nisi intellectiva. Dicit enim in XII Metaphys. quod primum movens movet caelum sicut desideratum, non quidem desiderio sensus, sed desiderio intellectus. Et in II de anima dicit: quibus inest ratiocinatio corruptibilium, his et reliqua omnia; quasi hoc non sit verum in corporibus incorruptibilibus, quibus opinatur intellectum vel rationem inesse absque aliis potentiis animae. | 415. Let us see, therefore, how much of this is in accord with the judgment of Aristotle, who seems to feel that no part of the soul but the intellective is found in the heavenly bodies. For he says in Metaphysics XII that the first mover moves the heaven as an object of desire, not indeed by the desire of sense, but by the desire of intellect. And in On the Soul II he says: "All corruptible things that possess reason possess all the rest" — as though this were not the case in incorruptible bodies, in which he believed intellect or reason to exist without the other powers of the soul. |
| Sed dubium videtur facere quod dicitur in III de anima. Non potest, inquit, corpus habere quidem animam et intellectum discretivum, sensum autem non habere, non mansivum existens, idest nisi maneat semper in eodem loco, sicut plantae et animalia immobilia, generabile autem, idest si sit generabile et corruptibile, sicut patet in hominibus et in aliis huiusmodi animalibus. Subdit autem: at vero neque ingenerabile; per quod videtur significare quod neque etiam si corpus aliquod sit ingenerabile et incorruptibile, sicut sunt caelestia corpora, quod scilicet habeant intellectum sine sensu. Et ad hoc probandum subdit: quare enim non habeant, scilicet sensum, cum habeant intellectum? Aut enim animae melius aut corpori: quasi dicat: aut hoc quod non habet sensum, est propter bonum animae, aut propter bonum corporis. Et subdit: nunc autem neutrum est: hoc quidem enim, scilicet anima, non magis intelliget sine sensu; hoc autem, scilicet corpus, nihil magis erit, idest non erit durabilius, propter illud, scilicet propter hoc quod non habet sensum. Unde concludit: nullum ergo habet animam corpus, non manens, sine sensu. Ex quo videtur sentire quod, si corpora caelestia sint animata anima rationali et intellectiva, quod habeant etiam sensum. | But a statement of his in On the Soul III raises a difficulty. He says, "A body cannot have a soul and a discerning intellect without possessing sensation, if it is not stationary," i.e., "if it is produced by generation," i.e., if it is generated and corruptible, as is evident in men and other animals of this sort. He continues: "Nor yet even if it were not produced by generation" — by which he seems to signify that, not even if a body is ungenerated and incorruptible, as are the heavenly bodies, would it have intellect without sensation. In proof of this he adds: "Why should it not have?" — i.e., not have sensation, seeing that it has intellect. "Because it were better so for the body or for the soul," which is as though saying that the lack of sensation is either for the good of the body or for the good of the soul. Then he goes on: "But clearly it would not be better for either —for the absence of sensation will not enable the one [the soul] to think better or the other [the body] to exist better [ice., more durably]." Then he concludes: "Therefore, no body which is not stationary has soul without sensation." From this he appears to feel that if heavenly bodies are animated with a rational and intellective soul, they also have sensation. |
| Sed huic sententiae obviat quod statim subdit: at vero si sensum habet, necesse est aut corpus esse aut simplex aut mixtum. Impossibile est autem simplex: tactum enim non haberet, est autem necesse hunc habere. Cum ergo corpora caelestia sint simplicia, impossibile est quod habeant sensum. | But what he immediately adds goes counter to this interpretation: "But if a body has sensation, it must be either simple or mixed. And simple it cannot be; for then it could not have touch, which is indispensable." Since, therefore, the heavenly bodies are simple, they cannot possess sensation. |
| Unde praedicta verba Aristotelis sic exponuntur et per Themistium et Averroem in suis commentis, ut hoc quod dicit, at vero neque ingenerabile, sic intelligatur: at vero neque incorruptibile, scilicet corpus caeleste, habet sensum. Quare enim non habebit? Quasi diceret: ista est causa quare non habet, aut enim animae melius aut corpori, idest, si haberet sensum corpus caeleste, aut hoc esset propter bonum animae aut propter bonum corporis. Nunc autem neutrum est: hoc quidem enim, scilicet anima caelestis corporis, non magis intelligit per sensum (non enim habet intellectum a sensibus accipientem, sicut anima intellectiva humana; sed intelligit talis anima per modum substantiae separatae, cui immediate continuatur in ordine rerum); hoc autem, scilicet corpus, nihil magis erit propter illud, idest non conservabitur in esse per sensum, sicut accidit in corporibus terrestrium animalium, quae praeservantur a corrumpentibus per sensum, sicut patet ex his quae praemiserat. | 416. Hence the above-quoted words of Aristotle are explained by Themistius and Averroes in their commentaries in the sense that the expression, "Not even if it were not produced by generation," means: "Not even that which is incorruptible," namely, a heavenly body, "has sensation. And why does it not have sensation?" — as though saying that this is the reason why it does not, namely, "Because it were better so either for the soul or for the body," i.e., if a heavenly body had sensation, it would possess it either for the good of the soul or for the good of the body. "But clearly it is not better for either, for the one [namely, the soul of the heavenly body], will not understand any better" [for its intellect is not the kind that receives from the senses as the human intellect does; rather such an intellect understands after the manner of a separated substance, to which it is immediately continuous in the hierarchy of things]; "nor will the other [namely, the body] exist any better. because of this," i.e., it will not be kept in existence through sensation as occurs with the bodies of earthly animals, which are preserved from corruptive things through sense, as is plain from what he had already said [in On the Soul ]. |
| Et haec quidem expositio videtur esse convenientior quantum ad efficaciam rationis. Ad hoc enim quod aliquid non sit frustra, magis oportet quaerere propter quid aliquid sit, quam propter quid aliquid non sit. Unde ad hoc quod caelum non habeat sensum, sufficit ostendere quod ex sensu nihil ei melius proveniat, quod ponitur secundum expositionem secundam. Nec oportet propter hoc ostendere quod melius sit ei non habere sensum, quod inquiritur secundum primam expositionem: quia hoc ipsum est sufficiens ratio non habendi sensum, si per sensum nihil ei melius adveniat. Sed conclusio quam infert, non videtur huic sententiae adaptari, sed magis priori: concludit enim consequenter: nullum ergo habet animam corpus, non manens, sine sensu. Quamvis possit dici quod haec conclusio non referatur ad immediate praecedentia, sed ad id quod supra dixerat de corporibus generabilibus. | Now this explanation seems to be more fitting than the other, so far as the efficacy of the argument is concerned. For in order to show that something is not without purpose [frustra], it is more necessary to show for what purpose something exists than to show for what purpose something does not exist. Hence, in order for the heaven not to possess sensation, it is enough to show that no advantage would come to it from sensation (and these are the lines according to which the second explanation proceeds). Accordingly, it is not necessary to show that it is better for it not to have sensation (which is the way the first explanation proceeds). For if no advantage would accrue to the heaven from sensation, that is reason enough for not having sensation. But the conclusion which he draws appears not to fit this understanding, but rather the previous one. For he subsequently concludes, "Therefore no body that is not stationary has soul without sensation." However, it could be said that this conclusion is connected not with what immediately preceded it, but with what he had said above about generable bodies. |
| Quia tamen haec sententia videtur aliquatenus esse extorta, videtur potius dicendum quod hoc quod dicit, at vero neque ingenerabile, est continuandum cum praecedentibus; ut sit sensus quod sicut corpus generabile non habet animam intellectivam sine sensu, ita nec corpus ingenerabile. Sed corpus ingenerabile non accipitur hic caelum: quod patet ex hoc quod caelum est mansivum in eodem loco secundum totum, ipse autem loquitur de corpore non mansivo. Unde videtur hic loqui de quibusdam corporibus animatis, quae Platonici Daemones nominabant, dicentes eos esse animalia corpore aerea, tempore aeterna, sicut Apuleius Platonicus dicit in libro de Deo Socratis. Ponebant autem huiusmodi corpora moveri motu progressivo, et non mansiva in eodem loco. | Yet, because this interpretation seems somewhat extorted, it seems better to say that the phrase, "Not even what is not produced by generation," should be continued with the preceding statement, so that its meaning would be: Just as a body which is produced by generation does not have an intellective soul without sensation, so also a body that is not produced by generation. But by the phrase, "A body that is not produced by generation," is not meant here the heaven — which is evident from the fact that the heaven remains in the same place as to its entirety, whereas he is here speaking of a body that is not stationary. Therefore, Aristotle seems to be speaking here of certain animated bodies which the Platonists called "demons," and described as being animals possessed of an airy body and eternal in time, as the Platonist Apuleius says in his book, on the God of Socrates. They posited such bodies as moving with progressive motion and not stationary in the same place. |
| Sed et si quis consideret ordinem corporum caelestium inter corpora naturalia, manifestum erit quod non convenit ei habere potentiam sensitivam. Primo quidem quia huiusmodi corpora non sunt passiva, sed activa: unde nec animabus eorum, si sint animata, convenit habere aliquas potentias sensitivas, quae sunt passivae. | 417. But anyone who considers the position of the heavenly bodies among natural bodies will see that it does not befit the former to have no sensitive potency. First, because these bodies are not passive, but active. Hence, it is not suitable for their souls, if the bodies are animate, to have sensitive potencies, which are passive. |
| Secundo quia huiusmodi corpora sunt uniformia, utpote sphaerica existentia. Oportet autem corpus habens animam sensitivam, habere diversitatem organorum: quia, cum sensus sit vis cognoscitiva particularium, oportet quod corpus sensitivum habeat diversas potentias sensitivas, si perfecte sentiat, quibus cognoscat diversa sensibilium genera; diversis autem sensibus adaptantur diversa organa. Unde uniformitas sphaerici corporis repugnat dispositioni animae sensitivae. | Secondly, because such bodies, being spherical, are uniform, whereas a body possessing sensitivity must have a variety of organs. For, since sense is a power knowing individual things, a body must have diverse sensitive powers if it is to sense perfectly, by which it may know the different genera of sensible things, different organs being adapted for different senses. Hence, the uniformity of the spherical body conflicts with the disposition of the sensitive soul. |
| Tertio quia corpora caelestia sunt quasi universales causae inferiorum effectuum; et ita effectus sensibiles sunt in corporibus caelestibus non secundum particularem, sed secundum universalem rationem, sicut in causis universalibus. Multo igitur magis rationes rerum sensibilium sunt in animabus caelestium corporum, si sint animata, non secundum rationem particularem, quae pertinet ad sensum, sed secundum rationem universalem, quae pertinet ad intellectum. | Thirdly, because the heavenly bodies are as though the universal causes of lower effects. Consequently, sensible effects pre-exist in the heavenly bodies not according to a singular, but according to a universal, notion, as being in universal causes. With much more reason, then, do the notions of sensible things exist in the souls of heavenly bodies (if they are animate), not according to a singular notion, which is proper to sense, but according to a universal notion, which belongs to intellect. |
| Corpora igitur caelestia, si sunt animata, habent intellectum sine sensu. Sed sicut intellectus substantiarum separatarum cognoscit non solum universalia, sed etiam particularia (habent enim per unam virtutem cognoscitivam quod nos habemus per plures), ita etiam est de animabus caelestibus, quod suo intellectu cognoscunt non solum universalia, sed etiam particularia. Ita enim est in omnibus, quod perfectiones quae attribuuntur inferiori per multa, superiori attribuuntur per unum; sicut imaginatio una est virtus omnium sensibilium cognoscitiva, quae tamen sensus percipit per diversas virtutes. | 418. The heavenly bodies, therefore, if they are animated, have intellect without sense. But just as the intellect of separated substances knows not only universals but also particulars (for they have by one knowing power what we have by several, so, too, the souls of heavenly bodies with their intellect know not only universals but particulars as well. For it is thus in all things, that the perfections which are attributed to the lower through many, a higher thing possesses through one — just as imagination is one power capable of knowing all sensible things, which things sense, however, perceives through different powers. |
| Et ex hoc excluditur obiectio Avicennae, qui in sua metaphysica ostendit quod oportet animam caelestis corporis habere vim imaginativam, per quam apprehendat particulares situs qui renovantur in caelo secundum motum eius; sicut intellectus noster practicus non movet secundum universalem apprehensionem sine particulari, ut dicitur in III de anima. Secundum enim praedicta, substantia quae movet caelum, sive sit substantia separata sive sit anima, potest apprehendere particulares situs per intellectum sine sensu, ut dictum est. | This also excludes an objection presented by Avicenna who, in his Metaphysics, shows that the soul of a heavenly body must have an imagination through which it may perceive the individual positions it assumes in the heaven by its motion, just as our practical intellect does not act according to a universal apprehension without a particular, as is said in On the Soul III. For, according to what has been said, the substance which moves the heaven — whether it be a separated substance or a soul — can perceive individual positions through the intellect without sense, as has been said. |
| Quod autem Simplicius obiicit, quod sentire pertinet ad nobilitatem inferioris corporis, unde magis natum est convenire corpori caelesti, dupliciter solvitur. Primo quidem quia, cum anima non sit propter corpus sed e converso, non est considerandum principaliter in potentiis animae id quod pertinet ad nobilitatem corporis, sed id quod pertinet ad rationem animae. Secundo quia id quod habent corpora inferiora, idest cognoscere sensibilia inferiori modo, scilicet per sensum, habent corpora caelestia superiori modo, scilicet per animam intellectivam eis unitam. | 419. The objection of Simplicius, that sensing pertains to the nobility of a lower body, and hence is even more appropriate for a heavenly body, is answered in two ways. First of all, because, since the soul is not for the sake of the body but vice versa, we should not, when considering the potencies of the soul, primarily consider what pertains to the nobility of the body, but what pertains to the notion of soul. Secondly, because that which lower bodies possess, namely, the ability to know sensible things, in an inferior way, that is, through sensation, is possessed by heavenly bodies in a higher way, namely, through an intellective soul united to them. |
Lecture 14:
Indirect and direct proof that heavenly bodies do not produce soundsChapter 9 Φανερὸν δ' ἐκ τούτων ὅτι καὶ τὸ φάναι γίνεσθαι φερομένων ἁρμονίαν, ὡς συμφώνων γινομένων τῶν ψόφων, κομψῶς μὲν εἴρηται καὶ περιττῶς ὑπὸ τῶν εἰπόντων, οὐ μὴν οὕτως ἔχει τἀληθές. 304 From all this it is clear that the theory that the movement of the stars produces a harmony, i.e. that the sounds they make are concordant, in spite of the grace and originality with which it has been stated, is nevertheless untrue. Δοκεῖ γάρ τισιν ἀναγκαῖον εἶναι τηλικούτων φερομένων σωμάτων γίγνεσθαι ψόφον, ἐπεὶ καὶ τῶν παρ' ἡμῖν οὔτε τοὺς ὄγκους ἐχόντων ἴσους οὔτε τοιούτῳ τάχει φερομένων ἡλίου δὲ καὶ σελήνης, ἔτι τε τοσούτων τὸ πλῆθος ἄστρων καὶ τὸ μέγεθος φερομένων τῷ τάχει τοιαύτην φορὰν ἀδύνατον μὴ γίγνεσθαι ψόφον ἀμήχανόν τινα τὸ μέγεθος. 305 Some thinkers suppose that the motion of bodies of that size must produce a noise, since on our earth the motion of bodies far inferior in size and in speed of movement has that effect. Also, when the sun and the moon, they say, and all the stars, so great in number and in size, are moving with so rapid a motion, how should they not produce a sound immensely great? Ὑποθέμενοι δὲ ταῦτα καὶ τὰς ταχυτῆτας ἐκ τῶν ἀποστάσεων ἔχειν τοὺς τῶν συμφωνιῶν λόγους, ἐναρμόνιον γίγνεσθαί φασι τὴν φωνὴν φερομένων κύκλῳ τῶν ἄστρων. 306 Starting from this argument and from the observation that their speeds, as measured by their distances, are in the same ratios as musical concordances, they assert that the sound given forth by the circular movement of the stars is a harmony. Ἐπεὶ δ' ἄλογον δοκεῖ τὸ μὴ συνακούειν ἡμᾶς τῆς φωνῆς ταύτης, 307 Since, however, it appears unaccountable that we should not hear this music, αἴτιον τούτου φασὶν εἶναι τὸ γιγνομένων εὐθὺς ὑπάρχειν τὸν ψόφον, ὥστε μὴ διάδηλον εἶναι πρὸς τὴν ἐναντίαν σιγήν πρὸς ἄλληλα γὰρ φωνῆς καὶ σιγῆς εἶναι τὴν διάγνωσιν ὥστε καθάπερ τοῖς χαλκοτύποις διὰ συνήθειαν οὐθὲν δοκεῖ διαφέρειν, καὶ τοῖς ἀνθρώποις ταὐτὸ συμβαίνειν. 308 they explain this by saying that the sound is in our ears from the very moment of birth and is thus indistinguishable from its contrary silence, since sound and silence are discriminated by mutual contrast. What happens to men, then, is just what happens to coppersmiths, who are so accustomed to the noise of the smithy that it makes no difference to them. Ταῦτα δή, καθάπερ εἴρηται πρότερον, ἐμμελῶς μὲν λέγεται καὶ μουσικῶς, ἀδύνατον δὲ τοῦτον ἔχειν τὸν τρόπον. Οὐ γὰρ μόνον τὸ μηθὲν ἀκούειν ἄτοπον, περὶ οὗ λέγειν ἐγχειροῦσι τὴν αἰτίαν, ἀλλὰ καὶ τὸ μηδὲν πάσχειν χωρὶς αἰσθήσεως. Οἱ γὰρ ὑπερβάλλοντες ψόφοι διακναίουσι καὶ τῶν ἀψύχων σωμάτων τοὺς ὄγκους, οἷον ὁ τῆς βροντῆς διίστησι λίθους καὶ (291a.) τὰ καρτερώτατα τῶν σωμάτων. Τοσούτων δὲ φερομένων, καὶ τοῦ ψόφου διιόντος πρὸς τὸ φερόμενον μέγεθος, πολλαπλάσιον μέγεθος ἀναγκαῖον ἀφικνεῖσθαί τε δεῦρο καὶ τὴν ἰσχὺν ἀμήχανον εἶναι τῆς βίας. 309 But, as we said before, melodious and poetical as the theory is, it cannot be a true account of the facts. There is not only the absurdity of our hearing nothing, the ground of which they try to remove, but also the fact that no effect other than sensitive is produced upon us. Excessive noises, we know, shatter the solid bodies even of inanimate things: the noise of thunder, for instance, splits rocks and the strongest of bodies. But if the moving bodies are so great, and the sound which penetrates to us is proportionate to their size, that sound must needs reach us in an intensity many times that of thunder, and the force of its action must be immense. Ἀλλ' εὐλόγως οὔτ' ἀκούομεν οὔτε πάσχοντα φαίνεται τὰ σώματα βίαιον οὐδὲν πάθος, διὰ τὸ μὴ ψοφεῖν. Ἅμα δ' ἐστὶ τό τ' αἴτιον τούτων δῆλον, καὶ μαρτύριον τῶν εἰρημένων ἡμῖν λόγων, ὥς εἰσιν ἀληθεῖς τὸ γὰρ ἀπορηθὲν καὶ ποιῆσαν τοὺς Πυθαγορείους φάναι γίγνεσθαι συμφωνίαν τῶν φερομένων ἡμῖν ἐστι τεκμήριον. 310 Indeed the reason why we do not hear, and show in our bodies none of the effects of violent force, is easily given: it is that there is no noise. But not only is the explanation evident; it is also a corroboration of the truth of the views we have advanced. For the very difficulty which made the Pythagoreans say that the motion of the stars produces a concord corroborates our view. Ὅσα (9) μὲν γὰρ αὐτὰ φέρεται, ποιεῖ ψόφον καὶ πληγήν ὅσα δ' ἐν φερομένῳ ἐνδέδεται ἢ ἐνυπάρχει, καθάπερ ἐν τῷ πλοίῳ τὰ μόρια, οὐχ οἷόν τε ψοφεῖν, οὐδ' αὐτὸ τὸ πλοῖον, εἰ φέροιτο ἐν ποταμῷ. Καίτοι τοὺς αὐτοὺς λόγους ἂν ἐξείη λέγειν, ὡς ἄτοπον εἰ μὴ φερόμενος ὁ ἱστὸς καὶ ἡ πρύμνα ποιεῖ ψόφον πολὺν τηλικαύτης νεώς, ἢ πάλιν αὐτὸ τὸ πλοῖον κινούμενον. Τὸ δ' ἐν μὴ φερομένῳ φερόμενον ποιεῖ ψόφον ἐν φερομένῳ δὲ συνεχὲς καὶ μὴ ποιοῦν πληγὴν ἀδύνατον ψοφεῖν. Ὥστ' ἐνταῦθα λεκτέον ὡς εἴπερ ἐφέρετο τὰ σώματα τούτων εἴτ' ἐν ἀέρος πλήθει κεχυμένῳ κατὰ τὸ πᾶν εἴτε πυρός, ὥσπερ πάντες φασίν, ἀναγκαῖον ποιεῖν ὑπερφυᾶ τῷ μεγέθει τὸν ψόφον, τούτου δὲ γινομένου καὶ δεῦρ' ἀφικνεῖσθαι καὶ διακναίειν. Ὥστ' ἐπείπερ οὐ φαίνεται τοῦτο συμβαῖνον, οὔτ' ἂν ἔμψυχον οὔτε βίαιον φέροιτο φορὰν οὐθὲν αὐτῶν, 311 Bodies which are themselves in motion, produce noise and friction: but those which are attached or fixed to a moving body, as the parts to a ship, can no more create noise, than a ship on a river moving with the stream. Yet by the same argument one might say it was absurd that on a large vessel the motion of mast and poop should not make a great noise, and the like might be said of the movement of the vessel itself. But sound is caused when a moving body is enclosed in an unmoved body, and cannot be caused by one enclosed in, and continuous with, a moving body which creates no friction. We may say, then, in this matter that if the heavenly bodies moved in a generally diffused mass of air or fire, as every one supposes, their motion would necessarily cause a noise of tremendous strength and such a noise would necessarily reach and shatter us. Since, therefore, this effect is evidently not produced, it follows that none of them can move with the motion either of animate nature or of constraint. ὥσπερ τὸ μέλλον ἔσεσθαι προνοούσης τῆς φύσεως, ὅτι μὴ τοῦτον τὸν τρόπον ἐχούσης τῆς κινήσεως οὐθὲν ἂν ἦν τῶν περὶ τὸν δεῦρο τόπον ὁμοίως ἔχον. 312 It is as though nature had foreseen the result, that if their movement were other than it is, nothing on this earth could maintain its character. Ὅτι μὲν οὖν σφαιροειδῆ τὰ ἄστρα καὶ ὅτι οὐ κινεῖται δι' αὑτῶν, εἴρηται. 313 That the stars are spherical and are not self-moved, has now been explained.
| Postquam philosophus determinavit de motu stellarum, hic determinat de sono earum, qui est effectus motus localis, ut dicitur in II de anima. Et circa hoc duo facit: | 420. After determining the matter of the motion of the stars, the Philosopher here treats of their sound, sound being an effect of local motion, as is said in On the Soul II. Concerning this he does two things: |
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primo excludit opinionem aliorum; secundo determinat veritatem, ibi: sed rationabiliter neque audimus et cetera. |
First he excludes the opinions of others; Secondly, he determines the truth, at 428. |
| Circa primum tria facit: | Regarding the first he does three things: |
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primo ponit quod intendit; secundo inducit rationem aliter sentientium, ibi: videtur autem quibusdam etc.; tertio ostendit quomodo dubitationi satisfacere nituntur, ibi: quoniam autem irrationabile et cetera. |
First he states his intention; Secondly, he presents the arguments of those who hold the opposite, 421; Thirdly, he shows how they try to account for a difficulty, at 423. |
| Dicit ergo primo manifestum esse ex his quae dicta sunt (quod scilicet stellae non moventur), quod si quis dicat quod ex motu earum accidit quaedam harmonia, idest sonus harmonicus, tanquam soni stellarum sibi invicem consonent, leviter loquitur, idest sine ratione sufficienti, et superflue: et hoc dicit quasi nulla utilitate ex huiusmodi sono sequente, sed magis maximo nocumento, ut patebit. Et etiam non ita se habet veritas, secundum quod ex praemissis demonstrationibus apparet. | He says therefore first [304] that it is clear from what has been said (namely, that the stars are not moved), that if anyone asserts that a certain "harmony," i.e., a harmonious sound, results from their motion as though the sounds of the stars harmonize with one another, such a one would be guilty both of "levity" for making assertions without sufficient reason, and of speaking "superfluously." He says this on the ground that such a sound would not be advantageous to anything, but rather most harmful, as will be clear below. Moreover, the truth is otherwise, according to what has so far been demonstrated. |
| Deinde cum dicit: videtur autem quibusdam etc., inducit rationem Pythagoricorum, quorum erat praedicta sententia. | 421. Then at [305] he presents the argument proposed by the Pythagoreans who held the aforesaid opinion. |
| Et primo ostendit quomodo probabant quod corpora caelestia suo motu faciunt magnum sonum. Tria enim sunt propter quae corpora quae apud nos moventur, magnum sonum facere videntur: scilicet propter magnitudinem corporum quae moventur, et propter velocitatem motus ipsorum, et propter multitudinem ipsorum. Corpora autem quae apud nos mota faciunt sonum, neque habent tantam magnitudinis molem, neque tam velocem motum, sicut sol et luna et aliae stellae: quod patet partim ex his quae sensu apparent, nam sol et luna quolibet die totum mundum circumeunt; partim ex his quae in astrologia manifestantur de magnitudinibus eorum et velocitate motus. Adhuc autem ad hoc facit multitudo stellarum. Multo igitur magis videtur quod sol et luna et aliae stellae suis motibus faciant maximos sonos. |
First he shows how they proved that the heavenly bodies produce a loud sound by their motion. For there are three things that seem to account for a loud sound made by bodies that are in motion among us, namely, such sounds are due to the size of the bodies that are in motion and to the velocity of their motion and to the number of bodies involved. Now the bodies that exist among us and cause sound have neither the size nor the speed of the sun and moon and other stars. This is evident in part from the fact that the sun and moon circle the whole world every day, and in part from what astronomy brings out about the sizes and the velocity of their motion. This is further confirmed by considering the great number of stars. Consequently there seems to be good reason why the sun and other stars should produce the greatest sounds in their course. |
| Secundo cum dicit: supponentes autem etc., ostendit quomodo probabant quod sonus eorum esset harmonicus. Manifestum est enim ex his quae in musica traduntur, quod velocitas motus facit sonum acutum, tarditas autem motus facit sonum gravem; determinata autem proportio secundum certos numeros acuti et gravis, est causa harmoniae in sonis; sicut proportio duorum ad unum facit diapason, proportio trium ad duo, quae dicitur sesquialtera, facit diapente, et sic de aliis. | 422. Secondly, at [306] he shows how they proved their sounds would produce a harmony. For it is evident from what is learned in music that swiftness of motion produces a sharp [high] sound, while slowness produces a grave [low] sound, Now a determinate proportion of high and low according to certain numbers is the cause of harmony in sounds — thus the ratio of 2 to 1 produces the diapason [octave]; the ratio of 3 to 2 produces the diapente [fifth] and so on for the others. |
| Ostensum est autem in praemissis quod quanto stella movetur in maiori circulo, tanto velocius movetur. Tanto autem est maior circulus in quo movetur stella, quanto in sphaera stellarum fixarum magis distat a polo; in planetis autem quanto magis distant a centro. Et ideo secundum proportionem elongationum stellarum ab invicem, sive etiam a centro vel a polis, comprehendebant fieri diversitatem velocitatum in motibus stellarum, et per consequens acuitatis et gravitatis in sonis earum. Inveniebant autem elongationem sive distantias esse secundum proportiones numerales, quae faciunt musicales consonantias; et ideo dicebant quod sonus astrorum quae moventur in circuitu, est harmonicus; quem vocabant vocem, propter hoc quod ponebant corpora caelestia esse animata. | Now it has been shown in what has gone before that the larger the circle in which a star is moved the greater is its speed, Such a circle for any given star is reckoned to be larger or smaller depending on its distance from the pole of that sphere in which the fixed stars are moved; while for a planet the size of its circle is reckoned from the center [of the universe]. Hence, according to the proportion of the distances of the stars between themselves, or from the center or the poles, they understood there to be a difference of speeds in the motions of the stars, and consequently, of high or low pitch in their sounds. For they found the elongation or distances to be according to numerical proportions, which produce musical harmonies. Therefore, said the Pythagoreans, the sound of the stars moving in their circuit is harmonious; and this sound they called a "voice," since they held the heavenly bodies to be animated. |
| Deinde cum dicit: quoniam autem irrationabile etc., ostendit quomodo obviabant cuidam dubitationi. | 423. Then at [307] he shows how they met a certain difficulty. |
| Primo ergo ponit dubitationem. Cum enim nos habeamus auditum quo nos sonum percipimus, videtur non esse rationabile quod non audiremus tam magnam vocem, si ex motu astrorum proveniret. | First, therefore, he presents the difficulty: Since we have hearing, by which we perceive sound, it does not seem reasonable that we should not hear such a loud voice if it were to proceed from the movement of the stars. |
| Secundo ibi: causam huius etc., ostendit quomodo huic dubitationi obviabant. Dicebant enim hanc esse causam quare hanc vocem non audimus, quia statim cum nascimur, coexistit nobis iste sonus; et ideo non potest nobis manifestari per suum oppositum, quod est silentium; haec enim duo, scilicet vox et silentium, per se invicem diiudicantur et discernuntur. Unde accidit hominibus de sono caelestium corporum, sicut accidit malleatoribus aeris, qui propter consuetudinem quasi non sentiunt differentiam soni et silentii, eo quod aures eorum sunt impletae huiusmodi sono. | Secondly, at [308] he shows how they met this difficulty. For they asserted that the reason why we do not hear this voice is that, as soon as we are born, that sound co-exists with us, and therefore it cannot make itself noticeable by its opposite which is silence. For these two things, namely, the voice and silence are judged and discerned the one by the other. Hence, in relation to the sound of the heavenly bodies men are in a situation similar to the people who hammer on bronze and become so accustomed to it that, as it were, they do not perceive the difference between sound and silence, so filled with this sound do their ears become. |
| Tertio ibi: haec autem quemadmodum etc., improbat dictam responsionem; dicens quod sicut etiam prius diximus, haec dicuntur ab eis allicienter, idest secundum quandam probabilem rationem quae allicit aures hominum, et musice, idest secundum musicas rationes, sed non secundum veritatem; impossibile enim est quod hoc modo se habeant. Quia si corpora caelestia facerent tam magnos sonos, non solum est inconveniens quod nihil eorum audiatur, quod ipsi solvere nituntur; sed etiam inconveniens est quod corpora inferiora nihil patiantur ab illis sonis, etiam si eos non sentiant. Videmus enim quod soni excellentes destruunt non solum auditum animalium, sed etiam quaedam corpora inanimata; sicut sonus tonitrui frangit lapides, et etiam alia corpora duriora, sicut ferrum et aedificia et alia huiusmodi. Quod quidem contingit non ita quod corpora inanimata patiantur a sono inquantum est quoddam sensibile per auditum, sed inquantum simul cum sono fit vehemens percussio aeris et motus ipsius, sicut philosophus dicit in II de anima. | 424. Thirdly, at [309] he attacks this explanation, declaring that as we said before, these statements are put forth by the Pythagoreans in an "alluring manner," i.e., according to a certain probable argument that appeals to the ears of men, and "musically," i.e., according to musical arguments, but without getting to the truth. For it is impossible that the reality be as they state. Because if heavenly bodies should make such great sounds, not only is it inconsistent that none of them is heard, which they try to solve, but also inconsistent that lower bodies do not suffer anything from these sounds, even though they do not perceive them. For we know that excessive sounds destroy not only the hearing of animals, but even certain inanimate objects — for example, the sound of thunder rends asunder stones and even harder bodies, such as iron, and buildings and the like. Now this happens not because inanimate bodies are affected by sound in the sense of something perceptible by hearing, but inasmuch as along with the sound, there is produced a violent striking and moving of the air, as the Philosopher says in On the Soul II. |
| Cum igitur corpora caelestia quae moventur, sint tam maximae quantitatis; et sonus eorum, si fit, oportet quod transcendat secundum excessum sonum tonitrui et quemlibet alium sonum, secundum proportionem magnitudinis corporum caelestium; multo magis necessarium est quod sonus caelestium corporum usque huc pertingeret, et quod esset intolerabilis fortitudo violentiae illius, quam inferret in inferioribus corporibus. | Since, therefore, heavenly bodies which are in motion, are of such great size, and since their sound, if produced, must be louder than thunder or any other sound, to a degree proportionate to their size, then certainly there is every reason that their sound should reach here and that there would be an unbearable power in the violence that it would do to lower bodies. |
| Patet etiam alio modo quod eorum solutio non est sufficiens: quia consuetudo audiendi magnos sonos, non solum aufert discretionem illorum sonorum, sed etiam aliorum; sicut malleatores aeris non possunt percipere alios sonos minimos. Unde si propter consuetudinem non possumus audire sonos caelestium corporum, pari ratione nec alios sonos audire possemus. | Their explanation is also plainly insufficient on yet another score, because continued exposure to strong sounds not only takes away the discernment of those sounds, but also that of others — as hammerers of bronze cannot distinguish other very slight sounds. Hence if it is through familiarity with them that we cannot hear the sounds of heavenly bodies, then for the same reason, we should not be able to hear any other sounds. |
| Videtur autem, ut Simplicius dicit in commento, sustineri posse Pythagorae positio contra ea quae hic Aristoteles dicit. Primo quidem quia potest dici quod soni caelestium corporum non sunt corruptivi, sed magis conservativi et vivificativi; sicut et motus caeli est ut vita quaedam omnibus natura existentibus, ut dicitur in VIII Physic. | 425. But, as Simplicius says in his Commentary, it seems that the position of Pythagoras can be maintained against the statements of Aristotle. First of all, because it can be said that the sounds of the heavenly bodies are not destructive but rather preservative and vivifying, just as the motion of the heaven is as a certain life for all things existing in nature, as is said in Physics VIII. |
| Similiter etiam quod nos non audimus sonos caelestium corporum, hoc non contingit propter consuetudinem, sicut hic dicitur; quia Pythagorici dicunt Pythagoram talem harmoniam quandoque audivisse, qui tamen consuetus fuit eam audire, sicut et alii. Sed hoc dicunt accidere quia non omnia sensibilia sunt proportionata omnibus sensibus, ut ab eis percipi possint; sicut multos odores percipiunt canes, quos homines percipere non possunt. Et similiter potest dici quod soni illi non sunt perceptibiles humano auditui, nisi aliquis habeat sensum elevatum et depuratum, sicut habuit Pythagoras. Quamvis dici possit quod Pythagoras audivit huiusmodi sonum non per sensum auditus, sed cognoscendo proportiones ex quibus illa harmonia constituitur. | Then, too, our failure to hear the sounds of heavenly bodies is not due to habit, as is said here, since the Pythagoreans claimed that Pythagoras at times heard this harmony, who, nevertheless, like others, was used to hearing it. But they say this occurred because not all sensible things are proportionate to all the senses, so as to be perceived by them — just as dogs perceive many odors that men cannot detect. In like manner, it can be said that those sounds are not perceptible to human hearing unless one have a sense uplifted and purified as did Pythagoras. It could also be said that Pythagoras heard such sounds not by hearing them but by knowing the proportions from which that harmony is formed. |
| Sed haec non videntur veritatem habere. | 426. But these explanations do not seem to contain the truth. |
| Primo quidem quia videmus quod, licet corpora caelestia sint causa vitae, et praecipue sol, tamen fulgor eius corrumpit visum nostrum, propter hoc quod eius proportionem excedit: et eadem ratione sonus qui ex motu illorum corporum proveniret, propter sui excessum nostrum auditum corrumperet. | First, because we know that although heavenly bodies are the cause of life, and especially the sun, yet its brilliance harms our sight, whose proportion it exceeds. For the same reason a sound coming from the motion of those bodies would on account of its excessive power destroy our hearing. |
| Secundo quia, sicut intellectus est perceptivus omnium intelligibilium, ita sensus est perceptivus omnium sensibilium, visus scilicet omnium visibilium, et auditus omnium audibilium: unde dicitur in III de anima quod anima quodammodo est omnia secundum sensum et secundum intellectum. Unde si esset aliquis auditus qui non esset perceptivus cuiuslibet soni, aut oporteret illum sonum aequivoce dici, aut etiam talem auditum. | Secondly, because, just as the intellect can perceive all intelligibles, so sensitivity can perceive all sensibles, for example, sight all that is visible and hearing all that is audible — wherefore in On the Soul III it is said that the soul is in a certain way all things according to sense and according to intellect. Hence if there were a hearing power that could not perceive any and every sound, then either the sound or the hearing would have to be called such only equivocally. |
| Potest quidem contingere quod aliquod animal delectetur in aliqua specie sensibilis secundum aliquem sensum, secundum quem non delectatur in ipso aliud animal; sicut homo delectatur secundum olfactum in odoribus rosarum et liliorum, non autem alia animalia; quia huiusmodi odores sunt convenientes hominibus secundum seipsos, aliis autem animalibus non conveniunt odores, nec delectant ea, nisi causa alimenti, sicut nec colores. Potest etiam contingere quod aliquod animal non cognoscat secundum aliquem sensum differentiam alicuius sensibilis, propter sensus debilitatem et sensibilis parvitatem; sicut homo, qui est debilis olfactus, non potest cognoscere differentiam aliquorum odorum, puta animalium transeuntium, quos cognoscunt canes: si tamen odores fuerint vehementes, etiam homines eos discernunt. Similiter etiam quaedam animalia secundum visum solis claritatem inspiciunt; quam oculi noctuarum ferre non possunt propter excellentiam eius, sed vitant eam sicut visus corruptivum. | Now it can happen that some animal may take pleasure in some kind of sensible thing according to a particular sense that does not delight some other animal according to that sense. For example, man takes pleasure according to the olfactory sense in the odors of roses and lilies, but the other animals do not, for odors of this kind are found agreeable to men for themselves, whereas for other animals odors do not befit them or give them pleasure, except as referring to food; and the same is true for colors. Also it can happen that an animal is unable to distinguish according to some sense the difference of some things because its sense is weak and because the object to be sensed is small. Thus, man, whose sense of smell is weak, cannot discern the difference between certain odors, for example, the odors of animals that are passing by, but dogs do. Yet if the odors were strong, men also could distinguish them. Similarly, some animals according to the sense of sight gaze on the sun's brilliance, which the owl's eyes cannot stand, and avoid as destructive of its vision. |
| Unde impossibile esset ex motibus caelestium corporum provenire sonos tam vehementes, nisi perciperentur ab hominibus, vel corrumperent eorum auditum: nisi forte dicatur quod soni illi aequivoce dicerentur. | Hence it would be impossible for such violent sounds to proceed from the movements of the heavenly bodies without being perceived by men or without harming their hearing; unless of course they are called sounds equivocally. |
| Quod videtur consonare positioni Simplicii, qui videtur arguere Alexandrum, dicentem quod colores, et si qua existunt caelestibus corporibus, tanquam accidentia et extrinsecus advenientia eis insunt. Contra quod ipse dicit quod accidentia et extrinsecus assequentia in corporibus caelestibus dicere, inconvenientissimum existimat, cum habeant substantialem et specificam virtutem: videbatur enim ei quod, quia corpora caelestia sunt causa formarum substantialium in his inferioribus, nullum accidens in eis esse possit. Et secundum hoc, cum sensus non sit cognoscitivus nisi accidentium, sequetur quod nihil illorum corporum sentire possimus. Unde ipse dicit quod neque astra ipsa videmus, neque magnitudines ipsorum aut figuras, neque excellentes pulchritudines, sed neque motum, propter quem fit sonus; sed velut illustrationem quandam ipsorum videmus, talem velut etiam solis circa terram lumen, non ipse sol videtur. | 427. And that seems to be the opinion of Simplicius who is seen to dispute Alexander's statement that colors and all such things, should they exist in the heavenly bodies, are present in them as accidents and extraneous additions. Against this he says that to posit accidents and extraneous additions in the stars he considers as most unacceptable, since they have substantial and specific power. For it seemed to him that, because heavenly bodies are the cause of the substantial forms in lower things, no accident could exist in them. And according to this, since sensation is aware only of accidents, it would follow that we cannot sense anything of these bodies. Wherefore he asserts that we neither perceive the stars themselves, nor their size or figures, nor their surpassing beauties, nor their motion — the cause of their sound; all we see is their luster, as it were — just as, for example, the light of the sun is seen around the earth, but the sun itself is not seen. |
| Sed hoc est expressissime falsum. Primo quidem quia Aristoteles dicit in II de anima quod non secundum quod aqua, neque secundum quod aer, diaphanum est; sed quoniam est natura eadem in his utrisque, et in perpetuo et superiori corpore. Et eadem ratione lumen, quod est actus diaphani, est eiusdem naturae in inferioribus corporibus et in caelesti corpore. Si ergo in huiusmodi inferioribus corporibus sunt accidentia sensu perceptibilia, pari ratione in corporibus caelestibus sunt accidentia perceptibilia sensu. | But this is most expressly false. First of all because Aristotle in On the Soul II says: "Neither air nor water is transparent because it is air or water; they are transparent because each of them has contained in it a certain nature which is the same in both and is also found in the eternal and uppermost body." And for the same reason light, which is the actuality of the transparent, possesses the same nature in lower bodies and in heavenly bodies. If, therefore, these inferior bodies possess accidents that can be perceived by sense, then by the same token there exist in the heavenly bodies accidents perceptible to sense. |
| Adhuc, figura et magnitudo sunt mathematica, quorum rationes sunt indifferentes in quocumque existant. Sicut igitur figura et magnitudo inferiorum corporum sunt accidentia sensibilia, ita etiam et in caelestibus corporibus. Item, si hoc esset, periret omnis certitudo astrologicae scientiae, quae procedit ex apparentibus secundum sensum circa corpora caelestia. | Furthermore, shape and size are mathematical things, whose notions are independent of that in which they may exist. Therefore, just as the shape and size of lower bodies are perceptible accidents, so too is this the case in heavenly bodies. Moreover, this position would destroy all certitude of the science of astronomy which proceeds from what appears to our senses about heavenly bodies. |
| Quomodo etiam esset possibile quod motus caelestium corporum esset eorum substantia, cum sit quid imperfectissimum? Sequeretur etiam quod idem esset in sole figura, lumen et motus, cum unius rei non sit nisi una substantia. Unde patet omnino impossibile esse quod dicit. | Again, how could the motion of the heavenly bodies be their very substance, since motion is something most imperfect? This position would force us to say that, in the sun, shape, light, and motion were one and the same thing, since of one thing there is but one substance. Hence it is plain that it is wholly impossible for what he says to be. |
| Nihil autem prohibet corpora caelestia specificam virtutem habere, et tamen quaedam accidentia in eis esse: nam in inferioribus corporibus sunt quaedam accidentalia, licet in eis sit virtus ad generandum sibi simile in specie. | Now there is nothing to prevent heavenly bodies from having a specific power and there being at the same time certain accidents in them — for in the lower bodies there are certain accidental entities, although they have the power to generate things akin. to them in kind. |
| Deinde cum dicit: sed rationabiliter neque audimus etc., determinat veritatem. | 428. Then at [310] he determines the truth. |
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Et primo proponit quod intendit; secundo manifestat propositum, ibi: quaecumque quidem et cetera. |
First he proposes what he intends; Secondly, he manifests his proposition, at 429. |
| Dicit ergo primo quod rationabile est quod non audimus sonum caelestium corporum, et quod inferiora corpora nullam violentam passionem ab eis pati videntur, propter hoc quod nullum sonum faciunt. Simul autem et per idem manifestabitur causa horum, scilicet quod non audimus sonos caelestium corporum, neque ab eis violentiam patimur; et testimonium accipiemus de veritate primorum sermonum, scilicet quod stellae non moventur per seipsas. Illud enim quod erat dubium circa sermones Pythagoricorum, dicentium fieri symphoniam, idest consonantiam musicalem, ex motu caelestium corporum, erit nobis argumentum quod stellae non per se moventur. | He says therefore first [310] that it is reasonable that we do not hear the sound of heavenly bodies and that lower bodies are seen to suffer no violent effects from them — because they make no sound. Now the very argument that will explain the reason for this, i.e., why we do not hear the sounds of the heavenly bodies and why we suffer no violence from them, will at the same time confirm the truth of the previous statements, namely, to the effect that the stars have no motion of their own. For the problem raised by the Pythagoreans' teaching that a "symphony," i.e., a musical harmony, resulted from the motion of the heavenly bodies, will serve as our argument that the stars are not moved on their own. |
| Deinde cum dicit: quaecumque quidem etc., manifestat propositum: | 429. Then at [311] he manifests his proposition. |
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et primo ratione sumpta ex causa effectiva soni; secundo ex causa finali, ibi: velut futurum et cetera. |
First, with an argument taken from the efficient cause of sound; Secondly, with one taken from the final cause at 430. |
| Dicit ergo primo quod quaecumque corpora in his inferioribus secundum seipsa localiter moventur, faciunt sonum, inquantum faciunt plagam, idest aeris percussuram. Sed quaecumque corpora non moventur secundum seipsa, sed sunt infixa, aut qualitercumque existunt in corpore quod localiter fertur, talia non est possibile sonare; sicut homines qui sedent in navi, non sonant navi mota; neque etiam partes navis quae sunt navi fortiter infixae, sonant ad motum navis, nisi forte propter debilitatem coniunctionis, et cum navis conquassatur. Neque etiam videmus quod navis sonum faciat si feratur in fluvio currenti, ita tamen quod motus navis non sit per seipsam, sed solum per motum aquae: si vero sit velocior motus navis quam motus aquae, tunc inquantum dividit aquam, sonabit. | He says therefore first [311] that whatever bodies among lower bodies are moved according to themselves, these produce a sound to the extent that they produce a "blow," i.e., a percussion, of the air. But bodies that are not moved on their own, but are embedded, or in some way exist, in a locally moving body cannot cause sound, just as people seated in a boat do not cause a sound when the boat is moved, any more than do the parts of the boat firmly attached to the boat, unless because of the weakness of the joint, or when the ship is buffeted. Moreover, we do not perceive that any sound is made by a ship when it is carried along by the current of a river, i.e., when the ship's motion is due entirely to the flow of the water; however, if the motion of the ship is swifter than that of the water, then it will make a sound insofar as it cuts the water. |
| Et tamen secundum easdem rationes quibus Pythagorici asserebant caelestia corpora sonum facere, poterit aliquis dicere inconveniens esse si malus, idest arbor navis, et puppis eius, cum habeat tantam magnitudinem, non faciant sonum; vel etiam ipsa navis, cum movetur in fluvio moto. Intelligendum tamen est quod hic excluditur sonus qui contingit ex divisione aquae, non autem sonus, si quis sit, ex divisione aeris, quantum ad partem navis quae aquae supereminet; quod praecipue apparet quando aer contra-resistit per impulsum venti. Sed illud quod movetur localiter per seipsum, non in aliquo corpore quod fertur, ita quod non faciat aliquam percussuram, impossibile est sonare. | Yet according to the very arguments by which the Pythagoreans asserted the heavenly bodies to make a sound, someone could say that it is inconsistent with this that the "tree," i.e., the mast, of a ship, and the poop, while being so large, make no sound" or that the ship itself makes no sound when it is carried along by the current. We must, of course, understand that he is excluding the sound due to cutting the water, but not the sound, if any, due to the air being cut by the part of the ship above water. Such a sound is heard especially when the air resists in gusts of wind. But whatever is moved locally on its own — and not in some body which is carried along —without causing any percussion, cannot make a sound. |
| Dicendum est ergo quod, si corpora stellarum per se moverentur, sive in aeris multitudine, sive intelligamus aerem per totum mundum diffusum, sive etiam in multitudine ignis, sicut omnes dicunt assignantes supremum locum inter corpora igni, necesse est quod faciant stellae suo motu sonum super omnem magnitudinem naturalis soni. Quod quidem si fieret, sequeretur quod sonus ille usque huc pertingeret, et non solum audiretur a nobis, sed etiam corrumperet corpora quae sunt hic. Sed quia hoc non videmus contingere, consequens est quod nulla stellarum moveatur per seipsam, neque motu violento, neque motu qui sit ab anima. Non enim possent moveri stellae per seipsas, nisi facerent divisionem vel ipsarum sphaerarum caelestium vel aliquorum corporum intermediorum. Ipsae autem sphaerae moventur per seipsas, nec tamen aliquod corpus dividunt: unde etiam ex eorum motu nullus provenit sonus. | It must be said, therefore, that if the bodies of the stars were moved by themselves, whether in a great body of air, or whether we understand air as diffused through the whole universe, or whether in a great body of fire, as all those say who assign the highest place in bodies to fire, then the stars in their motion would have to make a sound greater than any natural sound. If that were so, it would follow that that sound would reach us here, and not only would it be heard by us, but it would corrupt the bodies which exist here. But because we do not see this happen, it follows that none of the stars is moved on its own, neither by a violent motion, nor by a motion proceeding from its soul. For the stars could not be moved on their own without dividing either the celestial spheres or some intermediate bodies. Now the spheres are moved on their own, yet they do not divide any body — hence no sound results from their movement. |
| Patet etiam quod per hoc quod philosophus hic dicit, excludit imaginationem quorundam existimantium quod stellae non moventur in sphaeris, sed in quibusdam corporibus mediis, puta aere vel igne, aut aliquo huiusmodi. | It is clear that, by what he says here, the Philosopher excludes the imagining of those holding that the stars are not moved in the spheres but in certain intermediate bodies, such as air or fire or something of that sort. |
| Deinde cum dicit: velut futurum etc., ostendit idem ex causa finali. Ideo enim natura non dedit stellis motum per se, et per consequens nec sonos, ac si providisset quod, nisi ita se haberet motus stellarum quod non moverentur per se, sed solum per motum sphaerarum, sequeretur hoc inconveniens, quod nihil in his inferioribus esset similiter se habens, quasi per aliquod tempus in suo esse conservatum. | 430. Then at [312] he shows the same thing from the final cause. For nature has endowed the stars with no motion of their own, and consequently with no sounds, as though foreseeing that unless the stars' motion should be such that they would not move of themselves, there would follow the undesirable consequence that nothing among lower things would be "constant in itself," i.e., preserved for a certain space of time in its being. |
| Datur autem per hoc intelligi, sicut Alexander notat, quod Aristoteles hic sentit quod Deus habet providentiam de his quae sunt hic inferius: non enim potest naturae attribui providentia secundum quod est quaedam virtus in corporibus, sed solum per comparationem ad intellectum instituentem naturam. | One is given to understand by this, as Alexander notes, that Aristotle here feels that God exercises a providence over the things here below; for providence cannot be attributed to nature as it is a certain power in bodies, but only as it refers to a mind establishing nature. |
| Ultimo autem epilogando concludit dictum esse quod stellae sunt sphaericae figurae, et quod non moventur per seipsas. | In summing up he concludes [313] that we have said that the stars are spherical in shape and that they are not moved on their own. |
Lecture 15:
Swiftness and slowness in the motion of the planets proportionate to their distance from the first sphere and the earthChapter 10 Περὶ δὲ τῆς τάξεως αὐτῶν, ὃν μὲν τρόπον ἕκαστα κινεῖται τῷ τὰ μὲν εἶναι πρότερα τὰ δ' ὕστερα, καὶ πῶς ἔχει πρὸς ἄλληλα τοῖς ἀποστήμασιν, ἐκ τῶν περὶ ἀστρολογίαν θεωρείσθω λέγεται γὰρ ἱκανῶς. 314 With their order—I mean the position of each, as involving the priority of some and the posteriority of others, and their respective distances from the extremity—with this astronomy may be left to deal, since the astronomical discussion is adequate. Συμβαίνει δὲ κατὰ λόγον γίγνεσθαι τὰς ἑκάστου κινήσεις τοῖς ἀποστήμασι τῷ τὰς μὲν εἶναι θάττους τὰς δὲ βραδυτέρας ἐπεὶ γὰρ ὑπόκειται τὴν μὲν ἐσχάτην τοῦ οὐρανοῦ περιφορὰν ἁπλῆν τ' εἶναι (291b.) καὶ ταχίστην, τὰς δὲ τῶν ἄλλων βραδυτέρας τε καὶ πλείους (ἕκαστον γὰρ ἀντιφέρεται τῷ οὐρανῷ κατὰ τὸν αὑτοῦ κύκλον), εὔλογον ἤδη τὸ μὲν ἐγγυτάτω τῆς ἁπλῆς καὶ πρώτης περιφορᾶς ἐν πλείστῳ χρόνῳ διιέναι τὸν αὑτοῦ κύκλον, τὸ δὲ πορρωτάτω ἐν ἐλαχίστῳ, τῶν δ' ἄλλων τὸ ἐγγύτερον ἀεὶ ἐν πλείονι, τὸ δὲ πορρώτερον ἐν ἐλάττονι. Τὸ μὲν γὰρ ἐγγυτάτω μάλιστα κρατεῖται, τὸ δὲ πορρωτάτω πάντων ἥκιστα διὰ τὴν ἀπόστασιν τὰ δὲ μεταξὺ κατὰ λόγον ἤδη τῆς ἀποστάσεως, ὥσπερ καὶ δεικνύουσιν οἱ μαθηματικοί. 315 This discussion shows that the movements of the several stars depend, as regards the varieties of speed which they exhibit, on the distance of each from the extremity. It is established that the outermost revolution of the heavens is a simple movement and the swiftest of all, and that the movement of all other bodies is composite and relatively slow, for the reason that each is moving on its own circle with the reverse motion to that of the heavens. This at once leads us to expect that the body which is nearest to that first simple revolution should take the longest time to complete its circle, and that which is farthest from it the shortest, the others taking a longer time the nearer they are and a shorter time the farther away they are. For it is the nearest body which is most strongly influenced, and the most remote, by reason of its distance, which is least affected, the influence on the intermediate bodies varying, as the mathematicians show, with their distance.
| Postquam philosophus determinavit de natura et motu stellarum, hic determinat de ordine et situ earum, et maxime quantum ad planetas: nam de stellis fixis manifestum est quod omnes sunt in suprema sphaera situatae. Et circa hoc duo facit: | 431. After deciding about the nature and motion of the stars, the Philosopher here determines their order and position, and especially with respect to the planets — for with respect to the fixed stars it is plain that all are situated in the outermost sphere. Concerning this he does two things: |
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primo ostendit quid circa hoc naturalis a mathematico supponere debeat; secundo ostendit quid circa hoc proprie ad considerationem naturalis pertineat, ibi: accidit autem et cetera. |
First he shows that in this matter the natural philosopher should take the mathematician's suppositions; Secondly, he shows what pertains strictly to the natural philosopher to consider in this matter, at 432. |
| Dicit ergo primo quod de ordine stellarum, quomodo scilicet singulae sint dispositae, ita quod quaedam sint priores et quaedam posteriores, idest superiores et inferiores; et quomodo se habeant ad invicem secundum elongationes, idest quantum una distet ab alia; considerandum est ex his quae dicuntur in astrologia, ubi de his sufficienter determinatur. Haec enim non possunt cognosci per principia naturalis philosophiae, sed per principia mathematicae, idest per proportiones magnitudinum. | He says therefore [314] that in regard to the coordination of the stars, namely, as to how each is arranged, in such a way that some are "prior" and some "posterior," i.e., higher and lower, and how they are related as to "elongations," i.e., as to how far one is distant from another, must be considered from what is stated in astronomy where these particular aspects are sufficiently determined. For these matters cannot be derived from the principles of natural philosophy, but from mathematical principles, i.e., from the proportions existing between magnitudes. |
| Dicitur autem Anaximander primo invenisse rationem de magnitudinibus stellarum, et distantiis earum ab invicem et a terra; ordinem autem positionis planetarum dicuntur primi Pythagorici deprehendisse; quamvis cum maiori diligentia et perfectius sint haec considerata per Hipparchum et Ptolomaeum. | Now Anaximander is said to have been the first to find out the notions of the magnitudes of the stars, and of their distances one from the other and from the earth; while it is to the first Pythagoreans that credit is given for grasping the order of position of the planets, although these matters were given more careful and more perfect consideration by Hipparchus and Ptolemy. |
| Deinde cum dicit: accidit autem etc., ostendit quid circa hoc pertineat ad considerationem naturalis, scilicet velocitas et tarditas in motibus eorum. Dicit ergo quod rationabiliter accidit quod motus quarumlibet stellarum, secundum proportionem elongationis earum a prima sphaera et a terra, sunt velociores et tardiores. | 432. Then at [315] he shows what belongs to the natural philosopher to consider on these points, namely, the swiftness and slowness of their motions. He says, therefore, that it is reasonable for the motions of any stars to be slower and faster depending on their proportionate distance from the first sphere and from the earth. |
| Supponimus enim, tanquam sensu apparens, quod suprema caeli circulatio sit simplex, idest non composita ex pluribus motibus, quia in ea nulla irregularitas apparet: et est velocissima, utpote quae in brevissimo tempore, scilicet spatio unius diei, circuit maximum circulum continentem totum. Circulationes autem planetarum sunt et tardiores et plures; non solum quia diversorum planetarum diversi sunt motus, sed etiam quia motus uniuscuiusque planetae ex diversis motibus constituitur. Unusquisque enim planetarum, secundum proprium motum in suo circulo, fertur in contrarium motus primi caeli, large accipiendo contrarietatem (non enim in motibus circularibus proprie est contrarietas, sicut in primo habitum est): cum enim motus primi caeli sit ab oriente in occidentem, motus planetarum in propriis circulis sunt ab occidente in orientem. Unde rationabile est quod planeta qui est propinquissimus simplici et primae circulationi, contra quam fertur in suo circulo, in plurimo tempore pertranseat proprium circulum; sicut Saturnus in triginta annis suum circulum peragit. Planeta autem maxime distans a suprema sphaera, scilicet luna, in minimo tempore peragit circulum suum, scilicet in spatio unius mensis, vel etiam in minori. | For we suppose as sensibly evident that the outermost revolution of the heaven is "simple," i.e., not composed of several motions, because no irregularity appears in it; moreover, it is the swiftest of all, inasmuch as, in the briefest time, namely, in the course of one day it makes the circuit of the largest circle that encompasses the whole. But the circlings of the planets are both slower and plural, not only because the motions of the different planets are each different, but also because the motion of each planet is a composite of various motions. For each of the planets, as regards its peculiar motion in its own circle, has a movement contrary to the movement of the first heaven — here contrariety is taken in a wide sense, for, strictly speaking, contrariety does not exist among circular motions, as has been said in Book I — in the sense that the motion of the first heaven is from east to west, whereas the movements of the planets in their own circles are from west to east. Hence it is reasonable that the planet nearest to the simple and first revolution, against which it is moving in its own circle, should consume the most time in traversing its own circle—thus Saturn takes 30 [actually 29] years to traverse its orbit. |
| Inter alios autem planetas, propinquior supremae sphaerae semper in maiori tempore circulum suum pertransit, sicut Iupiter in duodecim annis, Mars in duobus, Venus, Mercurius et sol fere in anno. Et sic illud quod magis distat a suprema sphaera, in minori tempore pertransit suum circulum: quia prima sphaera maxime praevalet planetae sibi propinquissimo, et ex hoc motus contrarius fit tardior; planetae autem maxime distanti minime praevalet, propter eius distantiam, et ideo motus contrarius in eo est velocior, scilicet in luna. | On the other hand, the planet most distant from the outermost sphere, namely, the moon, traverses its orbit in the least time, namely, in the space of one month or even less. Among the other planets, that nearer to the outermost sphere always traverses its circle in a greater time — Jupiter in 12 years, Mars in two, Venus, Mercury and the Sun in a year, more or less. Thus the farther they are from the outermost sphere, the less time is required for traversing their orbit, the reason being that the first sphere most greatly dominates the planet closest to it, thus making its contrary motion slower, but dominates least the planet farthest away, because of its distance —hence the contrary motion is swifter in it, i.e., in the moon. |
| Intermedii autem planetae se habent secundum rationem distantiae, sicut mathematici ostendunt; ita scilicet quod superiores planetae tardius moventur in suis propriis motibus. Sed quantum ad motum quo moventur motu primi mobilis; quanto sunt superiores, tanto velociores sunt, ut supra habitum est. | The intermediate planets behave according to the proportion of the distance, as the mathematicians show, in such a way, namely, that the higher planets move more slowly in their proper motions. But with respect to the motion whereby they are moved with the motion of the first mobile body, the higher they are, the swifter they are, as has been shown above. |
| Videtur autem ex hoc quod Aristoteles hic dicit, quod in corporibus caelestibus sit aliquid violentum, si motus planetarum propinquiorum supremae sphaerae efficitur tardior ex hoc quod praevalet magis super ipsum motus primae sphaerae, propter propinquitatem. Si autem est ibi aliquid violentum, sequitur quod motus illi non sint sempiternae durationis sic se habentes, ut Aristoteles vult: nihil enim violentum potest esse sempiternum, ut supra habitum est. | 433. However, from what Aristotle says here, it seems that violence exists among the heavenly bodies, namely, if the motion of the planets nearer to the outermost sphere is slowed up by the greater influence exerted upon it by the motion of the first sphere on account of being near it. Now if there is any violence present, it follows that these motions would not last forever as Aristotle wishes — for nothing violent can be eternal, as was mentioned above. |
| Respondet igitur ad hoc Alexander quod praevalentia supremae sphaerae facit quidem in propinquiori planeta necessitatem tarditatis, non tamen violentiam. Motus enim illi caelestes sunt secundum intellectum et voluntatem; in motibus autem voluntariis non est violentum quod est secundum voluntatem, etiam si sit cum necessitate quadam. Est autem voluntas moventis supremum planetam, ad hoc quod moveat suum mobile secundum convenientiam ad motum superioris mobilis, cui desiderat similari: unde non sequitur tarditatem illam motus primi planetae esse violentam. | To this Alexander responds that although the domination of the outermost sphere does indeed produce a necessary slowing down in the nearer planet, yet not in a violent manner. For those heavenly motions are controlled by intellect and will. But in motions subject to will that is not violent which is in conformity with the will, even though there be an element of necessity involved. Now the aim of the will of the one moving the highest planet is to move its mobile body in accord with the motion of the higher mobile body, to which it desires to be likened. Consequently, it does not follow that the slowness in the motion of the first planet is violent. |
| Sed hoc non solvit totaliter dubitationem, ita ut salventur principia ab Aristotele supposita, qui ponit quod corpus maius velocius movetur proprio motu et naturali: unde si ille motus quo planeta movetur in proprio circulo, est proprius et naturalis, consequens est quod sphaera superioris planetae, cum sit maior, velocius moveatur proprio motu. | 434. But this does not wholly solve the difficulty in such a way as to preserve the principles supposed by Aristotle to the effect that a larger body is moved more swiftly by a proper and natural motion. Hence if that motion whereby a planet is moved in its own circle, is proper and natural to it, the consequence is that the sphere of a higher planet, since it is larger, will be moved more swiftly according to its own motion. |
| Similiter etiam non videtur ordinis convenientia salvari, si corpus quod est remotius a terra immobili, propinquius autem velocissimo motui primi mobilis, tardius in suo proprio motu moveatur. | Then, too, it seems that a strange order is being preserved if a body which is farther from the immobile earth, but nearer to the most rapid motion of the first mobile, should move slower in its own motion. |
| Unde et alii dixerunt quod in caelo non est nisi unus motus, scilicet quo totum caelum revolvitur per motum primi mobilis ab oriente in occidentem; et quantum ad hunc motum, superius corpus est velocioris motus, non solum quantum ad magnitudinem circuli, sed etiam quantum ad temporis brevitatem, ita scilicet quod superior sphaera in minori tempore percurrat maiorem circulum; et inde est quod inferior stella deficit a regrediendo ad idem punctum secundum tempus, non quod in contrarium primi motus moveatur. Et secundum hoc salvatur quod, ex hoc ipso quod superior planeta parum deficit ab attingendo primum motum, inferior autem plus, superior planeta est velocior, et inferior tardior. | 435. Hence, others said that in the heaven there is but one motion, namely, the one whereby the entire heaven is revolved from east to west by the motion of the first mobile: and with respect to this motion the higher body has the swifter motion not only according to the size of the circle but also according to the brevity of time, the result being that a higher sphere will traverse a greater circle in less time, Hence a lower star fails to return to the same point according to time, but not because it moves with a motion contrary to the first motion. This explanation saves the teaching that since the higher planet fails only by a little to match the first motion, whereas a lower planet fails more, the higher planet is swifter and the lower planet slower. |
| Et hoc quidem, sicut Ptolomaeus dicit, si motus planetarum contingat fieri super circulos aeque distantes ab aequinoctiali, et super eosdem polos. Cuius contrarium apparet, planetis declinantibus quandoque ad Septentrionem, quandoque ad meridiem. Unde magis videtur quod hoc quod planetae derelinquuntur a primo motu, sit secundum alium motum planetarum, quo moventur ab occidente in orientem, quam secundum solam deficientiam a primo motu, secundum quam videtur superior planeta tardius moveri. | 436. Indeed that is the situation if, as Ptolemy says, the motion of the planets takes place on circles equidistant from the equinoxial circle [equator] and upon the same poles. Yet the opposite is apparent, since the planets at one time decline to the north and at another time to the south. Hence, it seems that the failure to keep up with the first motion should be explained in terms of another motion of the planets, by which they are moved from west to east, rather than in terms of a sole failure to keep pace with the first motion, a failure that makes a higher planet seem to be moved more slowly. |
| Huius autem causam assignat Alexander aliam, praeter eam quam hic assignat Aristoteles ex praevalentia primi motus. Dicit enim quod ideo planeta superior in maiori tempore peragit circulum suum, non propter tarditatem motus, sed propter magnitudinem circuli: potest enim id quod in maiori tempore movetur, esse velocius vel aeque velox, si maior sit excessus magnitudinis quam pertransit, vel aequalis, quam excessus temporis. | 437. But Alexander assigns another cause to this besides the one which Aristotle assigns from the dominance of the first motion. For he says that a higher planet requires more time to traverse its circle, not because its motion is slower, but because the distance is greater. For a motion that requires more time can be swifter or as swift as another, if the excess in distance traversed is greater or equal to the excess of time. |
| Sed istud non apparet in planetis. Cum enim Saturnus peragat circulum suum in triginta annis, luna vero quasi in mense, oporteret quod proportio magnitudinis sphaerae Saturni ad sphaeram lunae esset secundum proportionem praedictorum temporum, vel etiam maior: quod nec hic videtur, nec in aliis planetis. | But this does not appear in the planets. For since Saturn traverses its circle in 30 years, while the moon traverses its circle in approximately one month, the ratio of the size of Saturn's sphere to that of the moon would have to be according to the ratio of the aforesaid times. But that is not observed in this case, nor in the other planets. |
| Unde aliter dicendum videtur, quod in universo est duplicem naturam considerare: scilicet naturam sempiternae permanentiae, quae est maxime in substantiis separatis; et naturam generabilem et corruptibilem, quae est in inferioribus corporibus. Corpora autem caelestia, cum sint media, utraque aliqualiter participant, secundum duos motus. Nam primus motus, qui est diurnus, est causa sempiternae durationis in rebus: secundus autem motus, qui est in circulo obliquo ab occidente in orientem, est causa generationis et corruptionis et aliarum transmutationum, ut patet per philosophum in II de Generat. | 438. Hence it seems that a different explanation should be given, namely, that we must consider two natures in the universe: first, the nature of eternal permanence which is above all in the separated substances, and secondly, generable and corruptible nature which is present in lower bodies. Now heavenly bodies, being intermediate, share somewhat in both, according to two motions. For the first motion, which is the diurnal, is the cause of eternal duration in things; but the second motion, which is in the oblique [i.e., zodiacal] circle from west to east, is the cause of generation and corruption and of other changes, is is plain from the words of the Philosopher in On Generation II. |
| Primum igitur mobile, tanquam nobilissimum et propinquissimum in ordine naturae substantiis separatis, habet solum primum motum, qui pertinet ad naturam uniformitatis. Alia vero corpora caelestia, inquantum magis recedunt a substantiis immobilibus, appropinquando substantiis generabilibus et corruptibilibus, aliquid participant de alio motu, qui pertinet ad naturam difformitatis; et tanto minus quanto corpus est superius et nobilius. Sic igitur superior planeta, scilicet Saturnus, minimum habet de secundo motu, propter nobilitatem suae naturae: unde hic motus in eo est tardior. Luna autem, propter propinquitatem suae naturae ad corpora generabilia et corruptibilia, plurimum participat de secundo motu, qui est in ea velocissimus. Medii autem planetae medio modo se habent: nam Iupiter, qui est immediate sub Saturno, peragit circulum suum proprio motu circa duodecim annos; Mars vero circa duos; sol, Venus et Mercurius fere uniformiter, scilicet per annum. | According to this, the first mobile, as being at once the most noble and the nearest to the separated substances in the order of nature, has only the first motion, which pertains to the nature of uniformity. But the other heavenly bodies, to the extent that they depart from the unchangeable substances and approach generable and corruptible substances, share somewhat in the other motion, which pertains to the nature of difformity, and to a lesser extent, according as the body is higher and more noble. According to this, then, the higher planet, namely, Saturn has the least portion of the second motion on account of the nobility of its nature; consequently this motion in Saturn is slower. But the moon, on account of the closeness of its nature to generable and corruptible bodies, shares the most in the second motion, which in it is most swift. The intermediate planets behave in an intermediate way: for Jupiter, which is immediately under Saturn traverses its circle with its own motion in about 12 years; Mars in about two years; the Sun, Venus and Mercury take nearly uniformly one year. |
| Nec tamen oportet quod sit proportio velocitatis secundum proportionem distantiarum. Quia motus caelestes non solum sunt naturales, sed voluntarii, et propter finem desideratum. Et ideo, inquantum motus illi sunt naturales, hoc communiter in eis invenitur, quod superiores planetae sunt tardioris motus: inquantum vero motus eorum sunt voluntarii, variatur proportio velocitatis eorum in speciali, non secundum proportionem distantiae, sed secundum id quod melius est. Unde quia motus Veneris et Mercurii quasi colligantur motui solis, utpote ei deservientes ad productionem sui effectus, quasi uniformiter cum ipso moventur. | 439. Nor does the proportion of speed need to be according to the proportion of the distances, because the heavenly motions are not only natural, but also voluntary and for a desired end. And therefore, insofar as these motions are natural, the general rule is that the higher planets are slower of motion; but insofar as their motions are voluntary, the proportion of their speed varies in a particular case, not according to distance, but according to what is better. Hence, because the motions of Venus and Mercury are, as it were, bound to the motion of the Sun, as serving the Sun in producing its effects, they are moved as though uniformly with the Sun. |
| Sic igitur quod Aristoteles dicit, quod suprema sphaera plus praevalet in supremum planetam et minus in remotum, non est intelligendum secundum aliquam coactionem, sed secundum naturalem impressionem; inquantum scilicet naturam superioris magis participat quod est ei propinquius, quam quod est ei remotius. | 440. Thus Aristotle's statement that the supreme sphere exercises more influence on the highest planet and less on a remote one, is not to be understood in the sense of a compulsory force, but in the sense of a natural impression insofar, namely, as the nature of a higher thing is participated in more by something closer to it than by something farther away from it. |
| Sic igitur salvantur principia Aristotelis. Nam licet planetae sit uterque motus naturalis, scilicet et diurnus et qui est in proprio circulo, tamen motus diurnus est ei naturalis secundum id quod est dignius in sua natura; et ideo solum secundum istum motum salvatur principium Aristotelis, quod corpus maius velocius movetur; sicut etiam in homine, in quo est natura sensitiva et intellectiva, dicimus quod quanto homo est dignior, tanto magis habet de motu dignioris naturae, scilicet intellectivae, minus autem de motu indignioris, scilicet sensitivae. | Thus are the principles of Aristotle preserved. For although both motions are natural to a planet, namely, the diurnal motion and that in its own circle, nevertheless the former is natural to it according to what is more noble in its nature. Therefore, it is only with respect to that motion that Aristotle's principle is saved, to the effect that a larger body is moved more swiftly. Likewise in man, who has a sensitive and an intellective nature, we say that the more a man is noble, the more he has of the motion of the nobler nature, namely, the intellective, and the less of the motion of the less noble, namely, the sensitive. |
Lecture 16:
By reason, and by what sensibly appears, the stars are proved to be spherical in shapeChapter 11 Τὸ δὲ σχῆμα τῶν ἄστρων ἑκάστου σφαιροειδὲς μάλιστ' ἄν τις εὐλόγως ὑπολάβοι. Ἐπεὶ γὰρ δέδεικται ὅτι οὐ πεφύκασι κινεῖσθαι δι' αὑτῶν, ἡ δὲ φύσις οὐδὲν ἀλόγως οὐδὲ μάτην ποιεῖ, δῆλον ὅτι καὶ σχῆμα τοιοῦτον ἀπέδωκε τοῖς ἀκινήτοις ὃ ἥκιστά ἐστι κινητικόν. Ἥκιστα δὲ κινητικὸν ἡ σφαῖρα διὰ τὸ μηδὲν ἔχειν ὄργανον πρὸς τὴν κίνησιν. Ὥστε δῆλον ὅτι σφαιροειδῆ ἂν εἴη τὸν ὄγκον. 316 With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she will have given things which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere. Ἔτι δ' ὁμοίως μὲν ἅπαντα καὶ ἕν, ἡ δὲ σελήνη δείκνυται διὰ τῶν περὶ τὴν ὄψιν ὅτι σφαιροειδής οὐ γὰρ ἂν ἐγίνετο αὐξανομένη καὶ φθίνουσα τὰ μὲν πλεῖστα μηνοειδὴς ἢ ἀμφίκυρτος, ἅπαξ δὲ διχότομος. Καὶ πάλιν διὰ τῶν ἀστρολογικῶν, ὅτι οὐκ ἂν ἦσαν αἱ τοῦ ἡλίου ἐκλείψεις μηνοειδεῖς. Ὥστ' εἴπερ ἓν τοιοῦτον, δῆλον ὅτι καὶ τἆλλα ἂν εἴη σφαιροειδῆ. 317 Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most part a crescent-shaped or gibbous figure, and only at one moment a half-moon? And astronomical arguments give further confirmation; for no other hypothesis accounts for the crescent shape of the sun's eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical also.
| Postquam philosophus determinavit de natura, motu et positione stellarum, hic determinat de figura earum. Et circa hoc duo facit: | 441. After determining the nature, motion, and position of the stars, the Philosopher here determines about their shape. Concerning this he does two things: |
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primo ostendit stellas esse figurae sphaericae, per rationem; secundo per ea quae sensibiliter apparent, ibi: adhuc autem similiter quidem et cetera. |
First he shows by reason that the stars are spherical in shape; Secondly, by what is apparent to sense, at 445. |
| Dicit ergo primo quod aliquis potest rationabiliter existimare figuram uniuscuiusque stellae esse sphaericam; non solum propter hoc quod sunt de natura caeli, ut supra probavit; sed etiam quia supra ostensum est quod stellae non sunt natae moveri per seipsas, sed moventur motibus circulorum sive sphaerarum. Natura autem nihil facit irrationabiliter neque frustra, quia tota naturae operatio est ordinata ab aliquo intellectu propter finem operante: unde manifestum est quod stellis immobilibus, idest quae per se non moventur, dedit talem figuram quae minime est apta ad motum progressivum. Talis autem, ut supra dixit, est figura sphaerica, propter hoc quod nullum habet organum deserviens ad motum progressivum: licet talis figura sit maxime apta ad motum circularem, quo aliquid secundum totum non mutat locum. Unde manifestum est quod stellae secundum molem suae magnitudinis sunt sphaericae figurae. | 442. He says therefore first [316], that someone can reasonably suppose that the figure of each star is spherical not only on the ground that they are of the nature of the heaven, as he proved above, but also because it has been shown above that the stars are not apt to be moved of themselves but are moved by the movements of their circles or spheres. Now nature does not do anything irrational or to no purpose, since the whole activity of nature is coordinated by an intellect acting for an end. Hence, it is plain that to the immovable stars, i.e., to those that are not moved on their own, this intellect gave a figure that is in no way suitable for progressive motion. Such a shape is, as he said above, the spherical, for the reason that it possesses no organ to serve for progressive motion. Yet, such a figure is most suitable for that type of circular motion in which the moved thing in its wholeness does not change its place. Thus it is plain that the stars, according to the mass of their magnitude, are spherical in figure. |
| Videtur autem haec probatio non esse conveniens. Nam supra Aristoteles probavit stellas non moveri per seipsas, ex eo quod sunt sphaericae figurae: unde cum hic probet e contra quod sint sphaericae figurae, per hoc quod sunt immobiles secundum seipsas, videtur quod sit probatio circularis. | 443. But this proof does not seem to be appropriate. For Aristotle proved above that the stars are not moved on their own, on the ground that they are spherical in shape — hence, when he now proves that they are spherical in shape on the ground that they cannot be moved on their own, he seems to be arguing in circles. |
| Respondet autem ad hoc Alexander quod ex hoc nullum sequitur inconveniens: quia Aristoteles probavit stellas non moveri per seipsas, non solum per hoc quod sunt sphaericae figurae, sed etiam per quaedam alia media. Similiter etiam ostendit stellas esse sphaericae figurae per quaedam alia media, et non solum per hoc quod sunt secundum se immobiles. | Alexander's answer to this is that nothing inappropriate follows from this —for Aristotle proved that the stars are not moved on their own, not only because they are spherical in shape but also through certain other middle terms. Likewise, he shows that the stars are spherical in shape through certain other middles and not only because they are of themselves immobile. |
| Obiicit autem contra hoc Simplicius, quod non impeditur ratio circularis demonstrationis per hoc quod utraque conclusio pluribus mediis ostenditur. | 444. Simplicius, however, argues against this that the charge of circular demonstration is not removed by the fact that both conclusions are shown by several middles. |
| Sed dicendum est quod, licet per hoc non tollatur ratio circularis demonstrationis, tollitur tamen inconveniens quod ex circulari demonstratione contingit, ut scilicet nihil manifestet. Quia non potest aliquid manifestari nisi per notius, non potest autem idem esse notius et minus notum: sed dum utraque conclusio per alia media manifestatur, una potest sumi ut manifestativa alterius, ad ostendendum convertibilitatem conclusionum. | But it should be stated that, although the notion of a circular demonstration is not thereby removed, yet there is removed the unacceptable situation arising from circular demonstration, namely, that it shows nothing. For the only way to manifest something is to use what is better known — and of course the same thing cannot be both better known and less known. However, when both conclusions are manifested by other middles, then one can be taken as manifestive of the other, in order to show the convertibility of the conclusions. |
| Deinde cum dicit: adhuc autem similiter quidem etc., ponit aliam rationem ad idem, quae sumitur ex his quae sensibiliter apparent. Et supponit quod omnia astra similiter se habent sicut unum. Ostenditur autem de uno eorum, scilicet de luna, per ea quae sensibiliter videntur, quod sit sphaericae figurae. Et hoc quidem ostendit dupliciter: | 445. Then at [317] he presents another argument for the same, based on what is sensibly apparent, and he supposes that as one star is, so all the others are. There is shown then, by one of them, namely, the moon, from the things apparent to sense, that it is spherical in shape. This he shows in two ways. |
| primo quidem per ea quae communiter ab omnibus considerantur, idest ex figuris quas luna mutat ex augmento et decremento. Dicit enim quod nisi luna esset sphaericae figurae, non fieret in suo augmento et decremento, secundum plurimum quidem lunularis vel novaculae habens figuram, aut etiam amphicurtos, aut etiam dichotomos. | First from what is generally considered by all, namely, from the shapes the moon goes through in waxing and waning. For he says that unless the moon were spherical in shape, then, as it waxes and wanes, it would not appear most of the time as having the shape of a crescent or scimitar, or amphicurtos [gibbous], or also "dichotomous." |
| Dicitur autem luna dichotoma, secundum quosdam, quando est plena, quia tunc mensem dividit in duo media: dichotomos enim dicitur a divisione in duo. Sed hoc repugnat ei quod infra dicetur, quod lunam vidimus dichotomam existentem, subintrantem autem Martem, et occultantem secundum nigrum ipsius, exeuntem autem secundum clarum et lucidum; ex quo patet quod dichotoma dicitur luna quando superficies eius quae est versus nos in duas partes dividitur, ita quod media pars eius est obscura, media clara. Et sic etiam accipitur hoc nomen in libro syntheseos Ptolomaei, translato de Graeco. | Some explain that the moon is said to be "dichotomous" when it is full, because it is then that it divides the month in half — for "dichotomous" refers to cutting in two. But this explanation conflicts with something that Aristotle will say later, namely, that we see the moon, when it is dichotomous, entering Mars and hiding it according to its dark part, but leaving according to its bright and shining part. From this it is clear that the moon is called "dichotomous" when its surface which is facing us is divided into two parts such that half is dark and half bright. This is also the meaning given to this word in Ptolemy's Synthesis translated from the Greek. |
| Est ergo considerandum quod Aristoteles non facit hic mentionem de figura lunae quam habet in principio aut termino augmenti seu decrementi, sed solum de ea quam habet dum crescit aut deminuitur. Semper enim, cum luna sit sphaericae figurae, unum eius hemisphaerium illuminatur a sole, et aliud remanet obumbratum. Quando ergo luna est in coniunctione ad solem, totum superius hemisphaerium, quod directe a sole respicitur, illuminatur a sole, ita quod inferius hemisphaerium remanet occultatum; et tunc videtur nobis luna obumbrata et obscurata. Paulatim autem luna recedente a sole, superius hemisphaerium ab una parte sua, qua magis distat a sole, desinit illustrari, et secundum eandem quantitatem incipit illustrari hemisphaerium inferius; et tunc videtur luna figurae lunularis, idest arcuosa. | 446. It is worthy of note that Aristotle makes no mention here of the shape which the moon has at the beginning or end of its waxing or waning, but only of the shape it has while it is waxing or waning. For, since the moon is spherical in shape, one of its hemispheres is always being illuminated by the sun and the other remains dark. When, therefore, the moon is in conjunction with the sun, its whole upper hemisphere, which is directly regarded by the sun, is illuminated by the sun, so that its lower hemisphere remains dark. It is then that the moon is seen by us as darkened and obscured. But as the moon gradually gets away from the sun, that part of its upper hemisphere which is farther from the sun ceases to be illuminated, and the lower hemisphere begins to be illuminated according to the same amount. At that time the moon appears "crescent-shaped," i.e., arc-shaped. |
| Et hoc procedit quousque distet a sole secundum quadraturam circuli, idest secundum quartam partem circuli; et tunc videtur superficies eius quae est versus nos, ex media parte obscura et ex media parte clara, quod est eam esse dichotomam. Postmodum autem, accedens ad solis oppositionem, incipit maior pars inferioris hemisphaerii eius illustrari a sole; et tunc dicitur amphicurtos, quousque sit in oppositione ad solem; tunc enim totum hemisphaerium eius inferius illustratur a sole, et dicitur plena. Postmodum vero paulatim incipit deficere, et fit amphicurtos, quousque distet secundum quartam partem circuli; et tunc dicitur dichotoma, quasi ex media parte clara; cuius claritas postmodum, dum citra dimidium deminuitur, fit lunularis, usque ad coniunctionem. | This goes on until it is a quadrant, i.e., a quarter circle, distant from the sun, and then its surface toward us is seen with one half dark and one half illuminated, and this makes it "dichotomous." After that, as the moon moves to opposition with the sun, more and more of its lower hemisphere begins to be illumined by the sun, and then it is called amphicurtos [gibbous] until it is in opposition with the sun. For at this time its entire lower hemisphere is illuminated by the sun and it is called "full." After that, it begins gradually to wane little by little until it is a quadrant distant, at which time it is called "dichotomous," as though half of it is bright. This brightness afterwards, when it diminishes below half, becomes crescent-shaped, until conjunction with the sun. |
| Sic igitur patet quod in augmento multoties, sive secundum plurimum, luna est arcualis seu lunularis, aut amphicurtos; sed semel in augmento est dichotoma et semel in decremento, quando scilicet distat a sole secundum quartam partem circuli. | Thus it is plain that as it waxes it is frequently or "mostly" arc-shaped or crescent-shaped, or gibbous; it is dichotomous just once as it is waxing and once in waning, namely, when it is distant from the sun by a quarter of a circle. |
| Hoc autem non contingeret si luna non esset sphaericae figurae. Manifestum est enim quod, si superficies eius quae est versus nos esset tota plana, simul inciperet illustrari a sole, et etiam obscurari, non successive per continuum augmentum et decrementum. Ex quo manifestum est quod habet sphaericam tumorositatem, per quam contingit quod paulatim augetur eius claritas vel obscuritas: quod non contingeret cuiuscumque esset alterius figurae quam sphaericae. | 447. Now all this would not happen if the moon were not spherical in shape. For it is plain that if its surface turned toward us were totally flat, it would begin to be illumined by the sun all at once, and also to get dark, instead of successively by a continuing increase and decrease. This shows that it has a spherical bulge by which its brightness or darkness comes to be increased little by little — which could not happen if it were any shape but spherical. |
| Secundo ostendit idem per astrologicas observationes, ex quibus manifestatur quod eclipses solis sunt lunulares, idest arcuales: incipit enim sol obscurari secundum arcualem figuram, per interpositionem lunae inter nos et solem. Quod non contingeret nisi luna esset sphaericae figurae: corpora enim sphaerica se invicem secant secundum arcuales sectiones, ut a mathematicis probatur. | 448. Secondly, he shows the same thing from astronomical observations, which reveal that the eclipses of the sun are "crescent-shaped," i.e., arcuate. For the sun begins to be obscured according to the figure of an arc, by the interposition of the moon between us and the sun. But this would not occur unless the moon were spherical, for spherical bodies cut each other according to arc-shaped sections, as is proved by mathematicians. |
| Sic igitur, si unum astrum est tale, scilicet luna, consequens est quod omnia etiam alia astra sint sphaericae figurae. Quod quidem fundatur super hoc quod omnes stellae sunt eiusdem naturae. | Therefore, if the situation is such with respect to one star, namely, the moon, it follows that all the other stars are also spherical in shape. This, of course, is based on all the stars' being of the same nature. |
| Dicit autem Averroes in suo commento quod sunt eiusdem naturae in specie, ita quod omnes stellae sunt sicut individua eiusdem speciei. Quod quidem manifeste est falsum. Primo quidem quia, si essent eiusdem speciei, haberent easdem specie operationes, et eosdem effectus, sicut patet in omnibus rebus naturalibus eiusdem speciei. | 449. However, Averroes, in his Commentary, says that they are of the same specific nature, in such a way that all the stars are as individuals of the same species. Now this is plainly false. First, because if they were all of the same species, they would have the same specific operations and the same effects, as is evident in all natural things of the same species. |
| Secundo quia, cum motus caelestium corporum sint naturales, sequeretur quod omnia corpora caelestia haberent uniformes motus: quod patet esse falsum tum de planetis per comparationem ad invicem, tum per comparationem ad stellas fixas. | Secondly, because, since the movements of the heavenly bodies are natural, it would follow that all the heavenly bodies would have uniform motions; but this is not true either of the planets in relation to one another, or in relation to the fixed stars. |
| Tertio quia hoc repugnat perfectioni caelestium corporum. Probavit enim in primo Aristoteles quod universum est perfectum, eo quod est unum (unum enim est in una specie): ex hoc enim apparet quod constat ex tota materia suae speciei. Unde et hoc ad perfectionem caelestium corporum pertinet, quod sit unum solum in una specie. Videmus enim in inferioribus corporibus multa individua esse unius speciei, propter aliquam impotentiam, vel quia unum individuum non potest semper durare; unde oportet quod species conservetur per successionem individuorum in eadem specie. Tum etiam quia unum individuum non sufficit ad perfectam operationem speciei; sicut maxime patet in hominibus, quorum unus iuvatur ab alio in sua operatione. Pertinet etiam magis ad perfectionem universi multiplicatio specierum, cum sit formalis, quam multiplicatio individuorum, quae est materialis. | Thirdly, because such a thing conflicts with the perfection of heavenly bodies. For in Book I Aristotle proved that the universe is perfect on the ground that it is one — for it is one in one species. From this fact one sees that it consists of the total matter of its species. Hence this also pertains to the perfection of the heavenly bodies, namely, that there be only one in one species. For we observe in the case of the lower bodies that there are many individuals of one species, on account of some lack of power or because one individual cannot exist forever — hence the species must be preserved by means of the succession of individuals in the same species. It is also because one individual is not sufficient for the perfect operation of the species — as is especially evident among men, one of whom is aided by another in his operation. Moreover, the multiplication of species, since it is formal, pertains more to the perfection of the universe than does the multiplication of individuals, which is material. |
| Patet etiam rationem quam inducit esse ridiculosam. Dicit enim quod si essent diversa corpora caelestia diversae species unius generis, sequeretur quod corpora caelestia essent materialia. Hoc enim multo magis sequitur, si ponamus, sicut ipse vult, diversa corpora caelestia esse sicut diversa individua unius speciei; quia multiplicatio individuorum in una specie fit per divisionem materiae. Quamvis non oporteat a corporibus caelestibus totaliter materiam excludere. Non sequitur etiam, si corpora caelestia habeant materiam, quod sint generabilia et corruptibilia, ut in primo habitum est. | It is plain, too, that the reason which Averroes gives is absurd. For he says that if heavenly bodies were diverse species of one genus it would follow that the heavenly bodies would be material. However, this would much more follow if we posited, as he desires, the diverse heavenly bodies to be diverse individuals of the same species, because multiplication of individuals in one species is made through the division of matter. However, matter is not to be wholly excluded from the heavenly bodies. For it does not follow, even if the heavenly bodies have matter, that they are generable and corruptible, as was had in Book I. |
| Sic igitur dicendum est quod corpora caelestia sunt unius naturae secundum genus, diversarum autem naturarum secundum speciem. Figura autem sphaerica sequitur in eis naturam generis, sicut et motus circularis. | Consequently, it must be said that the heavenly bodies are one in nature according to genus but of diverse natures according to species. Now their spherical shape, as well as their circular motion, follows in them upon the nature of the genus. |
Lecture 17:
Two difficulties proposed in connection with what has been determined about the starsChapter 12 Δυοῖν δ' ἀπορίαιν οὔσαιν, περὶ ὧν εἰκότως ἂν ὁστισοῦν ἀπορήσειε, πειρατέον λέγειν τὸ φαινόμενον, αἰδοῦς ἀξίαν εἶναι νομίζοντας τὴν προθυμίαν μᾶλλον ἢ θράσους, εἴ τις διὰ τὸ φιλοσοφίας διψῆν καὶ μικρὰς εὐπορίας ἀγαπᾷ περὶ ὧν τὰς μεγίστας ἔχομεν ἀπορίας. 318 There are two difficulties, which may very reasonably here be raised, of which we must now attempt to state the probable solution: for we regard the zeal of one whose thirst after philosophy leads him to accept even slight indications where it is very difficult to see one's way, as a proof rather of modesty than of overconfidence. Ἔστι δὲ πολλῶν ὄντων τοιούτων οὐχ ἥκιστα θαυμαστόν, διὰ τίνα ποτ' αἰτίαν οὐκ ἀεὶ τὰ πλεῖον ἀπέχοντα τῆς πρώτης φορᾶς κινεῖται πλείους κινήσεις, ἀλλὰ τὰ μεταξὺ πλείστας. Εὔλογον γὰρ ἂν δόξειεν εἶναι τοῦ πρώτου σώματος μίαν κινουμένου φορὰν τὸ πλησιαίτατον ἐλαχίστας κινεῖσθαι κινήσεις, οἷον δύο, τὸ δ' ἐχόμενον τρεῖς ἤ τινα ἄλλην τοιαύτην τάξιν. Νῦν δὲ συμβαίνει τοὐναντίον ἐλάττους γὰρ ἥλιος καὶ σελήνη κινοῦνται (292a.) κινήσεις ἢ τῶν πλανωμένων ἄστρων ἔνια καίτοι πορρώτερον τοῦ μέσου καὶ πλησιαίτερον τοῦ πρώτου σώματός εἰσιν αὐτῶν. 319 Of many such problems one of the strangest is the problem why we find the greatest number of movements in the intermediate bodies, and not, rather, in each successive body a variety of movement proportionate to its distance from the primary motion. For we should expect, since the primary body shows one motion only, that the body which is nearest to it should move with the fewest movements, say two, and the one next after that with three, or some similar arrangement. But the opposite is the case. The movements of the sun and moon are fewer than those of some of the planets. Yet these planets are farther from the centre and thus nearer to the primary body than they, Δῆλον δὲ τοῦτο περὶ ἐνίων καὶ τῇ ὄψει γέγονεν τὴν γὰρ σελήνην ἑωράκαμεν διχότομον μὲν οὖσαν, ὑπελθοῦσαν δὲ τῶν ἀστέρων τὸν τοῦ Ἄρεος, καὶ ἀποκρυφέντα μὲν κατὰ τὸ μέλαν αὐτῆς, ἐξελθόντα δὲ κατὰ τὸ φανὸν καὶ λαμπρόν. 320 as observation has itself revealed. For we have seen the moon, half-full, pass beneath the planet Mars, which vanished on its shadow side and came forth by the bright and shining part. Ὁμοίως δὲ καὶ περὶ τοὺς ἄλλους ἀστέρας λέγουσιν οἱ πάλαι τετηρηκότες ἐκ πλείστων ἐτῶν Αἰγύπτιοι καὶ Βαβυλώνιοι, παρ' ὧν πολλὰς πίστεις ἔχομεν περὶ ἑκάστου τῶν ἄστρων. 321 Similar accounts of other stars are given by the Egyptians and Babylonians, whose observations have been kept for very many years past, and from whom much of our evidence about particular stars is derived. Τοῦτό τε δὴ δικαίως ἀπορήσειεν ἄν τις, καὶ διὰ τίνα ποτ' αἰτίαν ἐν μὲν τῇ πρώτῃ φορᾷ τοσοῦτόν ἐστιν ἄστρων πλῆθος ὥστε τῶν ἀναριθμήτων εἶναι δοκεῖν τὴν πᾶσαν τάξιν, τῶν δ' ἄλλων ἓν χωρὶς ἕκαστον, δύο δ' ἢ πλείω οὐ φαίνεται ἐν τῇ αὐτῇ ἐνδεδεμένα φορᾷ. 322 A second difficulty which may with equal justice be raised is this. Why is it that the primary motion includes such a multitude of stars that their whole array seems to defy counting, while of the other stars each one is separated off, and in no case do we find two or more attached to the same motion? Περὶ δὴ τούτων ζητεῖν μὲν καλῶς ἔχει καὶ τὴν ἐπὶ πλεῖον σύνεσιν, καίπερ μικρὰς ἔχοντας ἀφορμὰς καὶ τοσαύτην ἀπόστασιν ἀπέχοντας τῶν περὶ αὐτὰ συμβαινόντων ὅμως δ' ἐκ τῶν τοιούτων θεωροῦσιν οὐδὲν ἄλογον ἂν δόξειεν εἶναι τὸ νῦν ἀπορούμενον. 323 On these questions, I say, it is well that we should seek to increase our understanding, though we have but little to go upon, and are placed at so great a distance from the facts in question. Nevertheless there are certain principles on which if we base our consideration we shall not find this difficulty by any means insoluble.
| Postquam determinavit philosophus de stellis, ostendens earum naturam, motum, ordinem et figuram, hic solvit quasdam dubitationes circa praedicta. Et circa hoc duo facit: | 450. Having determined the question of the stars and shown their nature, motion, order and figure, the Philosopher here solves certain difficulties with respect to what has been said. Concerning this he does two things: |
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primo ponit quaestiones; secundo solvit eas, ibi: sed nos ut de corporibus et cetera. |
First he presents the questions; Secondly, he resolves them (L. 18). |
| Circa primum tria facit: | As to the first he does three things: |
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primo excusat se a praesumptione pertractandi has difficiles quaestiones; secundo movet eas, ibi: adhuc autem etc.; tertio ostendit quaestionum difficultatem, ibi: de his quidem et cetera. |
First he excuses himself from presumption in dealing with these difficult questions; Secondly, he states the questions, at 451; Thirdly, he points out the difficulty of the questions, at 457. |
| Dicit ergo primo quod, cum circa stellas sint duae dubitationes de quibus rationabiliter quilibet potest dubitare, tentare debemus dicere circa istas dubitationes id quod nobis videtur; ita scilicet quod nos reputemus dignum esse quod promptitudo hominis considerantis huiusmodi quaestiones, magis debeat imputari verecundiae, idest honestati vel modestiae, quam audaciae, idest praesumptioni; si tamen ille qui huiusmodi dubitationes considerat, diligat etiam parvas sufficientias, idest parum sufficientes rationes, ad inveniendum de illis rebus, de quibus habemus maximas dubitationes; et hoc propter desiderium quod quis habet ad philosophiam, ut scilicet eius principia stent, idest firma permaneant. | He says therefore first [318] that since there are two doubts which anyone could reasonably raise with respect to the stars, we should try to state what we think about them. In so doing we deem it proper that a person's readiness to consider questions of this kind should be attributed rather to respect, i.e., to seemliness or modesty, than to boldness, i.e., presumption, if the one who tackles these doubts welcomes even "small sufficiencies," i.e., reasons that are only slightly sufficient, to discover the truth about these matters concerning which we have very great difficulties, and does this because of what he desires in philosophy, namely, that its principle may stand, i.e., abide firmly. |
| Deinde cum dicit: adhuc autem etc. (vel secundum aliam litteram, est autem etc.), movet dubitationes duas: quarum secunda incipit ibi: et hoc itaque et cetera. | 451. Then at [319] he presents the two difficulties, the second of which begins at 456. |
| Circa primum duo facit: | With regard to the first he does two things: |
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primo movet quaestionem; secundo probat quod supposuerat, ibi: palam autem hoc de quibusdam et cetera. |
First he raises the question; Secondly, he proves something he had presupposed, at 455. |
| Circa primum, tria praeconsideranda sunt ad intellectum huius dubitationis. Quorum primum est quod Aristoteles alium ordinem videtur assignare planetarum, quam astrologi nostri temporis. Primi enim astrologi posuerunt supremum planetam esse Saturnum, post quem posuerunt Iovem, tertio loco Martem, quarto solem, quinto Venerem, sexto Mercurium, septimo lunam. Astrologi autem qui fuerunt tempore Platonis et Aristotelis, mutaverunt hunc ordinem quantum ad solem, ponentes eum immediate supra lunam, sub Venere et Mercurio; quam positionem hic Aristoteles sequitur. Sed Ptolomaeus postea hunc ordinem planetarum correxit, ostendens verius esse quod antiqui dixerunt; quod etiam moderni astrologi sequuntur. | With respect to the first [319] there are three things to be considered for the understanding of this difficulty. The first of these is that Aristotle is seen to assign to the planets an order different from that of the astronomers of our time. For the earliest astronomers took Saturn as the outermost planet and after it Jupiter; Mars they put third, the Sun fourth, Venus fifth, Mercury sixth, and the Moon seventh. But the astronomers of Plato's and Aristotle's time changed this order as to the Sun, by putting it immediately above the Moon and under Venus and Mercury, which positing Aristotle follows here. Later on, Ptolemy corrected this order of the planets by showing that what the earlier astronomers said was truer, and this is the opinion held by current astronomers. |
| Secundo considerandum est quod circa motus planetarum quaedam anomaliae, idest irregularitates, apparent; prout scilicet planetae quandoque velociores, quandoque tardiores, quandoque stationarii, quandoque retrogradi videntur. Quod quidem non videtur esse conveniens caelestibus motibus, ut ex supra dictis patet. Et ideo Plato primus hanc dubitationem Eudoxo, sui temporis astrologo, proposuit; qui huiusmodi irregularitates conatus est ad rectum ordinem reducere, assignando diversos motus planetis; quod etiam posteriores astrologi diversimode facere conati sunt. Illorum tamen suppositiones quas adinvenerunt, non est necessarium esse veras: licet enim, talibus suppositionibus factis, apparentia salvarentur, non tamen oportet dicere has suppositiones esse veras; quia forte secundum aliquem alium modum, nondum ab hominibus comprehensum, apparentia circa stellas salvantur. Aristoteles tamen utitur huiusmodi suppositionibus quantum ad qualitatem motuum, tanquam veris. | Secondly, we must keep in mind that certain "anomalies," i.e., irregularities, appear with respect to the motions of the planets. For the planets seem to be now swifter, now slower, now stationary, now retrogressing. Now this does not seem to be appropriate to heavenly motions, as is evident from what has been said above. Therefore, Plato first proposed this problem to an astronomer of his time, named Eudoxus, who tried to reduce these irregularities to a right order by assigning diverse motions to the planets; a project also undertaken by later astronomers in various ways. Yet it is not necessary that the various suppositions which they hit upon be true — for although these suppositions save the appearances, we are nevertheless not obliged to say that these suppositions are true, because perhaps theme is some other way men have not yet grasped by which the things which appear as to the stars are saved. Aristotle nevertheless uses suppositions of this kind, in what regards the quality of the motions, as true. |
| Tertio considerandum est quod circa solem et lunam non apparent tot irregularitatum genera, sicut circa alios planetas: nam in sole et luna nunquam apparet statio vel retrogradatio, sicut in aliis planetis, sed solum velocitas et tarditas. Et ideo Eudoxus, qui primo conatus est has irregularitates dirigere, ad instantiam Platonis, pauciores motus assignavit soli et lunae, quos dicebat esse infimos planetas, quam superioribus planetis. | The third thing that must be considered is that not as many kinds of irregularities appear with respect to the sun and moon as with the other planets: for the sun and moon never appear to be stationary or to undergo retrograde movement as do the other planets, but present only swiftness and slowness. Accordingly, Eudoxus, who at Plato's request first tried to straighten out these irregularities, assigned fewer motions to the sun and moon, which he called the lowest planets, than to the higher ones. |
| Quorum unicuique assignabat quatuor motus, secundum quatuor sphaeras volventes corpus stellae infixum in infima earum: ita scilicet quod prima sphaera movet corpus stellae ab oriente in occidentem, secundum motum diurnum; secunda movet corpus stellae e converso ab occidente in orientem in zodiaco, qui dicitur motus longitudinis; tertia autem sphaera movet corpus stellae motu latitudinis, secundum quod contingit quod stella quandoque est Australior, quandoque borealior in zodiaco. Ponebat autem polos huius tertiae sphaerae esse in zodiaco; unde sequebatur quod circulus maior, aeque distans ab utroque polo, transiret per polos zodiaci; ex quo sequi videbatur quod planetae, secundum motum latitudinis, quandoque pervenirent usque ad polos zodiaci; quod tamen nunquam apparet. Unde ponebat quartam sphaeram, quae moveret stellam in oppositum huius motus, ita quod nunquam pervenit ad polos zodiaci. Soli autem et lunae non attribuit motum huius quartae sphaerae; sed apparentia eorum conatus est salvare, solum ponendo tres sphaeras, proportionales primis tribus sphaeris aliorum planetarum; ita tamen quod luna habet maiorem motum latitudinis quam sol, sicut expositum est in XII Metaphys. | To each of these he assigned four movements, according to the four spheres that revolved the stellar body fixed in the lowest of them. Thus the first sphere moves the stellar body from east to west according to the diurnal motion; the second moves the stellar body in the opposite direction of west to east in the Zodiac — and this is called longitudinal motion; the third sphere moves a stellar body latitudinally, according to which a star is now in a more southerly, now a more northerly, position in the Zodiac. Now he placed the poles of this third sphere in the Zodiac; hence it followed that a major circle, equidistant from the poles, would go through the poles of the Zodiac. From this it seemed to follow that the planets in their latitudinal motion would sometimes reach the very poles of the Zodiac — a situation that never appears. Hence, he posited a fourth sphere that would move a star in an opposite direction to this movement and thus prevent it from ever reaching the poles of the Zodiac. He did not, however, attribute the motion of this fourth sphere to the sun and the moon, but tried to save their appearances by positing only three spheres, proportional to the first three of the other planets, but in such a way that the latitudinal motion of the moon would be greater than the sun's, as is explained in Metaphysics XII. |
| Secundum hanc ergo positionem, Aristoteles hic quaestionem format. Et dicit quod, cum multa sint talia dubitabilia circa stellas, non minime videtur mirabile, propter quam causam non semper astra quae plus distant a motu primae sphaerae moventur pluribus motibus, sed intermedia moventur plurimis, scilicet quinque planetae, qui, secundum positionem Eudoxi, moventur quatuor motibus. Rationabile enim utique esse videtur quod, cum prima sphaera moveatur uno solo motu, quod astrum ei propinquissimum moveatur paucissimis motibus, puta duobus; habitum autem, idest consequenter se habens, moveatur tribus, vel quocumque tali ordine progrediatur. Sed nunc accidit contrarium, secundum positionem Eudoxi, secundum quem sol et luna moventur paucioribus motibus, idest solis tribus, quam quaedam stellarum errantium, quas ponebat habere quatuor motus; quamvis quinque planetae longius distent a medio mundi, idest terrae, et propinquiores sint primo corpori, idest supremae sphaerae, ipsis, idest sol et luna, secundum opinionem quae habebatur tempore Aristotelis et Platonis. | 452. With these considerations in mind Aristotle here formulates a question. And he says that while there are many such doubtful matters about the stars, not the least to be wondered at is why the stars farther from the motion of the first sphere are not always moved with a greater number of motions, but rather the intermediate ones are moved with the most, namely, the five planets, which, according to Eudoxus' theory, are moved with four motions. For it seems to be reasonable, if the first sphere is moved with one motion alone, that the star nearest it should be moved with the fewest motions, say two, and the "had," i.e., the next, with three or in some such progression. But now it is the contrary that happens according to Eudoxus' theory, which attributes fewer motions, i.e., only three, to the sun and moon than to some of the wandering stars which he posits as having four motions, although the five planets are farther from the middle [center] of the universe, i.e., from the earth, and closer to the "first body," i.e., the outermost sphere, "than they," i.e., than the sun and moon are, according to the opinion prevalent in Plato's and Aristotle's time. |
| Est autem ulterius sciendum quod, quia secundum suppositiones Eudoxi non poterant omnia apparentia circa stellas salvari, quidam alius astrologus, Callippus nomine, ad instantiam Aristotelis, correxit Eudoxi suppositiones; addens quidem Marti et Veneri et Mercurio, unicuique unam sphaeram et unum motum; soli autem et lunae, unicuique duos. Et sic Saturno et Iovi assignavit quatuor motus, unicuique autem inferiorum planetarum quinque: et sic non haberet locum dubitatio quam hic movet Aristoteles, quia superiores planetae, secundum hunc modum, paucioribus motibus moventur quam inferiores. Ponebat etiam unicuique planetarum quasdam alias sphaeras revolventes, ut expositum est in XII Metaphys. | 453. One should further know that, since the suppositions of Eudoxus could not save all the appearances concerning the stars, another astronomer named Callippus, at Aristotle's behest, corrected Eudoxus' suppositions. He added to Mars and Venus and Mercury one sphere and one motion apiece, and to the Sun and Moon two apiece. Thus to Saturn and Jupiter four motions were now assigned, and to each of the lower planets five. Consequently, the problem raised here by Aristotle would no longer be a problem, because the higher planets, according to this supposition, are now moved with fewer motions than the lower ones. Moreover, to each of the planets he also assigned certain other revolving spheres, as is explained in Metaphysics XII. |
| Sed nec secundum hanc positionem poterant omnia apparentia circa stellas salvari, praecipue quantum ad propinquitatem et remotionem stellarum a nobis; quae deprehenditur ex hoc quod planetae, eadem dispositione aeris existente, quandoque maiores, quandoque minores videntur. | 454. But even this theory could not account for all the appearances about the stars, especially as to their being near and far away from us — which is grasped from the fact that under the same disposition of the air, the planets are seen at one time larger and at another time smaller. |
| Similiter etiam inconveniens videbatur quod tanta multitudo sphaerarum ad movendum planetas concurreret; et praecipue videbatur superfluum quod cuilibet planetae attribueretur una sphaera quae ipsum revolveret ab oriente in occidentem motu diurno, cum hoc causari possit suprema sphaera, totum caelum hoc motu revolvente. | Also it seemed unacceptable that such a multitude of spheres should concur in order to move the planets. It seemed especially superfluous to assign to each planet a sphere to revolve it from east to west with its diurnal motion when this could be caused by the highest sphere revolving the entire heaven with this motion. |
| Et ideo Hipparchus et Ptolomaeus posuerunt unicuique planetae unam solam sphaeram; quam tamen posuerunt non esse supremae sphaerae concentricam, sed habere aliud centrum praeter terram; ita quod, cum planeta est in parte sphaerae magis distante a nobis, corpus planetae minus videtur et tardioris motus; cum autem est in opposita parte, videtur maius et velocioris motus. Praeter hoc autem posuerunt quosdam parvos circulos, quos epicyclos dicunt, qui moventur super huiusmodi sphaeris; ita quod corpora planetarum in huiusmodi epicyclis moventur, non tanquam infixa in huiusmodi circulis, sed quasi motu progressivo eos regyrant. | Therefore Hipparchus and Ptolemy posited for each planet a single sphere which however was not concentric with the supreme sphere but had a center other than the earth, [i.e., an "eccentric"], in such a way that when the planet is in that portion of the sphere that is farther from us, the body of the planet is seen as smaller and slower moving; but when it is in the opposite region, it is seen as larger and faster. In addition to this, they posited certain small circles which they call "epicycles," which are in motion upon these spheres in such a way that the bodies of the planets are in motion in these epicycles, not as though fixed in such circles, but as though turning through them with a progressive motion. |
| Sic igitur praeter motum diurnum, quem toti caelo attribuunt ex motu primae sphaerae, quatuor planetis, scilicet Saturno, Iovi, Marti et Veneri, attribuunt tres motus: quorum unus est secundum quem corpus stellae circuit epicyclum; secundus est secundum quem centrum epicycli circuit sphaeram; tertius autem est secundum quem ipsa sphaera movetur ab occidente in orientem, quibuslibet centum annis gradu uno, secundum motum stellarum fixarum, qui quidem dicitur motus augis vel apogaei, idest maximae distantiae in circulo excentrico. | Thus, in addition to the diurnal motion which they attribute to the entire heaven as due to the motion of the first sphere, they attribute to four planets, namely, Saturn, Jupiter, Mars and Venus, three motions apiece: according to one, the stellar body makes the circuit of its epicycle; according to the second, the center of the epicycle circles the sphere; according to the third, the sphere itself is moved from west to east, every hundred years, the distance of one degree in relation to the motion of the fixed stars. This last motion [the precession of the equinox], is called the motion of the increase [augus], or of the apogee, i.e., of the maximum distance in the eccentric circle. |
| Super hos autem tres motus addunt quartum motum Mercurio, quo dicunt centrum sphaerae ipsius moveri in quodam circulo parvo circa centrum mundi. Quos etiam quatuor motus attribuunt lunae, superaddentes ei quintum. Cum enim circulus sphaerae lunaris, super quem intelligitur moveri centrum epicycli eius, declinet a zodiaco ad meridiem et Septentrionem, necesse est quod huiusmodi circulus secet zodiacum in duobus punctis, qui dicuntur nodi, sive caput et cauda; in quibus tantum locis luna existente, possunt contingere eclipses lunares et solares; quae non semper contingunt in eadem parte circuli. | Now they add to Mercury, in addition to these motions, a fourth, according to which they say that the center of its sphere is moved in a small circle about the center of the world. They also attribute these four to the Moon with the addition of a fifth. For since the circle of the lunar sphere, along which the center of its epicycle is thought to be in motion, declines from the Zodiac to the south and to the north, it is necessary for this circle to intersect the Zodiac at two points called "nodes" or "head and tail." It is only when the moon is present at these points that eclipses of the sun and of the moon can occur; and these do not always occur at the same place on the circle. |
| Et ideo ex hoc ponunt quintum motum in luna, secundum quem praedicti nodi moventur; qui dicitur motus capitis et caudae. Corpus autem solis non dicunt moveri in aliquo epicyclo, sed in suo excentrico. Unde non attribuunt soli nisi duos motus: unum scilicet quo corpus solis movetur in excentrico; et alius est motus augis, quem attribuunt sphaerae solis, sicut attribuunt sphaeris aliorum planetarum. | This, therefore, caused them to posit a fifth motion in the moon according to which the aforesaid nodes are moved, and this is called the "movement of the head and tail." But they do not say the body of the sun to be moved in any epicycle, but in its own eccentric. Hence, they endowed the sun with just two motions: one, whereby the body of the sun is moved in the eccentric; the other is the motion of apogee which they assign to the sphere of the sun, just as they assign it to the spheres of the other planets. |
| Et sic patet quod vere secundum hanc positionem procedit dubitatio quam hic Aristoteles movet. Nam secundum hanc positionem Mercurius et luna, qui sunt infimi planetarum, habent plurimos motus; sol autem, quem ponunt medium, habet paucissimos; alii vero planetae medio modo se habent. | Thus it is evident that the problem Aristotle raises, arises also from the above position. For according to this supposition, Mercury and the Moon, the lowest of the planets, have the most motions, whereas the sun, which they place as intermediate, has the fewest, with the remaining planets being in between. |
| Deinde cum dicit: palam autem hoc de quibusdam etc., probat quoddam quod supposuerat, scilicet ordinem planetarum esse qualem dixerat. | 455. Then at [320] he proves something he had supposed, namely, that the order of the planets is as he had described. |
| Et primo quidem probat hoc quantum ad aliquid, per id quod ipse viderat: et dicit quod ordo quorundam planetarum manifestus est etiam visu. Dicit enim se vidisse quod luna, dichotoma existens, idest ex media parte illuminata, subintravit stellam Martis (nam ipsa est velocioris motus quam Mars); et luna secundum nigrum suum, idest secundum illam partem in qua erat obscura, occultavit Martem; et quod Mars exivit de sub luna pertranseunte ipsum, secundum partem lunae claram et lucidam. | First he proves it in one respect by means of something he had witnessed. And he says that the order of certain of the planets is evident even to sight. For he says that he saw the moon when it was "dichotomous," i.e., with half its face illumined, move in under the star of Mars (for its motion is swifter than Mars'), and the moon according to its blackness, i.e., according to that side which was darkened, concealed Mars, and Mars came out from under the moon passing it according to the bright and shining side of the moon. |
| Secundo, cum dicit: similiter autem etc., manifestat ordinem planetarum quantum ad alia, per ea quae alii viderunt. Et dicit quod similiter de ordine planetarum aliorum dicunt se vidisse illi, qui a multis temporibus retro talia observaverunt per multos annos, scilicet Aegyptii et Babylonii, quorum studium maxime fuit circa astrologiam; ex quorum dictis habemus multas credulitates de unaquaque stellarum, scilicet observationes eorum. | Secondly, at [321] he shows other details about the order of the planets through observations which others have made. And he says that others state themselves to have witnessed similar things concerning the order of the other planets, namely, those who from much time back have observed such things for many years, i.e., the Egyptians and Babylonians, whose study was concerned most with astronomy. From what they say we have many trustworthy statements about each of the stars, based on their observations. |
| Deinde cum dicit: et hoc itaque etc., movet secundam dubitationem. Et dicit quod merito potest aliquis dubitare quare in prima sphaera, quae movetur primo motu, est tanta multitudo astrorum, ut omnis ordo eorum videatur arithmeticorum esse, idest innumerabilium (non enim potest numerus eorum comprehendi a nobis); in aliis autem inferioribus orbibus invenitur singulariter una sola stella, ita quod non videntur duae vel plures de stellis erraticis infixae esse uni sphaerae mobili. | 456. Then at [322] he raises the second difficulty. And he says that with good reason one can wonder why it is that in the first sphere, which is moved by the first motion, there is such a great multitude of stars that their whole order appears to be of the "arithmetical," i.e., of things innumerable (for their number cannot be comprehended by us), whereas in the lower orbs we find one solitary star in each so that two or more of the wandering stars are not seen fixed in one mobile sphere. |
| Est autem hic considerandum quod tempore Aristotelis nondum erat deprehensus motus stellarum fixarum; quas Ptolomaeus ponit moveri ab occidente in orientem super polos zodiaci, quibuslibet centum annis gradu uno, ita quod tota revolutio earum compleatur in triginta sex millibus annorum. Et ideo antiqui ponebant sphaeram stellarum fixarum esse primum mobile, et eius esse tantum unum motum, qui est motus diurnus. Sed supposito motu stellarum fixarum, oportet ipsam moveri duobus motibus: scilicet motu proprio, qui est motus stellarum fixarum; et motu diurno, qui est motus supremae sphaerae, quae est sine stellis. | Here one should note that in Aristotle's time no motion had yet been discovered in the fixed stars, which Ptolemy posits as moved from west to east upon the poles of the Zodiac one degree every 100 years, so that they complete one full revolution in 36,000 years. Hence the ancients posited the sphere of the fixed stars as the first mobile and as endowed with but one motion, the diurnal. But if we assume a motion of the fixed stars, then this sphere must be moved by two motions: by its own motion, which is the motion of the fixed stars, and by the diurnal motion, which is the motion of the outermost sphere, which is without stars. |
| Deinde cum dicit: de his quidem etc., ostendit difficultatem harum quaestionum. Et dicit bonum esse inquirere de his dubitationibus: subdit autem: et ad eam quae ad plus intelligentiam. Quam quidem litteram Alexander dicit esse defectivam; et est subintelligendum quod ea quae circa hoc excedunt nostram intelligentiam, oportet magis suscipere, quam amplius quaerere per nos ipsos. Non autem est consuetudo Aristotelis, quamvis sit breviloquus, defectivis locutionibus uti, ut Simplicius dicit. Et ideo ipse sic exponit: quod de his bene se habet quaerere, sed hoc non ad quoslibet pertinet, sed solum ad eos qui plus intelligunt. Averroes autem in suo commento exponit secundum hoc, ut intelligamus quod inquirere de his quaestionibus et in se bonum est, et etiam ad hoc est utile quod homo magis ac magis intelligat: qui enim se exercitat circa intellectum difficilium, magis potest intelligere alia, ut dicitur in III de anima. | 457. Then at [323] he shows the difficulty of these questions. He says that it is good to investigate these doubtful matters, and adds, "for a greater understanding." This text, says Alexander, is defective, and one should understand it as meaning that whatever in these matters is too much for AU' intelligence one must simply accept, rather than make them a subject of further investigation by ourselves. But it is not Aristotle's custom, in spite of his laconic style, to employ defective language, as Simplicius says. Hence he explains it to the effect that, while it is good to investigate such things, it is not a task suited to just anyone but only those of wider understanding. However, Averroes in his Commentary explains it this way: namely, that we should understand that to investigate these matters is both good in itself, and also contributes to man's growth in understanding Therefore a person who exercises his mind by trying to understand difficult matters, can better understand others, as is said in On the Soul III. |
| Ista autem quae inquirenda sunt, difficultatem habent: quia modicum de causis eorum percipere possumus, et accidentia eorum magis sunt remota a cognitione nostra, quam etiam ipsa corpora elongentur a nobis secundum corporalem situm. Et tamen, si ex his quae dicentur contemplemur harum dubitationum veritatem, apparebit non esse irrationabile id quod inquirendo dubitabile videbatur. | Now the matters to be investigated are difficult, because we can perceive only a little about their causes; and their accidents are further removed from our ken than the bodies themselves are Physica lly distant from us. Yet, if what we shall say enables us to contemplate the truth of these doubtful matters, then what seemed to be doubtful at the beginning of our inquiry will be seen not to be devoid of all explanation. |
Lecture 18:
The first difficulty, concerning the number of motions of the stars, is solved. The number shown to agree with modern astronomers.Chapter 12 cont. Ἀλλ' ἡμεῖς ὡς περὶ σωμάτων αὐτῶν μόνον, καὶ μονάδων τάξιν μὲν ἐχόντων, ἀψύχων δὲ πάμπαν, διανοούμεθα δεῖ δ' ὡς μετεχόντων ὑπολαμβάνειν πράξεως καὶ ζωῆς οὕτω γὰρ οὐθὲν δόξει παράλογον εἶναι τὸ συμβαῖνον. 324 We may object that we have been thinking of the stars as mere bodies, and as units with a serial order indeed but entirely inanimate; but should rather conceive them as enjoying life and action. On this view the facts cease to appear surprising. Ἔοικε γὰρ τῷ μὲν ἄριστα ἔχοντι ὑπάρχειν τὸ εὖ ἄνευ πράξεως, τῷ δ' ἐγγύτατα διὰ ὀλίγης καὶ μιᾶς, τοῖς δὲ πορρωτέρω διὰ πλειόνων, 235 For it is natural that the best-conditioned of all things should have its good without action, that which is nearest to it should achieve it by little and simple action, and that which is farther removed by a complexity of actions, ὥσπερ ἐπὶ σώματος τὸ μὲν οὐδὲ γυμναζόμενον εὖ ἔχει, τὸ δὲ μικρὰ περιπατῆσαν, τῷ δὲ καὶ δρόμου δεῖ καὶ πάλης καὶ κονίσεως, 236 just as with men's bodies one is in good condition without exercise at all, another after a short walk, while another requires running and wrestling and hard training, πάλιν δ' ἑτέρῳ οὐδ' ὁποσαοῦν πονοῦντι τοῦτό γ' ἂν ἔτι ὑπάρξαι τἀγαθόν, ἀλλ' ἕτερόν τι. 237 and there are yet others who however hard they worked themselves could never secure this good, but only some substitute for it. Ἔστι δὲ τὸ κατορθοῦν χαλεπὸν ἢ τὸ πολλὰ ἢ τὸ πολλάκις, 238 To succeed often or in many things is difficult. οἷον μυρίους ἀστραγάλους Χίους βαλεῖν ἀμήχανον, ἀλλ' ἕνα ἢ δύο ῥᾷον. Καὶ πάλιν ὅταν τοδὶ μὲν δέῃ τοῦδ' ἕνεκα ποιῆσαι, τοῦτο δ' ἄλλου καὶ τοῦτο ἑτέρου, ἐν μὲν ἑνὶ ἢ δυσὶ ῥᾴδιον ἐπιτυχεῖν, ὅσῳ δ' ἂν διὰ πλειόνων, (292b.) χαλεπώτερον. 239 For instance, to throw ten thousand Coan throws with the dice would be impossible, but to throw one or two is comparatively easy. In action, again, when A has to be done to get B, B to get C, and C to get D, one step or two present little difficulty, but as the series extends the difficulty grows. Διὸ δεῖ νομίζειν καὶ τὴν τῶν ἄστρων πρᾶξιν εἶναι τοιαύτην οἵα περ ἡ τῶν ζῴων καὶ φυτῶν. Καὶ γὰρ ἐνταῦθα αἱ τοῦ ἀνθρώπου πλεῖσται πράξεις πολλῶν γὰρ τῶν εὖ δύναται τυχεῖν, ὥστε πολλὰ πράττειν, καὶ ἄλλων ἕνεκα. (Τῷ δ' ὡς ἄριστα ἔχοντι οὐθὲν δεῖ πράξεως ἔστι γὰρ αὐτὸ τὸ οὗ ἕνεκα, ἡ δὲ πρᾶξις ἀεί ἐστιν ἐν δυσίν, ὅταν καὶ οὗ ἕνεκα ᾖ καὶ τὸ τούτου ἕνεκα). Τῶν δ' ἄλλων ζῴων ἐλάττους, τῶν δὲ φυτῶν μικρά τις καὶ μία ἴσως ἢ γὰρ ἕν τί ἐστιν οὗ τύχοι ἄν, ὥσπερ καὶ ἄνθρωπος, ἢ καὶ τὰ πολλὰ πάντα πρὸ ὁδοῦ ἐστι πρὸς τὸ ἄριστον. 331 We must, then, think of the action of the lower stars as similar to that of animals and plants. For on our earth it is man that has the greatest variety of actions—for there are many goods that man can secure; hence his actions are various and directed to ends beyond them—while the perfectly conditioned has no need of action, since it is itself the end, and action always requires two terms, end and means. The lower animals have less variety of action than man; and plants perhaps have little action and of one kind only. For either they have but one attainable good (as indeed man has), or, if several, each contributes directly to their ultimate good. Τὸ μὲν οὖν ἔχει καὶ μετέχει τοῦ ἀρίστου, τὸ δ' ἀφικνεῖται [ἐγγὺς] δι' ὀλίγων, τὸ δὲ διὰ πολλῶν, τὸ δ' οὐδ' ἐγχειρεῖ, ἀλλ' ἱκανὸν εἰς τὸ ἐγγὺς τοῦ ἐσχάτου ἐλθεῖν οἷον εἰ ὑγίεια τέλος, τὸ μὲν δὴ ἀεὶ ὑγιαίνει, τὸ δ' ἰσχνανθέν, τὸ δὲ δραμὸν καὶ ἰσχνανθέν, τὸ δὲ καὶ ἄλλο τι πρᾶξαν τοῦ δραμεῖν ἕνεκα, ὥστε πλείους αἱ κινήσεις ἕτερον δ' ἀδυνατεῖ πρὸς τὸ ὑγιᾶναι ἐλθεῖν, ἀλλὰ πρὸς τὸ δραμεῖν μόνον ἢ ἰσχνανθῆναι, καὶ τούτων θάτερον τέλος αὐτοῖς. Μάλιστα μὲν γὰρ ἐκείνου τυχεῖν ἄριστον πᾶσι τοῦ τέλους εἰ δὲ μή, ἀεὶ ἄμεινόν ἐστιν ὅσῳ ἂν ἐγγύτερον ᾖ τοῦ ἀρίστου. Καὶ διὰ τοῦτο ἡ μὲν γῆ ὅλως οὐ κινεῖται, τὰ δ' ἐγγὺς ὀλίγας (20) κινήσεις οὐ γὰρ ἀφικνεῖται πρὸς τὸ ἔσχατον, ἀλλὰ μέχρι ὅτου δύναται τυχεῖν τῆς θειοτάτης ἀρχῆς. Ὁ δὲ πρῶτος οὐρανὸς εὐθὺς τυγχάνει διὰ μιᾶς κινήσεως. Τὰ δ' ἐν μέσῳ τοῦ πρώτου καὶ τῶν ἐσχάτων ἀφικνεῖται μέν, διὰ πλειόνων δ' ἀφικνεῖται κινήσεων. 332 One thing then has and enjoys the ultimate good, other things attain to it, one immediately by few steps, another by many, while yet another does not even attempt to secure it but is satisfied to reach a point not far removed from that consummation. Thus, taking health as the end, there will be one thing that always possesses health, others that attain it, one by reducing flesh, another by running and thus reducing flesh, another by taking steps to enable himself to run, thus further increasing the number of movements, while another cannot attain health itself, but only running or reduction of flesh, so that one or other of these is for such a being the end. For while it is clearly best for any being to attain the real end, yet, if that cannot be, the nearer it is to the best the better will be its state. It is for this reason that the earth moves not at all and the bodies near to it with few movements. For they do not attain the final end, but only come as near to it as their share in the divine principle permits. But the first heaven finds it immediately with a single movement, and the bodies intermediate between the first and last heavens attain it indeed, but at the cost of a multiplicity of movement.
| Praemissis duabus dubitationibus, hic ad earum solutiones accedit: | 458. Having proposed the two doubts, the Philosopher here starts to solve them. |
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et primo solvit primam quaestionem; secundo secundam, ibi: de dubitatione autem et cetera |
First he solves the first question; Secondly, the second one (L. 19). |
| Circa primum duo facit: | As to the first he does two things: |
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primo ostendit quid oporteat supponere, ad hoc ut de facili solvatur quaestio primo mota; secundo ponit solutionem, ibi: videtur autem et cetera. |
First he shows what ought to be assumed in order to make the first question easier to resolve; Secondly, he gives the solution, at 459. |
| Dicit ergo primo quod ideo prima quaestio difficilis videtur, quia nos inquirimus de corporibus caelestibus ac si essent sola corpora habentia quendam ordinem, absque hoc quod sint animata; et sic videtur nobis quod debeat in eis esse ordo motuum secundum ordinem numerorum, et secundum situm corporum. Sed ad hoc quod praedicta dubitatio solvatur, oportet opinionem habere de eis quod participent non solum vitam quamcumque, sed etiam actionem; quod est proprium habentium animam rationalem, quae agunt propter finem, tanquam habentia dominium sui actus, et non agunt ex solo naturae impetu, sicut omnia irrationalia. Hoc autem supposito, nihil videtur praeter rationem accidere, si multitudo motuum non procedat secundum corporum situm: quia magis est accipienda diversitas motuum et multitudo eorum secundum habitudinem ad bonum finale, quod est principium in omnibus agibilibus, ut patet per philosophum in VII Ethic. et II Physic. | He says therefore first [324] that the reason why the first question is difficult is that we investigate the heavenly bodies as though they were merely an orderly system of bodies without being animated. As a consequence, it seems to us that the order of their motions should be in accord with the order of numbers and according to the position of the bodies. But if the problem at hand is to be settled, we must assume that they have not only some sort of life but also actions — this being proper to things with a rational soul, which act for an end as being masters of their act, and do not act by the sole impulse of nature as do all irrational things. If this is assumed, nothing is seen to be occurring unreasonably if the number of their motions does not proceed according to the position of the bodies. For the diversity and number of the motions is to be taken more in terms of a relation to the final good, which is the principle in all things able to be done [i.e., voluntary actions], as is plain from the words of the Philosopher in Ethics VII and Physics II. |
| Et est attendendum quod, quantum ad hoc, non refert utrum ponamus corpora caelestia moveri a substantiis intellectualibus coniunctis per modum animae, vel etiam separatis. Non autem esset via solvendi, si moverentur per solum naturae impetum, sicut corpora gravia et levia. | One should note in this regard that it makes no difference whether we suppose that the heavenly bodies are moved by intellectual substances united to them after the manner of a soul, or by these as separated. But there would be no way to solve this question if they were moved by the sole impulse of nature, as heavy and light bodies are. |
| Deinde cum dicit: videtur autem etc., ponit solutionem. | 459. Then at [235] he presents his solution. |
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Et primo ponit solutionis principia; secundo applicat ad propositum, ibi: hoc quidem igitur habet et cetera. |
First he states the principles of the solution; Secondly, he applies them to the question at hand, at 463. |
| Circa primum duo facit: | With respect to the first he does two things: |
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primo ponit principia, ex quibus assignatur ratio quare superiores planetae moventur pluribus motibus, primum autem mobile uno solo motu; secundo ponit principia, ex quibus assignatur ratio quare superiores planetae moventur pluribus motibus, inferiores autem paucioribus, secundum suppositionem Eudoxi, ibi: iterum autem alteri et cetera. |
First he states the principles from which we obtain the reason why the higher planets are moved with a number of motions, while the first mobile is moved with only one; Secondly, he states the principles from which we obtain the reason why the higher planets are moved with a number of motions while the lower planets with fewer, according to the theory of Eudoxus, at 460. |
| Circa primum duo facit: | About the first he does two things: |
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primo ponit principium; secundo manifestat per exemplum, ibi: quemadmodum in corpore et cetera. |
First he states the principle; Secondly, he shows it with an example, at 459. |
| Dicit ergo primo quod in his quae possunt pervenire ad aliquod bonum perfectum, triplex gradus invenitur. Quorum supremus est eius quod optime se habet, et non indiget aliqua actione ad acquirendum bonum perfectum; sed hoc existit ei sine aliqua actione. Secundus gradus eius est quod est propinquissimum in bonitate dispositionis optimo, quod scilicet acquirit perfectum bonum per unam et modicam actionem. Tertius gradus est eorum quae magis distant ab optimo, quae tamen acquirunt perfectum bonum per plures operationes. | He says therefore first [325] that in things that can arrive at a perfect good, three degrees are found. The highest degree is that of a thing which is in the best state and does not need any action to acquire perfect good, which is already present to it without any action. The second degree is that of a thing which is nearest to the best in the goodness of its condition, and which, namely, acquires its perfect good by means of one slight action. The third degree belongs to things that are more removed from the best but still acquire their perfect good through several operations. |
| Deinde cum dicit: quemadmodum in corpore etc., manifestat per exemplum. Et dicit quod in corporibus videtur illud corpus optime esse dispositum, quod non indiget aliqua exercitatione ad bonam sui habitudinem (quae dicitur euechia); in secundo autem gradu est corpus quod per modicam deambulationem consequitur bonam habitudinem; in tertio autem gradu est corpus quod ad bonam habitudinem consequendam indiget multis exercitiis, puta cursu, lucta et pugna. | Then at [326] he manifests this by an example. And he says that among bodies, that body is seen to be in the best condition which does not require any exercise to maintain its good condition,(which is called euechia — "well-being'); in the second grade is a body which attains a good condition by walking just a bit; in the third grade is the body which in order to acquire a good condition needs many forms of exercise such as running, wrestling and boxing. |
| Deinde cum dicit: iterum autem alteri etc., ponit principia per quae solvitur secunda pars quaestionis, quare scilicet inferiores planetae paucioribus motibus moventur quam superiores. | 460. Then at [327] he states the principles with which to solve the second part of the question, namely, why the lower planets are moved with fewer motions than the higher planets. |
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Et primo ponit principia; secundo adhibet exemplum, ibi: propter quod oportet putare et cetera. |
First he states the principles; Secondly, he gives an example, at 461. |
| Circa primum tria facit: | As to the first, he does three things: |
| primo ponit esse quendam gradum inferiorem tribus praedictis. Et dicit quod invenitur in quarto gradu aliquid quod, quibuscumque laboribus, non potest pertingere ad hoc quod adipiscatur bonum perfectum, sed potest consequi quoddam aliud bonum minus perfecto bono; puta si aliquod corpus per nullum exercitium posset consequi perfecte bonam habitudinem, sed per aliqua exercitia consequeretur aliquantulum meliorem dispositionem quam prius habebat. | First he asserts that there is a certain grade below the three already mentioned [327], and he says that in the fourth degree is found something that, in spite of all its labors, cannot reach the state of attaining its perfect good; yet it can attain a certain other good less than the perfect good. For example, a case of this would be should a body be unable, in spite of all its exercise, perfectly to attain to a good condition, but should through certain exercises attain to a slightly better condition than it previously had. |
| Secundo, ibi: est autem dirigere etc., ostendit in hoc etiam gradu esse quandam diversitatem; dicens quod difficile est dirigere, idest rectificare, aut multa aut multoties: difficilius enim est rectum se habere in multis quam in paucis. Multitudo autem accipi potest vel secundum diversitatem rerum, vel secundum diversitatem actionum ordinatarum ad aliquid unum; ad quorum primum pertinet quod dicit multa, ad secundum pertinet quod dicit multoties, maxime si actiones non simul fuerint. Ex quo apparet quod maioris virtutis est quod per multa potest in aliquod bonum pertingere, quam quod in illa multa non potest, et ita non consequitur illud bonum. | Secondly, at [328] he shows that even in this grade there is a certain variety. And he says that it is difficult to "direct," i.e., to proceed rightly, in the case either of many things or many times, for it is more difficult to be correct in many things than in few. "Many" may be taken as referring either to a diversity of things or to a diversity of actions aimed at one objective — thus his statement, "many things," refers to the first; and his statement "many times," refers to the second, especially if the actions are not all at once. From this we understand that something which can achieve a good by means of many things is of greater power than something which cannot employ that many, and as a consequence does not attain the good in question. |
| Tertio, cum dicit: puta myrios etc., ponit exemplum de eo quod nunc dictum est. Et primo quantum ad hoc quod dixit multa; dicens quod difficile est proiicere myrios astragalos, idest decem millia astragalorum, quae sunt quaedam genera missilium, ex insula quae dicitur Chios, ubi sunt magni astragali (alia littera habet Coos, quae est alia insula Graeciae, in qua similiter sunt magni astragali); facile est autem quod aliquis iaciat unum ex his vel duo. | Thirdly, at [329] he gives an example of what he is talking about. And first of all with reference to the phrase, "many things." And he says that it is difficult to throw a "myriad," i.e., 10,000, astragals, which are a type of missile from the island of Chios where there are great astragal-throwers (another text has Coos, another Greek island, where there are also great astragal-throwers), but it is easy to throw one or two of them. |
| Secundo, ibi: et iterum etc., exemplificat quantum ad id quod dixit, multoties. Et dicit quod quando oportet operari aliquid huius gratia, et hoc alterius gratia, et illud adhuc alterius gratia (ita scilicet quod ad unum finem oporteat perveniri per multas actiones ad invicem ordinatas), facile est hunc finem adipisci, quando per unam actionem vel duas potest aliquis consequi finem; puta si aliquis emit equum ad hoc quod aequitet, et aequitando perveniat ad locum aliquem. Sed quando oportet ad finem pervenire per plures actiones, tunc hoc est difficilius; puta si non habeat pecuniam in promptu unde emat equum, sed oportet eam acquirere per operationem alicuius artificii, ad quae exercenda iterum indigeat quaerere instrumenta alicuius artificii. Manifestum est igitur quod maior virtus requiritur, et ex parte intellectus ordinantis et ex parte potentiae exequentis, per plures actiones pervenire in finem, quam per unam vel pauciores. | Secondly, he gives an example of his statement, "many times." And he says that whenever it is necessary to do one thing for the sake of another, and this for the sake of another and that for the sake of still another, in such a way, namely, that it is necessary to arrive at one goal by a series of subordinated actions, it is easy to obtain this goal when it can be achieved by one or two actions: for example, if someone buys a horse in order to ride and by riding reaches a certain place. But when a number of actions are required in order to achieve the goal, then it is more difficult. For example, if he should not have ready money with which to buy the horse, but must obtain it by working at some trade, in order to exercise which he must seek the tools required by that trade. It is plain, therefore, that greater power is required, both on the part of the ordering intellect, and on the part of the faculty carrying things out, to reach an objective by many actions, rather than by one or a few. |
| Deinde cum dicit: propter quod oportet putare etc., ponit exempla praemissi principii. Et dicit quod propter praemissa oportet existimare quod actio stellarum, secundum multitudinem vel paucitatem motus earum, sit similis actioni animalium et plantarum. Videmus enim quod in istis inferioribus homo, habens perfectam animae virtutem, habet multiplices operationes, quia potest multa bona adipisci: et propter hoc multa potest operari, non solum absolute, sed etiam secundum ordinem unius ad aliud, ut puta cum excogitat magnam seriem actionum ordinatarum in unum finem. Nec tamen propter hoc homo est optimum in universo: quia id quod est optimum in universo, scilicet Deus, nulla indiget actione quoad adipiscendum proprium bonum. Non enim habet aliquem finem extra se, quem oporteat adipisci per aliquam actionem, sed ipse est finis sui ipsius et omnium aliorum: actio autem quae est propter finem, semper in duobus consistit, cum oporteat ibi considerari et finem cuius gratia aliquid agitur, et id quod est ad finem, quod agitur gratia huius, scilicet finis. | 461. Then at [331] he gives examples of this principle. And he says that, in view of the foregoing, we must reckon that the action of the stars, so far as the multitude or fewness of their actions is concerned, is akin to the action of animals and plants. For we observe among these lower things that man, possessing perfect power of soul, has many operations, because he is able to attain to many goods — for which reason, he can do many things, not only absolutely, but according to the order of one thing to another, as, for example, when he plans a long series of actions all directed to one end. This does not mean, however, that man is the best thing in the universe — for that which is best in the universe, namely, God, needs no action in order to attain His own appropriate good. For He has no end outside Himself which must be obtained by some action, but He is His own end and the end of all other things. Now action which is for the sake of an end always involves two things, since it is necessary to consider the end for the sake of which something is done and that which is directed to the end, which is done for the sake of this, i.e., of the end. |
| Sed animalium praeter hominem sunt pauciores actiones quam hominis: tum quia non habent actiones intellectivae partis; tum quia in actionibus exterioribus habent determinatum modum praefixum sibi a natura, sicut hirundo semper eodem modo facit nidum. Sed plantae habent forte unam operationem tantum, scilicet nutritivam, et hanc parvam, idest imperfectam, respectu operationis sensitivae et intellectivae. | But animals other than man have fewer actions than man, both because they do not have actions of the intellectual part and because in their exterior actions they have a set pattern predetermined for them by nature — for example, a swallow always builds its nest in the same manner. But plants have perhaps one operation, namely, the nutritive and this "small," i.e., imperfect, in comparison to sentient and intellectual operation. |
| Et huius diversitatis ratio est, quia finis ad quem pervenitur, vel est unum aliquod bonum perfectum, puta ad quem pervenit homo, scilicet beatitudo, quam homo consequitur per multas operationes; aut sunt multa quae praeexiguntur ad perfectum bonum, ad quorum aliquod pertingunt plantae et animalia per unam vel paucas operationes. Puta ad beatitudinem praeexigitur primo conservatio vitae, deinde cognitio sensibilium, et ultimo apprehensio universalis veritatis, in qua consistit finalis beatitudo: et hanc solus homo consequitur, conservationem autem vitae consequitur planta per actum nutritivae partis, animalia autem irrationabilia super hoc consequuntur cognitionem singularium. | The explanation of this diversity is that the end which is reached is either some one perfect good, for example, the end which man reaches, namely, beatitude, which he acquires through many operations, or else the many things pre-requisite to the perfect good, to some one of which plants and animals attain through one or a few operations. For example, beatitude presupposes, first of all, the preservation of life, then knowledge of sensible things, and finally the apprehension of the universal truth, in which final beatitude lies. This last, man alone obtains, but preservation of life plants attain through the act of the nutritive part, while irrational animals, in addition to this, attain the knowledge of individual things. |
| Sic igitur patet ex omnibus praemissis quinque esse ordines rerum. Nam supremum in entibus est quod habet perfectum bonum sine actione; secundum autem est quod habet perfectum bonum per unum vel paucos motus; tertium autem est quod acquirit perfectum bonum per multas operationes, sicut homo. Quartus autem gradus est qui non potest acquirere perfectum bonum ullo modo, sed acquirit aliquid praevium per paucos motus vel per unum tantum, sicut animalia et plantae. Relinquitur autem infimum esse quod nihil horum potest acquirere, et propter hoc non habet participare aliquem motum. | 462. Therefore, it is plain from all the above that there are five orders of things. For the highest among beings is that which possesses perfect good without acting; the second is that which has perfect good through one or a few actions; the third is that which acquires perfect good through many actions, as does man. The fourth grade is that which cannot attain perfect good in any way, but acquires something preliminary to it by a few actions or just one, as is true of animals and plants. There remains for that to be the lowest which can acquire none of these, and because of this does not have as a property the participation in any motion. |
| Sic igitur quod aliquid omnino careat motu, potest dupliciter contingere: uno modo quia est perfectissimum, alio modo quia est imperfectissimum. Similiter etiam quod aliquid habeat unum vel paucos motus, potest dupliciter contingere: uno modo quia est propinquum perfectissimo, alio modo quia est propinquum imperfectissimo. Quod autem aliquid habeat multas actiones vel motus, contingit ex eo quod medio modo se habet. | Thus that a thing entirely lack motion can occur in two ways: in one way, because it is most perfect; in another, because it is most imperfect. Likewise, that a thing have one or a few motions can occur in two ways: in one way, because it is near to the most perfect; in another, because it is near to the most imperfect. But that a thing have many actions or motions is due to its being in a mediate position. |
| Deinde cum dicit: hoc quidem igitur habet etc., adaptat praedicta principia ad propositum. Et dicit quod in ordine rerum hoc quod supremum est, habet et participat optimo absque omni motu: quod quidem contingit substantiis separatis, quae sunt omnino immobiles. Dicit autem habet, propter supremam causarum, quae est Deus altissimus, qui est ipsa essentia bonitatis: dicit autem participat, propter inferiores substantias separatas, quae esse et bonum habent ex alio: nam participare nihil aliud est quam ab alio partialiter accipere. Hic est igitur primus et supremus ordo entium. | 463. Then at [332] he adapts the aforesaid principles to his purpose. And he says that in the order of things, that which is supreme has and participates in the best without any motion — which indeed happens with the separated substances, which are wholly immobile. Now he says "has" on account of the highest of the causes, which is the most high God, Who is the very essence of goodness; but he says "participates" on account of the lower separated substances, which receive being and goodness from another — for to "participate" is nothing other than to receive from another partially. This, therefore, is the first and supreme order of beings. |
| Secundum ordinem distinguit, dicens quod est aliquid quod de propinquo attingit illud optimum per paucos motus; sicut suprema sphaera, quae intantum dicitur appropinquare ad illud optimum, inquantum pertingit ad hoc quod sit causa universalis corporalium, et causa permanentiae ipsorum. Deinde ponit tertium gradum, dicens quod aliquid appropinquat ad bonum optimum per multos motus; sicut superiores planetae, qui etiam sunt causae universales effectuum in mundo, et permanentiae et fixionis rerum. Deinde ponit quartum gradum, dicens quod aliquid est quod non potest participare illud perfectum bonum, sed sufficit qualitercumque appropinquet. | He distinguishes a second order and says that it is something which from nearby attains that best thing by a few motions — thus, the highest sphere is said to approach that best thing to the extent that it attains to being the universal cause of bodily things as well as the cause of their permanence. Then he sets down a third degree, saying that something approaches the supreme good through many motions, as do the higher planets, which are also universal causes of effects in the world, and of the permanence and stability of things. After that he sets down a fourth degree, saying that there is something which cannot participate that perfect good but it suffices if it approach it in any way at all. |
| Et ad horum manifestationem subiungit exemplum, dicens quod, si ponamus sanitatem vitae finem, invenimus quantum ad hoc aliquid esse optimum, quod scilicet semper est sanum. In secundo autem gradu est quod fit sanum per solam extenuationem, idest subtractionem superfluorum. In tertio autem gradu est quod sanitatem quidem adipiscitur per extenuationem, sed ad hoc quod extenuetur indiget cursu, et ad hoc quod currat requiritur quod aliquid aliud agat, ut sit aptum ad cursum; et sic habet plures motus quibus pervenit ad finem sanitatis. Quartus autem gradus est quod non potest pervenire ad hoc quod sanetur, sed pervenit ad aliquid eorum quae sunt praevia sanitati, puta ad hoc solum quod currat, vel etiam ulterius quod extenuetur; quorum neutrum est finis, sed eorum est aliquis finis, scilicet sanitas, ut dictum est. | 464. In clarification of these, he adds an example, saying that if we suppose health as the objective of life, we find something as best in this regard, namely, what is always healthy. But in the second degree is found that which is made healthy by the sole process of "thinning," i.e., the withdrawing of what is superfluous. In the third degree is that which indeed acquires health by thinning, but which, in order to be thinned, requires running, and in order to run, must do something else in order to be fit for running — and which thus has a number of motions by which it arrives at the goal of health. In the fourth degree is that which cannot attain health but attains to something of the things that are preliminaries to health — for example, only to running, or even, beyond that, to becoming thin, neither of which is the goal, but rather they have a goal, namely, health, as has been said. |
| Et horum rationem assignat, dicens quod maxime optimum est omnibus finem sortiri qualitercumque, scilicet sive sine motu, sive per paucos, sive per multos motus. Si vero non contingat adipisci finem, semper tanto aliquid erit melius, quanto magis appropinquat ad optimum; puta quod pertingit ad extenuationem, quae est propinquissima sanitati, est melius quam quod pertingit ad cursum. Ex quo etiam patet quod in unoquoque horum ordinum possunt esse multi gradus. | He gives the reason for this, and says that the absolute best for all things is to attain in some way to the end, namely, whether without any motion, or with a few, or with many motions. However, if the end cannot be achieved, then a thing will always be better the closer it gets to the best — for example, should it reach thinning, which is the thing nearest to health, this is better than reaching the stage of running. From this it is also plain that in each one of these orders there can be many grades. |
| Et quia terra maxime distat ordine naturae a summo ordine rerum, ideo totaliter non movetur, quasi non valens appropinquare ad optimum per hunc modum quod sit causa aliorum. Illa vero quae sunt propinqua terrae, quae sunt in quarto ordine, paucis motibus moventur: quia non attingunt ad alterum extremum, ut scilicet sint universales causae permanentiae rerum; sed intantum moventur, inquantum possunt sortiri aliquid de similitudine primi et divinissimi principii, in hoc scilicet quod et ipsa sint aliorum principia. Sed primum caelum statim sortitur hanc similitudinem per unum motum: quod pertinet ad secundum gradum. Illa vero quae sunt intermedia inter primum caelum et extrema corpora, quae sunt in tertio ordine, attingunt similitudinem primi principii in causando, per plures motus. | 465. And because the earth is in the order of nature the most distant from the highest order of things, it is therefore absolutely without motion, being incapable as it were of approaching the best under the aspect of being a cause of other things. But the things that are near to the earth and are in the fourth order, are moved with few motions, because they do not attain to the other extreme, which is to be universal causes of the permanence of things; but they are moved to the extent of being able to acquire something of the likeness of the first and most divine principle, under the aspect of being principles of other things. But the first heaven obtains this likeness immediately by a single movement, which pertains to the second degree. But things that are between the first heaven and the outermost bodies, which are in the third order attain to a likeness of the first principle in being able to cause things, but through a number of motions, however. |
| In his autem quae dicta sunt, tria expressit: scilicet principium, quod habet et participat optimo: hoc enim exposuit esse divinissimum principium. Similiter etiam secundum ordinem, qui per paucos motus attingit perfectum bonum, attribuit primo caelo. Quintum etiam ordinem, qui propter imperfectionem omni caret motu, attribuit terrae. Remanet autem dubitatio de aliis duobus ordinibus, quibus sint attribuendi. Nam si tertium ordinem attribuamus superioribus planetis, eo quod per plures motus consequuntur perfectum bonum et durabile, videbitur attribuere quartum ordinem soli et lunae, ut dicamus quod non attingunt ad perfectum bonum: quod videtur inconveniens, praesertim cum sol videatur esse nobilissimus planetarum, et tam ipse quam luna videantur habere maximam efficaciam in inferioribus corporibus. | 466. So far, Aristotle has expressed three things: namely, the principle which has and participates in the best — this he has explained to be the "most divine principle." Also he has identified the second order, which attains to the perfect good by a few motions, with the first heaven. He has also assigned the fifth order, which, on account of its imperfections, has no motion, to earth. Now there remains a question about the other two orders; as to what are they to be attributed. For if we attribute the third order to the higher planets on the ground that they attain the perfect and lasting good by means of a number of motions, then the fourth order will seem to be assigned to the sun and moon, which will involve saying that they do not attain the perfect good. But this appears unacceptable, especially since the sun is seen to be the noblest of the planets, and both it and the moon to exercise the greatest influence on lower bodies. |
| Et ideo Averroes dicit in commento suo quod quartus ordo, eorum scilicet quae non attingunt perfectum bonum sed appropinquant ad ipsum per paucos motus, attribuitur tribus elementis, scilicet aquae, aeri et igni; quae quidem moventur duplici motu, scilicet motu proprio secundum naturam gravitatis vel levitatis, et motu quem consequuntur ex caelestibus corporibus; sicut ignis et superior pars aeris moventur circulariter secundum motum caeli, et mare fluit et refluit secundum motum lunae. Tertium autem ordinem attribuit omnibus planetis, qui consequuntur perfectum bonum, idest causalitatem universalem super haec inferiora, per plures motus. | 467. And therefore Averroes says in his commentary that the fourth order, which is the order of things that do not attain to perfect good but approach to it by means of a few motions, should be attributed to the three elements, namely, water, air and fire, which indeed are moved by a twofold motion, one being their proper motion according to the nature of lightness or heaviness, and the other being one that they obtain from the heavenly bodies — as fire and the upper region of air are moved circularly according to the motion of the heaven, while the sea flows back and forth according to the motion of the moon. But the third order he attributes to all the planets, which attain perfect good, that is, a universal causality over these lower things by means of a number of motions. |
| Sed secundum hunc intellectum, dubitatio quam movit Aristoteles remanet insoluta. Et ideo secundum intentionem Aristotelis dicere oportet quod quartus gradus attribuatur soli et lunae, qui secundum ipsum sunt infimi planetarum. Et secundum principia Aristotelis, eorum ordo in dignitate est secundum ordinem situs eorum; eo quod superior sphaera continet inferiorem, continens autem est nobilius et formalius contento, sicut dicitur in IV Physic., et sicut postea dicetur in capitulo de terra. | 468. But this interpretation leaves Aristotle's doubt unsolved. And therefore, to accord with Aristotle's intention one has to say that the fourth grade should be attributed to the sun and moon which, according to him, are the lowest of the planets. And according to Aristotle's principles, their order in dignity corresponds to the order of their position, on the ground that the higher sphere contains the lower and the container is more noble and more formal than the contained, as is said in Physics IV and as will be said later in the section treating of the earth. |
| Secundum hoc ergo intelligendum est quod optimum in rebus est permanentia. Quae quidem in substantiis separatis est absque omni motu; et quidquid permanentiae est in inferioribus rebus, illinc derivatur. Et inde est etiam quod supremum caelum, quod est propinquissimum substantiis separatis, suo motu diurno est causa sempiternitatis et permanentiae rerum: et ideo maxime attingit ad similitudinem primi principii. Superiores autem planetae sunt magis causa permanentiae et durationis quam inferiores: unde Saturno attribuuntur res fixae. Et inde est etiam quod, secundum Ptolomaeum in quadripartito, quod ea quae sunt Saturni attribuuntur ad universalia loca temporum; ea autem quae sunt Iovis, ad loca annualium temporum; ea vero quae sunt solis et Martis et Veneris et Mercurii, ad loca mensium; transitus vero lunae ad loca diurna. Coniunctiones etiam superiorum planetarum coaptantur effectibus magis universalibus et permanentibus, secundum astrologos. Sol autem et luna, qui sunt inferiores planetae secundum Aristotelem, habent maxime efficaciam ad causandum transmutationes in istis inferioribus corporibus: quod quidem non est optimum, sed aliquid ordinatum ad optimum et praevium ei; nam corpora inferiora per transmutationem generationis et corruptionis consequuntur perpetuitatem in specie, quam in individuo habere non possunt. | According to this, then, it must be understood that the optimum in things is permanence, which, in separated substances, is realized without any motion at all, and whatever of permanence exists in lower things is derived thence. And this explains why the outermost heaven, which is nearest to the separated substances, is by its diurnal motion the cause of the sempiternity and permanence of things; on which account, it ranks highest in resembling the first principle. Further, the higher planets are more a cause of permanence and duration than the lower — for which reason stable things are attributed to Saturn. Hence it is that, according to Ptolemy in his Quadripartite, what belongs to Saturn is attributed to the universal loci [events] of times, while what belongs to Jupiter to the annual loci of times, what belongs to the Sun, Mars, Venus and Mercury, to the loci of months, the phases of the moon to daily loci. Likewise the conjunctions of the higher planets cooperate, according to the astronomers, in producing more universal and permanent effects. But the sun and moon, which are according to Aristotle lower planets, have especial influence for causing transmutations in the lower bodies — which indeed is not itself the optimum but something order to the optimum and preliminary to it; for the lower bodies, through the transmutation of generation and corruption, attain to a perpetuity in the species which they are unable to attain in the individual. |
| Simplicius tamen dicit in commento quod non existimat ordinem nobilitatis esse in corporibus caelestibus secundum ordinem situs; sed quod unumquodque corporum caelestium, sive nobilius sive minus nobile, ibi ponitur ubi optimum est ipsum poni; et ideo luminaria mundi, scilicet sol et luna, secundum Aristotelem propinquissime situantur inferioribus corporibus, quae indigent illuminari ab eis. Illud tamen quod prius dictum est, magis verum esse videtur, secundum convenientiam principiorum naturalium. | 469. Simplicius, however, says in his commentary that he does not reckon the order of nobility of the heavenly bodies to be according to their position, but that each of the heavenly bodies, whether more noble or less noble, is put wherever it is best for it to be. That is why the lights of the world, namely, the sun and moon, are according to Aristotle situated nearest the lower bodies, which need their light. However, the prior interpretation seems truer in terms of agreement with natural principles. |
| Secundum vero suppositiones modernorum astrologorum, satis convenienter videtur dispositus numerus caelestium corporum, licet non secundum rationem quam Aristoteles hic assignat. Nam sicut supra dictum est, et sicut Aristoteles dicit in XII Metaphys., oportet in caelestibus motibus aliquid esse quod est causa perpetuitatis et durationis rerum, et oportet aliquid esse quod pertinet ad causam transmutationis; et in unoquoque ordine oportet esse aliquod summum. Sicut igitur in ordine causalitatis permanentiae rerum, post primum motum qui revolvit totum, praeeminentiam obtinet octava sphaera; ita etiam in ordine causalitatis transmutationis rerum, summum locum obtinet sphaera solis, quae quodammodo proportionaliter respondet in hoc ordine sphaerae stellarum fixarum; ita scilicet quod, sicut sphaera stellarum fixarum praeeminet in stellarum multitudine, quod congruit universalitati causalitatis eius, propter diversas effectuum species, ita etiam sphaera solis superabundat in magnitudine solaris corporis et luminositatis eius, propter efficaciam transmutandi inferiora corpora. Unde sicut sphaerae stellarum fixarum attribuuntur duo motus, scilicet motus proprius et motus superioris sphaerae; ita etiam soli attribuitur duplex motus, scilicet unus proprius, quo movetur in suo circulo, et alius quo movetur sphaera eius secundum motum sphaerae stellarum fixarum. Utrique autem sphaerae quasi deserviunt tres inferiores sphaerae. Ita scilicet quod sphaerae stellarum fixarum intelligantur deservire, ad causandum permanentiam in rebus et ad universales effectus, Saturnus, Iupiter et Mars: propter quod uniformes habent motus secundum numerum; nam sicut dictum est, unicuique eorum attribuuntur tres motus. Soli autem intelliguntur deservire tres inferiores planetae, ad causandum transmutationem in rebus: et ideo gradatim diversificantur in numero motuum; ita scilicet quod soli attribuantur duo motus, Veneri attribuantur tres, Mercurio quatuor, lunae quinque. | 470. According to the theories of present-day astronomers, the number of heavenly bodies seems to be disposed suitably enough, although it is not according to the notion which Aristotle here assigns. For, as has been said above and as Aristotle says in Metaphysics XII, there has to be among the heavenly motions something which is the cause of the perpetuity and duration of things, and something which pertains to the cause of their change; moreover, in each of these orders there must be something supreme. Therefore, just as in the order of the causality of the permanence of things, after the first motion which moves the whole, the eighth sphere obtains pre-eminence, so too in the order of the causality of change in things, the sphere of the sun holds the top place and is in a certain sense proportionate in this order to the sphere of the fixed stars. Thus, just as the sphere of the fixed stars is pre-eminent in having a multitude of stars which befits the universality of its causality, on account of the diverse kinds of its effects, so too the sphere of the sun superabounds in the magnitude of the solar body and its luminosity for the purpose of efficacy in changing lower bodies. Hence, just as two motions are assigned to the sphere of the fixed stars, namely, its own and that of the superior sphere; so also two motions are assigned to the sun, namely" one which is its own, whereby it is moved in its own circle, and the other by which its sphere is moved according to the motion of the sphere of the fixed stars. Now both spheres are, as it were, served by three inferior spheres. Thus, the sphere of the fixed stars is understood, in its role of causing permanence in things and in causing universal effects, to be served by Saturn, Jupiter and Mars, whence these have motions that are uniform in number, for, as has been said, the number of motions assigned to each of them is three. The sun, in its role of causing changes in things, is understood to be served by the three lower planets. And therefore they are differentiated by degrees in the number of their motions, so that two motions are assigned to the Sun, three to Venus, four to Mercury and five to the Moon. |
| Est etiam sciendum quod, quia Aristoteles hic terram ponit non participare aliquem motum, Alexander convenienter dicit eam esse inanimatam. Sed Simplicius in suo commento declarat, dicens terram esse animatam (sequitur enim in hoc errorem gentilium, qui cultum divinitatis terrae attribuebant). Quod Aristoteles reprobat in III de anima, ostendens quod nullum corpus simplex est animatum. Quod etiam evidenti signo apparet: quia quae in animalibus sunt magis terrea, sicut ossa, insensibilia sunt. Si autem corpus caeleste, simplex existens, est animatum, non impedit hanc rationem: quia corpus caeleste non subiacet contrarietati, sicut simplicia elementorum corpora. | 471. One should likewise know that, since Aristotle here assumes that the earth does not participate in any motion, Alexander fittingly says that it is inanimate. But Simplicius in his commentary says that the earth is animate (for on this point he follows the error of the pagans, who bestowed a divine worship upon the earth). But Aristotle rejects this in On the Soul III where he shows that no simple body is animate. And this is plain from an evident sign: for the parts of animals that are more from earth, e.g., bones, are incapable of sensing. If, however, a heavenly body, although simple, should be animate, this would not affect this argument, because a heavenly body is not a subject of contraries as are the simple bodies of the elements. |
| Nititur autem probare corpus terrae esse animatum, quia in aeternum durat, et ex eo quod aliquae partes terrae sunt animatae: non attendens quod ad corpora animata, terra et alia elementa habent habitudinem materiae, corpus autem caeleste habitudinem agentis. Agens autem nobilius est facto, sed factum nobilius est materia: unde etsi caelum habet nobiliorem formam quam corpora animata, elementa tamen habent formam minus nobilem. | But Simplicius tries to prove that the earth's body is animated because it endures forever and because some of its parts are animated, forgetting that earth and the other elements are related to animate bodies as matter, whereas celestial body is related to animate bodies as efficient cause. Now efficient cause is nobler than its product and the product nobler than its matter. Hence, even though the heaven has a nobler form than do animate bodies, the elements, however, have a less noble form. |
| Similiter etiam nititur ostendere quod non repugnat animationi terrae quod non movetur. Uno quidem modo quia etiam plantae sunt animatae, quae tamen non moventur secundum locum. Sed in hoc fallitur: quia quamvis non moveantur motu locali, moventur tamen motu augmenti et decrementi. Alio modo quia, cum etiam ea quae intelligunt dicat Aristoteles vivere, nihil prohibet terram esse animatam et viventem, licet non moveatur secundum locum: potest tamen esse quod intelligat. Sed hoc etiam est contra Aristotelem, qui dicit in II de anima quod in corporibus corruptibilium non est aliquid habens intellectum sine sensu; terram autem insensibilem esse, manifestum est ex eo quod quotidie scinditur et atteritur. Adhuc autem, cum eadem sit natura totius et partis, sicut et idem motus, si terra tota haberet animam intellectivam, oporteret quod quaelibet pars eius divisa esset animata et intelligens; et quod ulterius omnia corpora mixta, in quibus terra superabundat, essent talia; quod est derisibile. | Similarly, he tries to show that animation of earth is not ruled out by the fact that it is not moved. In one way, because plants although animated are not moved with respect to place. But in this he is deceived, because although they are not moved with respect to place, nevertheless they are moved by the motion of augmentation and decrease. In another way, because, since even things that understand [intellectually] are said to live; hence there is nothing to prevent the earth from being animate and living, even though it is not moved according to place — for it may be that it understands. But this, too, is contrary to Aristotle, who says in On the Soul II that among the bodies of corruptible things none has intellect without having sense. But that the earth lacks sense is evident from the fact that it is cut and broken up daily. Moreover, since there is the same nature in the whole and in the part and the same motion in each, if the whole earth had an intellective soul, then every separate part of it would have to be animate and intelligent, and furthermore, all compound bodies, in which there is a predominance of earth, would have to be such — which is laughable. |
| Addit etiam quod licet terra stet, habet tamen aliquam operationem, quae est ipsum stare; ut sicut caelestis corporis est operatio movere, ita terrae operatio est stare vel quiescere. Sed in hoc fallitur: quia stare vel quiescere non est operatio, sed privatio operationis vel motus. Unde cum cuiuslibet viventis corporis oporteat esse aliquam operationem vitae, quae appareat in ipso corpore, et non solum in anima (alioquin frustra corpori uniretur), manifestum est quod terra, in cuius corpore nulla vitae operatio apparet, non potest esse animata. | He also adds that, although the earth is stationary, nevertheless it has an operation, namely, "standing," so that, just as movement is an operation of a heavenly body, so the earth's operation is to be stationary or at rest. But in this he is deceived, because to stand or to be at rest is not an operation but a privation of operation or motion. Hence, since there must be in every living body some life operation which appears in the very body and not merely in the soul (for otherwise the soul would be united to that body without purpose), it is plain that earth, in whose body none of the operations of life appears, cannot be animated. |
Lecture 19:
The second difficulty of Lecture 17 is resolved.Chapter 12 cont. Περὶ δὲ τῆς ἀπορίας ὅτι κατὰ μὲν τὴν πρώτην μίαν οὖσαν φορὰν πολὺ πλῆθος συνέστηκεν ἄστρων, τῶν δ' ἄλλων χωρὶς ἕκαστον εἴληφεν ἰδίας κινήσεις, δι' ἓν μὲν ἄν τις πρῶτον εὐλόγως οἰηθείη τοῦθ' ὑπάρχειν νοῆσαι γὰρ δεῖ τῆς ζωῆς καὶ τῆς ἀρχῆς ἑκάστης πολλὴν ὑπεροχὴν εἶναι τῆς πρώτης πρὸς τὰς ἄλλας, 333 As to the difficulty that into the one primary motion is crowded a vast multitude of stars, while of the other stars each has been separately given special movements of its own, there is in the first place this reason for regarding the arrangement as a natural one. In thinking of the life and moving principle of the several heavens one must regard the first as far superior to the others. εἴη δ' ἂν ἥδε συμβαίνουσα κατὰ λόγον ἡ μὲν γὰρ πρώτη μία οὖσα πολλὰ κινεῖ τῶν σωμάτων τῶν θείων, αἱ δὲ πολλαὶ οὖσαι ἓν μόνον (293a.) ἑκάστη τῶν γὰρ πλανωμένων ἓν ὁτιοῦν πλείους φέρεται φοράς. Ταύτῃ τε οὖν ἀνισάζει ἡ φύσις καὶ ποιεῖ τινὰ τάξιν, τῇ μὲν μιᾷ φορᾷ πολλὰ ἀποδοῦσα σώματα, τῷ δ' ἑνὶ σώματι πολλὰς φοράς. 334 Such a superiority would be reasonable. For this single first motion has to move many of the divine bodies, while the numerous other motions move only one each, since each single planet moves with a variety of motions. Thus, then, nature makes matters equal and establishes a certain order, giving to the single motion many bodies and to the single body many motions. Καὶ ἔτι διὰ τόδε ἓν ἔχουσι σῶμα αἱ ἄλλαι φοραί, ὅτι πολλὰ σώματα κινοῦσιν αἱ πρὸ τῆς τελευταίας καὶ τῆς ἓν ἄστρον ἐχούσης ἐν πολλαῖς γὰρ σφαίραις ἡ τελευταία σφαῖρα ἐνδεδεμένη φέρεται, ἑκάστη δὲ σφαῖρα σῶμά τι τυγχάνει ὄν. Ἐκείνης ἂν οὖν κοινὸν εἴη τὸ ἔργον αὐτῇ μὲν γὰρ ἑκάστῃ ἡ ἴδιος φύσει φορά, αὕτη δὲ οἷον πρόσκειται, παντὸς δὲ πεπερασμένου σώματος πρὸς πεπερασμένον ἡ δύναμίς ἐστιν. 335 And there is a second reason why the other motions have each only one body, in that each of them except the last, i.e. that which contains the one star, is really moving many bodies. For this last sphere moves with many others, to which it is fixed, each sphere being actually a body; so that its movement will be a joint product. Each sphere, in fact, has its particular natural motion, to which the general movement is, as it were, added. But the force of any limited body is only adequate to moving a limited body. Ἀλλὰ περὶ μὲν τῶν τὴν ἐγκύκλιον φερομένων κίνησιν ἄστρων εἴρηται ποῖ' ἄττα κατά τε τὴν οὐσίαν ἐστὶ καὶ κατὰ τὸ σχῆμα, περί τε τῆς φορᾶς καὶ τῆς τάξεως αὐτῶν. 336 The characteristics of the stars which move with a circular motion, in respect of substance and shape, movement and order, have now been sufficiently explained.
| Praemissa solutione primae dubitationis, hic solvit dubitationem secundam, qua scilicet quaerebatur quare, cum in sphaera primi motus sint innumerabiles stellae, in qualibet aliarum inferiorum non est nisi una. | 472. Having given a solution to the first problem, he [the Philosopher] here solves the second one, which asks why it is that, whereas there are innumerable stars in the sphere of the first motion, there is but one in each of the other lower spheres. |
| Ponit autem ad hoc tres solutiones. Quarum prima est sumpta ex excellentia primae sphaerae ad alias. Et dicit quod, circa dubitationem qua dubitatur quare secundum motum primae sphaerae, qui est unus, invenitur magis multitudo astrorum, in aliis autem sphaeris inferioribus planetarum unaquaeque stella seorsum accipit proprios motus (ut scilicet alii sint motus Saturni, alii Iovis, et sic de aliis, cum tamen omnes stellae fixae sint locatae secundum unum motum), dicendum est quod aliquis potest existimare hoc rationabile esse, primo quidem propter hoc unum, quia oportet intelligere quod prima sphaera habeat magnam excellentiam in comparatione ad alias sphaeras: tum quantum ad vitam, quia scilicet habet nobiliorem vitam, utpote habens nobiliorem animam; tum quantum ad hoc quod est esse principium uniuscuiusque, quia scilicet universalis causalitas magis competit primae sphaerae quam alicui aliarum. Quae quidem excellentia considerari potest ex tribus: primo quidem quia immediatius ordinatur ad primum motorem; secundo quia continet et revolvit omnes alias sphaeras; tertio autem quia habet motum simplicissimum et velocissimum. Manifestum est autem quod id quod est nobilissimum et magis activum in corporibus caelestibus, est stella; quod ostendit luminositas ipsius. Et ideo conveniens est quod prima sphaera abundet in multitudine stellarum, per comparationem ad alias sphaeras. | 473. To this he gives three answers. The first of these is based on the excellence of the first sphere as compared to the others. And he says [333] that to the question why it is that a multitude of stars is found to be connected with the motion of the first sphere, which is one, while in the other lower spheres of the planets each star has separately its own motions (so that the motions of Saturn are distinct from those of Jupiter, and so on for all the others, whereas all the fixed stars are located according to one motion), to this the answer must be given that this is reasonable first of all for one reason, namely, because we must understand that the first sphere has a great excellence in comparison to the other spheres, both in point of life, since it has a nobler life as having a nobler soul, and in point of being a principle of each, since, namely, universal causality is truer of the first sphere than of any of the others. Now this excellence can be considered from three facts: first, it [the first sphere] is more immediately ordered to the first mover; secondly, it contains and revolves all the other spheres; and thirdly, it has the simplest and the swiftest motion. It is plain that that which is noblest and more acting in the heavenly bodies is the star, and this is proved by its luminosity. And therefore, it is fitting that the first sphere should abound with a multitude of stars as compared with the other spheres. |
| Si vero supponamus quod sphaera stellarum fixarum non sit suprema sphaera, sed sit alia sphaera ea superior, in qua nulla est stella, nihil differt ad propositum. Quia motus sphaerae non est nisi propter motum stellae, ut dicitur in XII Metaphys.: unde ille motus supremae sphaerae, quae caret stellis, ordinatur ad motum stellarum fixarum; sicut, secundum antiquos astrologos, unusquisque planeta habet multas sphaeras carentes stella, ordinatas ad motum stellae infixae in ultima earum. Et secundum hoc, quantum ad ordinem motus, illa sphaera prima cadit in eundem ordinem cum sphaera stellarum fixarum. Propter quod etiam Aristoteles signanter dicit esse multas stellas secundum primam lationem, non autem secundum primam sphaeram: quia lationes determinantur secundum stellas, propter quas deferendas moventur sphaerae, non autem secundum sphaeras. Hoc autem solum infert quod motus stellarum fixarum non erit omnino simplex, ut Aristoteles supponit, sed compositus ex duobus motibus. | 474. But if we suppose that the sphere of the fixed stars is not the outermost sphere but that there is another above it, in which there is no star, our proposition is not affected. For the motion of the sphere exists only for the motion of the star, as is said in Metaphysics XII — hence, that motion of the supreme sphere that lacks stars is ordained to the movement of the fixed stars, just as, according to the ancient astronomers, each planet has many spheres lacking a star but ordained to the motion of the star fixed in the last of them. Therefore, according to this, so far as the coordination of motion is concerned, that first sphere falls into the same order as the sphere of the fixed stars. For this reason also Aristotle significantly says that there are many stars connected with the first "carrying," but not connected with the first "sphere," since the carryings are determined with respect to the stars, for the sake of carrying which along the spheres are moved, and not with respect to the spheres. This only implies, then, that the motion of the fixed stars will not be wholly simple, as Aristotle supposes, but composed of two motions. |
| Secundam rationem ponit ibi: erit autem utique etc.; quae quidem sumitur secundum proportionem multitudinis stellarum ad multitudinem motuum. Et dicit hoc quod in dubitatione ponitur, secundum rationem accidere. Nam prima latio cum sit una, secundum eam moventur multa caelestium corporum (quae vocat corpora divina, propter sui perpetuitatem): inferiores autem lationes, multae earum movent unum corpus solum; quia quaelibet stellarum errantium, idest planetarum, movetur pluribus motibus, ut supra dictum est. Sic igitur natura facit quandam proportionis aequalitatem inter stellas fixas et planetas, et ordinate eas disponit: ita scilicet quod uni primo motui attribuit multa corpora, idest multas stellas; e converso autem circa planetas, uni corpori, idest uni stellae, attribuit multos motus. | 475. The second argument is at [334] and it is based on the proportion of the multitude of stars to the multitude of motions. And he says that that about which the problem is raised occurs according to reason. For the first carrying along, although it is one, nevertheless many of the heavenly bodies (which he here calls "divine bodies," because of their perpetuity), are moved with it, whereas in the case of the lower carryings, many of them move one body alone, because each of the "wandering" stars, i.e., the planets, is moved with several motions, as has been said above. In this way, then, nature makes a certain equality of proportion between the fixed stars and the planets, and disposes them in good order, in the sense that, to the one first motion it assigns "many bodies," i.e., many stars, but conversely, as to the planets, to "one body," i.e., to one star, it assigns many motions. |
| Et rationabiliter ita distribuit. Nam planetae sunt quasi instrumenta quaedam supremae sphaerae, quasi principaliter agentis in corporibus, inquantum planetis mediantibus quodammodo deferuntur et coaptantur multiplices virtutes stellarum fixarum ad haec inferiora. Instrumentum autem agit inquantum est motum, principale autem agens agit secundum formam et virtutem propriam: et ideo conveniens est quod suprema sphaera abundet in multitudine stellarum, in quibus radicantur diversae virtutes activae, planetae autem abundant in multitudine motuum. | And this distribution [by nature] is reasonable. For the planets are as though certain instruments of the supreme sphere, which is as though the principal agent with respect to bodies, insofar as, through the medium of the planets, there are in a certain way transmitted and applied to these lower bodies the manifold powers of the fixed stars. Now an instrument acts insofar as it is moved, while a principal agent acts according to its own form and proper power. Consequently, it is fitting that the supreme sphere abound with a multitude of stars, in which diverse active powers are rooted, while the planets abound in a multitude of motions. |
| Salvatur autem haec ratio etiam secundum positionem modernorum astrologorum. Nam etsi sphaera stellarum fixarum habeat duos motus, minimum tamen de secundo eorum participat, qui tardissimus est in ea. | This explanation is valid even in the light of the suppositions of present-day astronomers. For even though the sphere of the fixed stars has two motions, it shares in a minimum way in the second, since it is most slow in it. |
| Tertiam rationem ponit ibi: et adhuc propter hoc etc.; quae quidem sumitur ex multitudine sphaerarum moventium unumquemque planetarum, secundum positiones antiquorum astrologorum. Et dicit quod ideo in quolibet apparenti motu planetarum invenitur unum tantum corpus stellae quae movetur, quia multa corpora sphaerica sunt quae movent stellam; ita scilicet quod illae quae primae, idest superiores, sunt motivae illius sphaerae quae est in fine, et quae habet in se ipsam stellam; quia stella movetur infixa in ultima sphaera multarum sphaerarum ordinatarum ad motum unius sphaerae (vel potest intelligi quod ultima sphaera est quodammodo alligata superioribus sphaeris, et secundum earum motum movetur). | 476. He gives the third explanation at [335] and it is based on the multitude of spheres moving each of the planets, according to the theory of the ancient astronomers. And he says that the reason why in each apparent motion of the planets there is found but one stellar body in motion, is that there are many spherical bodies moving the star, so arranged that those which are "first," i.e., the higher, are movers of that sphere which is at the end and which contains the star. For the star is moved as fixed in the last of many spheres ordered to moving one sphere. Or one can understand that the last of the spheres is in some way connected with the higher spheres and is moved according to their motion. |
| Manifestum est autem quod unaquaeque harum sphaerarum est corpus quoddam. Sic igitur commune opus omnium sphaerarum revolventium planetam est illius, idest sphaerae supremae in illo ordine, quae revolvit omnes inferiores: quia motus infimae sphaerae, in qua est planeta, est proprius motus et naturalis ipsius planetae; motus autem superiorum sphaerarum quasi apponuntur ad dirigendum irregularitatem quae videtur in motu planetae, scilicet secundum velocitatem et tarditatem, retrogradationem, directionem et stationem. Et sic patet quod, cum sphaera superior moveat omnes inferiores ordinatas ad motum eiusdem planetae, si cum hoc haberet movere plures stellas, esset ei laboriosum: quia cuiuslibet corporis est virtus finita per comparationem ad aliud corpus; ostensum est enim in VIII Physic. quod in magnitudine finita non est virtus infinita. | Now it is evident that each of these spheres is a certain body. Thus, therefore, the common work of all the spheres revolving a given planet belongs "to it," i.e., to the sphere which is supreme in that system and which revolves all the lower — for the motion of the lowest sphere, in which the planet exists, is the proper and natural motion of that planet, while the motions of the higher spheres are, so to speak, added to correct the irregularity that appears in the planet's motion, namely, of swiftness and slowness, retrogression, advancing and standing still. Accordingly, it is plain that, since the higher sphere moves all the lower that are ordered to the motion of the same one planet, then, if in addition to that it had to move several stars, it would be laborious for it — each body's strength being finite in comparison to another body, it having been shown in Physics VIII that there is not infinite power in a finite magnitude. |
| Non autem est intelligendum quod ista difficultas accideret ex eo quod in stellis sit ponderositas aut aliquid resistens motui, sed quia oportet esse excessum moventis ad mobile: non autem posset esse excessus superioris sphaerae secundum virtutem, si in inferioribus simul cum multitudine sphaerarum esset multitudo stellarum, cum in corporibus stellarum abundet virtus caelestium corporum. | 477. It should not be thought that this difficulty would derive from there being weight in the stars or from anything that resists motion, but rather it is because there is required an excess of the mover over the mobile. But there could not be an excess of the superior sphere in power if in the lower things there was together with a multitude of spheres also a multitude of stars, because in the bodies of stars the power of the heavenly bodies most abounds. |
| Est autem diligenter attendendum quod finitam proportionem ponit sphaerae moventis ad corpora mota, ex eo quod sphaera movens est corpus. Ex quo patet quod motor separatus, qui est substantia incorporea et immaterialis, non habet, secundum intentionem Aristotelis, finitum excessum supra corpus quod ab eo movetur, sed infinitum, utpote extra totum corpus magnitudinis existens, et per materiam non determinatum. Ex quo patet falsum esse quod Averroes dicit in suo commento, quod additio primi motoris supra potentiam moti non est infinita nisi in tempore infinito. Qualiter autem, si potentia motoris separati est infinita, non moveat velocitate infinita, scilicet in instanti; et qualiter, si potentia corporis est finita, corpus possit durare tempore infinito, manifestum est in VIII Physic. | It should also be diligently noted that he posits a finite proportion between the movent sphere and the moved bodies on the ground that the movent sphere is a body. This indicates that the separated mover, which is an incorporeal and immaterial substance, does not, according to the intention of Aristotle, finitely exceed the body which is moved by it, but infinitely, as existing outside the whole body of magnitude and not determined by matter. This reveals that Averroes is in error in his commentary when he says that the addition of the first mover over the power of the moved is not infinite except in infinite time. But how, If the power of the separated mover is infinite, it does not move with infinite speed, i.e., in an instant, and how, if the power of a body is finite, that body can endure for an infinite time, has been shown in Physics VIII. |
| Sciendum vero est quod tertia ratio non habet locum secundum modernos astrologos, qui non ponunt planetis multas sphaeras, quarum una movet omnes, sicut ponebant antiqui astrologi: qui tamen ponebant multas stellas fixas non moveri nisi ab una sphaera. | It should be noted that this third argument does not apply to the position of the modern astronomers, who do not assign to the planets a number of spheres, one of which moves all the others, as the ancient astronomers did; nevertheless, these latter did hold that the many fixed stars were not moved except by one sphere. |
| Ultimo autem epilogando dicit quod dictum est de stellis, quae moventur motu circulari, qualia sint secundum substantiam suae naturae et secundum figuram: dictum est etiam de motu et ordine ipsarum. | 478. In summing up [336], he says we have stated of the stars, which are moved with a circular motion, what they are according to the substance of their nature and according to their shape. Moreover, we have discussed their motion and order. |
Lecture 20:
Opinions of the philosophers as to the site of the earth. Pythagorean theory, of fire in the center relectedChapter 13 Λοιπὸν δὲ περὶ τῆς γῆς εἰπεῖν, οὗ τε τυγχάνει κειμένη, καὶ πότερον τῶν ἠρεμούντων ἐστὶν ἢ τῶν κινουμένων, καὶ περὶ τοῦ σχήματος αὐτῆς. 337 It remains to speak of the earth, of its position, of the question whether it is at rest or in motion, and of its shape. Περὶ μὲν οὖν τῆς θέσεως οὐ τὴν αὐτὴν ἅπαντες ἔχουσι δόξαν, ἀλλὰ τῶν πλείστων ἐπὶ τοῦ μέσου κεῖσθαι λεγόντων, ὅσοι τὸν ὅλον οὐρανὸν πεπερασμένον εἶναί φασιν, ἐναντίως οἱ περὶ τὴν Ἰταλίαν, καλούμενοι δὲ Πυθαγόρειοι λέγουσιν ἐπὶ μὲν γὰρ τοῦ μέσου πῦρ εἶναί φασι, τὴν δὲ γῆν, ἓν τῶν ἄστρων οὖσαν, κύκλῳ φερομένην περὶ τὸ μέσον νύκτα τε καὶ ἡμέραν ποιεῖν. Ἔτι δ' ἐναντίαν ἄλλην ταύτῃ κατασκευάζουσι γῆν, ἣν ἀντίχθονα ὄνομα καλοῦσιν, 338 I. As to its position there is some difference of opinion. Most people—all, in fact, who regard the whole heaven as finite—say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the centre. They further construct another earth in opposition to ours to which they give the name counterearth. οὐ πρὸς τὰ φαινόμενα τοὺς λόγους καὶ τὰς αἰτίας ζητοῦντες, ἀλλὰ πρός τινας λόγους καὶ δόξας αὑτῶν τὰ φαινόμενα προσέλκοντες καὶ πειρώμενοι συγκοσμεῖν. 339 In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accommodate them to certain theories and opinions of their own. Πολλοῖς δ' ἂν καὶ ἑτέροις συνδόξειε μὴ δεῖν τῇ γῇ τὴν τοῦ μέσου χώραν ἀποδιδόναι, τὸ πιστὸν οὐκ ἐκ τῶν φαινομένων ἀθροῦσιν ἀλλὰ μᾶλλον ἐκ τῶν λόγων. 340 But there are many others who would agree that it is wrong to give the earth the central position, looking for confirmation rather to theory than to the facts of observation. Τῷ γὰρ τιμιωτάτῳ οἴονται προσήκειν τὴν τιμιωτάτην ὑπάρχειν χώραν, εἶναι δὲ πῦρ μὲν γῆς τιμιώτερον, τὸ δὲ πέρας τοῦ μεταξύ, τὸ δ' ἔσχατον καὶ τὸ μέσον πέρας ὥστ' ἐκ τούτων ἀναλογιζόμενοι οὐκ οἴονται ἐπὶ τοῦ μέσου τῆς σφαίρας κεῖσθαι αὐτήν, ἀλλὰ μᾶλλον (293b.) τὸ πῦρ. 341 Their view is that the most precious place befits the most precious thing: but fire, they say, is more precious than earth, and the limit than the intermediate, and the circumference and the centre are limits. Reasoning on this basis they take the view that it is not earth that lies at the centre of the sphere, but rather fire. Ἔτι δ' οἵ γε Πυθαγόρειοι καὶ διὰ τὸ μάλιστα προσήκειν φυλάττεσθαι τὸ κυριώτατον τοῦ παντός, τὸ δὲ μέσον εἶναι τοιοῦτον, [ὃ] Διὸς φυλακὴν ὀνομάζουσι τὸ ταύτην ἔχον τὴν χώραν πῦρ 342 The Pythagoreans have a further reason. They hold that the most important part of the world, which is the centre, should be most strictly guarded, and name it, or rather the fire which occupies that place, the 'Guardhouse of Zeus', ὥσπερ τὸ μέσον ἁπλῶς λεγόμενον, καὶ τὸ τοῦ μεγέθους μέσον καὶ τοῦ πράγματος ὂν μέσον καὶ τῆς φύσεως. Καίτοι καθάπερ ἐν τοῖς ζῴοις οὐ ταὐτὸν τοῦ ζῴου καὶ τοῦ σώματος μέσον, οὕτως ὑποληπτέον μᾶλλον καὶ περὶ τὸν ὅλον οὐρανόν. Διὰ μὲν οὖν ταύτην τὴν αἰτίαν οὐθὲν αὐτοὺς δεῖ θορυβεῖσθαι περὶ τὸ πᾶν, οὐδ' εἰσάγειν φυλακὴν ἐπὶ τὸ κέντρον, ἀλλ' ἐκεῖνο ζητεῖν τὸ μέσον, ποῖόν τι καὶ ποῦ πέφυκεν. Ἐκεῖνο μὲν γὰρ ἀρχὴ τὸ μέσον καὶ τίμιον, τὸ δὲ τοῦ τόπου μέσον ἔοικε τελευτῇ μᾶλλον ἢ ἀρχῇ τὸ μὲν γὰρ ὁριζόμενον τὸ μέσον, τὸ δ' ὁρίζον τὸ πέρας. Τιμιώτερον δὲ τὸ περιέχον καὶ τὸ πέρας ἢ τὸ περαινόμενον τὸ μὲν γὰρ ὕλη, τὸ δ' οὐσία τῆς συστάσεώς ἐστιν. 343 as if the word 'centre' were quite unequivocal, and the centre of the mathematical figure were always the same with that of the thing or the natural centre. But it is better to conceive of the case of the whole heaven as analogous to that of animals, in which the centre of the animal and that of the body are different. For this reason they have no need to be so disturbed about the world, or to call in a guard for its centre: rather let them look for the centre in the other sense and tell us what it is like and where nature has set it. That centre will be something primary and precious; but to the mere position we should give the last place rather than the first. For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which is limited, seeing that the latter is the matter and the former the essence of the system. Περὶ μὲν οὖν τοῦ τόπου τῆς γῆς ταύτην ἔχουσί τινες τὴν δόξαν, 344 II. As to the position of the earth, then, this is the view which some advance,
| Postquam philosophus determinavit de corpore caelesti, quod movetur circulariter, hic determinat de terra, circa quam caelum movetur. Non autem intendit hic determinare de terra secundum quod est unum quatuor elementorum; sed secundum quod est centrum caelestis motus, sicut de ea tractant astrologi. | 479. After determining about the heavenly body which is moved circularly, the Philosopher here determines the question of the earth, around which the heaven is moved. But he does not intend to determine here concerning the earth as one of the four elements but as it is the center of heavenly motion, as astronomers deal with it. |
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Primo ergo dicit de quo est intentio; secundo prosequitur propositum, ibi: de positione quidem et cetera. |
First, therefore, he states his intention; Secondly, he pursues it, at 480. |
| Dicit ergo primo quod, cum dictum sit de caelo, relinquitur dicere de terra. De qua tria dicit se determinaturum: | He says, therefore, first [337] that, since the heaven has been discussed, there remains the earth to be discussed. Concerning this, he says there are for him three things to be settled: |
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primo de situ eius, ubi scilicet sit posita; secundo de quiete eius, utrum scilicet sit de numero eorum quae quiescunt, vel quae moventur; tertio de figura eius, utrum scilicet sit sphaericae figurae, vel cuiuscumque alterius. |
First, its situation, namely, where is it positioned; Secondly, its rest, namely, whether it is one of the things that rest or that are moved; Thirdly, its shape, namely, whether it has a spherical shape or some other. |
| Deinde cum dicit: de positione quidem etc., exequitur propositum. | 480. Then at [338] he executes his proposal: |
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Et primo prosequitur praedicta tria secundum opinionem aliorum; secundo secundum veritatem, ibi: nos autem dicamus et cetera. |
First he pursues the above-mentioned three things according to the opinion of others; Secondly, according to truth (L. 26). |
| Circa primum duo facit: | Concerning the first he does two things: |
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primo ponit falsas opiniones quorundam circa terram; secundo assignat falsas rationes aliorum circa veram positionem de quiete terrae, ibi: haesitare (vel dubitare) quidem igitur et cetera. |
First he presents the false opinions of certain ones concerning earth; Secondly, he presents the false reasons alleged about the true theory concerning the earth's state of rest (L. 22). |
| Circa primum tria facit: | As to the first he does three things: |
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primo ponit opiniones aliorum circa situm terrae; secundo circa quietem et motum, ibi: similiter autem et de mansione etc.; tertio quantum ad figuram, ibi: similiter autem et de figura et cetera. |
First he presents others' opinions about the position of the earth; Secondly, about its rest and motion (L. 21); Thirdly, about its shape (L. 21). |
| Circa primum tria facit: | About the first he does three things: |
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primo ponit opiniones aliorum circa situm terrae; secundo ponit rationes eorum, ibi: non ad apparentia etc.; tertio solvit, ibi: tanquam medium et cetera. |
First he presents others' opinions about the position of earth, 481; Secondly, he gives their reasons, at 482; Thirdly, he solves them, at 485. |
| Dicit ergo primo quod de situ terrae non omnes philosophi habent eandem opinionem. Quicumque enim posuerunt totum universum esse infinitum, non potuerunt assignare terrae determinatum situm, eo quod in infinito non est accipere medium et extrema. Sed plures eorum qui posuerunt totum mundum esse finitum, dixerunt terram esse positam in medio mundi, sicut Anaximander, Anaxagoras, Democritus, Empedocles et Plato. Sed quidam philosophi qui dicuntur Pythagorici, in partibus Italiae commorantes, e contra dixerunt quod ignis positus est in medio mundi: terra autem, ad modum unius stellarum, movetur circulariter circa medium mundi, et suo motu facit noctem et diem, secundum diversam habitudinem sui ad solem. Ponebant etiam et aliam terram, similiter circulariter motam circa medium mundi, quam vocabant antichthona, eo quod est contraposita huic terrae; quae tamen a nobis videri non potest, propter hoc quod sequitur in suo motu terram istam, in qua nos habitamus, ita quod semper totum corpus terrae interponitur inter visus nostros et alteram terram. | 481. He says therefore first [338] that not all philosophers have the same opinion about the position of the earth. For whichever ones held that the entire universe is infinite were unable to assign a definite position to the earth, since in the infinite no middle and no boundary can be determined. But a number of those who posited the whole world as finite said that earth is positioned in the middle of the world, as did Anaximander, Anaxagoras, Democritus, Empedocles and Plato. But certain philosophers called "Pythagoreans" who sojourned in the region of Italy said on the contrary that fire is positioned in the middle of the world and that the earth, after the manner of one of the stars, moved circularly around the center of the world, and by its motion makes day and night, according to its different relation to the sun. They also posited another earth — likewise in circular motion about the middle of the world — which they called antichtona on account of its contraposition to our earth. But this other earth is not visible to us because in its motion it follows the earth in which we live, in such a way that the entire body of our earth is always interposed between our sights and this other earth. |
| Et licet haec Pythagorici dicerent secundum apparens suorum sermonum, intelligebant tamen, metaphorice loquentes, ignem esse in medio, quia calor naturalis ex sole et aliis stellis procreatus, usque ad medium mundi pertingit, omnia quodammodo contemperans et conservans. Terram autem dicebant esse stellam, quia est causa diei et noctis per suam habitudinem ad solem. Terram autem aliam vocabant lunam: vel quia obsistit solari lumini, sicut et terra, ut in eclipsibus patet; vel quia est terminus caelestium corporum versus nos, sicut et terra est terminus elementorum. | And although the Pythagoreans said these things according to the face value of their words, they nevertheless understood in their metaphor that fire was in the center since the natural heat produced from the sun and other stars reaches the middle of the world, in a certain way keeping all things in balance and preserving them. But earth they said to be a star because it causes day and night, depending on its relation to the sun. The other earth they called a moon, either because it is interposed to the sun's light as our earth is, as is plain from eclipses, or because it is the boundary facing us of the heavenly bodies, just as the earth is the boundary of the elements. |
| Deinde cum dicit: non ad apparentia etc., ponit rationes eorum. Et circa hoc duo facit: | 482. Then at [339] he presents their reasons. Concerning this he does two things: |
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primo ponit qualitatem rationis eorum; secundo ponit ipsas rationes, ibi: honorabilissimo enim et cetera. |
First he describes the quality of their reason; Secondly, he presents the reasons themselves, at 483. |
| Circa primum duo facit: | About the first he does two things: |
| primo ponit qualibus rationibus Pythagorici utebantur. Et dicit quod Pythagorici non quaerebant hoc modo rationes et causas, ut applicarent eas ad ea quae sensu apparent; sed e converso ea quae sensu apparent, conabantur reducere, et per quandam violentiam attrahere ad quasdam rationes et opiniones intelligibiles, quas ipsi praecogitabant. Quod quidem conveniens est in his quae ab homine fiunt, quorum principium est intellectus humanus: in his autem quae arte divina sunt facta, oportet e converso ex ipsis operibus quae videntur, considerare operum rationes: sicut artifex ex rationibus praeconceptis assimilat domum quam facit, sed quicumque alius videret domum iam factam, ex ipso opere viso consideraret operis rationes. |
First he describes the kind of reasons the Pythagoreans used [339] and says that they did not search for reasons and causes in such a way as to apply them to what is sensibly apparent; rather, what was apparent to sense they tried to reduce to, and by a certain violence align with, certain preconceived intelligible reasons and opinions. Now such a method is suitable in things that are man-made, and whose principle is the human intellect; but in things that are the product of divine art, it is necessary, on the contrary, to consider the notions of the works from the works themselves that are seen. Thus? an artisan conforms a house he makes to preconceived plans, but whoever else might see the constructed house would consider the ideas of the work from the sight of the work. |
| Secundo ibi: multis autem utique etc., ostendit quod eisdem rationibus Pythagoricorum, multos alios possibile est moveri. Et dicit quod multis aliis praeter Pythagoricos videri poterit quod non oporteat mediam regionem assignare terrae; dum considerant id quod oportet credere, non ex his quae apparent, sed magis ex intelligibilibus rationibus. Quod quidem non dicit quasi aliqui praeter Pythagoricos hoc posuerunt ante Aristotelem; sed quia possibile erat alios ex his rationibus moveri. Unde dicitur post Aristotelem huius opinionis Archedemus fuisse. | Secondly, at [340] he shows that it is possible for many others to be moved by these same reasons of the Pythagoreans. And he says that it might seem to many others besides the Pythagoreans that one should not assign the middle region to earth, "if it is their wont to consider things, not as they appear, but according to intelligible reasons." He says this, not as though any of Aristotle's predecessors besides the Pythagoreans posited this, but because it was possible that others would be swayed by these reasons. Hence it is said that after Aristotle's time Archedemus was of this opinion. |
| Deinde cum dicit: honorabilissimo enim etc., ponit duas rationes. Quarum prima est quod putabant honorabilissimo corpori honorabilissimam competere regionem, idest locum; eo quod loca proportionantur corporibus secundum eorum naturam. Manifestum est autem quod ignis est honorabilior quam terra; tum propter claritatem, tum propter virtutem activam, tum etiam propter subtilitatem ipsius. Manifestum est etiam quod termini sunt nobiliores his quae sunt intermedia inter terminos, sicut terminus terminato, et continens contento. Illud autem quod est extremum, idest supremum, in mundo, et medium mundi, ponebant esse quasi terminos; quae propter hoc ponebant esse nobilissima loca. Et ideo, ista cogitantes, non ponebant terram in medio sphaerae mundialis, sed magis ignem, qui tenet secundum locum nobilitatis post caelestia corpora, quae sunt in extremo. | 483. Then he gives two reasons. The first of these is that they thought that the most honorable "region," i.e., place, should belong to the most honorable body, on the ground that places are proportionate to bodies according to their nature. But it is plain that fire is more honorable than earth, not only because of its brightness, but also on account of its active power and on account of its subtility. It is plain, too, that boundaries are nobler than the intermediates between them, as the terminus is nobler than the thing terminated and a container than the contained. But that which is "extreme," i.e., highest, in the world, and that which is the middle of the world, they thought of as being boundaries. For this reason, they set them down as the noblest places. And therefore, thinking in this wise, they did not place earth in the middle of the sphere of the world, but rather fire, which holds the place of nobility after the heavenly bodies, which are at the boundaries. |
| Secundam rationem ponit ibi: adhuc autem Pythagorici et cetera. Et dicit quod Pythagorici ponebant ignem in medio mundi, propter hoc quod, cum sit principalissimum inter elementa, maxime debet conservari, sicut res pretiosas diligentius custodimus: medius autem locus videtur habere talem conservandi dispositionem, quasi vallatus et firmatus ex omnibus quae exterius circumstant medium. Et inde est quod Pythagorici, metaphorice loquentes, nominabant hanc regionem quae habet ignem, esse carcerem vel custodiam Iovis. Et hoc si intelligamus ignem esse custoditum. Si autem intelligamus ignem esse custodientem, oportet e converso intelligere quod ignis qui habet hanc regionem, idest qui tenet medium locum, dicatur carcer Iovis, quasi habens virtutem custodiendi. | 484. He gives their second reason at [342] and says that the Pythagoreans put fire in the middle of the world because, since it is the most principal of the elements it should be most of all preserved — as we more carefully guard precious things. Now the middle place seems to have such a disposition for preserving, as though walled up and strengthened by all the things that surround the middle. That is why the Pythagoreans, speaking metaphorically, called this region which has fire, the "guard-house" or "fortress" of Jupiter. This is the case if we understand that the fire is guarded. But if we understand that fire is the guardian, then, conversely, we must understand that the fire which has this region, i.e., which holds the middle place, is Jupiter's guardhouse in the sense that it has the power of guarding. |
| Deinde cum dicit: tanquam medium etc., solvit praedictam rationem. Et dicit quod Pythagorici in praedicta ratione utebantur nomine medii, ac si simpliciter, idest univoce, diceretur medium magnitudinis, et id quod est medium rei secundum naturam, per quod scilicet natura rei conservatur: sicut videmus in animalibus quod non est idem medium a quo natura animalis conservatur, quod est cor, et quod est medium quantum ad corporis magnitudinem, quod est magis umbilicus. Et ita est etiam aestimandum in toto caelo, idest in toto universo. Et propter hoc non oportet eos dubitare circa totum universum, quasi indigeat custodia, ita quod oporteat carcerem sive custodiam universi attribuere centro, quod est medium magnitudinis: sed oportet quaerere de eo quod est medium naturae in universo, sicut in animali, quale sit secundum naturam, et quis locus ei naturaliter competat. | 485. Then at [343] he refutes the aforesaid reason and says that in the aforesaid reason the Pythagoreans used the word "middle" as though one called "middle" absolutely, i.e., univocally, both the middle of a magnitude, and the middle of a thing according to nature, i.e., that through which the nature of a thing is preserved — as we see in animals that the middle by which the nature of an animal is preserved, namely, the heart, is not the same as the middle of the body's size, for that would be the umbilicus. A similar viewpoint must be taken with respect to the whole heaven, i.e., to the whole universe. Hence they should not be concerned with the whole universe as though it needs a guardhouse in such a way that such a prison or guardhouse would have to be assigned to the center, which is the middle of magnitude. It is necessary, rather, to seek that which is the middle of nature in the universe, as in the case of an animal, and ask what is its condition according to nature, and which place naturally befits it. |
| Et haec duo manifestat: primo quidem ostendens quale sit medium universi quod proportionatur cordi animalis. Et dicit quod est principium aliorum corporum, et maxime honorabile inter alia corpora: et haec est sphaera stellarum fixarum. | He explains these two things, showing first how the middle of the universe is as corresponding to the heart of an animal. And he says that it is a principle of other bodies, and most honorable among other bodies: and this is the sphere of the fixed stars. |
| Non autem competit ei locus medius, sed magis locus extremi continentis: quia id quod est medium magnitudinis inter loca universi, magis assimilatur ultimo quam principio. Et hoc ideo, quia medium est contentum et determinatum omnibus aliis; id autem quod est finis, idest extremum inter corpora secundum ordinem locorum, habet rationem determinantis et continentis. Manifestum est autem quod continens est honorabilius contento, et finis quam finitum: quia contentum et finitum pertinent ad rationem materiae, esse autem continens et finiens, ad rationem formae, quae est substantia totius consistentiae rerum. Et ita corpora continentia sunt magis formalia, corpora autem contenta sunt magis materialia. Et ideo in toto universo, sicut terra, quae ab omnibus continetur, in medio localiter existens, est maxime materialis et ignobilissima corporum; ita etiam suprema sphaera est maxime formalis et nobilissima, et inter elementa ignis est maxime continens et maxime formalis. | But it is not the middle place but rather the place of the outermost container that belongs to it, for that which is the magnitudinal middle among the places of the universe is more like an ultimate than like a principle. The reason is that the middle is contained and determined by all the others, while that which is the "end," i.e., the extremity, among bodies according to the order of place, has the nature of a determinant and container. But it is manifest that the container is more honorable than the contained, and the end more honorable than the thing ended — since the contained and the terminated pertain to the notion of matter, but to be a container and that which terminates to the notion of form, which is the substance of the whole consistency of things. Consequently, containing bodies are more formal and contained bodies are more material. And therefore, in the whole universe, just as the earth which is contained by all, being in the middle, is the most material and ignoble among bodies, so the outermost sphere is most formal and most noble, while among the elements fire is above all containing and formal. |
| Ultimo autem epilogando concludit quod de loco terrae quidam habent talem opinionem sicut dictum est. | Finally, he sums up [344] and concludes that in regard to the place of earth, some have an opinion such as has been described. |
Lecture 21:
Different opinions of the motion, rest, and shape of the earthChapter 13 cont. ὁμοίως δὲ καὶ περὶ μονῆς καὶ κινήσεως οὐ γὰρ τὸν αὐτὸν τρόπον ἅπαντες ὑπολαμβάνουσιν, ἀλλ' ὅσοι μὲν μηδ' ἐπὶ τοῦ μέσου κεῖσθαί φασιν αὐτήν, κινεῖσθαι κύκλῳ περὶ τὸ μέσον, οὐ μόνον δὲ ταύτην, ἀλλὰ καὶ τὴν ἀντίχθονα, καθάπερ εἴπομεν πρότερον. Ἐνίοις δὲ δοκεῖ καὶ πλείω σώματα τοιαῦτα ἐνδέχεσθαι φέρεσθαι περὶ τὸ μέσον, ἡμῖν ἄδηλα διὰ τὴν ἐπιπρόσθησιν τῆς γῆς. 345 and the views advanced concerning its rest or motion are similar. For here too there is no general agreement. All who deny that the earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the counter-earth as well. Some of them even consider it possible that there are several bodies so moving, which are invisible to us owing to the interposition of the earth. Διὸ καὶ τὰς τῆς σελήνης ἐκλείψεις πλείους ἢ τὰς τοῦ ἡλίου γίγνεσθαί φασιν τῶν γὰρ φερομένων ἕκαστον ἀντιφράττειν αὐτήν, ἀλλ' οὐ μόνον τὴν γῆν. 346 This, they say, accounts for the fact that eclipses of the moon are more frequent than eclipses of the sun: for in addition to the earth each of these moving bodies can obstruct it. Ἐπεὶ γὰρ οὐκ ἔστιν ἡ γῆ κέντρον, ἀλλ' ἀπέχει τὸ ἡμισφαίριον αὐτῆς ὅλον, οὐθὲν κωλύειν οἴονται τὰ φαινόμενα συμβαίνειν ὁμοίως μὴ κατοικοῦσιν ἡμῖν ἐπὶ τοῦ κέντρου, ὥσπερ κἂν εἰ ἐπὶ τοῦ μέσου ἦν ἡ γῆ οὐθὲν γὰρ οὐδὲ νῦν ποιεῖν ἐπίδηλον τὴν ἡμίσειαν ἀπεχόντων τῆς διαμέτρου. 347 Indeed, as in any case the surface of the earth is not actually a centre but distant from it a full hemisphere, there is no more difficulty, they think, in accounting for the observed facts on their view that we do not dwell at the centre, than on the common view that the earth is in the middle. Even as it is, there is nothing in the observations to suggest that we are removed from the centre by half the diameter of the earth. Ἔνιοι δὲ καὶ κειμένην ἐπὶ τοῦ κέντρου φασὶν αὐτὴν ἴλλεσθαι καὶ κινεῖσθαι περὶ τὸν διὰ παντὸς τεταμένον πόλον, ὥσπερ ἐν τῷ Τιμαίῳ γέγραπται. 348 Others, again, say that the earth, which lies at the centre, is 'rolled', and thus in motion, about the axis of the whole heaven, So it stands written in the Timaeus. Παραπλησίως δὲ καὶ περὶ τοῦ σχήματος ἀμφισβητεῖται τοῖς μὲν γὰρ δοκεῖ εἶναι σφαιροειδής, τοῖς δὲ πλατεῖα καὶ τὸ σχῆμα (294a.) τυμπανοειδής 349 III. There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and drum-shaped. ποιοῦνται δὲ τεκμήριον ὅτι δύνων καὶ ἀνατέλλων ὁ ἥλιος εὐθεῖαν ἀλλ' οὐ περιφερῆ τὴν ἀπόκρυψιν φαίνεται ποιούμενος ὑπὸ τῆς γῆς, ὡς δέον, εἴπερ ἦν σφαιροειδής, 350 For evidence they bring the fact that, as the sun rises and sets, the part concealed by the earth shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to be circular. περιφερῆ γίνεσθαι τὴν ἀποτομήν, οὐ προσλογιζόμενοι τό τε ἀπόστημα τοῦ ἡλίου πρὸς τὴν γῆν καὶ τὸ τῆς περιφερείας μέγεθος, ὡς ἐν τοῖς φαινομένοις μικροῖς κύκλοις εὐθεῖα φαίνεται πόρρωθεν. Διὰ μὲν οὖν ταύτην τὴν φαντασίαν οὐδὲν αὐτοὺς ἀπιστεῖν δεῖ μὴ κυκλοτερῆ τὸν ὄγκον εἶναι τῆς γῆς 351 In this they leave out of account the great distance of the sun from the earth and the great size of the circumference, which, seen from a distance on these apparently small circles appears straight. Such an appearance ought not to make them doubt the circular shape of the earth. ἀλλ' ἔτι προστιθέασι, καὶ φασὶ διὰ τὴν ἠρεμίαν ἀναγκαῖον τὸ σχῆμα τοῦτ' ἔχειν αὐτήν. Καὶ γὰρ δὴ οἱ περὶ τῆς κινήσεως καὶ τῆς μονῆς εἰρημένοι τρόποι πολλοὶ τυγχάνουσιν. 352 But they have another argument. They say that because it is at rest, the earth must necessarily have this shape. For there are many different ways in which the movement or rest of the earth has been conceived.
| Postquam philosophus posuit opiniones de situ terrae, hic ponit opiniones de motu et quiete ipsius. | 486. After presenting opinions about the position of the earth, the Philosopher here presents opinions about its motion and rest. |
| Et ponit duas opiniones: | He presents two opinions; |
| quarum secundam ponit ibi: quidam autem et positam et cetera. | The second of these is at 490. |
| Circa primum tria facit: | With respect to the first he does three things: |
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primo ponit positiones; secundo inducit quandam probationem ipsorum, ibi: propter quod et lunae etc.; tertio ostendit quomodo obviabant rationibus in contrarium inductis, ibi: quoniam enim non est terra et cetera. |
First he presents the theories; Secondly, he induces a certain proof thereof, at 488; Thirdly, he shows how they meet arguments brought against them, at 489. |
| Dicit ergo primo quod, sicut de loco terrae diversimode loquuntur philosophi, ita etiam de motu et quiete ipsius. Sed quicumque dicunt ipsam non esse positam in medio mundi, sicut Pythagorici, attribuunt ei motum circularem, quo movetur circa medium. Nec dicunt hanc solam terram moveri in qua nos habitamus, sed etiam quandam aliam, quam vocant antichthona, idest contrapositam huic terrae, sicut supra dictum est. Et hoc ponebant propter perfectionem denarii numeri; ut cum sint octo corpora caelestia circulariter mota, scilicet sphaera stellarum fixarum et septem planetae, impleatur denarius numerus, positis duabus terris circulariter motis. | 487. He says therefore first [345] that just as philosophers have spoken in various ways about the place of the earth, so also about its motion and rest. But those who say that it is not positioned in the middle of world, such as the Pythagoreans, assign to it a circular motion by which it is moved about the middle. Nor do they say that it is just this earth in which we live that is moved but also a certain other one which they called "antichtona," i.e., in counter-opposition to this earth, as has been said above. This they posited on account of the perfection of the number 10, in order that, since there are 8 heavenly bodies circularly moved, namely, the sphere of the fixed stars and the 7 planets, the number of 10 might be fulfilled by positioning two earths circularly moved. |
| Quidam autem Pythagoricorum sunt, qui non solum ponunt quod sint duae terrae circulariter motae, sed quod sint plura alia corpora terrea circa medium mota. Quae quidem sunt nobis immanifesta propter hoc, quod haec terra in qua habitamus, superponitur aliis, ita scilicet quod aliae sequantur motum ipsius: et ideo interpositio huius terrae inter visus nostros et illas, occultat eas a nobis. | Now there are some Pythagoreans who claim that there are not only two earths circularly moved, but also several other bodies of earth in motion about the middle. These indeed are imperceptible to us because this earth on which we live is superimposed on the others, in such a way that the others follow its motion. Consequently, the interposition of this earth between out vision and those earths hides them from us. |
| Deinde cum dicit: propter quod et lunae etc., inducit eius quod ultimo dictum est probationem, secundum eos. Manifestum est enim quod, sicut eclipsis solis contingit propter interpositionem lunae inter nos et solem, ita eclipsis lunae contingit propter interpositionem terrae inter solem et lunam. Pluries autem eclipsatur luna quam sol. Quod quidem dicebant accidere propter hoc, quod una sola luna est quae eclipsat solem, interposita inter nos et ipsum; lunam autem non solum eclipsat ista terra in qua nos habitamus, sed plures aliae. | 488. Then at [346] he presents their proof of what we have just stated. Now it is plain that just as an eclipse of the sun is due to the interposition of the moon between us and the sun, so the eclipse of the moon is due to the interposition of the earth between the sun and the moon. But the moon is eclipsed more often than the sun. This they said is due to the fact that there is but one solitary moon to eclipse the sun when interposited between us and it, but the moon is eclipsed not only by the earth on which we live but by several other earths. |
| Sed haec ratio eorum nulla est: quia nunquam invenitur luna eclipsari, nisi per interpositionem huius terrae inter lunam et solem, quando scilicet luna subintrat umbram huius terrae. Accidit autem pluries eclipsari lunam quam solem, quia eclipsis solis impeditur plerumque propter diversitatem aspectus. | But this argument of theirs is of no worth, because the moon is never found to be eclipsed except by the interposition of this earth between the moon and the sun, namely, when the moon enters the shadow of this earth. Eclipses of the moon occur more frequently than those of the sun, because a solar eclipse is very often impeded on account of the diversity of aspect. |
| Deinde cum dicit: quoniam enim non est terra etc., ostendit quomodo obviabant rationibus contra se inductis. Quarum tamen praecipua est quod, nisi terra esset in medio mundi, horizon, qui est superficies transiens per visum nostrum, non secaret semper sphaeram totam et maximos circulos eius in duo media, ita scilicet quod semper apparerent nobis sex signa super terram, et sex signa sub terra. | 489. Then at [347] he shows how they meet arguments leveled against them. The chief of these is that, unless the earth were in the middle of the world, the horizon which is a plane passing through our sight would not always cut the entire sphere and the greatest circles into two halves, in such a way, namely, that six signs [of the Zodiac] are always visible to us above the earth and six are under the earth. |
| Sed ad hoc ipsi respondebant quod tota terra non est centrum: quia centrum est indivisibile et punctuale, terra autem est corpus magnitudinem habens. | But their answer to this was that the whole earth is not a center, because a center is indivisible and a point, whereas the earth is a body possessing size. |
| Unde circulus noster, qui est in superficie terrae, distat per totum hemisphaerium terrae a centro: et tamen hoc non impedit quin omnia accidant nobis apparere, sicut si oculus noster esset in centro. Et hoc est propter parvitatem terrae, quae quasi nullius est quantitatis in comparatione ad totum caelum. Et similiter existimabant quod, si terra in qua nos habitamus non sit in medio, quod omnia apparentia accidant sicut si terra esset in medio mundi: quia etiam nunc non manifestatur distantia a medio quantum ad apparentiam, quamvis visus noster distet a medio mundi per totam medietatem terrae. | Hence, our circle which is on the surface of the earth is a full hemisphere's distance from the center — yet this does not prevent everything from appearing to us as though our eye were in the center. The reason for this is the smallness of the earth, which is as though nothing in size in comparison with the whole heaven. In like manner, they thought that if the earth on which we live is not in the middle, all things would appear to us as though the earth were in the middle of the universe, because even now the distance from the middle is not manifest as to appearance, although our sight is distant from the middle of the universe by half the earth. |
| Sed hoc intelligi posset si terra per modicum spatium distaret a medio: non autem si distaret per multum spatium. Sunt autem quaedam alia apparentia, quae non salvarentur si terra non esset in medio; puta quae accidunt circa eclipsim lunae, per directam oppositionem lunae ad solem. Nisi enim terra semper esset in medio, non semper sequeretur eclipsis lunae, quando est in oppositione existens in capite vel in cauda: et tamen in eclipsi lunae nihil operatur aspectus noster. | But this could be understood if the earth were a small distance from the middle but not if it were at a great distance therefrom. There are also certain other appearances which would not be saved if the earth were not in the middle —for example, what occurs in an eclipse of the moon, when there is direct opposition of the moon to the sun. For, unless the earth were always in the middle, an eclipse of the moon would not always occur when it is in opposition in the head or tail — yet our aspect counts for nothing in an eclipse of the moon. |
| Deinde cum dicit: quidam autem et positam etc., ponit secundam opinionem. Et dicit quod, licet quidam dicant terram in centro positam, dicunt tamen ipsam moveri et revolvi circa polum semper statutum, idest circa axem mundi (nam polus quandoque dicitur caelum, quandoque autem dicitur axis, quandoque vero dicitur extrema pars axis, sicut dicitur polus Arcticus et Antarcticus). Et hoc dicit scriptum esse in Timaeo. Est autem notandum quod illud quod hic dicitur revolvi vel converti, sumpsit Aristoteles ex eo quod Plato in Timaeo, secundum linguam Graecam dixit, illomenam circa eum qui per omne ordinatum polum. Hoc autem quod dicitur illomenum, si in Graeco scribatur per iota, significat alligationem; si vero scribatur per diphthongum, significat prohibitionem. Videtur autem a Platone sumptum istud vocabulum secundum quod significat alligationem, ut patet per ea quae ipse dicit de terra in libro Phaedonis, ubi asserit eam in medio quiescentem et quasi ligatam: et sic videtur contra intentionem Platonis, Aristoteles verba eius assumpsisse. | 490. Then at [348] he presents a second opinion. And he says that some, although they say that the earth is in the center, yet say it is moved and revolved "about the never-shifting pole," i.e., about the axis of the world (for sometimes the heaven is called the "pole," sometimes the axis is, and sometime the ends of the axis, as when we speak of the arctic and antarctic pole). And this opinion, he says, is found in the Timaeus. But it should be noted that Aristotle took what is here called "revolved" or "turned," from Plato's statement in the Timaeus: in Greek, "illomenum" about the pole in every way ordered Now if illomenum is written in Greek with an iota, it means a "binding," but if written with a diphthong, it means "a hindrance." Now this word seems to be taken by Plato as it means a "binding," as is plain from what he says about the earth in the Phaedo, where he asserts it to be at rest in the middle and, as it were, held fast. Consequently, Aristotle seems to have taken the words of Plato in a way not intended by him. |
| Dicit igitur Alexander, Aristotelem excusans, quod hoc quod dicitur illomenum, significat proprie prohibitionem vel violentiam: sed quia ista significatio non competit secundum ea quae ibi intendit Plato, Aristoteles intellexit quod illomenum translative acciperetur a Platone, prout consuevit translatum significare conversionem, quae designat motum. Nec pertinet aliquid ad rationem praesentem, si Plato alibi aliter dixit ab his quae dixerat in Phaedone, motus ex aliqua alia ratione: nam Aristoteles hic proponit id quod in Timaeo scribitur, sive hoc sit inductum tanquam Platoni placens, sive tanquam Timaei opinio, quam Plato non approbat: unde non dicit quemadmodum Plato dicit, sed quemadmodum in Timaeo scriptum est. | Therefore, Alexander, excusing Aristotle, says that illomenum, properly signifies "preventing" or "compulsion," but because that meaning does not fit what Plato intends to say here Aristotle understood him as taking it in the extended sense of meaning, as transferred, "turning," which denotes motion. Nor does it make any difference in the present argument whether Plato has said elsewhere something that differed from what he had said, in the Phaedo, for some other reason. For Aristotle is here proposing what is written in Timaeus; whether it be introduced as an opinion accepted by Plato, or as the opinion of Timaeus, which he does not approve. That is why he does not say "as Plato says," but "as is written in the Timaeus." |
| Sed contra hoc multipliciter obiicit Simplicius. Primo quidem quia Timaeus ibi probat terram in medio esse locatam et firmatam. Secundo quia illomenam ibi scribitur per unum iota, prout significat alligationem. Tertio quia conversio non semper significat motum: dicuntur enim circulares figurae conversae, idest ad omnem partem versae, etiam si sint quiescentes. Quarto quia, cum dictio multa significet, non oportuit significationem eius trahere ad manifestum sensum contra intentionem Platonis. | But Simplicius has a barrage of objections against this. First, because Timaeus there proves the earth is located and settled in the middle. Secondly, because there the word illomenum is written with an iota, and thus signifies a "holding fast." Thirdly, because a "turning" does not always imply motion — for circular figures are said to be "turned," i.e., facing [turned] in every direction, even if they are at rest. Fourthly, because, since this word has many meanings, one should not have bent its meaning to a sense plainlySed contra hoc iterum obiicit Simplicius: quia non est probabile quod Aristoteles ignoraret aut significationem vocabuli, aut intentionem Platonis. contrary to Plato's intention. |
| Sed contra hoc iterum obiicit Simplicius: quia non est probabile quod Aristoteles ignoraret aut significationem vocabuli, aut intentionem Platonis. Et ideo potest dici quod, quia possibile erat aliquos false intelligere verba Platonis, Aristoteles removet falsum intellectum qui ex his verbis haberi posset, sicut frequenter consuevit facere circa verba Platonis. | But, against this, Simplicius again objects that it is not probable that Aristotle was ignorant either of the meaning of the word or of Plato's intention. Consequently, it can be said that, because it was possible for some to falsely interpret Plato's words, Aristotle removes the false understanding that could be obtained from these words, as he frequently does with passages from Plato. |
| Vel potest dici quod hoc quod dicitur et moveri, est ab aliquo alio appositum. In Graeco autem dicitur illesthai, pro quo hic est translatum revolvi: potest autem significare quod in Graeco positum est, et alligationem et motum: ita quod intelligamus quod, postquam Aristoteles posuit opinionem Pythagoricorum de motu terrae circa medium, hic ponit opinionem Platonis de quiete terrae in medio. | Or it can be said that the phrase, "and to be moved," is an interpolation by another. In the Greek there is stated illesthai, which is here translated, "to be revolved." Now what is written in the Greek can signify both a "holding fast" and "motion," so that we can understand that after Aristotle presented the Pythagorean theory of the motion of the earth about the middle, he here presents Plato's theory about the earth being at rest in the middle. |
| Possumus autem et brevius dicere quod quidam Heraclitus Ponticus posuit terram in medio moveri, et caelum quiescere; cuius opinionem hic Aristoteles ponit. Quod autem addit, quemadmodum in Timaeo scriptum est, referendum est non ad id quod dictum est, revolvi et moveri, sed ad id quod sequitur, quod sit super statutum polum. | We can also say more briefly that one Heraclitus of Pontus posited the earth to be in motion in the center and the heaven to be at rest, and that it is his opinion that Aristotle is here introducing. The fact that he adds, "as stands written in the Timaeus," is to be referred, not to what was said, namely, "it is revolved and moved," but to what follows, namely, "that it is upon a fixed pole." |
| Deinde cum dicit: similiter autem et de figura etc., ponit opiniones de figura terrae. Et primo ponit opiniones, dicens quod similiter dubitatur de figura terrae, sicut de motu et situ: quibusdam enim videtur quod terra sit sphaerica; quibusdam autem videtur quod sit lata, habens figuram tympani. | 491. Then at [349] he gives the theories about the shape of the earth. And first he presents the theories, and states that there are likewise problems about the shape of the earth, as there are about its motion and position. For some think that it is spherical, others that it is wide and having the shape of a tambourine. |
| Secundo ibi: faciunt autem argumentum etc., ponit rationes duas huius secundae opinionis. Quarum prima est quod faciunt argumentum accipientes hoc signum, quod sol occidens et oriens secatur a terra secundum rectam lineam, et non circularem, quando scilicet pars solis est apparens super terram, pars autem occultatur: si autem terra esset sphaerica, videtur quod oporteret quod secatio illa esset circularis, quia duo corpora sphaerica se intersecant intersectione circulari. | 492. Secondly, he presents two reasons used to support this second theory. The first of these [350] is that they make an argument of the fact that as the sun rises and sets, it is cut by the earth according to a straight, and not a circular, line — namely, when part of the sun appears above the earth, and part is hidden. Now if the earth were spherical, the line of section would seem to have to be circular, because two spherical bodies intersect with a circular intersection. |
| Hoc autem argumentum excludit ibi: non attendentes et cetera. Et dicit quod illi qui ponunt hoc argumentum, non attendunt distantiam solis a terra, et magnitudinem rotunditatis, scilicet utriusque. Videmus enim quod etiam parvi circuli, a longe apparentes, videntur secundum modum lineae rectae: unde multo magis portiones magnorum circulorum a longe rectae videntur, quia sunt minus curvae. Sed hoc praecipue intelligendum est quando circulus est in eadem superficie cum visu: nam secatio solis et lunae quae non est in eadem superficie cum visu nostro, non videtur recta, sed circularis, ut supra dictum est, cum ageretur de figura stellarum. | But he excludes this argument at [3513, and says that those who present this argument do not consider the sun's distance from the earth and the greatness of the rotundity of each. For we sometimes see that even small circles, seem: from afar, appear after the manner of a straight line. There is all the more reason, therefore, for portions of large circles to appear straight from a distance, because they are less curved. However, this must be principally understood when the circle is in the same surface as our vision — for the intersection of the sun and moon, which is not in the same surface with our sight, is not seen as straight but as circular, as was said above when discussing the shape of the stars. |
| Secundam rationem ponit ibi: sed adhuc etc.; dicens quod adhuc addunt rationem ad idem, dicentes quod necesse est terram, ad hoc quod quiescat, habere figuram latam. Nam figura sphaerica facile mobilis est, quia in modico tangit superficiem: sed figura lata secundum se totam tangit superficiem, et ideo est apta ad quietem. | 493. He gives a second argument at [352] and says that they add a further argument for the same, namely, that if the earth is to be at rest, it has to be flat. For a spherical shape is easy to move, because so little of it is in contact with a plane; but a wide shape is totally in contact with a plane, and is consequently apt for rest. |
| Et ne credatur quod haec causa quietis terrae communiter ab omnibus assignetur, subiungit quod de motu et quiete terrae multi modi dicuntur, ut patebit ex his quae infra dicentur. | And lest anyone believe that this explanation of the earth's rest is generally assigned by everyone, he adds that there are many different ways in which the motion and rest of the earth has been conceived, as will be plain from what will be said below. |
Lecture 22:
The problem about the earth's restChapter 13 cont. Τὸ μὲν οὖν ἀπορῆσαι πᾶσιν ἀναγκαῖον ἐπελθεῖν τάχα γὰρ ἀλυποτέρας διανοίας τὸ μὴ θαυμάζειν πῶς ποτε μικρὸν μὲν μόριον τῆς γῆς, ἂν μετεωρισθὲν ἀφεθῇ, φέρεται καὶ μένειν οὐκ ἐθέλει, καὶ τὸ πλεῖον ἀεὶ θᾶττον, πᾶσαν δὲ τὴν γῆν εἴ τις ἀφείη μετεωρίσας, οὐκ ἂν φέροιτο. Νῦν δ' ἠρεμεῖ τοσοῦτον βάρος. Ἀλλὰ μὴν κἂν εἴ τις τῶν φερομένων μορίων αὐτῆς, πρὶν πεσεῖν, ὑφαιροίη τὴν γῆν, οἰσθήσεται κάτω μηθενὸς ἀντερείσαντος. Ὥστε τὸ μὲν ἀπορεῖν εἰκότως ἐγένετο φιλοσόφημα πᾶσιν 353 The difficulty must have occurred to every one. It would indeed be a complacent mind that felt no surprise that, while a little bit of earth, let loose in mid-air moves and will not stay still, and more there is of it the faster it moves, the whole earth, free in midair, should show no movement at all. Yet here is this great weight of earth, and it is at rest. And again, from beneath one of these moving fragments of earth, before it falls, take away the earth, and it will continue its downward movement with nothing to stop it. The difficulty then, has naturally passed into a common place of philosophy; τὸ δὲ τὰς περὶ τούτου λύσεις μὴ μᾶλλον ἀτόπους εἶναι δοκεῖν τῆς ἀπορίας, θαυμάσειεν ἄν τις. 354 and one may well wonder that the solutions offered are not seen to involve greater absurdities than the problem itself. Οἱ μὲν γὰρ διὰ ταῦτα ἄπειρον τὸ κάτω τῆς γῆς εἶναί φασιν, ἐπ' ἄπειρον αὐτὴν ἐρριζῶσθαι λέγοντες, ὥσπερ Ξενοφάνης ὁ Κολοφώνιος, ἵνα μὴ πράγματ' ἔχωσι ζητοῦντες τὴν αἰτίαν 355 By these considerations some have been led to assert that the earth below us is infinite, saying, with Xenophanes of Colophon, that it has 'pushed its roots to infinity',—in order to save the trouble of seeking for the cause. διὸ καὶ Ἐμπεδοκλῆς οὕτως ἐπέπληξεν, εἰπὼν ὡς εἴ περ ἀπείρονα γῆς τε βάθη καὶ δαψιλὸς αἰθήρ, ὡς διὰ πολλῶν δὴ γλώσσης ῥηθέντα ματαίως ἐκκέχυται στομάτων, ὀλίγον τοῦ παντὸς ἰδόντων. 356 Hence the sharp rebuke of Empedocles, in the words 'if the deeps of the earth are endless and endless the ample ether—such is the vain tale told by many a tongue, poured from the mouths of those who have seen but little of the whole. Οἱ δ' ἐφ' ὕδατος κεῖσθαι. Τοῦτον γὰρ ἀρχαιότατον παρειλήφαμεν τὸν λόγον, ὅν φασιν εἰπεῖν Θαλῆν τὸν Μιλήσιον, ὡς διὰ τὸ πλωτὴν εἶναι μένουσαν ὥσπερ ξύλον ἤ τι τοιοῦτον ἕτερον (καὶ γὰρ τούτων ἐπ' ἀέρος μὲν οὐθὲν πέφυκε μένειν, ἀλλ' ἐφ' ὕδατος), 357 Others say the earth rests upon water. This, indeed, is the oldest theory that has been preserved, and is attributed to Thales of Miletus. It was supposed to stay still because it floated like wood and other similar substances, which are so constituted as to rest upon but not upon air. ὥσπερ οὐ τὸν αὐτὸν λόγον ὄντα περὶ τῆς γῆς καὶ τοῦ ὕδατος τοῦ ὀχοῦντος τὴν γῆν οὐδὲ γὰρ τὸ ὕδωρ πέφυκε μένειν μετέωρον, ἀλλ' ἐπί τινός (294b.) ἐστιν. 358 As if the same account had not to be given of the water which carries the earth as of the earth itself! It is not the nature of water, any more than of earth, to stay in mid-air: it must have something to rest upon. Ἔτι δ' ὥσπερ ἀὴρ ὕδατος κουφότερον, καὶ γῆς ὕδωρ ὥστε πῶς οἷόν τε τὸ κουφότερον κατωτέρω κεῖσθαι τοῦ βαρυτέρου τὴν φύσιν; 359 Again, as air is lighter than water, so is water than earth: how then can they think that the naturally lighter substance lies below the heavier? Ἔτι δ' εἴπερ ὅλη πέφυκε μένειν ἐφ' ὕδατος, δῆλον ὅτι καὶ τῶν μορίων ἕκαστον νῦν δ' οὐ φαίνεται τοῦτο γιγνόμενον, ἀλλὰ τὸ τυχὸν μόριον φέρεται εἰς βυθόν, καὶ θᾶττον τὸ μεῖζον. 360 Again, if the earth as a whole is capable of floating upon water, that must obviously be the case with any part of it. But observation shows that this is not the case. Any piece of earth goes to the bottom, the quicker the larger it is. Ἀλλ' ἐοίκασι μέχρι τινὸς ζητεῖν, ἀλλ' οὐ μέχρι περ οὗ δυνατὸν τῆς ἀπορίας. Πᾶσι γὰρ ἡμῖν τοῦτο σύνηθες, μὴ πρὸς τὸ πρᾶγμα ποιεῖσθαι τὴν ζήτησιν ἀλλὰ πρὸς τὸν τἀναντία λέγοντα καὶ γὰρ αὐτὸς ἐν αὑτῷ ζητεῖ μέχρι περ ἂν οὗ μηκέτι ἔχῃ ἀντιλέγειν αὐτὸς αὑτῷ. Διὸ δεῖ τὸν μέλλοντα καλῶς ζητήσειν ἐνστατικὸν εἶναι διὰ τῶν οἰκείων ἐνστάσεων τῷ γένει, τοῦτο δ' ἐστὶν ἐκ τοῦ πάσας τεθεωρηκέναι τὰς διαφοράς. 361 These thinkers seem to push their inquiries some way into the problem, but not so far as they might. It is what we are all inclined to do, to direct our inquiry not by the matter itself, but by the views of our opponents: and even when interrogating oneself one pushes the inquiry only to the point at which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of all the differences.
| Postquam philosophus exclusit opiniones eorum qui falsas opiniones circa terram habebant, hic prosequitur opiniones eorum qui, veram opinionem circa terram habentes, scilicet quod ipsa quiesceret, inconvenientes rationes quietis terrae assignabant. | 494. After rejecting the opinions of those who held false theories about the earth, the Philosopher here pursues the opinions of those who, while holding a true theory about the earth, namely, that it is at rest, assigned unsuitable explanations for the earth's rest. |
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Et primo movet dubitationem; secundo proponit solutionum insufficientiam, quas alii assignabant, ibi: solutiones autem de hoc etc.; tertio prosequitur singulas solutiones, ibi: hi quidem enim propter hoc et cetera. |
First he poses the problem; Secondly, he points out where the solutions which others proposed are insufficient, at 496; Thirdly, he examines these solutions, each in turn, at 497. |
| Dicit ergo primo quod necessarium videtur quod omnibus superveniat quaedam dubitatio circa terram. Quia si quis de hoc non miretur, videtur irrationabilem mentem habere, quasi qui non possit difficultatem percipere: quomodo scilicet, si aliquando elevetur per violentiam aliqua parva terrae particula, et postea dimittatur, fertur deorsum et non vult manere, idest non habet aptitudinem naturalem ut quiescat; et quanto maior fuerit terrae particula, tanto velocius feretur inferius; videtur autem quod, si tota terra posset ab aliquo elevari a suo loco in sursum, et postea dimittatur, non ferretur inferius. Et hoc quidem videtur per hoc quod nunc accidit circa totam terram. Cum enim habeat intensam gravitatem, non movetur inferius, sed quiescit in suo loco: unde videtur quod, in quocumque situ mundi poneretur, quod ibi quiesceret, eadem ratione qua nunc in hoc loco quiescit. Et hoc quantum ad illos qui existimant omnem locum indifferenter se habere ad quodlibet corporum. | 495. He says therefore first [353] that it seems necessary that a certain problem about the earth should occur to everyone. For if someone did not wonder about this, he would seem to have an irrational mind, as though not being able to perceive the difficulty, namely, as to how it is that, if some small particle of earth be raised against its nature and then released, it is borne downward and "does not wish to remain," i.e., has no natural tendency to rest, and the larger the particle of earth is, so much the faster does it move downward. Yet it seems that if the whole earth could be raised by someone on high out of its place, and then let loose, it would not move down. This seems so from what presently happens in regard to the whole earth. For, while it does have great heaviness, it does not move downward but remains at rest in its place. Hence, it seems that no matter where in the world the earth might be set, it would rest there, for the same reason that it now rests in this place. This, indeed, is in keeping with the opinion of those who suppose that any place at random is suitable for just any body. |
| Et quia posset aliquis dicere quod partes terrae elevatae, cum dimittuntur, feruntur deorsum usque ad hunc locum in quo modo est terra, non autem amplius; ideo, ad dubitationem augendam, adiungit quod, si aliquis sursum ferat aliquas particulas terrae, et contingat quod antequam illae particulae terrae cadentes revertantur ad terram, aliquis removeat terram a suo loco; partes terrae sursum elevatae feruntur deorsum, idest magis infra quam sit locus unde fuerant assumptae, ex quo iam non est aliquid impediens. Et hoc potest aliquis coniicere de toto ex parte: si enim aliquis lapidem sursum proiiciat, et antequam cadat, foveam faciat in terra, descendet lapis ille quousque resistentiam inveniat. Et ita videtur quod, cum tota terra nullam resistentiam habeat ab aliquo impediente descensum ipsius, mirum esse quod non descendit. | But someone could say that the particles of earth, when lifted and then released, move down no farther than the place where earth now is. Therefore, in order to augment the difficulty, he adds that if someone were to raise some particles of earth, and it should happen that, before the falling particles returned to earth, someone should remove the earth from their place, then those clods would move "downward," i.e., farther downward than the place from which they were picked up, since nothing would now be there to stop them. Now we can guess about the whole from the part — for if someone should throw a stone upward and then, before it fell, dig a ditch in the earth, that stone would fall until it encountered an obstacle; and thus it seems strange that, since the earth as a whole has no resistance from anything impeding its descent, it does not move downward. |
| Concludit ergo quod hoc ipsum quod est stupere, idest vehementer admirari, circa hoc, omnibus philosophis factum est philosophema, idest philosophiae consideratio, vel philosophandi occasio; sicut in principio Metaphys. dicitur quod ex admirari incoeperunt homines philosophari. | He concludes therefore that the "stupor," i.e., the great wonder, evoked by this made it a "philosophema," i.e., a consideration of philosophy or occasion for philosophizing for all philosophers — just as in the beginning of the. Metaphysics it is said that it is from wonder that men began to philosophize. |
| Deinde cum dicit: solutiones autem de hoc etc., proponit insufficientiam solutionum a philosophis circa hoc assignatarum. Et dicit quod non solum aliquis admiratur de hoc quod sic accidit circa terram; sed etiam aliquis potest admirari quod philosophi, volentes solvere praedictam dubitationem, non viderunt quod solutiones de hac dubitatione assignatae ab eis, sunt magis inconvenientes quam sit ipsa dubitatio. Improbabiliora enim dixerunt eo ex quo dubitatio consurgit: unde ipsae solutiones magis augent dubitationem. | 496. Then at [354] he presents the inadequacy of the solutions proposed on this point by the philosophers. And he says that one can wonder, not only at the way things happen thus with regard to the earth, but also why philosophers trying to solve this problem have not seen that their solutions given to this problem are more at odds than the problem itself. For they have given forth theories more improbable than the situation which gives rise to the problem — hence those solutions only increase the problem. |
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Deinde cum dicit: hi quidem enim propter hoc etc., ponit quinque solutiones praedictae dubitationis. Secunda incipit ibi: hi autem in aqua etc.; tertia ibi: Anaximenes autem etc.; quarta ibi: quoniam autem manet etc.; quinta ibi: sunt autem quidam et cetera. |
497. Then at [355] he presents five solutions of the aforesaid problem:
The second one begins at 499; The third at Lecture 23; The fourth at Lecture 24; The fifth at Lecture 25. |
| Circa primum duo facit. | With respect to the first he does two things: |
| Primo proponit solutionem primam. Et dicit quod quidam propter hoc, ut scilicet evitarent difficultatem praedictam, dicunt quod deorsum terrae est infinitum. Quod quidem potest intelligi dupliciter. Uno modo sic, quod aer qui est infra terram, sit infinitus; quasi terra ob hoc non moveatur inferius, quia nihil movetur ad infinitum. Alio modo, et verius, intelligitur quod ipsa terra versus partem inferiorem sit infinita; et ita in infinitum superior pars eius retinetur ab inferiori, ut non descendat; quod promptius est ad intelligendum. Huius autem opinionis dicitur fuisse Xenophanes Colophonius. Quod quidem dixerunt, non quidem quia secundum se verisimile videatur, sed ut non cogerentur laborare ad inquirendam causam quietis terrae. |
First he presents the first solution [355]. And he says that some, for the sake of this, i.e., in order to evade the problem, assert that the earth's downward direction is infinite. Now this can be understood in two ways: In one way, that the air below the earth is infinite, implying that the reason why the earth is moved no farther down is because nothing is moved to an infinite goal. In the other and truer interpretation, it is taken to mean that the earth itself is infinite on its nether side, and thus the upper part is sustained by a lower part extending to infinity. This is more quickly understood and is said to have been the theory of Xenophanes of Colophon. They put this forth, not because it seemed more plausible in itself, but in order to save the trouble of laboring to find the cause of the earth's rest. |
| Secundo ibi: propter quod et Empedocles etc., ponit quomodo Empedocles hanc solutionem derisit. Et dicit quod, quia praedicti homines hoc non dicebant quasi aliquid verisimile, sed ut quaestionem vitarent, Empedocles obstupuit, idest vehementer admiratus est de eorum errore, sic dicens in suis versibus, quos de philosophia composuit: siquidem, inquit, infinitae sunt terrae profunditates (quasi diceret: terra est in infinitum profunda), et aether, idest aer vel ignis, est etiam immensus in altum. Et dixit quod haec vane, idest sine ratione, effusa sunt, idest divulgata, cum sint dicta per linguam multorum (quasi diceret: ex ore multorum hominum), intelligentium modicum totius, idest modicum intelligentium de natura universi. Per quod dedit intelligere quod ex defectu intellectus provenit quod hoc aliqui dixerunt solo ore, cum interius consideratum non sit verisimile. | 498. Secondly, he tells how Empedocles derided this solution. And he says that, since the aforesaid men did not assert this as though plausible but in order to sidestep the question, Empedocles was "stupefied," i.e., greatly astonished at their error, speaking as follows in the verses he composed oh philosophy: "Are indeed the deeps of the earth endless" (as though to say: Is the earth infinitely deep?) "and endless too the ether?" i.e., air or fire And he says that these opinions have been "vainly poured out," i.e., asserted without reason, "since they have been told by many a tongue" (as if to say: from the mouths of many men) "who understood but little of the whole," i.e., understanding but little about the nature of the universe. In these words, h= gives us to understand that it is from a lack of intelligence that some said this with their mouths alone, while, as interiorly considered, it is not plausible. |
| Fuit autem contentus Aristoteles de hac Empedoclis reprehensione, tum propter improbabilitatem eius quod dicitur, tum etiam quia supra in primo ostensum est quod non potest esse gravitas infinita. | Now Aristotle contented himself with this rebuke by Empedocles, both on account of the improbability of what is said and because it has been previously shown in Book I that there cannot be infinite weight. |
| Deinde cum dicit: hi autem in aqua etc., prosequitur secundam solutionem. | 499. Then at [357] he takes up the second solution. |
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Et primo proponit eam; secundo improbat, ibi: tanquam non eadem etc.; tertio assignat rationem defectus huiusmodi solutionum, ibi: sed videntur et cetera. |
First he proposes it; Secondly, he refutes it, at 500; Thirdly, he underscores the reason for the defects in solutions of this kind, at 503. |
| Dicit ergo primo quod, sicut praedicti posuerunt terram sustentari a terra in infinitum, ita quidam dixerunt terram poni super aquam. Quae quidem est antiquissima opinio, quam, ut dicunt, Thales Milesius posuit, qui fuit unus de septem qui dicti sunt sapientes, et primus se intromisit de philosophia naturali, et posuit aquam esse principium omnium rerum, ut dicitur in I Metaphys. Unde et posuit terram esse locatam super aquam, ut quiescat ibi per modum supernatationis, sicut accidit de ligno et de similibus; quorum nihil naturaliter manet in aere, sed in aqua manent huiusmodi propter supernatationem. Et simile dicebant accidere de terra. | He says therefore first [357] that just as the aforesaid philosophers posited the earth to be held up by earth ad infinitum, so others declared the earth to be set on water. This indeed is the oldest theory, proposed, they say, by Thales of Miletus, who was one of the seven called "Wise Men," and the first to interest himself in natural philosophy. It was he who posited water as the principle of all things, as is said in Metaphysics I. Hence he posited the earth to be set upon water and to rest there in the manner of flotation, as occurs with wood and other similar substances, none of which naturally remains. in air, but they do remain in water in this wise because of floating. And the same thing happens with the earth, they claimed. |
| Deinde cum dicit: tanquam non eadem etc., improbat quod dictum est, tribus rationibus. Et dicit quod sic assignata est praedicta solutio, tanquam non sit eadem ratio de terra, et aqua quam ponunt sustentare terram. Videmus enim quod sicut terra, si elevetur, non manet nisi sustentetur ab aliquo, ita nec aqua elevata nata est manere, sed oportet quod sit in aliquo sustentante, ad hoc quod quiescat. Et ideo si terra sustentaretur ab aqua, remaneret eadem difficultas, a quo sustentaretur aqua. | 500. Then at [358] he refutes what has been said with three arguments. And he says that the previous solution was proposed as though the same account had not to be given of the water which sustains the earth as of the earth itself. For we see that just as earth, if raised up, does not remain unless it is supported by something, so neither is water, when raised, apt to remain so, but it must be in something supporting it, if it is to remain at rest. Therefore, if earth were sustained by water, the same problem would remain — by what is the water supported? |
| Secundam rationem ponit ibi: adhuc autem quemadmodum et cetera. Et dicit quod sicut aer est levior quam aqua, ita et aqua est levior quam terra, vel minus gravis. Est autem de ratione levioris, quod superemineat graviori secundum naturam. Non est ergo possibile quod aqua, quae est levior, ponatur magis deorsum quam terra, quae est gravior, secundum naturam; nisi forte quis dicat quod partes mundi non sunt ordinatae secundum naturam, quod est inconveniens. | 501. He gives the second argument at [359], namely, that just as air is lighter than water, so water is lighter than earth, or less heavy. Now it is the nature of something lighter to rise above that which is heavier by nature. Therefore, it is not possible for water, which is lighter, to be placed lower than earth, which is heavier, according to nature — unless someone should say that the parts of the world are not ordered according to nature, which is unacceptable. |
| Tertiam rationem ponit ibi: adhuc autem si quidem etc.; quae ratio talis est. Sicut in primo habitum est, idem est motus naturalis, et etiam quies est eadem, totius terrae et partis eius. Si ergo tota terra nata est manere in aqua, supernatando ipsi, manifeste sequitur quod quaelibet particularum eius possit manere in aqua per supernatationem. Sed hoc non videmus accidere: quinimmo quaelibet pars terrae posita in aqua fertur ad fundum ipsius; et tanto velocius, quanto fuerit maior. Ergo multo velocius tota terra fertur inferius, si sit superposita aquae. | 502. The third reason at [360] is this: As was had in Book I, natural motion, and the rest as well, of the entire earth and of a clod is the same. If, therefore, the whole earth is apt to remain in water and float on it, it plainly follows that any particle of it could remain afloat on the water. But this is not what we see happening; rather, any particle of earth placed in water sinks to the bottom, the quicker the larger it is. Therefore, much more quickly would the whole earth sink, if it were set upon water. |
| Deinde cum dicit: sed videntur etc., assignat causam defectus dictarum solutionum. Et dicit hoc accidisse, quod tam defectivas solutiones assignaverunt, quia videntur quaerere circa dubitationes usque ad aliquem terminum, et non quousque possibile sit dubitari. Oportet autem eum qui vult recte solvere, ut perducat solutionem usque ad id ubi non sit amplius dubitatio; quod isti non faciunt. | 503. Then at [361] he indicates the reason why these arguments are deficient. And he says that the reason why they give such defective solutions is that they seem to investigate a problem up to a certain point but not as far as it is possible to inquire. But anyone who desires to solve problems properly must push his solution to the point where no doubts remain. This is something they failed to do. |
| Cuius rationem assignat, connumerans se aliis, causa vitandae iactantiae; dicens quod omnibus nobis dubitationes solventibus hoc videtur esse consuetum, ut inquisitio fiat non ad rem, sed ad contraria dicentem, idest non quousque natura rei requirit, sed quousque adversarius non habeat ulterius contradictionem: quia etiam hoc quilibet observat ad seipsum, ut cum ipse dubitat de aliquo, quaerat in seipso quousque ipse non habeat in promptu unde sibi contradicat. Sed illud non sufficit: quia cum aliquis vult veram solutionem invenire, oportet quod non sit contentus obiectionibus quas habet in promptu, sed diligenter inquirat eas. Et propter hoc, sicut ipse subdit, oportet eum qui vult bene inquirere veritatem, esse promptum ad hoc quod instet et sibi ipsi et aliis; non per instantias sophisticas, sed per instantias reales et rationabiles, proprias, idest convenientes, generi de quo inquiritur. Et hoc quidem contingit ex hoc quod homo considerat omnes differentias rerum, ex quarum similitudine quaestio solvitur. Sicut Thales solvit quaestionem praesentem ex similitudine ligni ad terram: fuisset autem ei consideranda differentia utriusque: nam lignum, quia multum habet de aere, supernatat aquae; quod terrae non congruit. | He assigns the reason for this, and counts himself in with the others, to avoid being boastful, and says that it seems to be the practice of all of us when resolving problems to investigate, "not in terms of the thing, but in terms of the one contradicting," i.e., not as far as the nature of the matter requires but until an adversary offers no further contradiction. A man even does this with himself — when wondering about something he interrogates himself until he can no longer find to hand anything to contradict his view. But this is not enough. When someone wants to find a true solution, he must not be content merely with answering the objections he has to hand, but must diligently seek them out. Wherefore, as he says, anyone who wishes to be a good inquirer after truth must be ready to object against himself and others, not with sophistries but with real and reasonable objections proper to, i.e., befitting the genus under investigation. This arises when a man considers all the differences of the things from whose similarities a problem is solved. For example, Thales solved the present question on the basis of wood's similarity to water, but he should have considered the difference between them as well, For wood, because it contains much air, floats on water, which is not true of earth. |
Lecture 23:
The cause of the earth's rest is not supporting airChapter 13 cont. Ἀναξιμένης δὲ καὶ Ἀναξαγόρας καὶ Δημόκριτος τὸ πλάτος αἴτιον εἶναί φασι τοῦ μένειν αὐτήν. Οὐ γὰρ τέμνειν ἀλλ' ἐπιπωμάζειν τὸν ἀέρα τὸν κάτωθεν, ὅπερ φαίνεται τὰ πλάτος ἔχοντα τῶν σωμάτων ποιεῖν ταῦτα γὰρ καὶ πρὸς τοὺς ἀνέμους ἔχει δυσκινήτως διὰ τὴν ἀντέρεισιν. Ταὐτὸ δὴ τοῦτο ποιεῖν τῷ πλάτει φασὶ τὴν γῆν πρὸς τὸν ὑποκείμενον ἀέρα, (τὸν δ' οὐκ ἔχοντα μεταστῆναι τόπον ἱκανὸν ἀθρόως [τῷ] κάτωθεν ἠρεμεῖν,) ὥσπερ τὸ ἐν ταῖς κλεψύδραις ὕδωρ. Ὅτι δὲ δύναται πολὺ βάρος φέρειν ἀπολαμβανόμενος καὶ μένων ὁ ἀήρ, τεκμήρια πολλὰ λέγουσιν. 362 Anaximenes and Anaxagoras and Democritus give the flatness of the earth as the cause of its staying still. Thus, they say, it does not cut, but covers like a lid, the air beneath it. This seems to be the way of flat-shaped bodies: for even the wind can scarcely move them because of their power of resistance. The same immobility, they say, is produced by the flatness of the surface which the earth presents to the air which underlies it; while the air, not having room enough to change its place because it is underneath the earth, stays there in a mass, like the water in the case of the water-clock. And they adduce an amount of evidence to prove that air, when cut off and at rest, can bear a considerable weight. Πρῶτον μὲν οὖν εἰ μὴ πλατὺ τὸ σχῆμα τῆς γῆς ἐστι, διὰ τοῦτο μὲν οὐκ ἂν ἠρεμοῖ. 363 Now, first, if the shape of the earth is not flat, its flatness cannot be the cause of its immobility. Καίτοι τῆς μονῆς οὐ τὸ πλάτος αἴτιον ἐξ ὧν λέγουσιν, ἀλλὰ τὸ μέγεθος μᾶλλον διὰ γὰρ τὴν στενοχωρίαν οὐκ ἔχων τὴν πάροδον ὁ ἀὴρ μένει διὰ τὸ πλῆθος πολὺς δ' ἐστὶ διὰ τὸ ὑπὸ μεγέθους πολλοῦ ἐναπολαμβάνεσθαι τοῦ τῆς γῆς. Ὥστε τοῦτο μὲν ὑπάρξει, κἂν σφαιροειδὴς μὲν ᾖ, τηλικαύτη δὲ τὸ μέγεθος μενεῖ γὰρ κατὰ τὸν ἐκείνων λόγον. 364 But in their own account it is rather the size of the earth than its flatness that causes it to remain at rest. For the reason why the air is so closely confined that it cannot find a passage, and therefore stays where it is, is its great amount: and this amount great because the body which isolates it, the earth, is very large. This result, then, will follow, even if the earth is spherical, so long as it retains its size. So far as their arguments go, the earth will still be at rest. Ὅλως δὲ πρὸς τοὺς οὕτω λέγοντας περὶ τῆς κινήσεως οὐ περὶ μορίων ἐστὶν ἡ ἀμφισβήτησις, ἀλλὰ περὶ ὅλου τινὸς καὶ παντός. Ἐξ ἀρχῆς γὰρ διοριστέον πότερόν ἐστί τις τοῖς σώμασι φύσει κίνησις ἢ οὐδεμία, καὶ πότερον φύσει μὲν οὐκ ἔστι, βίᾳ δ' ἔστιν. Ἐπεὶ δὲ (295a.) περὶ τούτων διώρισται πρότερον ὅσα κατὰ τὴν παροῦσαν δύναμιν εἴχομεν, χρηστέον ὡς ὑπάρχουσιν. Εἰ γὰρ μηδεμία φύσει κίνησίς ἐστιν αὐτῶν, οὐδὲ βίαιος ἔσται εἰ δὲ μή ἐστι μήτε φύσει μήτε βίᾳ, ὅλως οὐδὲν κινηθήσεται περὶ γὰρ τούτων ὅτι ἀναγκαῖον συμβαίνειν, διώρισται πρότερον, καὶ πρὸς τούτοις ὅτι οὐδ' ἠρεμεῖν ἐνδέχεται ὥσπερ γὰρ κίνησις ὑπάρχει ἢ βίᾳ ἢ φύσει, οὕτω καὶ ἠρεμία. Ἀλλὰ μὴν εἴ γέ ἐστι κίνησίς τις κατὰ φύσιν, οὐκ ἂν ἡ βίαιος εἴη φορὰ μόνον οὐδ' ἠρέμησις ὥστ' εἰ βίᾳ νῦν ἡ γῆ μένει, καὶ συνῆλθεν ἐπὶ τὸ μέσον φερομένη διὰ τὴν δίνησιν ταύτην γὰρ τὴν αἰτίαν πάντες λέγουσιν ἐκ τῶν ἐν τοῖς ὑγροῖς καὶ περὶ τὸν ἀέρα συμβαινόντων ἐν τούτοις γὰρ ἀεὶ φέρεται τὰ μείζω καὶ βαρύτερα πρὸς τὸ μέσον τῆς δίνης. Διὸ δὴ τὴν γῆν πάντες ὅσοι τὸν οὐρανὸν γεννῶσιν, ἐπὶ τὸ μέσον συνελθεῖν φασίν 365 In general, our quarrel with those who speak of movement in this way cannot be confined to the parts; it concerns the whole universe. One must decide at the outset whether bodies have a natural movement or not, whether there is no natural but only constrained movement. Seeing, however, that we have already decided this matter to the best of our ability, we are entitled to treat our results as representing fact. Bodies, we say, which have no natural movement, have no constrained movement; and where there is no natural and no constrained movement there will be no movement at all. This is a conclusion, the necessity of which we have already decided, and we have seen further that rest also will be inconceivable, since rest, like movement, is either natural or constrained. But if there is any natural movement, constraint will not be the sole principle of motion or of rest. If, then, it is by constraint that the earth now keeps its place, the so-called 'whirling' movement by which its parts came together at the centre was also constrained. (The form of causation supposed they all borrow from observations of liquids and of air, in which the larger and heavier bodies always move to the centre of the whirl. This is thought by all those who try to generate the heavens to explain why the earth came together at the centre.
| Praemissis duabus solutionibus, quarum prima assignabat causam quietis terrae ex infinitate eius quod in terra subsidet, secunda vero ex aqua subsidente terrae, hic ponit tertiam solutionem, quae assignatur a parte aeris subsidentis terrae. | 504. Having presented two solutions, the first of which derived the cause of the earth's rest from the infinitude of the nether part of the earth, while the second derived it from water being under the earth, he here gives a third solution in which the cause is ascribed to air supporting the earth. |
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[1314] In De caelo, lib. 2 l. 23 n. 1 Et primo ponit solutionem; secundo improbat eam, ibi: primum quidem et cetera. |
First he presents the solution; Secondly, he refutes it, at 505. |
| Dicit ergo primo quod Anaximenes et Anaxagoras et Democritus posuerunt causam quietis terrae esse latitudinem eius; ex qua contingit quod terra non dividit inferiorem aerem, sed superequitat ipsum. | He says therefore first that Anaximenes and Anaxagoras and Democritus gave the broadness of the earth as the cause of its state of rest. That is why it happens that the earth does not cut the air beneath it, but rides upon it. |
| Quod quidem videntur facere corpora artificialiter facta cum aliqua latitudine ad obviandum aeri sive vento: huiusmodi enim corpora lata non de facili videntur moveri a ventis, propter hoc quod resistunt eis secundum totam ipsorum latitudinem. Et hoc ipsum videtur facere terra, propter sui latitudinem, per comparationem ad aerem sub ea existentem; quia videlicet non dividit ipsum, sed resistendo comprimit eum. Et cum aer non habeat locum quo transferatur ne sit sub terra, propter terrae latitudinem, sufficiens est quiescere terram propter multitudinem aeris deorsum existentis et compressi; sicut patet de aqua in clepsydris. Si enim sit aliquod vas habens in sui summitate parvum foramen obturatum, et in lateribus aliud non obturatum, et subito submergatur in aquam, aer interior conclusus, quia non habet quo diffugiat, prohibebit aquam intrare. Et similiter aer subsidens terrae, compressus ab ea et non potens diffugere, non permittit eam descendere. | Now this is indeed what seems to be done by bodies purposely made wide in order to resist air and wind: for such very wide bodies do not seem to be easily moved by winds because they resist them along their entire width. This, too, the earth, because of its width, seems to do with respect to the air under it, i.e., instead of cleaving it, the earth resists and compresses it. And, since the air has no place to move in order not to be under the earth, because of the earth's width, the vast amount of pressed air under the earth is sufficient to uphold it, like the water in the case of the water-clock. For if a vessel with a small opening in the top, which is stopped up, and in the side another such opening not so stopped up, be suddenly submerged in water, the air imprisoned within, having no place to escape to, will keep water from entering. Similarly, the air residing under the earth, being pressed down by it and unable to escape, prevents the earth from falling. |
| Inducunt autem multa argumenta, idest sensibilia signa, ad ostendendum quod aer conclusus et quiescens, idest qui non potest ex aliqua parte effugere, sustinet magnam gravitatem: et hoc maxime fit evidens ex utribus inflatis, qui possunt magnum pondus sustinere. | And they adduce many "arguments," i.e., sensible signs, to show that air imprisoned and at rest, i.e., which cannot escape in any direction, sustains a great heaviness. And this is particularly true of inflated skins, which can support a great weight. |
| Deinde cum dicit: primum quidem etc., improbat praedictam solutionem tribus rationibus. Quarum prima est quia supponit haec solutio terram esse latae figurae; quod est falsum, ut infra patebit. Unde si figura terrae non est lata, sed sphaerica, sequetur quod non quiescet propter latitudinem, sicut isti dicebant. | 505. Then at [363] he refutes this solution with three arguments. The first of these is that this solution assumes the earth to be broad. But as we shall see later, this is false. Hence, if the earth is not broad but spherical, it will follow that its width will not account for its state of rest, as they alleged. |
| Secundam rationem ponit ibi: quamvis mansionis et cetera. Et dicit quod, licet ipsi assignarent latitudinem terrae causam quietis eius, tamen secundum ea ex quibus procedunt, non videtur causa mansionis terrae latitudo, sed magis magnitudo ipsius. Dicunt enim quod aer, non habens quo transeat, propter hoc quod coarctatur a terra, manet propter sui multitudinem; et propter hoc sustinet terram. Quod autem multus aer coarctetur a terra, contingit propter hoc quod aer comprehenditur a multa magnitudine terrae. Unde videtur quod eadem ratio esset, si terra ponatur esse sphaericae figurae, et tantae magnitudinis quod possit tantundem de aere coarctare: quia sic etiam manebit et aer et terra, secundum rationem quam assignant. | 506. He gives the second argument at [364]. And he says that although they assign the earth's width as the cause of its rest, yet, according to that from which _they proceed, it seems that it is the earth's size rather than its width that causes it to rest. For they say that the air, having no place to go because it is prevented by the earth, remains because there is so much of it, and because of this holds up the earth. But the reason why a vast amount of air is kept in confinement by the earth is that it is compressed by the enormous magnitude of the earth. Hence it seems that the same argument would hold if the earth were assumed to be spherical and of such a great size that it could confine the same amount of air — for then, too, the air and the earth would remain, according to the reason they give. |
| Tertiam rationem ponit ibi: totaliter autem et cetera. Et dicit quod contra eos qui sic loquuntur de motu et quiete corporum naturalium, consurgit dubitatio non de parte, idest non de aliquo particulari corpore, puta terra vel aqua, sed de toto universo et de omni corpore naturali. Hoc enim videtur a principio in talibus dubitationibus determinandum, utrum corpora habeant aliquem motum naturalem vel nullum; et utrum, si non habent motum naturalem, possint habere motum violentum. Et quia de his determinatum est prius, scilicet in primo libro, oportet ut nunc utamur tanquam existentibus, idest veris, omnibus his quae supra habuimus probata, secundum virtutem quae tunc aderat nostro ingenio. | 507. He gives the third argument at [365] and he says that against those who thus speak about the motion and rest of natural bodies there arises a doubt not "about the part," i.e., concerning any particular body, such as earth or water, but concerning the entire universe and every natural body. For the first thing that seems to have to be determined in such problems is whether bodies have some natural motion, or none, and whether, if they do not have a natural motion, they can have violent [compulsory] motion. And because this question has already been determined, namely, in Book I, we must now use as "in existence," i.e., as true, all that we have previously established on this point according to the power that was then present in our talent. |
| Supra enim ostensum est quod, si nullus est motus naturalis corporum, neque etiam erit aliquis motus violentus eorum: quia violentum est quasi excisio quaedam eius quod est secundum naturam, ut supra habitum est. Si autem non est aliquis motus corporum neque per naturam neque per violentiam, sequitur quod totaliter nihil moveatur: et quod hoc necessarium sit accidere, supra determinatum est. Et ad hoc etiam addendum est, secundum prius determinata, quod pari ratione non contingit aliquid quiescere: sicut enim est aliquis motus naturalis et violentus, ita est etiam aliqua quies naturalis et violenta. Et si est aliquis motus naturalis, non erit solum motus violentus, neque sola quies violenta: quia in loco ad quem aliquid movetur naturaliter, etiam quiescit naturaliter. | For it has been shown above that, if there is no natural motion of bodies, neither can there be any compulsory motion thereof, because the compulsory is, as it were, a departure from that which is according to nature, as has been had above. But if there is neither a natural nor a compulsory motion of bodies, it follows that nothing is in motion at all — that this is so has been previously determined. To this must be added, according to what has been previously determined, that for the same reason nothing can be at rest — for just as there is motion which is natural and compulsory, so too, rest which is natural and compulsory. But if natural motion does exist, then there will not be compulsory motion alone nor compulsory rest alone — because, into whatever place a thing is moved naturally, there it also rests naturally. |
| His ergo praemissis quasi principiis, argumentatur ad propositum, concludens ex praemissis quod, si quies terrae in medio non est naturalis sed violenta, sequitur quod motus eius ad medium non sit naturalis, sed propter violentiam circumgyrationis caeli. Omnes enim qui terram dicunt per violentiam quiescere in medio, assignant hanc causam motus terrae ad medium, idest circumgyrationem caeli; considerantes ex his quae accidunt in liquidis et etiam in aere, in quibus propter gyrationem ea quae sunt maiora et graviora congregantur ad medium, quasi violentius repulsa ex violentia gyrationis. Unde omnes qui ponunt mundum per generationem incoepisse, dicunt quod terra venit ad medium propter praedictam causam, idest propter violentiam circumgyrationis caeli. Et sic auferunt terrae quietem naturalem et motum naturalem. Quod est inconveniens: quia sequitur, secundum praedicta, quod totaliter corpora naturalia nec moveantur nec quiescant. | Having prefaced these points as principles, he argues to his proposition and concludes from these premises that, if the earth's rest in the middle is not natural but compulsory, it follows that its motion to the middle is not natural. but is due to compulsion exercised by the circumgyration of the heaven. For all who maintain that the earth rests in the middle through compulsion assign this cause of the motion of the earth to the middle, namely, the circumgyration of the heaven, basing themselves on the consideration of what happens in the case of liquids, and also of air, namely, that the larger and heavier masses are gathered in the middle as though more violently repelled by the violence of the gyration. Hence all who posit a world that began by generation say that the earth came to the middle for the reason stated, i.e., on account of the compulsion induced by the heaven's circumgyration. They thus take from the earth both natural rest and natural motion. But this is unacceptable, because it follows, according to what has been said, that in their entirety natural bodies are neither in motion nor at rest. |
Lecture 24:
Earth's rest not from gyration of the heavenChapter 13 cont. ὅτι δὲ μένει, ζητοῦσι τὴν αἰτίαν, καὶ λέγουσιν οἱ μὲν τοῦτον τὸν τρόπον, ὅτι τὸ πλάτος καὶ τὸ μέγεθος αὐτῆς αἴτιον, οἱ δ' ὥσπερ Ἐμπεδοκλῆς, τὴν τοῦ οὐρανοῦ φορὰν κύκλῳ περιθέουσαν καὶ θᾶττον φερομένην ἢ τὴν τῆς γῆς φορὰν κωλύειν, καθάπερ τὸ ἐν τοῖς κυάθοις ὕδωρ καὶ γὰρ τοῦτο κύκλῳ τοῦ κυάθου φερομένου πολλάκις κάτω τοῦ χαλκοῦ γινόμενον ὅμως οὐ φέρεται κάτω, πεφυκὸς φέρεσθαι, διὰ τὴν αὐτὴν αἰτίαν. 366 They then seek a reason for its staying there; and some say, in the manner explained, that the reason is its size and flatness, others, with Empedocles, that the motion of the heavens, moving about it at a higher speed, prevents movement of the earth, as the water in a cup, when the cup is given a circular motion, though it is often underneath the bronze, is for this same reason prevented from moving with the downward movement which is natural to it.) Καίτοι μήτε τῆς δίνης κωλυούσης μήτε τοῦ πλάτους, ἀλλ' ὑπείκοντος τοῦ ἀέρος, ποῖ ποτ' οἰσθήσεται; Πρὸς μὲν γὰρ τὸ μέσον βίᾳ, καὶ μένει βίᾳ κατὰ φύσιν δέ γε ἀναγκαῖον εἶναί τινα αὐτῆς φοράν. Αὕτη οὖν πότερον ἄνω ἢ κάτω, ἢ ποῦ ἐστιν; Εἶναι μὲν γάρ τινα ἀναγκαῖον εἰ δὲ μηδὲν μᾶλλον κάτω ἢ ἄνω, ὁ δ' ἄνω ἀὴρ μὴ κωλύει τὴν ἄνω φοράν, οὐδ' ἂν ὁ ὑπὸ τῇ γῇ κωλύοι τὴν κάτω τὰ γὰρ αὐτὰ τῶν αὐτῶν ἀναγκαῖον εἶναι αἴτια τοῖς αὐτοῖς. 367 But suppose both the 'whirl' and its flatness (the air beneath being withdrawn) cease to prevent the earth's motion, where will the earth move to then? Its movement to the centre was constrained, and its rest at the centre is due to constraint; but there must be some motion which is natural to it. Will this be upward motion or downward or what? It must have some motion; and if upward and downward motion are alike to it, and the air above the earth does not prevent upward movement, then no more could air below it prevent downward movement. For the same cause must necessarily have the same effect on the same thing. Ἔτι δὲ πρὸς Ἐμπεδοκλέα κἂν ἐκεῖνό τις εἴπειεν. Ὅτε γὰρ τὰ στοιχεῖα διειστήκει χωρὶς ὑπὸ τοῦ νείκους, τίς αἰτία τῇ γῇ τῆς μονῆς ἦν; Οὐ γὰρ δὴ καὶ τότε αἰτιάσεται τὴν δίνην. 368 Further, against Empedocles there is another point which might be made. When the elements were separated off by Hate, what caused the earth to keep its place? Surely the 'whirl' cannot have been then also the cause. Ἄτοπον δὲ καὶ τὸ μὴ συννοεῖν ὅτι πρότερον μὲν διὰ τὴν δίνησιν ἐφέρετο τὰ μόρια τῆς γῆς πρὸς τὸ μέσον νῦν δὲ διὰ τίν' αἰτίαν πάντα τὰ βάρος ἔχοντα φέρεται πρὸς αὐτήν; Οὐ γὰρ ἥ γε δίνη (295b.) πλησιάζει πρὸς ἡμᾶς. 369 It is absurd too not to perceive that, while the whirling movement may have been responsible for the original coming together of the art of earth at the centre, the question remains, why now do all heavy bodies move to the earth. For the whirl surely does not come near us. Ἔτι δὲ καὶ τὸ πῦρ ἄνω φέρεται διὰ τίν' αἰτίαν; Οὐ γὰρ διά γε τὴν δίνην. Εἰ δὲ τοῦτο φέρεσθαί που πέφυκεν, δῆλον ὅτι καὶ τὴν γῆν οἰητέον. 370 Why, again, does fire move upward? Not, surely, because of the whirl. But if fire is naturally such as to move in a certain direction, clearly the same may be supposed to hold of earth. Ἀλλὰ μὴν οὐδὲ τῇ δίνῃ γε τὸ βαρὺ καὶ κοῦφον ὥρισται, ἀλλὰ τῶν πρότερον ὑπαρχόντων βαρέων καὶ κούφων τὰ μὲν εἰς τὸ μέσον ἔρχεται, τὰ δ' ἐπιπολάζει διὰ τὴν κίνησιν. Ἦν ἄρα καὶ πρὶν γενέσθαι τὴν δίνην τὸ μὲν βαρὺ τὸ δὲ κοῦφον, ἃ τίνι διώριστο καὶ πῶς ἐπεφύκει φέρεσθαι ἢ ποῦ; ἀπείρου γὰρ ὄντος ἀδύνατον εἶναι ἄνω ἢ κάτω, διώρισται δὲ τούτοις τὸ βαρὺ καὶ κοῦφον. Οἱ μὲν οὖν πλεῖστοι περὶ τὰς αἰτίας ταύτας διατρίβουσιν 371 Again, it cannot be the whirl which determines the heavy and the light. Rather that movement caused the pre-existent heavy and light things to go to the middle and stay on the surface respectively. Thus, before ever the whirl began, heavy and light existed; and what can have been the ground of their distinction, or the manner and direction of their natural movements? In the infinite chaos there can have been neither above nor below, and it is by these that heavy and light are determined. It is to these causes that most writers pay attention:
| Praemissis tribus rationibus de quiete terrae, quae sumebantur ex parte inferiorum corporum, scilicet ipsius terrae, aquae et aeris, hic ponit alias rationes, quae sumuntur ex parte caelestis corporis. | 508. Having presented three reasons for the earth's rest, taken on the part of the lower bodies, namely, earth,. water and air, he here presents other arguments taken on the part of the heavenly body. |
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Et primo ponit quartam rationem quietis terrae, quam ponebat Empedocles; secundo improbat eam, ibi: quamvis neque gyratione et cetera. |
First he gives the fourth reason for the earth's rest, namely, the one which Empedocles gave; Secondly, he refutes it, at 509. |
| Dicit ergo primo quod, cum omnes philosophi qui ponunt mundum generatum esse, assignant causam motus terrae ad medium, violentiam circumgyrationis caeli, quaerunt etiam causam huius quod terra quiescit in medio. Et quidam dicunt quod causa huius est latitudo et magnitudo terrae, sicut supra dictum est; quidam autem, sicut Empedocles, dicunt quod motus caeli circa terram, propter sui velocitatem, prohibet terram moveri. Et ponunt exemplum de aqua contenta in cyathis, idest in quibusdam vasis aereis. Si enim vas illud in circuitu velocius moveatur, et sit aliquod foramen in aliqua parte aerei vasis, multoties vase circulariter moto, aqua descendet ad inferiora vasis aerei, ubi est foramen, et tamen non cadet inferius extra vas, secundum quod habet aptitudinem naturalem, propter eandem causam; quia scilicet prohibetur ex velocitate motus ipsius vasis, ita quod aqua ante rapiatur a motu vasis quam possit cadere. Et simili ratione dicunt quod terra impeditur a velocitate motus caeli ne deorsum cadere possit. | He says therefore first [366] that, since all the philosophers who assert than the world was generated, assign, as the cause of the earth's movement to the middle, the violence of the heaven's circumgyration, they also inquire into the reason why the earth rests in the middle. Some say that the cause of this is the earth's width and size, as was said above; but others, such as Empedocles, assert that the motion of the heaven around the earth is so swift that it keeps the earth from being moved. And they give the example of water contained in cyathi, i.e., certain bronze vessels. For if that vessel be given a quite rapid circular motion and there is an opening in some part of the bronze vessel, then, after the vessel is spun a number of times, the water will descend to the bottom of the bronze vessel where the opening is; yet it will not fall out of the vessel (as it normally should according to its natural inclination) for the same reason, namely, because it is prevented by the speed of the vessel's motion in such a way that the water is seized by the motion of the vessel before it can fall. With a like argument, they say that the earth. is prevented by the speed of the heaven's motion from being able to fall downwards. |
| Deinde cum dicit: quamvis neque gyratione etc., improbat praedictam rationem. | 509. Then at [367] he rejects this reason. |
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Et primo quantum ad quietem terrae; secundo quantum ad motum, ibi: inconveniens autem et cetera. |
First with respect to the earth's rest; Secondly, with respect to its motion. |
| Circa primum duo facit: | In regard to the first he does two things: |
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primo improbat causam quietis terrae communiter, tam quantum ad illos qui causam quietis terrae ponunt latitudinem vel magnitudinem terrae, quam etiam quantum ad Empedoclem; secundo specialiter improbat hanc positionem quantum ad Empedoclem, qui posuit causam quietis terrae velocitatem motus caeli; et hoc ibi: adhuc autem ad Empedoclem et cetera. |
First he rejects the cause of the earth's rest in general, both with respect to those who assign the width or size of the earth as the cause of its rest, and also with respect to Empedocles; Secondly, he specifically rejects this theory as far as it pertains to Empedocles, who assigned the speed of the heaven's motion as the cause of the earth's rest, at 510. |
| Dicit ergo primo quod, ex quo praedicti philosophi causam quietis terrae ponunt motum caeli vel latitudinem terrae, quae coarctat inferiorem aerem ut non possit diffugere, necessarium videtur quod, si gyratio caeli non prohiberet motum terrae, neque etiam prohiberet ipsum latitudo terrae, coarctans aerem, sed aer libere veniret et recederet, quod terra alicubi ferretur: quia tunc, remotis causis quietis, oporteret eam moveri. Non autem videtur secundum eorum positionem, quod ferretur ad medium secundum suam naturam: si enim, sicut ipsi ponunt, terra fertur ad medium per violentiam, necesse est quod per violentiam quiescat in medio; quod etiam ipsi ponunt. | He says therefore first [367] that, since the aforesaid philosophers declare that the cause of the earth's rest is the motion of the heaven, or the earths width which corners the lower air so that it cannot escape, then it seems necessary that, if the heaven's gyration should not. restrain the earth from moving; and if the earth's width should not restrain it by confining the air, but the air should freely come and go, the earth would be carried somewhere —since now, the causes of rest removed, it would have to move. But it does not seem, according to their theory, that it would be carried to the middle according to its nature. If, then, as they say, the earth is carried to the middle by compulsion, then it would have to rest in the middle by compulsion, which they also posit. |
| Sed tamen necesse est quod terra habeat aliquem motum naturalem, cessante omni violentia: oportet enim corporibus naturalem motum assignare, sicut supra dictum est. Restat igitur quaerendum versus quam partem naturaliter moveretur, violentia cessante; scilicet utrum sursum vel deorsum, vel versus aliquam aliam differentiam, puta ad dextrum vel sinistrum: quia omnino oportet quod habeat aliquem motum naturalem. Nec est dare quod ad aliquam aliam partem naturaliter moveatur nisi deorsum et ad medium, ut patet ex motu partium terrae, quae ad nullam aliam partem naturaliter moventur. Sic igitur male assignant causam quietis terrae in medio ex aliqua violentia. | However, the earth has to have some natural motion after all compulsion ceases — for all bodies have some motion that is natural, as has been said above. It remains, therefore, to investigate in which direction the earth would be moved naturally, if all compulsion ceased — whether upward, or downward, or in some other direction, e.g., to the right or to the left, for it certainly must have some natural motion. Nor can a reason be found for it to be naturally moved in any other direction except down and to the middle, as is evident from the motion of particles of earth, which are naturally moved in no other direction. Consequently, in assigning compulsion as the cause of the earth's rest in the middle, they make a poor choice. |
| Si vero dicant quod terra, secundum motum suum naturalem, non magis habet quod moveatur deorsum quam sursum, videtur sequi quod, sicut aer qui est supra terram, non prohibet eam moveri sursum, ita etiam nec aer qui est sub terra, prohibebit eam moveri deorsum, vel propter comprehensionem eius a latitudine terrae, vel propter revolutionem eius ex motu caeli: quia in eisdem rebus, quantum ad eosdem effectus, necesse est ponere easdem causas. | But if they say that the natural motion of the earth does not incline it downward any more than upward, it seems to follow that, just as the air which is atop the earth does not keep it from being moved upward, so too neither will the air under the earth keep it from being moved downward, whether on account of the air's being confined by the earth's width or on account of its being revolved by the motion of the heaven — because, in dealing with the same things as to the same effects, the same causes must be posited. |
| Deinde cum dicit: adhuc autem ad Empedoclem etc., improbat specialiter solutionem Empedoclis. Considerandum est autem quod Empedocles ponebat quatuor elementa materialia et duo moventia, scilicet litem et amicitiam; quae per congregationem et segregationem elementorum, sunt causa generationis et corruptionis mundi, et omnium quae in mundo sunt. Dicit ergo quod aliquis potest quaestionem movere contra Empedoclem: quando elementa erant ab invicem separata propter litem, oportebat terram quiescere (non enim coniungebat se aliis elementis, dominio litis durante): est ergo quaerendum quae fuit tunc causa quod terra quiesceret. Nec potest assignari pro causa gyratio caeli; quia caelum nondum erat generatum. Videtur ergo quod nullo modo oporteat dicere gyrationem caeli causam quietis terrae. | 510. Then at [368] he specifically disproves Empedocles' solution. Here it should be kept in mind that Empedocles posited four material elements and two movers, namely, friendship and strife, which, by associating and disassociating the elements, are the cause of the generation and corruption of the world and all things in the world. Aristotle says, therefore, that someone can bring against Empedocles the following difficulty: When the elements were separated from one another by strife, earth had to be at rest — because it did not join itself to the other elements so long as strife ruled. Therefore, one should ask what caused earth to be at rest at that time. One cannot give as a cause the gyration of the heaven, because the heaven had not yet been generated. It seems, therefore, that one can in no way say that the gyration of the heaven is the cause of the earth's rest. |
| Sed de hac ratione videtur esse dubium. Videtur enim lis esse causa generationis mundi, distinguendo elementa ab invicem; amicitia autem esse causa corruptionis eiusdem, congregando elementa in unum chaos. Unde nunc videtur esse litis dominium, propter hoc quod elementa sunt ab invicem distincta. | But there seems to be some problem about this argument. For strife seems to be the cause of the generation of the world by disassociating the elements from one another, while friendship seems to be the cause of its corruption by uniting the elements into one chaos. Hence, one seems to have at present the rule of strife, since the elements are disassociated from one another. |
| Et ideo Alexander exposuit haec verba sic: quando elementa distabant seorsum, non quidem ab invicem, sed a lite; idest quando lis ab elementis aberat, tempore scilicet quo amicitia dominabatur. | Accordingly, Alexander expounds these words in the following manner: "When the elements were apart," means, not "from one another," but "from strife," i.e., at the time when strife was disassociated from the elements, namely, at the time when friendship ruled. |
| Sed quia haec expositio videtur esse extorta, ideo exponenda est, sicut Simplicius dicit: quando elementa distabant seorsum, scilicet ab invicem, et hoc a lite, idest propter litem. Est enim considerandum quod Empedocles ponebat mundum generari non ex sola lite, sed etiam cum admixtione amicitiae. Et sicut ipse per verba Empedoclis probat, ex dominio amicitiae provenit circumgyratio caeli, quia motus caeli quasi omnia convolvit in unum. Et ideo convenienter Aristoteles quaerit, antequam gyratio caeli per amicitiam causaretur, secundum Empedoclem, quae erat causa quietis terrae. | But because this explanation seems extorted, it should be explained as Simplicius says, as follows: "When the elements were apart," i.e., "from one another," and this "from strife," i.e., on account of strife. For it must be remembered that Empedocles explained the generation of the world, not in teems of strife alone, but with an admixture of friendship as well. And, as he [Simplicius] proves from the words of Empedocles, it is from the dominance of friendship that the circumgyration of the heaven comes, since the motion of the heaven masses, as it were, all things into one. Therefore, it is suitable for Aristotle to ask: What was the cause of the earth's rest before the gyration of the world was, according to Empedocles, caused by friendship? |
| Deinde cum dicit: inconveniens autem etc., improbat rationem quam assignant communiter de motu terrae, tribus rationibus. Circa quarum primam dicit quod inconveniens est non considerare quare, si prius, quando generabatur mundus, partes terrae ferebantur ad medium propter gyrationem caeli, nunc non est talem causam assignare quare, sicut videmus, omnia gravia ferantur ad medium. Gyratio enim caeli simul circumgyrat ignem et superiorem partem aeris, non autem hanc inferiorem aeris partem: et ita illa gyratio non attingit usque ad nos. Videmus enim quod gravia feruntur ad medium et in hoc aere propinquo. Non ergo gyratio caeli debet poni causa motus gravium ad medium: quia remota causa, removetur effectus. | 511. Then at [369] he rejects the reason which they assign in general for the motion of the earth. This he does with three arguments. With respect to the first of which, he says that it is unacceptable not to consider why it is that if before, when the world was being generated, the parts of earth were carried to the middle on account of the heaven's gyration, now, when such a cause can no longer be assigned, we still see all heavy things carried to the middle. For the heaven's gyration rotates at once fire and the upper region of air, but not this lower region of air — and, consequently, this gyration does not reach as far as us. Yet we observe that heavy things are carried to the middle in this air near us. Therefore, the gyration of the heaven ought not be posited as the cause of heavy things' being moved to the middle — because if the cause is taken away, so too the effect. |
| Secundam rationem ponit ibi: adhuc autem et ignis et cetera. Et dicit quod considerare oportet propter quam causam ignis feratur sursum. Non enim potest dici quod hoc sit propter gyrationem caeli: non enim ad hoc se extendit exemplum ab eis inductum. Si vero ignis feratur ad aliquem locum propter suam aptitudinem naturalem, manifestum est quod est idem existimare de terra, quae habet contrarietatem ad ignem, ut supra dictum est: contrariorum enim sunt contrarii motus, et si unum contrariorum est naturale, et aliud naturale esse oportet, ut supra dictum est. | 512. At [370] he presents the second argument. And he says that we must consider why it is that fire is borne upwards. For it cannot be said that this s due to the heaven's gyration — since the example they give does not extend this far. However, if it is on account of its natural inclination that fire is borne to some certain place, then it is plain that the same should be thought of earth, which has contrariety to fire, as has been said above — for the motions of contraries are themselves contrary, and if one of the contraries is natural, the other too must be natural, as has been said. |
| Tertiam rationem ponit ibi: sed adhuc neque gyratione et cetera. Et dicit quod si quis eorum verba et exempla consideret, non videtur dicendum quod grave distinguatur a levi in corporibus propter ipsam gyrationem caeli; sed praesupposita distinctione gravium et levium, quaedam veniunt ad medium, scilicet gravia, quaedam autem, scilicet levia, conantur sursum ferri, propter motum, inquantum repelluntur a loco medio a corporibus gravibus in ipsum latis. Et sic solum per accidens gyratio caeli causat motum ignis sursum. Quod autem gyratio non distinguat grave et leve, sed eorum distinctionem praesupponat, potest videri ex exemplo quod inducunt: in gyratione enim aeris et liquidorum, ea quae prius erant gravia, feruntur ad medium. Sic igitur antequam esset gyratio caeli, erat grave et leve. Quae secundum aliquid distinguebantur, scilicet secundum aptitudinem ad hoc quod aliquo modo et ad aliquem locum moveantur: nam grave dicitur aliquid vel leve, propter inclinationem ad aliquem motum localem. Et ita gyratio non est causa quare levia moventur sursum, vel gravia deorsum. | 513. He presents the third reason at [371] and says that if anyone considers their words and examples, it does not seem that one should say that the heavy is distinguished from the light among bodies on account of the heaven's gyration, but that, if we presuppose the distinction between the heavy and the light, then some, namely, the heavy, move to the middle, while others, namely, the light, try to move upward, insofar as they are repelled from the middle place by the heavy bodies carried there. Consequently, it is only by accident that the heaven's gyration causes the upward motion of fire. But that the gyration of the heaven does not distinguish the heavy from the light, but pre-supposes their distinction, can be seen from the example they adduce — for it: the gyration of air and liquids, things that are already heavy are carried to the middle. Consequently, before there was a gyration of the heaven, there existed heavy and light. These were distinguished according to something, namely, their aptitude to be moved in some way and to some certain place —for a thing is called "heavy" or "light" on account of an inclination to some certain local motion. Consequently, gyration is not the reason why light things are moved upward or heavy things downward. |
| Poterant autem hi distinguere grave et leve, et loca eorum, quae sunt sursum et deorsum, quia non ponebant universum esse infinitum: non enim impossibile est distinguere sursum vel deorsum, si apud istos distinguitur grave et leve, sicut dictum est. Et quia aliqui ponebant universum infinitum, scilicet Anaximenes et Xenophanes, ideo signanter dicit quod plurimi, non autem omnes, sunt detriti, idest consueti et exercitati, circa istas causas motus et quietis gravium et levium. | Now these could distinguish heavy and light and their places, which are above and below, because they did not posit the universe to be infinite. For it is not impossible to distinguish up and down, if they distinguish heavy and light. And because some assumed an infinite universe, namely, Anaximenes and Xenophanes, Aristotle therefore says significantly that "many" of them, but not all, were "worn out," i.e., accustomed to, and practiced in, the matter of the causes of the motion and rest of heavy and light things. |
Lecture 25:
Reason for earth's rest not from same relation to every part of the heavenChapter 13 cont. εἰσὶ δέ τινες οἳ διὰ τὴν ὁμοιότητά φασιν αὐτὴν μένειν, ὥσπερ τῶν ἀρχαίων Ἀναξίμανδρος μᾶλλον μὲν γὰρ οὐθὲν ἄνω ἢ κάτω ἢ εἰς τὰ πλάγια φέρεσθαι προσήκει τὸ ἐπὶ τοῦ μέσου ἱδρυμένον καὶ ὁμοίως πρὸς τὰ ἔσχατα ἔχον ἅμα δ' ἀδύνατον εἰς τὸ ἐναντίον ποιεῖσθαι τὴν κίνησιν ὥστ' ἐξ ἀνάγκης μένειν. 372 but there are some, Anaximander, for instance, among the ancients, who say that the earth keeps its place because of its indifference. Motion upward and downward and sideways were all, they thought, equally inappropriate to that which is set at the centre and indifferently related to every extreme point; and to move in contrary directions at the same time was impossible: so it must needs remain still. Τοῦτο δὲ λέγεται κομψῶς μέν, οὐκ ἀληθῶς δέ κατὰ γὰρ τοῦτον τὸν λόγον ἀναγκαῖον ἅπαν ὅ τι ἂν τεθῇ ἐπὶ τοῦ μέσου, μένειν, ὥστε καὶ τὸ πῦρ ἠρεμήσει τὸ γὰρ εἰρημένον οὐκ ἴδιόν ἐστι τῆς γῆς. 373 This view is ingenious but not true. The argument would prove that everything, whatever it be, which is put at the centre, must stay there. Fire, then, will rest at the centre: for the proof turns on no peculiar property of earth. Ἀλλὰ μὴν οὐκ ἀναγκαῖον. Οὐ γὰρ μόνον φαίνεται μένουσα ἐπὶ τοῦ μέσου, ἀλλὰ καὶ φερομένη πρὸς τὸ μέσον. Ὅπου γὰρ ὁτιοῦν φέρεται μόριον αὐτῆς, ἀναγκαῖον ἐνταῦθα φέρεσθαι καὶ τὴν ὅλην οὗ δὲ φέρεται κατὰ φύσιν, καὶ μένει ἐνταυθοῖ κατὰ φύσιν. Οὐκ ἄρα διὰ τὸ ὁμοίως ἔχειν πρὸς τὰ ἔσχατα τοῦτο μὲν γὰρ πᾶσι κοινόν, τὸ δὲ φέρεσθαι πρὸς τὸ μέσον ἴδιον τῆς γῆς. 374 But this does not follow. The observed facts about earth are not only that it remains at the centre, but also that it moves to the centre. The place to which any fragment of earth moves must necessarily be the place to which the whole moves; and in the place to which a thing naturally moves, it will naturally rest. The reason then is not in the fact that the earth is indifferently related to every extreme point: for this would apply to any body, whereas movement to the centre is peculiar to earth. Ἄτοπον δὲ καὶ τοῦτο μὲν ζητεῖν, διὰ τί ποτε μένει ἡ γῆ ἐπὶ τοῦ μέσου, τὸ δὲ πῦρ μὴ ζητεῖν διὰ τί ἐπὶ τοῦ ἐσχάτου. Εἰ μὲν γὰρ κἀκείνῳ φύσει τόπος ὁ ἔσχατος, δῆλον ὅτι ἀναγκαῖον εἶναί τινα καὶ τῇ γῇ φύσει τόπον εἰ δὲ μὴ ταύτῃ οὗτος ὁ τόπος, ἀλλὰ διὰ τὴν ἀνάγκην μένει τὴν τῆς ὁμοιότητος (ὥσπερ ὁ περὶ τῆς τριχὸς λόγος τῆς ἰσχυρῶς μὲν ὁμοίως δὲ πάντῃ τεινομένης, ὅτι οὐ διαρραγήσεται, καὶ τοῦ πεινῶντος καὶ διψῶντος σφόδρα μέν, ὁμοίως δέ, καὶ τῶν ἐδωδίμων καὶ ποτῶν ἴσον ἀπέχοντος καὶ γὰρ τοῦτον ἠρεμεῖν ἀναγκαῖον), ζητητέον αὐτοῖς περὶ τῆς τοῦ πυρὸς μονῆς ἐπὶ τῶν ἐσχάτων. 375 Again it is absurd to look for a reason why the earth remains at the centre and not for a reason why fire remains at the extremity. If the extremity is the natural place of fire, clearly earth must also have a natural place. But suppose that the centre is not its place, and that the reason of its remaining there is this necessity of indifference—on the analogy of the hair which, it is said, however great the tension, will not break under it, if it be evenly distributed, or of the men who, though exceedingly hungry and thirsty, and both equally, yet being equidistant from food and drink, is therefore bound to stay where he is—even so, it still remains to explain why fire stays at the extremities. (296a.) Θαυμαστὸν δὲ καὶ τὸ περὶ μὲν τῆς μονῆς ζητεῖν, περὶ δὲ τῆς φορᾶς αὐτῶν μὴ ζητεῖν, διὰ τίν' αἰτίαν τὸ μὲν ἄνω φέρεται, τὸ δ' ἐπὶ τὸ μέσον, μηδενὸς ἐμποδίζοντος. 376 It is strange, too, to ask about things staying still but not about their motion,—why, I mean, one thing, if nothing stops it, moves up, and another thing to the centre. Ἀλλὰ μὴν οὐδ' ἀληθές ἐστι τὸ λεγόμενον. Κατὰ συμβεβηκὸς μέντοι τοῦτό γ' ἀληθές, ὡς ἀναγκαῖον μένειν ἐπὶ τοῦ μέσου πᾶν ᾧ μηθὲν μᾶλλον δεῦρο ἢ δεῦρο κινεῖσθαι προσήκει. Ἀλλὰ διά γε τοῦτον τὸν λόγον οὐ μενεῖ, ἀλλὰ κινηθήσεται, οὐ μέντοι ὅλον, ἀλλὰ διεσπασμένον. Ὁ γὰρ αὐτὸς ἁρμόσει λόγος καὶ ἐπὶ τοῦ πυρός ἀνάγκη γὰρ τεθὲν μένειν ὁμοίως ὥσπερ τὴν γῆν ὁμοίως γὰρ ἕξει πρὸς τῶν σημείων τῶν ἐσχάτων ὁτιοῦν ἀλλ' ὅμως οἰσθήσεται ἀπὸ τοῦ μέσου, ὥσπερ καὶ φαίνεται φερόμενον, ἂν μή τι κωλύῃ, πρὸς τὸ ἔσχατον πλὴν οὐχ ὅλον πρὸς ἓν σημεῖον (τοῦτο γὰρ ἀναγκαῖον μόνον συμβαίνειν ἐκ τοῦ λόγου τοῦ περὶ τῆς ὁμοιότητος) ἀλλὰ τὸ ἀνάλογον μόριον πρὸς τὸ ἀνάλογον τοῦ ἐσχάτου, λέγω δ' οἷον τὸ τέταρτον μέρος πρὸς τὸ τέταρτον μέρος τοῦ περιέχοντος οὐθὲν γὰρ στιγμὴ τῶν σωμάτων ἐστίν. Ὥσπερ δὲ κἂν ἐκ μεγάλου συνέλθοι πυκνούμενον εἰς ἐλάττω τόπον, οὕτω κἂν ἐξ ἐλάττονος εἰς μείζω μανότερον γιγνόμενον ὥστε κἂν ἡ γῆ τοῦτον τὸν τρόπον ἐκινεῖτο ἀπὸ τοῦ μέσου διά γε τὸν τῆς ὁμοιότητος λόγον, εἰ μὴ φύσει τῆς γῆς οὗτος ὁ τόπος ἦν. 377 Again, their statements are not true. It happens, indeed, to be the case that a thing to which movement this way and that is equally inappropriate is obliged to remain at the centre. But so far as their argument goes, instead of remaining there, it will move, only not as a mass but in fragments. For the argument applies equally to fire. Fire, if set at the centre, should stay there, like earth, since it will be indifferently related to every point on the extremity. Nevertheless it will move, as in fact it always does move when nothing stops it, away from the centre to the extremity. It will not, however, move in a mass to a single point on the circumference—the only possible result on the lines of the indifference theory—but rather each corresponding portion of fire to the corresponding part of the extremity, each fourth part, for instance, to a fourth part of the circumference. For since no body is a point, it will have parts. The expansion, when the body increased the place occupied, would be on the same principle as the contraction, in which the place was diminished. Thus, for all the indifference theory shows to the contrary, earth also would have moved in this manner away from the centre, unless the centre had been its natural place. Ὅσα μὲν οὖν τυγχάνει περί τε τοῦ σχήματος αὐτῆς ὑπολαμβανόμενα καὶ περὶ τόπου καὶ μονῆς καὶ κινήσεως, σχεδὸν ταῦτ' ἐστίν. We have now outlined the views held as to the shape, position, and rest or movement of the earth.
| Praemissa quarta solutione, secundum quam sumebatur ratio quietis terrae ex violentia gyrationis caeli, hic ponit quintam solutionem, secundum quam assignatur ratio quietis terrae ex simili habitudine caeli ad terram ex omni parte. | 514. Having presented the fourth solution according to which the explanation of the earth's rest was taken from the violence of the heaven's gyration, he [the Philosophe] here presents the fifth solution in which the explanation of the earth's rest is based on the fact of a similar relation of the heaven to the earth from all directions. |
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Et primo assignat hanc rationem; secundo improbat eam, ibi: hoc autem dicitur et cetera. |
First he presents this explanation; Secondly, he disproves it, at 515. |
| Dicit ergo primo quod quidam dixerunt terram quiescere in medio propter similitudinem, idest similem eius habitudinem ad omnem partem caeli. Et hoc inter antiquos dixit Anaximander. Per quod dat intelligere quod etiam aliquibus sui temporis hoc videbatur. Dicitur enim Plato hoc posuisse: sed tamen Aristoteles hoc ei non imponit, quia supra ei imposuerat quod moveretur in medio circa axem mundi. | He says therefore first that some have said that the earth rests in the middle because of "likeness,"' i.e., on account of its being similarly related to every part of the heaven. Among the ancients, Anaximander held this opinion. By this he gives us to understand that some of his contemporaries believed this. For Plato is said to have posited this; yet Aristotle does not attribute it to him because above he had attributed to him the opinion that the earth was moved in the middle about the axis of the world. |
| Ideo autem dicebant terram propter similitudinem manere, quia nulla est ratio quare id quod est in medio collocatum, magis moveatur sursum vel deorsum, aut versus alias plagas caeli, cum similiter se habeat undique ad extrema; impossibile est autem quod simul moveatur ad contrarias partes; ergo relinquitur quod ex necessitate quiescat in medio. | Now the reason why they said that the earth stays put on account of likeness, is that there is no reason why that which is placed in the middle should be moved upward or downward, or toward other reaches of the heaven, since it is related in the same way to the extremes in every direction. Now it is impossible for it to be moved simultaneously in contrary directions. Therefore it remains that it necessarily rests in the middle. |
| Deinde cum dicit: hoc autem dicitur etc., improbat praedictam rationem. | 515. Then at... he disproves this explanation. |
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Et primo ex hoc quod ratio non est necessaria; secundo ex hoc quod supponit falsum, ibi: sed adhuc neque verum quod dicitur et cetera. |
First on the ground that the argument does not have necessity; Secondly, on the ground that it supposes something false, at 519. |
| Dicit ergo primo quod id quod dictum est, videtur persuasibiliter dici, non tamen vere. Et hoc probat quatuor rationibus. Quarum prima est quia, secundum praedictam rationem, necessarium esset quiescere omne quod ponitur in medio (et sic sequeretur quod etiam ignis, si poneretur in medio, quiesceret; quod patet esse falsum): quia id quod assignatur pro causa quietis, scilicet esse in medio, non accipitur ut proprium terrae; cum tamen effectus, scilicet quiescere in medio, sit proprium terrae. | He says therefore first 1577 that the statements they make appear persuasive, but are not truly so. And this he proves with four arguments. The first of these is that, if the above explanation were true, then everything placed in the middle would have to rest there (and thus it would follow that fires if it were put in the middle, would remain at rest, which is patently false), because the cause of rest assigned here, namely, being in the middle, is not taken to be peculiar to earth yet the effect, namely, to be at rest in the middle, is peculiar to earth. |
| Secundam rationem ponit ibi: sed et non necessarium et cetera. Et dicit quod non est necessarium dicere quod terra quiescat in medio propter similitudinem, cum inveniatur alia convenientior causa. Terra enim non solum videtur quiescere in medio, sed etiam ferri ad medium, etsi non secundum se totam, tamen secundum suas partes. Eadem enim est ratio de motu totius et partis: quocumque enim fertur pars eius, fertur de necessitate et totum, si extra suum locum esset. Ubi autem fertur secundum naturam, ibi et quiescit secundum suam naturam. Sic ergo patet quod terra quiescit in medio propter suam naturam, et non propter hoc quod similiter se habeat ad extrema: quia hoc potest esse commune omnibus, ut ponantur in medio; sed naturaliter ferri ad medium est proprium terrae. | 516. The second argument is presented at 717, and he says that it is not necessary to say that the earth rests in the middle on account of likeness, since a more suitable cause is available. For earth seems not only to rest in the middle, but to be borne toward the middle, if not according to the whole, nevertheless according to its parts. Now there is the same explanation for the motion of the whole and for that of the part. For whithersoever a part of the earth is borne, there too the whole would be necessarily borne, should it be outside its proper place. But wherever it is borne according to its nature, there it also rests according to its nature. Accordingly, it is plain that the earth rests in the middle on account of its very nature and not because it is related in a "liken way to the extremes, since to be put in the middle can be common to all things — but to be naturally borne to the middle is peculiar to earth. |
| Tertiam rationem ponit ibi: inconveniens autem etc.; quae ostendit etiam insufficientiam huius rationis. Et dicit quod inconveniens est quaerere propter quid terra quiescat in medio, et non quaerere quare ignis quiescat in extremo. Si enim ignis quiescit ibi, quia locus extremus naturaliter convenit ei, eadem ratione dicendum est quod terra habeat quendam locum naturalem in quo quiescat. Si enim hic locus qui est medius, non sit locus in quo naturaliter quiescit, sed manet in medio propter necessitatem similitudinis, restat eis quaerere quare ignis maneat in extremis. | 517. He gives his third argument, which also shows the insufficiency of this explanation. And he says it is inappropriate to investigate why the earth rests in the middle and not investigate why fire rests in the extreme confine. For if fire rests there because the extreme place naturally suits it, then for the same reason it should be said that earth too has a natural place in which to rest. And if the middle is not the place where earth naturally rests, but it remains in the middle on account of the necessity of likeness, then they must investigate why fire remains in the extremes. |
| Et ponit exempla de quiete terrae in medio, secundum quasdam rationes sophistarum, qui probare videbantur quod si trichos, idest capillus, fortiter extendatur, quod non frangetur; quia similiter undique extenditur, et non est ratio quare magis frangatur in uno loco quam in alio. Sed haec ratio sophistica est: primo quidem quia difficile est ut similiter sit undique extensus; secundo quia, hoc etiam posito, frangetur in medio, quia ibi concurrit violentia quae ex utraque parte infertur. | And he gives examples of the earth's rest in the middle based on certain arguments of the sophists, who seemed to prove that a "trichos," i.e., a hair, if vigorously stretched, would not break, because it would be stretched alike in every direction and there is no reason why it should break at one point rather than at another. But this argument is sophistical: first, because it is difficult for it to be stretched everywhere in the same way; secondly, because, even supposing this, it would break in the middle, because it is there that the violence exerted from both directions meets. |
| Aliud exemplum ponit de eo qui aequaliter esurit et sitit, et habet cibum et potum in aequali distantia: concludunt enim sophistae quod talis quiesceret, et ad neutrum moveretur. Sed hoc non sequitur: primo quidem quia sitis magis agit quam fames; secundo quia, si aequaliter distarent duo cibi vel duo potus aequaliter desiderabiles, curreret ad alterum quodcumque contingeret. | He gives another example, namely, of a person subject to an equal degree of hunger and thirst and having food and drink at an equal distance. The sophists conclude that such a person would remain where he is, and be moved to neither. But this does not follow: first of all, because thirst is stronger than hunger; secondly, because, if two meals or two drinks were equally desirable, he would run to whichever one he should happen to run to. |
| Quartam rationem ponit ibi: mirabile autem etc.; quae etiam ostendit insufficientiam praedictae rationis. Et dicit quod mirabile fuit quod quaerebant rationem quietis corporum, et non quaerebant rationem motuum ipsorum; propter quam scilicet causam unum corporum movetur sursum, aliud vero deorsum, si non sit aliquid impediens; natura enim est principium motus et quietis in eo in quo est, ut dicitur in II Physic. | 518. He presents his fourth argument, which also shows the insufficiency of the aforesaid. And he says that it was strange for them to inquire into the reason why bodies rest and not inquire into the reason for their motion, namely, as to why one body is moved upward and another downward when no obstacle detains them. For nature is the principle of motion and rest in that in which it is, as is said in Physics II. |
| Deinde cum dicit: sed adhuc neque verum quod dicitur etc., improbat praedictam rationem ex eo quod supponit falsum. Et dicit quod id quod dicitur in praedicta ratione, non est verum per se et universaliter: est enim hoc verum per accidens, quod omne, idest totum; necesse est manere in medio, ad quod nihil magis pertinet quod moveatur huc quam illuc. Sed si habeat inclinationem ut moveatur ad aliquam partem, propter hanc rationem, quia scilicet est in medio, non ex necessitate quiescet, sed movebitur; non tamen secundum totum, sed divisum in partes, sicut patet de igne. | 519. Then he disproves the aforesaid explanation on the ground that it assumes something that is false. And he says that what is said in the aforesaid explanation is not true per se and universally. For it ism' accid~ true that "everything," i.e., a whole, must remain in the middle if there is no greater reason for it to be moved here than there. But if it should have an inclination to be moved in some direction, then, because of the fact that it is in the middle, it will not rest of necessity, but it will be moved — yet not as a whole, but divided into parts, as is evident with fire. |
| Si enim verum est quod dicunt, necesse est quod, si poneretur ignis in medio mundi, quod quiesceret ibi, sicut terra quiescit, eo quod similiter se haberet ad quodlibet punctum in caelo signatum: et tamen ignis in medio positus moveretur a medio usque ad extremum, si nihil prohiberet, sicut et nunc videtur moveri. Sed tamen non totum movetur ad unum punctum: et hoc solum removebatur in praedicta ratione, ut scilicet totum moveretur ad unam partem. Sed movebitur unaquaeque pars ignis ad partem caeli sibi proportionatam, puta quarta pars ignis ad quartam partem continentis, scilicet caeli: corpus enim non est aliquod punctum indivisibile. Sicut autem partes terrae, si essent dispersae circa extremum caeli, condensarentur, ad hoc quod venirent in minorem locum, scilicet in medium, sic oporteret e converso: quia si ignis moveretur a medio usque ad extremum, oporteret quod per rarefactionem ex parvo loco moveretur ad locum maiorem. | For if what they say is true, then, if fire were put in the middle of the world, it would have to remain there, as the earth does, on the ground that it would be similarly related to every point that can be designated in the heaven; yet if fire were put in the middle, it would be moved to the extreme if nothing stopped it, as it is even now seen to be moved. But yet, not all is moved to one point — and this alone was removed in the previous argument, namely, that the whole should be moved in one direction. But each portion of the fire will be moved to a part of the heaven suitable to it — for example, a fourth part of the fire to a fourth part of the "container," i.e., the heaven; for a body is not an indivisible point. Just as parts of earth, if dispersed toward the confines of the heaven, would be condensed to come to a lesser place, namely, the middle, so also conversely, if fire were moved from the middle to the extreme, it would have, by rarefaction, to be moved from a small place to a larger place. |
| Et sic cessat obiectio, qua posset aliquis resistere supradictis, dicens impossibile esse quod singulae partes ignis ferrentur ad singulas partes caeli, propter hoc quod locus extremus excedit locum medium in quantitate. Sed hoc removetur, quia ignis per rarefactionem extenderetur in maiorem locum. Et ex hoc concludit quod, si locus medius non esset naturalis terrae, quod propter rationem similitudinis hoc modo moveretur a medio versus extremum, quod singulae partes eius moverentur ad singulas partes extremi, sicut de igne dictum est. | 520. And thus ceases the objection upon which someone could gainsay the foregoing and declare that it is impossible for individual portions of fire to be borne to individual parts of the heaven on the ground that the extreme place exceeds the middle in quantity. For this is forestalled by the fact that through rarefaction the fin: would be extended to occupy a greater place. And from this he concludes that if the middle place were not natural to earth, then, on account of likeness, it would be moved in such a way from the middle to the extreme that each of its parts would be moved to individual parts of the extreme, as was said of fire. |
| Ultimo autem epilogat, dicens fere haec esse omnia quae antiqui suspicati sunt circa figuram terrae et locum ipsius, et motum eius vel quietem. | Finally, he sums up and says that this is practically all that the ancient philosophers suspected about the shape and place of the earth and about its place and its motion or rest. |
Lecture 26:
Proof of the earth's rest in the middleChapter 14 Ἡμεῖς δὲ λέγωμεν πρῶτον πότερον ἔχει κίνησιν ἢ μένει καθάπερ γὰρ εἴπομεν, οἱ μὲν αὐτὴν ἓν τῶν ἄστρων εἶναι ποιοῦσιν, οἱ δ' ἐπὶ τοῦ μέσου θέντες ἴλλεσθαι καὶ κινεῖσθαί φασι περὶ τὸν πόλον μέσον. Ὅτι δ' ἐστὶν ἀδύνατον, δῆλον λαβοῦσιν ἀρχὴν ὡς εἴπερ φέρεται εἴτ' ἐκτὸς οὖσα τοῦ μέσου εἴτ' ἐπὶ τοῦ μέσου, ἀναγκαῖον αὐτὴν βίᾳ κινεῖσθαι ταύτην τὴν κίνησιν οὐ γὰρ αὐτῆς γε τῆς γῆς ἐστιν καὶ γὰρ ἂν τῶν μορίων ἕκαστον ταύτην εἶχε τὴν φοράν νῦν δ' ἐπ' εὐθείας πάντα φέρεται πρὸς τὸ μέσον. Διόπερ οὐχ οἷόν τ' ἀΐδιον εἶναι, βίαιόν γ' οὖσαν καὶ παρὰ φύσιν ἡ δέ γε τοῦ κόσμου τάξις ἀΐδιος. 379 Let us first decide the question whether the earth moves or is at rest. 380 For, as we said, there are some who make it one of the stars, and others who, setting it at the centre, suppose it to be 'rolled' and in motion about the pole as axis. 381 That both views are untenable will be clear if we take as our starting-point the fact that the earth's motion, whether the earth be at the centre or away from it, must needs be a constrained motion. It cannot be the movement of the earth itself. If it were, any portion of it would have this movement; but in fact every part moves in a straight line to the centre. Being, then, constrained and unnatural, the movement could not be eternal. But the order of the universe is eternal. Ἔτι πάντα τὰ φερόμενα τὴν φορὰν τὴν ἐγκύκλιον ὑπολειπόμενα φαίνεται καὶ κινούμενα πλείους (296b.) μιᾶς φορὰς ἔξω τῆς πρώτης, ὥστε καὶ τὴν γῆν ἀναγκαῖον, εἴτε περὶ τὸ μέσον εἴτ' ἐπὶ τοῦ μέσου κειμένη φέρεται, δύο κινεῖσθαι φοράς. Τούτου δὲ συμβαίνοντος ἀναγκαῖον γίγνεσθαι πάροδον καὶ τροπὰς τῶν ἐνδεδεμένων ἄστρων. Τοῦτο δ' οὐ φαίνεται γιγνόμενον, ἀλλ' ἀεὶ ταὐτὰ κατὰ τοὺς αὐτοὺς ἀνατέλλει καὶ δύεται τόπους αὐτῆς. 382 Again, everything that moves with the circular movement, except the first sphere, is observed to be passed, and to move with more than one motion. The earth, then, also, whether it move about the centre or as stationary at it, must necessarily move with two motions. But if this were so, there would have to be passings and turnings of the fixed stars. Yet no such thing is observed. The same stars always rise and set in the same parts of the earth. Ἔτι δ' ἡ φορὰ τῶν μορίων καὶ ὅλης αὐτῆς ἡ κατὰ φύσιν ἐπὶ τὸ μέσον τοῦ παντός ἐστιν διὰ τοῦτο γὰρ καὶ τυγχάνει κειμένη νῦν ἐπὶ τοῦ κέντρου 383 Further, the natural movement of the earth, part and whole alike, is the centre of the whole—whence the fact that it is now actually situated at the centre— διαπορήσειε δ' ἄν τις, ἐπεὶ ταὐτὸν ἀμφοτέρων ἐστὶ τὸ μέσον, πρὸς πότερον φέρεται τὰ βάρος ἔχοντα καὶ τὰ μόρια τῆς γῆς κατὰ φύσιν πότερον ὅτι τοῦ παντός ἐστι μέσον, ἢ διότι τῆς γῆς. 384 but it might be questioned since both centres are the same, which centre it is that portions of earth and other heavy things move to. Is this their goal because it is the centre of the earth or because it is the centre of the whole? Ἀνάγκη δὴ πρὸς τὸ τοῦ παντός καὶ γὰρ τὰ κοῦφα καὶ τὸ πῦρ εἰς τοὐναντίον φερόμενα τοῖς βάρεσι πρὸς τὸ ἔσχατον φέρεται τοῦ περιέχοντος τόπου τὸ μέσον. Συμβέβηκε δὲ ταὐτὸ μέσον εἶναι τῆς γῆς καὶ τοῦ παντός φέρεται γὰρ καὶ ἐπὶ τὸ τῆς γῆς μέσον, ἀλλὰ κατὰ συμβεβηκός, ᾗ τὸ μέσον ἔχει ἐν τῷ τοῦ παντὸς μέσῳ. 385 The goal, surely, must be the centre of the whole. For fire and other light things move to the extremity of the area which contains the centre. It happens, however, that the centre of the earth and of the whole is the same. Thus they do move to the centre of the earth, but accidentally, in virtue of the fact that the earth's centre lies at the centre of the whole. Ὅτι δὲ φέρεται καὶ πρὸς τὸ τῆς γῆς μέσον, σημεῖον ὅτι τὰ φερόμενα βάρη ἐπὶ ταύτην οὐ παρ' ἄλληλα φέρεται ἀλλὰ πρὸς ὁμοίας γωνίας, ὥστε πρὸς ἓν τὸ μέσον φέρεται, καὶ τὸ τῆς γῆς. 386 That the centre of the earth is the goal of their movement is indicated by the fact that heavy bodies moving towards the earth do not parallel but so as to make equal angles, and thus to a single centre, that of the earth. Φανερὸν τοίνυν ὅτι ἀνάγκη ἐπὶ τοῦ μέσου εἶναι τὴν γῆν καὶ ἀκίνητον, διά τε τὰς εἰρημένας αἰτίας, 387 It is clear, then, that the earth must be at the centre and immovable, not only for the reasons already given, καὶ διότι τὰ βίᾳ ῥιπτούμενα ἄνω βάρη κατὰ στάθμην πάλιν φέρεται εἰς ταὐτό, κἂν εἰς ἄπειρον ἡ δύναμις ἐκριπτῇ. 388 but also because heavy bodies forcibly thrown quite straight upward return to the point from which they started, even if they are thrown to an infinite distance. Ὅτι μὲν οὖν οὔτε κινεῖται οὔτ' ἐκτὸς κεῖται τοῦ μέσου, φανερὸν ἐκ τούτων 389 From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre. πρὸς δὲ τούτοις δῆλον ἐκ τῶν εἰρημένων τὸ αἴτιον τῆς μονῆς. Εἰ γὰρ φύσει πέφυκε φέρεσθαι πάντοθεν πρὸς τὸ μέσον, ὥσπερ φαίνεται, καὶ τὸ πῦρ ἀπὸ τοῦ μέσου πάλιν πρὸς τὸ ἔσχατον, ἀδύνατον ἐνεχθῆναι ὁτιοῦν μόριον αὐτῆς ἀπὸ τοῦ μέσου μὴ βιασθέν μία γὰρ φορὰ τοῦ ἑνὸς καὶ ἁπλῆ τοῦ ἁπλοῦ, ἀλλ' οὐχ αἱ ἐναντίαι ἡ δ' ἀπὸ τοῦ μέσου τῇ ἐπὶ τὸ μέσον ἐναντία. Εἰ τοίνυν ὁτιοῦν μόριον ἀδύνατον ἐνεχθῆναι ἀπὸ τοῦ μέσου, φανερὸν ὅτι καὶ τὴν ὅλην ἔτι ἀδυνατώτερον εἰς ὃ γὰρ τὸ μόριον πέφυκε φέρεσθαι, καὶ τὸ ὅλον ἐνταῦθα πέφυκεν ὥστ' (297a.) εἴπερ ἀδύνατον κινηθῆναι μὴ ὑπὸ κρείττονος ἰσχύος, ἀναγκαῖον ἂν εἴη μένειν αὐτὴν ἐπὶ τοῦ μέσου. 390 From what we have said the explanation of the earth's immobility is also apparent. If it is the nature of earth, as observation shows, to move from any point to the centre, as of fire contrariwise to move from the centre to the extremity, it is impossible that any portion of earth should move away from the centre except by constraint. For a single thing has a single movement, and a simple thing a simple: contrary movements cannot belong to the same thing, and movement away from the centre is the contrary of movement to it. If then no portion of earth can move away from the centre, obviously still less can the earth as a whole so move. For it is the nature of the whole to move to the point to which the part naturally moves. Since, then, it would require a force greater than itself to move it, it must needs stay at the centre. Μαρτυρεῖ δὲ τούτοις καὶ τὰ παρὰ τῶν μαθηματικῶν λεγόμενα περὶ τὴν ἀστρολογίαν τὰ γὰρ φαινόμενα συμβαίνει μεταβαλλόντων τῶν σχημάτων οἷς ὥρισται τῶν ἄστρων ἡ τάξις, ὡς ἐπὶ τοῦ μέσου κειμένης τῆς γῆς. 391 This view is further supported by the contributions of mathematicians to astronomy, since the observations made as the shapes change by which the order of the stars is determined, are fully accounted for on the hypothesis that the earth lies at the centre. Περὶ μὲν οὖν τοῦ τόπου καὶ μονῆς καὶ κινήσεως, ὃν τρόπον ἔχει, τοσαῦτα εἰρήσθω περὶ αὐτῆς. 392 Of the position of the earth and of the manner of its rest or movement, our discussion may here end.
| Postquam philosophus prosecutus est aliorum opiniones de terra, hic determinat de ea secundum veritatem. | 521. After pursuing the opinions of others concerning the earth, the Philosopher here determines about it according to the truth. |
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Et primo determinat de loco et quiete terrae; secundo de figura ipsius, ibi: figuram autem habere sphaericam et cetera. |
First he determines the question of the earth's place and rest; Secondly, that of its shape (L. 27). |
| Circa primum duo facit: | As to the first he does two things: |
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primo determinat veritatem per rationes naturales; secundo per signa astrologica, ibi: testificantur autem his et cetera. |
First he determines the truth by arguments of nature; Secondly, by signs taken from astronomy, at 530. |
| Circa primum duo facit: | Regarding the first he does two things: |
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primo ostendit quod impossibile est terram moveri; secundo ex praemissis assignat veram rationem quietis terrae, ibi: adhuc autem palam et cetera. |
First he shows that it is impossible for the earth to be in motion; Secondly, from the foregoing he assigns the true reason of the earth's rest, at 529. |
| Circa primum tria facit. | Regarding the first he does three things: |
| Primo dicit de quo est intentio, scilicet quod primo dicendum est utrum terra habeat motum vel quiescat. Ex motu enim debemus accedere ad alia quae sunt circa terram consideranda; et ideo hoc primo ponit, ut assumat hoc tanquam principium ad sequentia. | First he states his intention [379], namely, that we must first say whether the earth is in motion or at rest. For it is from motion that we must approach the other points to be considered about the earth. Therefore he presents this first in order to take it as a principle of what is to follow. |
| Secundo, ibi: quemadmodum enim diximus etc., assignat necessitatem praedictae inquisitionis. Sicut enim supra dictum est, quidam, scilicet Pythagorici, posuerunt eam moveri circa medium mundi, ac si esset una stellarum; alii vero, sicut in Timaeo scribitur, ponentes terram esse in medio, dicunt eam revolvi circa medium Poli, idest circa axem dividentem caelum per medium. | Secondly, at [380] he states why it is necessary to make this enquiry For, as has been said above, some, namely, the Pythagoreans, assumed that it is in motion about the middle of the world, as though it were one of the stars; but others, as is written in the Timaeus, assuming that the earth is in the middle, assert that it is revolved about the "middle of the pole," i.e., about the axis which divides the heaven through the middle. |
| Tertio, ibi: quod autem est impossibile etc., ostendit quod impossibile est terram sic moveri, quatuor rationibus. In quarum prima accipit hoc pro principio, quod si terra movetur circulariter, sive existens in medio mundi sive extra medium mundi, necesse est quod talis motus sit ei violentus. Manifestum est enim quod motus circularis non est proprius et naturalis motus terrae: quia si esset ei hic motus naturalis, oporteret quod quaelibet particula eius haberet hunc motum, quia idem est motus naturalis totius et partis, ut supra dictum est; hoc autem videmus esse falsum, nam omnes partes terrae moventur motu recto versus medium mundi. Si vero motus terrae circularis sit violentus et praeter naturam, non potest esse sempiternus: quia, sicut in praecedenti habitum est, nullum violentum est sempiternum. Sed si terra movetur circulariter, necesse est quod talis motus sit sempiternus, supposito quod mundus sit aeternus, secundum eius opinionem: quia secundum hoc oportet quod ordo mundi sit sempiternus, motus autem vel quies partium principalium mundi pertinet ad ordinem ipsius. Sic ergo sequitur quod terra non movetur circulariter. | 522. Thirdly, at [381] he shows that it is impossible for the earth to be thus in motion with four arguments. In the first of these he takes as a principle the fact that, if the earth is moved circularly, whether in the middle of the world or outside the middle, such a motion, as far as the earth is concerned, would have to be a compulsory one. For it is manifest that a circular motion is not the proper and natural motion for the earth, because, if it were, then every particle of earth would have to have this motion, since the natural motion of the whole and of the part is the same, as was said above. Now observation shows that this is false, for all the parts of earth are moved with a straight motion toward the middle of the world. But if a circular motion of earth is a compulsory one and beside its nature, it cannot be eternal, because, as was held in a previous lecture, nothing compulsory is eternal. But if the earth is in circular motion, that motion has to be eternal, supposing, according to his opinion, that the world is eternal — because, according to this, the world's order must be eternal, and the motion, or rest, of the chief parts of the world pertain to its order. Thus it follows, therefore, that the earth is not being moved circularly. |
| Secundam rationem ponit ibi: adhuc omnia etc.; quae talis est. Omnia corpora quae circulariter moventur, videntur esse haesitantia, idest non semper uniformem situm habentia, ex eo quod quodlibet eorum movetur pluribus motibus et non uno solo, excepta prima sphaera, quae movetur uno motu: et haec, secundum ipsum, est sphaera stellarum fixarum. Si ergo terra habet motum circularem, sive in medio existens sive extra medium, oportet quod moveatur pluribus motibus, scilicet motu primae sphaerae circa polos aequinoctialis, et aliquo alio motu proprio circa polos zodiaci. | 523. The second argument at [382] is this: All bodies in circular motion seem to be "hesitant," i.e., they do not always retain a uniform position, since each of them is moved by several motions and not just one, except the first sphere, which is moved with one motion, and this, according to him, is the sphere of the fixed stars. If, therefore, the earth has a circular motion, whether being in the middle or outside the middle, it would have to be moved with several motions, namely, with the motion of the first sphere about the poles of the equinoctial circle and with another proper motion about the poles of the Zodiac. |
| Quod non potest esse: quia si hoc esset, contingeret fieri mutationes et versiones stellarum fixarum per respectum ad terram, quae propter proprium motum suum deficeret, et non rediret ad idem punctum simul cum stella fixa, vel ipsa tota terra vel aliqua pars eius signata, sicut accidit de planetis; et ita sequeretur quod stellae fixae non semper viderentur oriri et occidere secundum eandem partem terrae. Quod non accidit, sed semper oriuntur et occidunt secundum eadem loca designata. Non ergo terra circulariter movetur. | But this cannot be, because, if it were, there would be changes and turnings of the fixed stars in relation to the earth, which, because of its own motion, would fail [i.e., be slowed up] and would not return to the same point simultaneously with a fixed star, either in the case of the whole earth or of some indicated part, as happens with the planets. Consequently, it would follow that the fixed stars would not always be seen to rise and set according to the same part of the earth. But this does not happen — rather they always rise and set according to the same designated places. Therefore, the earth is not circularly moved. |
| Tertiam rationem ponit ibi: adhuc autem latio etc., quae quidem procedit ex motu partium terrae et totius. Unde circa hoc tria facit: | 524. At [383] he gives a third argument which takes its start from the motion of the parts of the earth and of the whole. Hence with respect to this he does three things: |
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primo proponit qualis sit motus naturalis terrae et partium eius; secundo circa hoc movet quandam dubitationem, ibi: hoc enim utique etc.; tertio concludit quod intendit. |
First he proposes the condition of the natural motion of the earth and of its parts; Secondly, he raises a problem on this point, at 525; Thirdly, he concludes to what he intended, at 527. |
| Dicit ergo primo quod motus partium terrae, secundum suam naturam, est ad medium mundi totius; et similiter, si tota terra esset extra medium mundi, moveretur ad medium mundi secundum suam naturam, quia idem est motus naturalis totius et partis. | He says therefore first [383] that the motion of parts of the earth is, according to their nature, to the middle of the whole world. In like manner, if the whole earth were outside the middle of the world, it would be moved to the middle of the world according to its nature, because the natural motion of the whole and of the part is the same. |
| Deinde cum dicit: hoc enim utique etc., movet circa hoc quandam dubitationem. Et primo proponit ipsam: et dicit quod si ponatur quod terra sit in medio mundi vel centro, hoc modo quod idem sit centrum totius mundi et ipsius terrae, potest dubitari ad quod horum moveantur secundum naturam corpora gravia, et specialiter partes terrae; utrum videlicet ad medium ea ratione qua est medium mundi, vel ea ratione qua est medium terrae. | 525. Then at [384] he raises a certain problem on this point. First he proposes it, and says that if it be assumed that the earth is in the middle or center of the world, in such a way that the center of the whole world and of the earth is the same, there can be a problem as to which of these middles do heavy bodies, and especially parts of the earth move according to nature, namely, whether to the middle as it is the middle of the world, or as it is the middle of the earth. |
| Secundo ibi: necesse itaque etc., solvit dubitationem, dicens necessarium esse quod corpora gravia moveantur ad medium, ea ratione qua est medium totius mundi. Motus enim gravium contrariatur motui levium; sed corpora levia, et specialiter ignis, moventur ad extremum caelestis corporis; ergo corpora gravia, et specialiter terra, moventur ad medium mundi. Sed quia accidit quod idem sit medium terrae et medium mundi, consequens est quod partes terrae moveantur ad medium terrae, non per se sed per accidens, prout scilicet idem est subiecto medium terrae et medium mundi; sicut si cognosco Coriscum, per accidens cognosco venientem, quia Coriscus est veniens. | Secondly, at [385] he solves the problem, saying that it is necessary that heavy bodies be moved to the middle as it is the middle of the whole world. For the motion of heavy bodies is contrary to the motion of the light. But light bodies, and in particular, fire, are moved toward the outer boundary of the heavenly body; therefore, heavy bodies, and in particular, earth, are moved to the middle of the world. But because it happens that the middle of the earth and the middle of the world are the same, the consequence is that the parts of earth are moved to the middle of the earth, not per se, but per accidens, namely, insofar as the middle of the earth and the middle of the world are the same as to subject — thus, if I know Coriscus, I know per accidens the one who is approaching, because Coriscus is the one approaching. |
| Tertio ibi: quoniam autem fertur etc., probat quod supposuerat, scilicet quod corpora gravia et partes terrae moventur ad medium. Et dicit huius signum esse, quod corpora gravia feruntur naturaliter versus terram non iuxta invicem, idest non secundum aeque distantes lineas, quae nunquam concurrunt, sed ad similes angulos, idest ad rectos angulos respectu superficiei vel lineae contingentis superficiem terrae; et hoc ex quacumque parte corpus grave movetur usque ad terram. | 526. Thirdly, at [386] he proves what he had assumed, namely, that heavy bodies and the parts of earth are moved to the middle. And he says that a sign of this is that heavy bodies are naturally borne toward the earth, "not side by side," i.e., not along equidistant lines that never meet, but "according to similar angles," i.e., right angles with respect to the surface, or a line tangent to the earth's surface. And this happens no matter from which direction a heavy body is moved toward the earth. |
| Et huius signum est quod, si columna in quacumque parte terrae non statuatur secundum rectos angulos, sed inclinationem habens, cadet versus illam partem ex qua facit angulum acutum. Est autem probatum in III Euclidis quod, si aliqua linea contingat circulum, et protrahatur alia linea recta perpendiculariter super lineam contingentem in loco contactus, necesse est lineam illam, si protrahatur, transire centrum circuli. Et sic patet quod omnia corpora gravia moventur versus centrum terrae; ita quod, si non esset aliquid impediens, ex diversis partibus mota concurrerent in centro terrae; propter hoc quod quodlibet eorum moveretur secundum lineam rectam perpendiculariter cadentem super lineam contingentem, et in loco contactus. Et sic oportet quod omnia corpora gravia ferantur ad unum medium totius mundi et terrae. | And a sign of this is that if a pillar anywhere on earth is not erected according to right angles, but leans, it will fall in the direction with which it makes an acute angle. Now it is proved in Book III of Euclid that, if a line is tangent to a circle, and another line is drawn down perpendicular to the tangent line at the point of contact with the circle, necessarily it will, if extended, pass through the center of the circle. Thus it is plain that all heavy bodies are moved toward the center of the earth, in such a way that, if there were no obstacle, things moved from different directions would meet in the center of the earth. The reason for this is that each of them would be moving along a straight line falling perpendicularly on a tangent at its point of contact [with the earth]. Consequently all heavy bodies must be borne toward the one middle of the world and of the earth. |
| Deinde cum dicit: manifestum igitur etc., concludit propositum. Et infert duas conclusiones. Quarum prima est quod terra sit in medio mundi. Quod quidem concluditur sic ex praemissis. Omnia corpora gravia moventur per se ad medium mundi; omnia etiam moventur ad medium terrae, ut probatum est; ergo medium terrae est medium mundi. Et ita terra est in medio mundi. | 527. Then at [387] he concludes his proposition. And he draws two conclusions. The first of these is that the earth is in the middle of the world. This conclusion is derived thus from the foregoing. All heavy bodies are moved per se to the middle of the world. But all are likewise moved to the middle of the earth, as has been proved. Therefore, the middle of the earth is the middle of the world. And so the earth is in the middle of the world. |
| Secunda conclusio est quod terra sit immobilis. Quod quidem concluditur ex praemissis sic. Nihil movetur in loco ad quem naturaliter movetur, quia ibi naturaliter quiescit; sed terra naturaliter movetur ad medium mundi; ergo non movetur in medio. Non est autem nisi in medio mundi, ut probatum est; ergo terra nullo modo movetur. | The second conclusion is that the earth is immovable. This is concluded from the foregoing as follows: Nothing is moved in the place toward which it is naturally moved. But the earth is naturally moved to the middle of the world. Therefore, it is not in motion there. But it is nowhere but in the middle of the world, as has been proved, Therefore the earth is not in motion in any way |
| Quartam rationem ponit ibi: et quia vi proiecta et cetera. Videmus enim quod, si lapis superpositus alicui tabulae, proiiciatur sursum in directum, et iterum cadat secundum eandem rectitudinem, secundum quam sursum motus est; si tabula non moveatur, cadet lapis in eundem locum ubi prius erat; si autem tabula moveatur, cadet lapis in alium locum, tanto magis distantem, quanto magis lapis fuerit in altum proiectus; quia secundum hoc erit maius tempus inter principium proiectionis et terminum casus. Videmus autem quod gravia proiecta sursum secundum regulam, idest secundum rectam lineam, iterum revertuntur in eundem locum terrae unde fuerunt proiecta. Et ne aliquis dicat quod accidit propter tarditatem motus terrae, quod imperceptibilis est distantia utriusque loci; subiungit quod hoc idem accidit, si infinities, una vice post aliam, aliquis proiiciat lapidem sursum; ita scilicet quod magnitudo temporis faciat distantiam locorum esse perceptibilem. Et ita patet quod terra non movetur. | 528. He gives a fourth argument at [388] For we observe that if a stone at rest on a tablet is thrown straight up into the air and then falls along the same straight line that it described in its upward flight, and the tablet is not moved, the stone will fall into the same place where it previously was. But if the tablet is moved, the stone will fall in another place [than the tablet], so much the more distant as the stone was thrown higher — since, according to this, there will be more time between the beginning of the throwing and the end of the fall. However, when heavy objects are thrown upward "according to rule," i.e., according to a straight line, they again return to the same place on earth whence they were thrown. And lest anyone should say that this happens due to the slowness of the earth's motion, which makes the difference between the two places to be imperceptible, he adds that the same thing will happen if someone throws the stone up an infinite number of times, one after the other, i.e., long enough to make perceptible the distance intervening between the places. Thus it is plain that the earth is not in motion. |
| Deinde epilogando concludit manifestum esse ex praemissis quod terra neque movetur, neque habet situm extra medium mundi. | Then in summing up he concludes [3891 that it is plain from the foregoing that the earth is neither in motion nor has any position outside the middle of the earth. |
| Deinde cum dicit: adhuc autem palam etc., assignat causam quietis terrae. Et dicit quod ex praemissis manifestum est quae sit causa quietis eius. Sicut enim dictum est, terra naturaliter nata est ferri ex omni parte ad medium, sicut sensibiliter apparet (et similiter ad sensum apparet quod ignis naturaliter movetur a medio mundi ad extremum). Unde sequitur quod nulla particula terrae, vel parva vel magna, potest moveri a medio, nisi per violentiam: sicut enim in primo habitum est, unius corporis est unus motus naturalis, et simplex motus simplicis corporis, non autem possunt esse uni corpori simplici duo motus contrarii naturales; motus autem a medio contrarius est motui ad medium. Et sic, si ita est quod quaecumque pars terrae non possit ferri a medio nisi per violentiam, manifestum est quod multo impossibilius est quod tota terra moveatur a medio. | 529. Then at [390] he assigns the cause of the earth's rest. And he says that from the foregoing it is plain what the cause of its rest is. For, as has been said, earth is naturally inclined to be borne to the middle from every direction, as our sense observations indicate — and similarly it is apparent to sense that fire is naturally moved from the middle of the world to the extreme. Hence it follows that no particle of earth, small or large, can be moved from the middle except by violence; for, as was had in Book I, one body has one natural motion, and to a simple body belongs a simple motion, so that two contrary motions cannot belong to a simple body. But a motion from the middle is contrary to one toward the middle. And so, if it is true that no portion of earth can be borne from the middle except through violence, it is plainly much more impossible that the entire earth be moved from the middle. |
| Posset autem aliquis obviare, dicens quod tota terra non movetur ad medium. Sed ipse hoc excludit, dicens quod illuc nata est ferri tota terra, quo nata est ferri pars terrae: et ita, si pars terrae movetur ad medium naturaliter, et tota terra illuc movebitur naturaliter. Et ita impossibile est quod moveatur a medio: unde necessarium est quod quiescat in medio. | However, someone could object that the whole earth is not in motion to the middle. But he excludes this by saying that the whole earth is apt to be borne whither a part is apt to be borne. And so, if a part of the earth is naturally moved to the middle, then the whole earth will be naturally moved thither. And so it is impossible that it be moved from the middle; hence it is necessary that it rest in the middle. |
| Deinde cum dicit: testificantur autem his etc., confirmat quae dicta sunt de situ et quiete terrae, per dicta astrologorum. Et dicit quod his quae dicta sunt, scilicet quod terra sit in medio et quod quiescat, attestantur ea quae dicta sunt a mathematicis circa astrologiam: ea enim quae sensibiliter apparent circa translationem configurationum, quae determinantur secundum astrorum situm et ordinem, hoc modo salvari possunt, si terra sit in medio quiescens, et non aliter. | 530. Then at [391] he uses the findings of astronomers to confirm his teachings about the earth's position and state of rest. And he says that what has been said, namely, that the earth is in the middle and rests there, is attested to by the statements of the mathematicians concerning astronomy. For what sensibly appears concerning the shifting of configurations, determined by the position and order of the stars, can be saved if the earth is at rest in the middle and not otherwise. |
| Ut enim Ptolomaeus dicit, si terra non esset in medio, oporteret eam altero trium modorum esse dispositam. Quorum unus est quod axis mundi extra terram esset, et tamen terra distaret aequaliter ab utroque polorum. Secundus modus est quod terra esset in axe, et magis appropinquaret ad unum polorum quam ad alium. Tertius modus est quod neque esset terra in axe, neque aequaliter distaret ab utroque polorum. | For as Ptolemy says, if the earth were not in the middle, then it would have to be subject to one of three dispositions. One of these is that the axis of the world would be outside the earth, and yet the earth would be equidistant from each of the poles. The second is that the earth would be on the axis and would approach closer to one pole than to the other. The third is that the earth is neither on the axis nor equidistant from each of the poles. |
| Si autem terra esset sita primo modo, ut scilicet terra esset extra axem aequaliter distans ab utroque polo; si quidem esset supra axem vel infra, oporteret quod horizon habitantium in sphaera recta divideret aequinoctialem et omnes circulos aequidistantes in partes inaequales, et ita nunquam in sphaera recta fieret aequinoctium. In sphaera vero obliqua vel nunquam fieret aequinoctium, vel non fieret in medio duorum solstitiorum: quia horizon nunquam posset dividere maximum circulorum aequidistantium in duo media, sed forte aliquem aliorum. Si vero terra declinaret ab axe ad partem Orientalem vel Occidentalem, sequeretur primo quidem quod stellae non viderentur aequales in ortu et occasu, propter inaequalem distantiam. Iterum secundo sequeretur quod non esset aequale spatium temporis ab ortu solis usque ad maximam exaltationem eius, quando maxime appropinquat capitibus nostris, spatio temporis quod est usque ad occasum. | Now if the earth were situated in the first way, namely, so that the earth would be outside the axis but equidistant from each pole, then, whether it were above or below the axis, the horizon of people living in the right sphere would have to divide the equinoctial circle and all equidistant circles into unequal parts; consequently, there would never be an equinox in the right sphere. In the oblique sphere either there never would be an equinox, or else it would not occur between two solstices — because the horizon could never divide the greatest of the equidistant circles into two halves, although perhaps one of the others. But if the earth leaned away from the axis in either an easterly or westerly direction, it would follow, first of all, that the stars would not appear equal in their rising and setting on account of the inequality of distance. Secondly, it would follow that the interval of time from sunrise to highest elevation, when it is most above our heads, would not be equal to the space of time until sunset. |
| Si vero terra esset disposita secundo modo, scilicet quod terra esset in axe, sed appropinquaret magis ad unum polorum quam ad alium, sequerentur duo inconvenientia. Primo quidem quia in sola recta sphaera horizon divideret caelum in duo media: in sphaera vero obliqua semper esset minor pars caeli ex parte Poli apparentis, maior autem ex parte Poli occultati. Et ita sequeretur quod horizon obliquae sphaerae non divideret zodiacum in duo media: cuius contrarium apparet ex hoc quod semper sex signa videmus super terram. Secundo quia, si terra non esset directe posita sub aequinoctiali, sequeretur quod umbrae corporum erectorum in aequinoctiis Orientales, non fierent in directo Occidentalibus: cuius contrarium ubique apparet. | But if the earth were disposed in the second way, namely, with the earth on the axis but nearer to one of the poles than to the other, two unacceptable things would follow. First of all, because it would be in the right sphere alone that the horizon would divide the heaven into two halves, whereas in the oblique sphere the smaller part of the heaven would always be related to the visible pole, and the larger part to the hidden pole. And thus it would follow that the horizon of the oblique sphere would not divide the Zodiac into two halves; the contrary of which is apparent from the fact that we see six signs over the earth. Secondly, because if the earth were not directly situated under the equinoctial circle [i.e., the equator], it would follow that the eastern shadows of erect bodies at the equinoxes would not be in a straight line with those of the west — but the contrary of this is observed. |
| Et ex hoc patet quod neque tertius modus esse potest, ut scilicet terra neque sit in axe, neque distet aequaliter ab utroque polorum: quia ad hanc positionem sequuntur omnia praedicta inconvenientia. Qualitercumque etiam terra non esset in medio mundi, confunderetur omnis ordo qui consideratur circa augmentum et deminutionem dierum et noctium. Similiter etiam perturbarentur regulae eclipsium: non enim semper eclipses lunae fierent in directa oppositione solis et lunae, si terra non esset in medio. | And from this it is plain that neither is the third way possible, namely, that the earth be neither on the axis nor equidistant from each of the poles, because, on this position, all the aforesaid impossibilities would follow. Moreover, no matter which way the earth should fail to be in the middle of the world, the entire order in the increasing and decreasing of days and nights would be confused. Similarly disturbed would be the rules of eclipses; for eclipses of the moon would not always occur when sun and moon are in direct opposition, if the earth were not in the middle. |
| Quod autem terra non moveatur transiens de loco ad locum, contingit ex hoc quod terra semper est in medio. Et iterum sequeretur, quocumque motu moveretur, quod propter velocitatem sui motus occultarentur a nobis omnes alii motus, vel nubium vel animalium: non enim videtur moveri quod tardius movetur iuxta corpus velocius motum. | 531. That the earth is not in a motion that passes from place to place is due to its always being in the middle. And again it would follow, no matter with what sort of motion it were moved, that the swiftness of its motion would conceal from us all other motions whether of clouds or of animals. For a slower moving object does not seem to be in motion when side by aide with a faster moving object. |
| Sic igitur epilogando concludit philosophus quod de loco et motu et quiete terrae, quomodo se habeant, tanta dicta sint. | Thus, therefore, in summary, the Philosopher concludes [392] that so much has been said above about the manner of the earth's place and its motion and rest. |
Lecture 27:
Proof of the earth's spherical shape, from motionChapter 14 cont. Σχῆμα δ' ἔχειν σφαιροειδὲς ἀναγκαῖον αὐτήν ἕκαστον γὰρ τῶν μορίων βάρος ἔχει μέχρι πρὸς τὸ μέσον, καὶ τὸ ἔλαττον ὑπὸ τοῦ μείζονος ὠθούμενον οὐχ οἷόν τε κυμαίνειν, ἀλλὰ συμπιέζεσθαι μᾶλλον καὶ συγχωρεῖν ἕτερον ἑτέρῳ, ἕως ἂν ἔλθῃ ἐπὶ τὸ μέσον. 393 Its shape must necessarily be spherical. For every portion of earth has weight until it reaches the centre, and the jostling of parts greater and smaller would bring about not a waved surface, but rather compression and convergence of part and part until the centre is reached. Δεῖ δὲ νοῆσαι τὸ λεγόμενον ὥσπερ ἂν εἰ γιγνομένης τὸν τρόπον ὃν καὶ τῶν φυσιολόγων λέγουσί τινες γενέσθαι. Πλὴν ἐκεῖνοι μὲν βίαν αἰτιῶνται τῆς κάτω φορᾶς βέλτιον δὲ τιθέναι τἀληθές, καὶ φάναι τοῦτο συμβαίνειν διὰ τὸ φύσιν ἔχειν φέρεσθαι τὸ βάρος ἔχον πρὸς τὸ μέσον. Ἐν δυνάμει οὖν ὄντος τοῦ μίγματος τὰ διακρινόμενα ἐφέρετο ὁμοίως πάντοθεν πρὸς τὸ μέσον. 394 The process should be conceived by supposing the earth to come into being in the way that some of the natural philosophers describe. Only they attribute the downward movement to constraint, and it is better to keep to the truth and say that the reason of this motion is that a thing which possesses weight is naturally endowed with a centripetal movement. When the mixture, then, was merely potential, the things that were separated off moved similarly from every side towards the centre. Εἴτ' οὖν ὁμοίως ἀπὸ τῶν ἐσχάτων διῃρημένα τὰ μόρια συνήχθη πρὸς τὸ μέσον, εἴτ' ἄλλως ἔχοντα, ποιήσει ταὐτόν. Ὅτι μὲν οὖν ὁμοίως γε πανταχόθεν ἀπὸ τῶν ἐσχάτων φερομένων πρὸς ἓν μέσον ἀναγκαῖον ὅμοιον γίγνεσθαι πάντῃ τὸν ὄγκον, φανερόν ἴσου γὰρ πάντῃ προστιθεμένου ἴσον ἀνάγκη ἀπέχειν τοῦ μέσου τὸ ἔσχατον τοῦτο δὲ τὸ σχῆμα σφαίρας ἐστίν. Οὐδὲν δὲ διοίσει πρὸς τὸν λόγον, οὐδ' εἰ μὴ πανταχόθεν ὁμοίως συνέθει πρὸς τὸ μέσον τὰ μόρια αὐτῆς. Τὸ γὰρ πλεῖον ἀεὶ τὸ πρὸ αὑτοῦ ἔλαττον προωθεῖν ἀναγκαῖον μέχρι τοῦ μέσου τὴν ῥοπὴν ἐχόντων ἀμφοῖν, καὶ τοῦ βαρυτέρου προωθοῦντος μέχρι τούτου τὸ ἔλαττον βάρος. 395 Whether the parts which came together at the centre were distributed at the extremities evenly, or in some other way, makes no difference. If, on the one hand, there were a similar movement from each quarter of the extremity to the single centre, it is obvious that the resulting mass would be similar on every side. For if an equal amount is added on every side the extremity of the mass will be everywhere equidistant from its centre, i.e. the figure will be spherical. But neither will it in any way affect the argument if there is not a similar accession of concurrent fragments from every side. For the greater quantity, finding a lesser in front of it, must necessarily drive it on, both having an impulse whose goal is the centre, and the greater weight driving the lesser forward till this goal is reached. Ὃ γὰρ ἄν τις ἀπορήσειε, τὴν αὐτὴν ἔχει τούτοις λύσιν εἰ γὰρ οὔσης ἐπὶ τοῦ μέσου καὶ σφαιροειδοῦς τῆς γῆς πολλαπλάσιον βάρος ἐπιγένοιτο πρὸς θάτερον ἡμισφαίριον, οὐκ ἔσται τὸ αὐτὸ μέσον τοῦ ὅλου καὶ τὸ τῆς γῆς ὥστε ἢ οὐ μενεῖ ἐπὶ τοῦ μέσου, ἢ εἴπερ, ἠρεμήσει γε καὶ (297b.) μὴ τὸ μέσον ἔχουσα, ᾗ πέφυκε κινεῖσθαι καὶ νῦν. Τὸ μὲν οὖν ἀπορούμενον τοῦτ' ἔστιν 396 In this we have also the solution of a possible difficulty. The earth, it might be argued, is at the centre and spherical in shape: if, then, a weight many times that of the earth were added to one hemisphere, the centre of the earth and of the whole will no longer be coincident. So that either the earth will not stay still at the centre, or if it does, it will be at rest without having its centre at the place to which it is still its nature to move. Such is the difficulty. ἰδεῖν δ' οὐ χαλεπὸν μικρὸν ἐπιτείναντας, καὶ διελόντας πῶς ἀξιοῦμεν ὁποσονοῦν μέγεθος φέρεσθαι πρὸς τὸ μέσον, βάρος ἔχον. Δῆλον γὰρ ὡς οὐχὶ μέχρι τοῦ ἅψασθαι τοῦ κέντρου τὸ ἔσχατον, ἀλλὰ δεῖ κρατεῖν τὸ πλέον ἕως ἂν λάβῃ τῷ αὑτοῦ μέσῳ τὸ μέσον μέχρι τούτου γὰρ ἔχει τὴν ῥοπήν. Οὐδὲν τοίνυν τοῦτο διαφέρει λέγειν ἐπὶ βώλου καὶ μορίου τοῦ τυχόντος ἢ ἐπὶ ὅλης τῆς γῆς οὐ γὰρ διὰ μικρότητα ἢ μέγεθος εἴρηται τὸ συμβαῖνον, ἀλλὰ κατὰ παντὸς τοῦ ῥοπὴν ἔχοντος ἐπὶ τὸ μέσον. Ὥστε εἴτε ὅλη ποθὲν ἐφέρετο εἴτε κατὰ μέρος, ἀναγκαῖον μέχρι τούτου φέρεσθαι ἕως ἂν πανταχόθεν ὁμοίως λάβῃ τὸ μέσον, ἀνισαζομένων τῶν ἐλαττόνων ὑπὸ τῶν μειζόνων τῇ προώσει τῆς ῥοπῆς. 397 A short consideration will give us an easy answer, if we first give precision to our postulate that any body endowed with weight, of whatever size, moves towards the centre. Clearly it will not stop when its edge touches the centre. The greater quantity must prevail until the body's centre occupies the centre. For that is the goal of its impulse. Now it makes no difference whether we apply this to a clod or common fragment of earth or to the earth as a whole. The fact indicated does not depend upon degrees of size but applies universally to everything that has the centripetal impulse. Therefore earth in motion, whether in a mass or in fragments, necessarily continues to move until it occupies the centre equally every way, the less being forced to equalize itself by the greater owing to the forward drive of the impulse. Εἴτ' οὖν ἐγένετο, τοῦτον ἀναγκαῖον γενέσθαι τὸν τρόπον, ὥστε φανερὸν ὅτι σφαιροειδὴς ἡ γένεσις αὐτῆς, εἴτ' ἀγένητος ἀεὶ διατελεῖ μένουσα, τὸν αὐτὸν τρόπον ἔχειν ὅνπερ κἂν εἰ γιγνομένη τὸ πρῶτον ἐγένετο. 398 If the earth was generated, then, it must have been formed in this way, and so clearly its generation was spherical; and if it is ungenerated and has remained so always, its character must be that which the initial generation, if it had occurred, would have given it.
| Postquam philosophus determinavit veritatem circa locum et motum vel quietem terrae, hic determinat veritatem circa figuram ipsius. | 532. Having determined the truth about the earth's place and about its motion or rest, the Philosopher here determines the truth about its shape. |
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Et primo probat terram esse sphaericam, rationibus naturalibus, quae accipiuntur ex parte motus; secundo rationibus mathematicis et astrologicis, quae accipiuntur ex his quae apparent secundum sensum, ibi: adhuc autem et per apparentia et cetera. |
First he proves that the earth is spherical with natural reasons taken on the part of motion; Secondly, with mathematical and astronomical reasons based on sense observations (L. 28). |
| Circa primum duo facit: | About the first he does two things: |
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primo ostendit propositum, ratione sumpta ex ipsa specie naturalis motus terrae; secundo ex figura motus ipsius, ibi: et quia omnia et cetera. |
First he shows his proposition with an argument taken from the species of the natural motion of earth; Secondly, from the figure of its motion (L. 28). |
| Circa primum tria facit: | Regarding the first he does three things: |
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primo ponit rationem; secundo comparat eam rationi quam antiqui assignabant, ibi: oportet autem intelligere etc.; tertio excludit quasdam obviationes ad rationem praedictam, ibi: sive igitur similiter et cetera. |
First he presents his reason; Secondly, he compares it with the reason assigned by the ancients, 534; Thirdly, he excludes certain objections to the aforesaid reason, at 535. |
| Dicit ergo primo quod necesse est terram habere sphaericam figuram, hac ratione; quia quaelibet partium eius habet gravitatem ad medium, idest, sua gravitate naturaliter movetur ad medium, ut ex supra dictis patet. Est etiam hic considerandum circa motum partium terrae, quod maior pars depellit minorem, quousque ipsa maior pars perveniat ad medium. Cuius ratio est, quia maior pars terrae habet maiorem gravitatem, et per consequens maiorem virtutem ut moveatur ad medium; semper autem minor virtus vincitur a maiori. Et ideo non est possibile quod, partibus terrae motis versus medium, aliqua pars terrae intumescat vel fluctuet, ita scilicet quod elevetur in situ una pars terrae super aliam, sicut accidit in mari fluctuante, quasi terra sit alicubi non compressa et alicubi compressa: sed oportet quod, cum omnes partes terrae tendant versus medium, superiores partes terrae comprimant inferiores, et una quasi consentiat alteri cedendo ei, quousque perveniatur ad medium. Et sic oportet quod, partibus terrae quasi undique aequaliter compressis versus medium, terra habeat sphaericam figuram. | 533. He says therefore first [393] that. it is necessary that the earth have a spherical shape for this reason, namely, that each of its parts "has heaviness toward the middle," i.e., is naturally moved to the middle by its heaviness, as is plain from what has been said above. But we must here consider, with respect to the motion of parts of the earth, that a larger part crowds out a smaller until the larger part reaches the middle. The reason for this is that a larger portion of earth has greater heaviness, and consequently greater power to be moved to the middle, a lesser power being always overcome by a greater. And therefore it is not possible that, as portions of earth are moved to the middle, any part should billow or rise and fall, so that one part of earth should have a position above another, as occurs in the waves of the sea, as though the earth were here not compressed and there compressed. Rather, since all parts of earth tend toward the middle, the upper parts of earth must press down on the lower, and one part, as it were, consent to another by yielding to it, until the middle is reached. And so, as a result, the parts of earth being, as it were, from all sides compressed toward the middle, the earth must have a spherical shape. |
| Deinde cum dicit: oportet autem intelligere etc., manifestat praedictam rationem, comparando ipsam ad rationem de figura terrae ab aliis assignatam. Et dicit quod oportet praedictam rationem intelligere ac si positum esset quod terra esset generata de novo, concurrentibus undique partibus terrae versus medium, sicut antiqui naturales posuerunt. In hoc tamen differentia est, quod illi ponunt motum partium terrae versus medium causari ex violentia gyrationis caeli, sicut supra dictum est: melius autem et verius est, ut ponamus motum partium terrae accidere naturaliter, propter hoc quod partes terrae habent gravitatem inclinantem eas versus medium. Si ergo ponamus quod terra prius erat in potentia, sicut antiqui posuerunt, consequens erit quod partes eius, dispersae et disgregatae prius, quando fuerunt in actu graves, ferentur simili modo ex omni parte ad medium; et ex hoc constituetur terra sphaericae figurae. | 534. Then at [394] he clarifies the foregoing reason by comparing it with the reason others assigned for the shape of the earth. And he says that the foregoing reason must be understood as though one were positing that the earth was newly generated by the parts of earth coming together from all directions to the middle, as the ancient natural philosophers posited. Nevertheless, there is this difference, namely, that whereas they posit that this motion of parts of earth toward the middle is caused by the violence of the heaven's gyration, as was said above, it is better and truer to suppose that this motion of the parts of earth occurs naturally, on account of the parts of earth possessing heaviness that inclines them toward the middle. If, therefore, we posit that the earth was at first in potency, as the ancients posited, the consequence will be that its parts, at first dispersed and unconnected, will have been borne, when become heavy in act, from every direction to the middle. And from this will result an earth spherical in shape. |
| Deinde cum dicit: sive igitur similiter etc., excludit tres obviationes contra praemissam rationem. Quarum prima est, quod potest aliquis dicere quod praedicta ratio non cogit figuram terrae esse sphaericam, nisi supposito quod in ipsa generatione terrae, undique partes terrae similiter et aequaliter concurrant ad medium. Sed potuit contingere quod in illa disgregatione partium terrae, plures partes terrae inventae fuerint ad unam partem superioris loci quam ad aliam; et sic plures partes terrae aggregatae sunt ad unam partem eius quam ad aliam; quod est contra rationem sphaericae figurae. | 535. Then at [395] he excludes three objections against the foregoing reason. The first of these is that someone can say that the foregoing reason does not force the earth's shape to be spherical, unless one supposes that, during the coming-to-be of the earth, parts of earth from all sides similarly and equally moved together to the middle. But it could have happened that when the parts were still disassociated, more parts of earth were found in one region of the place above than in another; consequently, more parts of earth have been assembled at one part of it than at another — which is against the nature of a spherical shape. |
| Sed ipse dicit quod idem contingit circa figuram terrae, sive partes terrae quae prius erant disgregatae, similiter conveniant ab extremis terrae versus medium, sive aliter se habeant. Est autem manifestum quod, si partes terrae similiter et aequaliter undique ab extremis ferantur ad medium, necesse est quod moles terrae undique fiet aequalis: quia cum aequalis quantitas partium apponatur medio undique, necesse est quod extremum terrae undique distet aequaliter a medio. Et in hoc salvatur ratio sphaerae: quia sphaera nihil aliud est quam corpus a cuius medio omnes lineae ductae ad extrema, sunt aequales. | 536. But he says that the same results as to the shape of the earth whether the previously disassociated parts of earth come together similarly from the extremities of the earth to the middle or something other is the case. For it is manifest that, if the parts of the earth are carried in a similar fashion and in equal amounts from all directions to the middle, then of course the resulting mass of earth will be everywhere equal — since, because an equal quantity of parts is added to the middle on all sides, necessarily the periphery of the earth will be everywhere equidistant from the middle. And that makes for a sphere, because a sphere is nothing else than a body from the center of which all lines to its surface are equal. |
| Nec differt quantum ad hanc rationem, si aliquis dicat quod partes terrae non similiter et aequaliter conveniunt ad medium: quia semper illud quod est plus, cum sit gravius, propellit id quod est minus grave, usque ad hoc, idest usque ad medium. | This argument is not affected if someone should insist that the parts do not gather in the middle in a similar way and in equal amounts, since the larger portions, being heavier, always jostle the smaller portions "so far," i.e., until the middle is reached. |
| Quod quidem potest intelligi dupliciter. Uno modo sic ut intelligatur quod id quod est minus grave, propellatur a graviori quousque minus grave pertingat ad medium. Sed hoc non convenit secundum intentionem Aristotelis: quia praedicta positione facta, adhuc remanebit maior quantitas versus unam partem terrae, ad quam plures partes concurrunt. | Now this can be interpreted in two ways. In one way, as meaning that a less heavy part would be pushed until it reached the middle, by a heavier part. But this does not fit Aristotle's intention, because, on the basis of such an interpretation, there will still remain a greater amount in one region of the earth, where more parts come together. |
| Alio modo potest intelligi usque ad hoc, idest quousque ipsum corpus gravius attingat medium. Et hoc convenientius dicitur: quia unumquodque corpus grave naturaliter tendit ad hoc ut ipsum sit in suo loco, non autem ad hoc quod aliquid aliud in suo loco statuatur. Et inde est quod corpus gravius, ad hoc quod ipsum magis appropinquet medio, repellit per violentiam corpus minus grave a medio; sicut patet de lapide proiecto in aquam, qui repellit aquam a contactu terrae. | In another way "so far" can mean, "until the heavier body reaches the middle." And this interpretation is more fitting, because every heavy body naturally tends to this, namely, that it be in its own place, and not that something else be in its own place. Wherefore, a heavier body, in striving to get closer to the middle, violently shoves a less heavy body from the middle — as in the case of a stone thrown into water, which shoves aside the water from contact with the earth. |
| Et secundum hoc procedit ratio Aristotelis: nam si versus unam partem terrae sit maior quantitas, ad hoc quod ipsa magis appropinquet medio, depellit minorem partem per violentiam a medio, quousque aequale pondus ex omni parte terrae inveniatur. | It is along these lines that Aristotle's reason proceeds. For if a larger quantity of earth finds itself in one section of the earth, then, in order to get closer to the middle, it violently jostles a smaller part from the middle until there is found an equal weight everywhere on the earth. |
| Secundam obviationem excludit ibi: quod enim utique et cetera. Et primo ponit ipsam obviationem; eo quod, sicut ipse dicit, eandem habet solutionem cum his quae dicta sunt. Est autem dubitatio talis. Ponamus quod terra existat in medio, et quod sit sphaericae figurae, et quod versus unum hemisphaerium terrae superapponatur multo maior quantitas quam ex alia parte (quod quidem dicit ad excludendum obiectionem quae posset fieri de montibus, qui videntur supereminere aliis partibus terrae: nam quantitas montium nihil est in comparatione ad totam quantitatem terrae, sicut si pilus apponeretur ex una parte sphaerae cupreae). Dato autem quod tantum de corpore gravi superadderetur versus unam partem, quod haberet notabilem quantitatem respectu totius terrae, sequeretur quod non esset idem medium mundi totius et terrae. Unde sequeretur quod vel non quiesceret in medio; vel si quiesceret, etiam non in medio existens, etiam nunc quando est in medio, sit nata moveri. Haec igitur est dubitatio. | 537. A second objection is excluded at [396]. First he states it because, as he says, it has the same solution as that which has gone before. The problem is this: Let us suppose that the earth does exist in the middle, that it is spherical in shape, and that much more quantity is accumulated on one hemisphere of earth than on the other (this is cited in order to exclude an objection that could be raised on account of the mountains, which are seen to rise above other parts of the earth; for the size of mountains is as nothing in comparison with the total quantity of the earth, but is rather like a hair laid on the side of a copper sphere). Now, if we suppose that enough of a heavy body were added to one place so that it would have a notable quantity with respect to the whole earth, the result would be that there would not be the same middle of the world and of the earth. Hence it would follow either that the earth would not be at rest in the middle or if it did rest, without being in the middle, then now, when it is in the middle, it is capable of being in motion. This therefore is the problem. |
| Secundo ponit solutionem, ibi: videre autem et cetera. Et dicit quod illud non est difficile videre, si aliquis velit modicum considerare, et distinguere qualiter dignum ducimus quod aliqua magnitudo gravitatem habens feratur ad medium mundi. Manifestum est enim quod feretur ad medium mundi, non solum usque ad hoc quod infima extremitas tangat centrum mundi; sed, nisi aliud impediat, oportet quod, praevalente maiori parte super minorem, usque ad hoc feratur quod corpus motum medio sui tangat medium mundi, ad quod habent inclinationem omnia corpora gravia. Puta si non esset in mundo aliud corpus grave nisi unus lapis qui demitteretur ab alto, oporteret ipsum tandiu descendere, quousque medium lapidis tangeret medium mundi; propter hoc quod maior pars eius repellit minorem a medio, quousque undique inveniatur aequalis gravitas, sicut supra dictum est. | 538. Secondly, he gives the solution at [397]. And he says that the solution is not difficult to see if someone is willing to consider only slightly and distinguish how we hold that any magnitude having heaviness is borne to the middle of the world. For it is manifest that it will be borne to the middle of the world, not just until its lower surface touches the center of the world, but, unless prevented, it must be borne, with a greater part prevailing over a lesser, to the point where the center of the moved body coincides with the center of the world, in accordance with the inclination that all heavy bodies have. Thus, if the only heavy body in the world were one stone dropped from on high, it would have to keep falling until the center of the stone touched the center of the world. This would be because a greater part of it would repel a lesser from the middle until an equal heaviness should be everywhere found, as was said above. |
| Concludit ergo quod nihil differt hoc quod dictum est dicere in quacumque parte terrae, aut in tota terra. Non enim hoc contingit propter magnitudinem aut parvitatem, quod dictum est de motu gravis ad medium: sed verificatur de omni eo quod habet inclinationem ad medium, ratione suae gravitatis. Unde sive tota terra ab aliqua parte caeli feratur ad medium, sive partes eius, necesse est usque ad hoc fieri motum, donec ex omni parte terra similiter appropinquet ad medium, per hoc quod minores partes adaequantur maioribus per impulsionem minorum a maioribus, ut dictum est. | He concludes therefore that it makes no difference whether we apply this to a clod of earth or to the whole earth. For what has been said about the movement of the heavy to the middle is not due to largeness or smallness; rather, it is verified of everything that has an inclination to the middle by reason of its heaviness. Hence, whether the whole earth is being borne from some part of the heaven to the middle, or parts of it, the motion must continue until earth approaches the center in a similar way from all sides, and this is brought about by the smaller parts being made equal to the larger ones through the displacing of the smaller by the larger, as has been said. |
| Tertiam obiectionem excludit ibi: sive igitur facta est et cetera. Posset enim aliquis dicere quod praedicta ratio procedit supposita generatione terrae. Sed ipse hoc excludit, dicens quod sive terra sit generata, necesse est quod hoc modo sit facta in medio existens, sicut supra dictum est (ita scilicet quod medio sui tangat medium mundi), et ita figura eius erit sphaerica: sive etiam non sit generata, oportet quod hoc modo se habeat sicut si esset generata; quia terminus generationis est natura rei; unde illud quod non est generatum, oportet tale esse quale fieret si generaretur. | 539. The third objection he excludes at [398]. For someone could say that the foregoing argument proceeds on the assumption that the earth is generated. But this he rejects when he says that, whether the earth was generated, it has to have so come to exist in the middle as has been described, namely, in such a way that its middle touches the middle of the world, and so its figure will be spherical; or whether it was not generated, it must be in the same state as if it had been generated — for the terminus of generation is the nature of the thing; hence anything that is not generated must be such as it would have been had it been generated. |
| Et secundum hoc concludit figuram terrae esse sphaericam. | And it is according to this that he concludes the shape of the earth to be spherical. |
Lecture 28:
Proofs, of the earth's sphericity from the angle of motion of its parts, and from astronomyChapter 14 cont. Κατὰ τοῦτόν τε δὴ τὸν λόγον ἀναγκαῖον εἶναι τὸ σχῆμα σφαιροειδὲς αὐτῆς, καὶ ὅτι πάντα φέρεται τὰ βαρέα πρὸς ὁμοίας γωνίας, ἀλλ' οὐ παρ' ἄλληλα τοῦτο δὲ πέφυκε πρὸς τὸ φύσει σφαιροειδές. Ἢ οὖν ἐστι σφαιροειδής, ἢ φύσει γε σφαιροειδής. Δεῖ δ' ἕκαστον λέγειν τοιοῦτον εἶναι ὃ φύσει βούλεται εἶναι καὶ ὑπάρχειν, ἀλλὰ μὴ ὃ βίᾳ καὶ παρὰ φύσιν. 399 But the spherical shape, necessitated by this argument, follows also from the fact that the motions of heavy bodies always make equal angles, and are not parallel. This would be the natural form of movement towards what is naturally spherical. Either then the earth is spherical or it is at least naturally spherical. And it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature. Ἔτι δὲ καὶ διὰ τῶν φαινομένων κατὰ τὴν αἴσθησιν οὔτε γὰρ ἂν αἱ τῆς σελήνης ἐκλείψεις τοιαύτας ἂν εἶχον τὰς ἀποτομάς νῦν γὰρ ἐν μὲν τοῖς κατὰ μῆνα σχηματισμοῖς πάσας λαμβάνει τὰς διαιρέσεις (καὶ γὰρ εὐθεῖα γίνεται καὶ ἀμφίκυρτος καὶ κοίλη), περὶ δὲ τὰς ἐκλείψεις ἀεὶ κυρτὴν ἔχει τὴν ὁρίζουσαν γραμμήν, ὥστ' ἐπείπερ ἐκλείπει διὰ τὴν τῆς γῆς ἐπιπρόσθησιν, ἡ τῆς γῆς ἂν εἴη περιφέρεια τοῦ σχήματος αἰτία σφαιροειδὴς οὖσα. 400 The evidence of the senses further corroborates this. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave—but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth's surface, which is therefore spherical. Ἔτι δὲ διὰ τῆς τῶν ἄστρων φαντασίας οὐ μόνον φανερὸν ὅτι περιφερής, ἀλλὰ καὶ τὸ μέγεθος οὐκ οὖσα μεγάλη μικρᾶς γὰρ γιγνομένης μεταστάσεως ἡμῖν πρὸς μεσημβρίαν καὶ ἄρκτον ἐπιδήλως ἕτερος γίγνεται ὁ ὁρίζων κύκλος, ὥστε τὰ (298a.) ὑπὲρ κεφαλῆς ἄστρα μεγάλην ἔχειν τὴν μεταβολήν, καὶ μὴ ταὐτὰ φαίνεσθαι πρὸς ἄρκτον τε καὶ μεσημβρίαν μεταβαίνουσιν ἔνιοι γὰρ ἐν Αἰγύπτῳ μὲν ἀστέρες ὁρῶνται καὶ περὶ Κύπρον, ἐν τοῖς πρὸς ἄρκτον δὲ χωρίοις οὐχ ὁρῶνται, καὶ τὰ διὰ παντὸς ἐν τοῖς πρὸς ἄρκτον φαινόμενα τῶν ἄστρων ἐν ἐκείνοις τοῖς τόποις ποιεῖται δύσιν. Ὥστ' οὐ μόνον ἐκ τούτων δῆλον περιφερὲς ὂν τὸ σχῆμα τῆς γῆς, ἀλλὰ καὶ σφαίρας οὐ μεγάλης οὐ γὰρ ἂν οὕτω ταχὺ ἐπίδηλον ἐποίει μεθισταμένοις οὕτω βραχύ. Διὸ τοὺς ὑπολαμβάνοντας συνάπτειν τὸν περὶ τὰς Ἡρακλείας στήλας τόπον τῷ περὶ τὴν Ἰνδικήν, καὶ τοῦτον τὸν τρόπον εἶναι τὴν θάλατταν μίαν, μὴ λίαν ὑπολαμβάνειν ἄπιστα δοκεῖν λέγουσι δὲ τεκμαιρόμενοι καὶ τοῖς ἐλέφασιν, ὅτι περὶ ἀμφοτέρους τοὺς τόπους τοὺς ἐσχάτους ὄντας τὸ γένος αὐτῶν ἐστιν, ὡς τῶν ἐσχάτων διὰ τὸ συνάπτειν ἀλλήλοις τοῦτο πεπονθότων. 401 Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent. Hence one should not be too sure of the incredibility of the view of those who conceive that there is continuity between the parts about the pillars of Hercules and the parts about India, and that in this way the ocean is one. As further evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the common characteristic of these extremes is explained by their continuity. Καὶ τῶν μαθηματικῶν δὲ ὅσοι τὸ μέγεθος ἀναλογίζεσθαι πειρῶνται τῆς περιφερείας, εἰς τετταράκοντα λέγουσιν εἶναι μυριάδας. Ἐξ ὧν τεκμαιρομένοις οὐ μόνον σφαιροειδῆ τὸν ὄγκον ἀναγκαῖον εἶναι τῆς γῆς, ἀλλὰ καὶ μὴ μέγαν πρὸς τὸ τῶν ἄλλων ἄστρων μέγεθος. 402 Also, those mathematicians who try to calculate the size of the earth's circumference arrive at the figure 400,000 stades. This indicates not only that the earth's mass is spherical in shape, but also that as compared with the stars it is not of great size.
| Praemissa ratione ad probandum rotunditatem terrae, quae sumebatur ex specie motus partium eius, hic inducit aliam rationem ad idem, quae sumitur ex figura motus partium terrae. | 540. Having given an argument for the rotundity of the earth taken from the type of motion of its parts, he here adduces another argument for the same taken from the figure of the motion of the parts of earth. |
| Et dicit quod omnia corpora gravia, ex quacumque parte caeli moveantur, feruntur ad terram ad similes angulos, idest secundum rectos angulos, quos facit linea recta per quam est motus corporis gravis, cum linea contingente terram (quod manifestatur per hoc quod gravia non stant firmiter super terram nisi secundum lineam perpendicularem): non autem feruntur corpora gravia ad terram iuxta invicem, idest secundum lineas aequidistantes. Quod quidem ordinatur ad hoc quod terra apta nata sit esse sphaerica: quia similem inclinationem habent gravia ad locum terrae, ex quacumque parte caeli demittantur; et ita similiter et aequaliter nata est fieri appositio ad terram ex omni parte, quod constituit eam sphaericae figurae. Si vero terra naturaliter esset lata in superficie sua, sicut quidam dicebant, fieret motus corporum gravium a caelo ad terram non undecumque secundum similes angulos. Oportet igitur quod vel terra sit sphaerica, vel quod naturaliter sit sphaerica. | And he says [399] that all heavy bodies, from whatever region of the heaven ', they are moved, are carried to the earth "at like angles," i.e., according to right angles formed by the straight line of the body's motion with a line tangent to the earth (which is evident from the fact that heavy objects do not stand firmly on the earth unless they are perpendicular to it); but heavy bodies are not carried to the earth "side by side," i.e., according to parallel lines. Now all this is ordered to the fact that the earth is naturally apt to be spherical: because heavy bodies have a like inclination to the place of earth no matter from what part of the heaven they are released. And so there is an aptitude for additions to the earth to be made in a like and equal manner on all sides, which makes it to be spherical in shape. But if the earth were naturally wide [flat] in its surface, as some claimed, the motions of heavy bodies from the heaven to earth would not be from all sides at similar angles. Therefore, the earth must either be spherical or be "spherical by nature." |
| Hoc autem ideo apposuit, propter tumorositates montium et concavitates vallium, quae videntur rotunditatem terrae impedire. Sed huiusmodi sunt ex aliqua causa accidentali, et non ex eo quod per se convenit terrae: nec hoc habet aliquam quantitatem notabilem in comparatione ad totam terram, ut supra dictum est. Oportet autem unumquodque dicere esse tale quale est secundum suam naturam, et non quale est per aliquam causam violentam vel praeternaturalem: et ideo, licet per accidens terra non sit omnino sphaerica ex aliquo accidente, quia tamen naturam habet ad hoc quod sit sphaerica, simpliciter dicendum est eam sphaericam esse. | He added this last phrase on account of the bulges of mountains and the depressions of valleys which seem to militate against a rotund earth. But such [deviations] arise from some accidental cause and not from what belongs or se to earth; nor does this amount to an appreciable quantity in relation to the whole earth, as has been said above. Now one must say each thing to be as it is according to its nature and not as it is by reason of some violent or preternatural cause. And therefore, although by accident the earth may not be perfectly spherical due to some chance happening, yet, because it is naturally apt to be spherical, it should, absolutely speaking, be called spherical. |
| Deinde cum dicit: adhuc autem et per apparentia etc., probat terram esse sphaericam, rationibus astrologicis, per ea quae apparent secundum sensum. Et inducit tres probationes. Quarum prima sumitur ex eclipsi lunae. Et dicit quod adhuc manifestum est per ea quae apparent secundum sensum, quod terra sit sphaerica. Nisi enim terra esset sphaerica, eclipsis lunae non semper haberet circulares decisiones: videmus enim quod semper quando luna eclipsatur, obscurum ipsius et lucidum distinguuntur per lineam circularem. Accidit autem eclipsis lunae per hoc quod ipsa subintrat umbram terrae: unde apparet umbram terrae esse rotundam. Ex quo apparet terram, quae facit talem umbram, esse sphaericam: solum enim corpus sphaericum natum est semper facere sphaericam umbram. Si enim corpus lucidum, scilicet sol, sit maius terra, oportet quod faciat terra umbram pyramidalem, cuius conus sit in alto, et basis in ipsa terra; si vero sol esset minor terra, faceret quidem umbram similiter secundum figuram rotundae pyramidis, tamen e converso conus illius pyramidis esset in terra, basis autem eius in alto; si vero sol esset aequalis terrae, faceret umbram cylindricam, idest columnarem: quidquid autem horum esset, sequeretur, propter hoc quod terra est sphaerica, quod umbra eius secundum lineam circularem abscinderet lunam. | 541. Then at [400] he proves that the earth is spherical with astronomical arguments, based on what appears according to sense. And he brings in three proofs. The first of these is taken from the eclipse of the moon. And he says that it is further manifest by what appears according to sense, that the earth is spherical. For unless the earth were spherical, an eclipse of the moon would not always reveal circular segments; for we observe that whenever the moon is eclipsed, its dark and its shining portions are distinguished by a curved line. Now an eclipse of the moon results from its entering the earth's shadow — hence the earth's shadow appears to be round. From this it appears that the earth, which makes such a shadow, is round — for only a spherical body is apt always to cast a round shadow. For if the shining body, namely, the sun is larger than the earth, the earth must make a pyramidical shadow, whose cone is above and base on earth; if the sun should be smaller than the earth, it would likewise produce a shadow according to the figure of a round pyramid [i.e., a cone], but, conversely [the summit of] the cone of this pyramid would be on the earth and its base in the heaven; if the sun were equal to the earth, the shadow made would be cylindrical, i.e., columnar. Now, no matter which of these it should be, it would follow, on account of the earth's sphericity, that its shadow would cut the moon according to a circular line. |
| Posset autem aliquis dicere quod ista circularis abscissio lunae non est propter rotunditatem terrae, sed propter rotunditatem lunae. Sed ad hoc excludendum, subdit quod in augmento et decremento lunae, quod accidit per singulos menses, sectio lunae accipit omnes differentias figurarum: nam quandoque dividitur secundum lineam rectam, sicut quando dividitur per medium, puta cum est septima vel vigesima prima; quandoque autem fit amphicurtos, idest habens circularem sectionem vel arcualem, scilicet a septima luna usque ad vigesimam primam; quandoque autem est concava, puta cum est prima, et a prima usque ad septimam, et a vigesima prima usque ad defectum; quod contingit propter diversam habitudinem eius ad solem, ut supra dictum est. Sed in eclipsibus semper linea dividens ipsam est gibbosa, idest circularis. Quia igitur luna eclipsatur propter terrae interpositionem, rotunditas terrae, cum sit sphaerica, est causa talis figurae circa divisionem lunae. | Now someone could say that this circular section is not due to the earth's rotundity but to the moon's. But to exclude this he adds that in the monthly waxing and waning of the moon, the section of the moon takes all differences of shape — for sometimes it is divided by a straight line, as when it is divided through the center, for example, on the 7th and the 21st days; at other times, it is amphicurtos [gibbous], having a circular or arc-like section, namely from the 7th to the 21st; at still other times it is concave [crescent], as from the 1st to the 7th, and from the 21st to its total waning. All this happens according to its position in relation to the sun, as has been said above. But during eclipses the line dividing the moon is always "gibbous," i.e., circular. Since, therefore, the moon is eclipsed by the interposition of the earth, the rotundity of the earth, since it is spherical, is the cause of such a shape with respect to the division of the moon. |
| Secundam probationem ponit ibi: adhuc autem per astrorum etc.; quae sumitur ex apparentia stellarum. Et dicit quod ex diversitate apparentiae stellarum apparet quod terra non solum est rotunda, sed etiam parva in comparatione ad corpora caelestia. Si enim modicum moveamur versus meridiem vel Septentrionem, manifeste diversificatur nobis horizon. | 542. The second proof is given at [401] and is based on the appearance of the stars. And he says that from the difference in the appearance of the stars it appears that the earth is not only round, but also small in comparison with the heavenly bodies. For if we move a slight distance to the south or north, our horizon is noticeably changed. |
| Quod apparet quantum ad duo. Primo quidem quantum ad polum horizontis, qui est punctum caeli existens supra summitatem capitis nostri; quod quidem punctum manifeste diversificatur secundum modicam distantiam, ut apparet ex stellis fixis; quia in modica distantia diversae stellae apparent super summitatem capitis. | This change is particularly evident in two respects. First, with respect to the horizon's pole, which is the point of the heaven above our head. This point markedly varies in proportion to a short distance, as is apparent from the fixed stars — since with a slight change of location on our part different stars appear overhead. |
| Secundo apparet diversitas horizontis ex diversa abscissione caeli per horizontem. Et hoc manifestat quia moventibus se versus Septentrionem vel meridiem, non videntur eaedem stellae. In his enim qui habitant in sphaera obliqua, polus Septentrionalis elevatur supra horizontem ipsorum, et omnes stellae quae non distant a polo ultra elevationem Poli supra orizontem, sunt perpetuae apparitionis; et in aequali spatio circa alium polum stellae existentes, sunt perpetuae occultationis. Quia igitur, propter diversitatem horizontis, in terris Septentrionalibus polus Septentrionalis magis elevatur, et polus oppositus magis deprimitur, contingit quod quaedam stellae quae sunt propinquae polo Antarctico, non sunt perpetuae occultationis, sed videntur quandoque in terris magis meridionalibus, puta in Aegypto et circa Cyprum, quae nunquam videntur in terris magis Septentrionalibus: et e converso quaedam stellae sunt perpetuae apparitionis in regionibus magis Septentrionalibus, quae tamen in regionibus magis meridionalibus magis occultantur per occasum. | Secondly, a difference of horizon appears from the different cutting of the heaven by the horizon. And he shows this from the fact that, as one moves to the north or to the south, the same stars are not visible. To those who live in the oblique sphere, the north pole is above their horizon, and all the stars which are not farther from the pole than the elevation of the pole above the horizon are perpetually visible, while all the stars at an equal distance from the other pole are perpetually hidden. Since, therefore, because of the difference of horizon, in northern lands the north pole is higher, and the opposite pole is lower, it happens that certain stars which are near to the ant-arctic pole are not perpetually hidden, but are sometimes seen in lands more to the south, for example in Egypt and about Cyprus, which are never seen in the more northerly region. Conversely, certain stars are always visible in the more northern regions, which in more southern regions are hidden by setting. |
| Et ex hoc apparet quod terra est figurae rotundae, praecipue secundum aspectum ad duos polos: si enim esset superficiei planae, omnes habitantes in tota terrae superficie ad meridiem et Septentrionem, haberent eundem horizontem, et eaedem stellae eis apparerent et occultarentur, nullo impedimento facto ex tumorositate. Et simili ratione probatur quod terra sit rotunda versus ortum et occasum: alioquin non prius oriretur astrum quodcumque his qui sunt in oriente, quam his qui sunt in occidente. Si enim terra esset figurae concavae, sidus oriens prius appareret his qui sunt in occidente: si vero terra haberet planam superficiem, simul appareret omnibus. Manifestum est autem quod sidus oriens prius apparet his qui sunt in oriente, per eclipsim lunae; quae si appareat in regione magis Orientali circa mediam noctem, in regione magis Occidentali apparebit ante mediam noctem, secundum quantitatem distantiae; ex quo patet quod sol prius oritur et occidit in regione magis Orientali. | And from this it appears that the earth is rotund in shape especially according to its aspect at the two poles — for if it were flat, all those dwelling on the whole face of the earth to the south and north would have the same horizon and the very same stars would appear to them and be hidden from them, no impediment arising from the bulge of the earth. And with a similar argument it is proved that the earth is round toward the east and west — otherwise no star would rise any earlier for people in the east than for those in the west. For if the earth were concave, a rising star would appear first to people in the west; but if the earth were flat, it would appear to everyone at the same time. But it is evident that a rising star appears first to those in the east, if we consider a lunar eclipse. If such an eclipse appears in a more easterly region about midnight, it will appear before midnight in a more westerly region, depending on the amount of the distance. From this it is plain that the sun rises earlier and sets earlier in a more easterly region. |
| Per hoc autem, ut Aristoteles dicit, apparet quod non sit magna quantitas rotunditatis terrae. Si enim esset magnae quantitatis, non in tam parva distantia fieret ita cito diversitas circa apparentiam stellarum. Et ideo non videntur valde incredibilia opinari, qui volunt coaptare, secundum similitudinem et propinquitatem, locum in extremo occidentis situm, qui dicitur esse circa Heracleas columnas (quas scilicet Hercules statuit in signum suae victoriae), loco qui est circa mare Indicum in extremo orientis, et dicunt esse unum mare, Oceanum, quod continuat utraque loca. Et similitudinem utrorumque locorum coniiciunt ex elephantibus, qui circa utrumque locum oriuntur, non autem in mediis regionibus. Quod quidem est signum convenientiae horum locorum, non autem propinquitatis. | This also shows, as Aristotle says, that the earth's rotundity is of no great quantity. For if it were, in so small a distance there would not so soon be made a change in the appearance of the stars. And therefore, we would not consider as very absurd the view of those who wish to link, on the basis of similarity and nearness, the region situated in the far west about the pillars of Hercules (which Hercules set up as a memorial of his victory), and the region in the far east about the Indian Ocean, and who say there is one sea, the Ocean, bordering on both places. And they make a conjecture as to the similarity of both places from the elephants which arise in both places but are not found in the regions between them. This of course is a sign of the agreement of these places but not necessarily of their nearness to one another. |
| Tertiam probationem inducit ibi: et mathematicorum etc.; quae quidem sumitur ex mensura terrae. Et dicit quod quicumque mathematicorum attentaverunt ratiocinari de magnitudine rotunditatis terrae, dicunt quod rotunditas terrae attingit usque ad quadraginta myriades stadiorum, idest quadragesies decem millia, quod est quadringentesies millia stadiorum. Est autem stadium octava pars milliaris; octava autem pars praedicti numeri est quinquaginta millia; et secundum hoc rotunditas terrae erit quinquaginta millia milliariorum. | 543. He adduces a third proof at [402], and it is based on measurements of the earth. And he says that whatever mathematicians have attempted to reason about the size of the earth's rotundity assert that its circumference reaches 40 myriads of stades, i.e., 40 times 10,000, which is 400,000 stades. Now a stadium is 1/8 of 1,000 paces. But 1/8 of the aforesaid number is 50,000. Therefore, according to this, the circumference of the earth will be 50,000 times a thousand paces. |
| Secundum autem diligentiorem considerationem modernorum astrologorum, est rotunditas terrae multo minor, idest viginti millia milliaria et quadringenta, ut Alfraganus dicit; vel decem et octo myriades stadiorum, idest centum octoginta millia stadiorum, ut Simplicius dicit; quod quasi in idem redit, nam viginti millia est octava pars centum sexaginta millium. | But according to the more careful measurent of present-day astronomers, the earth's circumference is much less, i.e., 20,000 times 1,000 paces and 400, as Al Fargani says; or 180,000 stades, as Simplicius says — which is about the same, since 20,000 is 1/8 of 160,000. |
| Hoc autem astrologi perpendere potuerunt, considerantes quantum spatium in terra facit diversitatem unius gradus in caelo: et invenerunt quod quingenta stadia, secundum Simplicium; vel quinquaginta sex milliaria et duas tertias milliarii, secundum Alfraganum. Unde multiplicantes hunc numerum per trecenta sexaginta, qui est numerus graduum caeli, apprehenderunt rotunditatem terrae esse praedictae quantitatis. | Now astronomers were able to calculate this by considering how much space on earth makes for a difference of one degree in the heaven; and they found that it was 500 stadia according to Simplicius, or 56 2/3 times 1,000 paces according to Al Fargani. Hence, multiplying this number by 360, which is the number of degrees in the heaven, they found the size of the earth's circumference. |
| Et sic ex his possumus argumentari quantitatem terrae non solum esse sphaericam, sed etiam non magnam in comparatione ad magnitudines aliorum astrorum: nam solem probant astrologi esse centies septuagesies maiorem terra; cum tamen, propter distantiam, videatur nobis pedalis. Dicit autem aliorum astrorum, propter opinionem Pythagorae, qui posuit terram esse unam de stellis. Et in hoc terminatur sententia secundi libri. | And so, from all of this, we can argue that the earth's quantity is not only spherical, but not large in comparison to the sizes of the other stars. For astronomers prove that the sun is 170 times greater than the earth, even though its distance from us makes it seem to be only a foot in diameter. He says, "of the other stars," because of Pythagoras' opinion, who held that the earth is one of the stars. — And with this is terminated the doctrine of Book II. |
Γ
ON THE HEAVEN: BOOK IIILecture 1:
What has gone before and what remains to be treatedChapter 1 Περὶ μὲν οὖν τοῦ πρώτου οὐρανοῦ καὶ τῶν μερῶν, ἔτι δὲ περὶ τῶν ἐν αὐτῷ φερομένων ἄστρων, ἐκ τίνων τε συνεστᾶσι καὶ ποῖ' ἄττα τὴν φύσιν ἐστί, πρὸς δὲ τούτοις ὅτι ἀγένητα καὶ ἄφθαρτα, διεληλύθαμεν πρότερον. 403 WE have already discussed the first heaven and its parts, the moving stars within it, the matter of which these are composed and their bodily constitution, and we have also shown that they are ungenerated and indestructible. Ἐπεὶ δὲ τῶν φύσει λεγομένων τὰ μέν ἐστιν οὐσίαι, τὰ δ' ἔργα καὶ πάθη τούτων (λέγω δ' οὐσίας μὲν τά τε ἁπλᾶ σώματα, οἷον πῦρ καὶ γῆν καὶ τὰ σύστοιχα τούτοις, καὶ ὅσα ἐκ τούτων, οἷον τόν τε σύνολον οὐρανὸν καὶ τὰ μόρια αὐτοῦ, καὶ πάλιν τά τε ζῷα καὶ τὰ φυτὰ καὶ τὰ μόρια τούτων, πάθη δὲ καὶ ἔργα τάς τε κινήσεις τὰς τούτων ἑκάστου καὶ τῶν ἄλλων, ὅσων ἐστὶν αἴτια ταῦτα κατὰ τὴν δύναμιν τὴν ἑαυτῶν, ἔτι δὲ τὰς ἀλ(298b.) λοιώσεις καὶ τὰς εἰς ἄλληλα μεταβάσεις), φανερὸν ὅτι τὴν πλείστην συμβαίνει τῆς περὶ φύσεως ἱστορίας περὶ σωμάτων εἶναι πᾶσαι γὰρ αἱ φυσικαὶ οὐσίαι ἢ σώματα ἢ μετὰ σωμάτων γίγνονται καὶ μεγεθῶν. Τοῦτο δὲ δῆλον ἔκ τε τοῦ διωρίσθαι τὰ ποῖά ἐστι φύσει, καὶ ἐκ τῆς καθ' ἕκαστα θεωρίας. 404 Now things that we call natural are either substances or functions and attributes of substances. As substances I class the simple bodies—fire, earth, and the other terms of the series—and all things composed of them; for example, the heaven as a whole and its parts, animals, again, and plants and their parts. By attributes and functions I mean the movements of these and of all other things in which they have power in themselves to cause movement, and also their alterations and reciprocal transformations. It is obvious, then, that the greater part of the inquiry into nature concerns bodies: for a natural substance is either a body or a thing which cannot come into existence without body and magnitude. This appears plainly from an analysis of the character of natural things, and equally from an inspection of the instances of inquiry into nature. Περὶ μὲν οὖν τοῦ πρώτου τῶν στοιχείων εἴρηται, καὶ ποῖόν τι τὴν φύσιν, καὶ ὅτι ἄφθαρτον καὶ ἀγένητον λοιπὸν δὲ περὶ τοῖν δυοῖν εἰπεῖν. 405 Since, then, we have spoken of the primary element, of its bodily constitution, and of its freedom from destruction and generation, it remains to speak of the other two. Ἅμα δὲ συμβήσεται περὶ τούτων λέγουσι καὶ περὶ γενέσεως καὶ φθορᾶς διασκέψασθαι γένεσις γὰρ ἤτοι τὸ παράπαν οὐκ ἔστιν, ἢ μόνον ἐν τούτοις τοῖς στοιχείοις καὶ τοῖς ἐκ τούτων ἐστίν. Αὐτὸ δὲ τοῦτο πρῶτον ἴσως θεωρητέον, πότερον ἔστιν ἢ οὐκ ἔστιν. 406 In speaking of them we shall be obliged also to inquire into generation and destruction. For if there is generation anywhere, it must be in these elements and things composed of them. This is indeed the first question we have to ask: is generation a fact or not?
| Postquam philosophus determinavit de corporibus quae moventur motu circulari, hic procedit ad determinandum de corporibus quae moventur motu recto. | 544. After determining the question of bodies that are moved circularly, the Philosopher here goes on to determine that of bodies that move in a straight line. |
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Et primo praemittit prooemium, in quo explicat suam intentionem; secundo prosequitur propositum, ibi: prius quidem igitur philosophantes et cetera. |
First he prefaces an introduction in which he explains his intention; Secondly, he pursues his intention (L. 2). |
| Circa primum duo facit: | Regarding the first he does two things: |
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primo continuat se ad praecedentia, ostendens de quibus iam supra dictum sit; secundo ostendit de quibus restat dicendum, ibi: quoniam autem eorum quae natura et cetera. |
First he establishes continuity with what has gone before by showing what has already been covered; Secondly, he states what remains to be discussed, at 546. |
| Dicit ergo primo se in praecedentibus pertransivisse, idest breviter tractasse, de primo caelo et partibus, scilicet eius. Possumus autem per primum caelum intelligere totum universum, quod est primum perfectione, et partes eius accipere corpora quae moventur motu circulari et motu recto; ut sic videatur hic tangere etiam ea quae in primo libro determinata sunt. Sed huic expositioni videtur obsistere quod subditur, adhuc autem de astris latis in ipso: non autem proprie dicuntur ferri astra in toto universo, sed in caelo, quod circulariter fertur. Et ideo videtur melius quod dicit de primo caelo, esse intelligendum de corpore quod circulariter fertur. | 545. He says therefore first [403] that in what has preceded he has "gone through," i.e., treated briefly, "the first heaven and the parts," namely, of it. Now we can understand by "first heaven" the whole universe, which is first in perfection, and take as its "parts" the bodies that are moved with circular and with straight motion. In this way it would seem that he is touching also what was determined in the first book. But this interpretation seems to be belied by his next phrase, "and also the stars that are moved in it." Now, the stars are not properly said to be carried along in the whole universe, but in the heaven which is circularly moved. Hence it seems better to understand what he says of the first heaven to refer to the body which is moved circularly. |
| Sed quia non dicit simpliciter de caelo, sed de primo caelo, potest hoc referri ad primam sphaeram, quae est stellarum fixarum: quod autem dicit et partibus, refertur ad dextrum et sinistrum et alias positionis differentias, quas in caelo esse ostendit. Sed secundum hoc non esset sufficiens commemoratio, nec eorum quae dicta sunt in toto primo libro, nec etiam omnium eorum quae dicta sunt in secundo, in quo habitum est etiam de sphaeris planetarum. Et ideo melius videtur dicendum quod per primum caelum intelligitur hic totum corpus quod circulariter fertur; quod quidem dicitur primum in comparatione ad corpora inferiora, respectu quorum est primum et ordine situs, et perpetuitate durationis, et virtute causalitatis. Quod autem subdit et partibus, referendum est ad diversas sphaeras, quae sunt partes totius caelestis corporis. | But because he does not say absolutely "heaven," but "first heaven," this can be referred to the first sphere, which is that of the fixed stars; and "parts" to the right and left and the other different positions that he showed to exist in the heaven. But according to this interpretation there would not be a sufficient recalling, either of what was treated in the entire first book, or of all those things treated in the second, in which the spheres of the planets were also discussed. Consequently, it seems better to say that by "first heaven" is here understood the entire body which is circularly moved, and that it is called "first" in comparison to the lower bodies, in relation to which it is first in the order of position, and by reason of the eternity of its duration, and the power of its causality. The added expression, "and the parts," would then refer to the various spheres which are parts of the whole celestial body. |
| Dictum est etiam de stellis quae moventur in toto caelo, et quantum ad stellas fixas et quantum ad planetas. De quibus dictum est ex quibus constant: ostensum est enim quod sunt de natura caelestis corporis. Dictum est etiam qualia sint secundum naturam: quia sunt animata et sphaerica. Dictum est etiam quod non sunt subiecta generationi et corruptioni. | The stars that are moved in the whole heaven have also been treated, both the fixed stars and the planets Concerning them it has been stated of what they are composed: for it was shown that they are of the nature of the heavenly body. It has also been stated how they are according to nature, namely, that they are animated and spherical. Likewise it has been said that they are not subject to generation and decay. |
| Et si quidem in primo libro determinavit de toto universo, sicut supra diximus secundum opinionem Alexandri, sic recapitulatio se extendit solum ad secundum librum. Si vero etiam in primo libro intendit determinare de caelo principaliter, ut Simplicius dicit, sic recapitulatio se extendit etiam ad primum librum. | If the first book was a discussion of the whole universe, as we have said it was according to the opinion of Alexander, then this present review refers only to the second book. But if his [Aristotle's] intention in the first book also was to talk mainly about the heaven, as Simplicius avers, then this review extends even to the first book. |
| Deinde cum dicit: quoniam autem eorum quae natura etc., ostendit de quibus restat dicendum. | 546. Then at [404] he shows what remains to be treated. |
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Et primo manifestat in quo consistat tota consideratio naturalis philosophiae; secundo ex hoc concludit quid post praemissa restat dicendum, ibi: de primo quidem et cetera. |
First he shows in what the entire consideration of natural philosophy consists; Secondly, from this he concludes what remains to be said, after what has gone before, at 549. |
| Circa primum utitur tali ratione. Omnes substantiae naturales sunt corpora; sed tota consideratio naturalis est de substantiis naturalibus et earum accidentibus; ergo tota consideratio scientiae naturalis est circa corpora. | In regard to the first [404], he uses the following argument: All natural substances are bodies; but the whole consideration of natural science is about natural substances and their accidents; therefore the whole consideration of natural science is concerned with bodies. |
| Primo igitur praemittit minorem, dicens quod eorum quae dicuntur esse secundum naturam, quaedam sunt substantiae naturales, quaedam autem sunt operationes et passiones substantiarum naturalium. Et ad hoc manifestandum, primo exponit quae sunt substantiae naturales. Inter quas primo enumerat corpora simplicia. Et inter ea primo exemplificat de igne et terra, et de aliis quae sunt simul elementa corporum cum eis, sicut sunt aer et aqua: et ad horum naturam pertinent corpora mixta quae ex eis componuntur, sicut lapides et metalla. Deinde exemplificat de alio corpore simplici praeter elementa, quod est totum caelum et partes eius. Ultimo autem ponit corpora mixta animata, sicut animalia et plantas et partes eorum. | 547. First, therefore, he presents the minor, saying that among the things said to be according to nature, some are natural substances and some are the operations and passions of natural substances. In order to manifest this, he first explains which are the natural substances. Among these he first numbers simple bodies. And among these he gives as the first examples, fire and earth, and those others that are the elements of bodies together with these, as are air and water. And to the nature of these pertain the mixed [compound] bodies composed of them, such as stones and metals. Then he mentions another body beyond the elements, namely, the whole heaven and its parts. Lastly, he mentions animated composites, such as animals and plants and their parts. |
| Deinde manifestat quae sint operationes harum substantiarum. Et dicit quod primo quidem sunt motus locales uniuscuiusque horum corporum, et etiam aliorum quorum ista corpora sunt causa, vel materialis, sicut elementa, vel effectiva, sicut caelum (et tamen causatis corporibus congruit motus secundum virtutem corporum simplicium, ex quibus causantur). Deinde opera et passiones praedictarum substantiarum dicit esse alterationes et transmutationes earum in invicem, quae sunt secundum generationem et corruptionem. | After this he manifests what the operations of these substances are. And he says that first, indeed, are the local motions of each of these bodies and also of the bodies of which these bodies are the cause, either the material cause, as are the elements, or the efficient, as is the heaven (and yet motion suits caused bodies according to the power of the simple bodies out of which they are caused). Then he says that the activities and passions of the aforesaid substances are their alterations and transmutations into one another according to generation and corruption. |
| Secundo infert conclusionem. Et dicit ex praemissis manifestum esse quod plurimum historiae (idest narrationis) naturalis est circa corpora. Per hoc autem quod dicit plurimam, intelligit omnem; sed utitur hoc modo loquendi propter philosophicum temperamentum. Vel dicit plurimam, propter hoc quod in scientia naturali aliquid etiam traditur de primo motore et de anima intellectiva. | Secondly, he infers the conclusion and says that from the foregoing it is plain that most of "natural history" (i.e., the relating of the contents) deals with bodies. In saying "most," he means "all," but he uses this mode of expression on account of his philosophic temperament. Or he says "most" on account of the fact that in natural science something is also said about the first mover and the intellective soul. |
| Tertio ponit maiorem, scilicet quod omnes substantiae naturales aut sunt corpora, aut generantur cum corporibus et magnitudinibus, sicut sunt formae naturales quae dicuntur substantiae. Et hoc quidem dicit esse manifestum dupliciter. Primo per hoc quod determinatum est quae sunt secundum naturam, paulo ante, quae omnia vel sunt corpora vel cum corporibus; ut determinatum est in II Physic. quod secundum naturam sunt ea quae habent in seipsis principium motus et quietis, huiusmodi autem sunt sola corpora, quia nihil movetur nisi corpus. Secundo dicit hoc esse manifestum per inductionem, considerando per singula ea quae in scientia naturali traduntur: invenimus enim omnia esse corpora, vel cum corporibus. Et est advertendum quod haec eadem supra in primo libro praemisit. | 548. Thirdly, he presents the major, namely, that all natural substances are either bodies, or are generated with bodies and magnitudes, as are the natural forms, which are called "substances." And he says that this is evident in two ways: First, from what has just been decided as being according to nature —all of which are either bodies or with bodies; and in Physics II it was determined that those things are according to nature which have within themselves their own principle of motion and rest; such things are bodies and only bodies, because only bodies are moved. Secondly, he says that this is manifest by induction, if we consider one by one the things treated in natural science — for we find that all are bodies or with bodies. And it should be noted that he mentioned all this as a preface to Book I. |
| Deinde cum dicit: de primo quidem etc., ostendit quid post dicta restet dicendum. Et primo quantum ad substantias; dicens dictum esse de primo corpore inter elementa, idest de caelo (quod vocat elementum, secundum Alexandrum quia est pars mundi, secundum autem Simplicium quia est corpus simplex); de quo dictum est quale sit secundum naturam, quia est animatum et sphaericum, et quia etiam est incorruptibile et ingenitum. Unde reliquum est dicere de aliis duobus corporibus. Ostensum est enim in primo libro esse tria corpora, unum scilicet quod movetur circa medium, de quo iam dictum est; aliud quod movetur a medio; et tertium quod movetur ad medium; de quibus duobus restat dicendum (nam de terra supra dictum est non quantum ad suam naturam, sed quantum ad habitudinem quam habet ad caelum). | 549. Then at [405] he states what remains to be discussed. First with regard to substances, saying that the heaven has been discussed, i.e., the first body among the elements, which he calls an "element" because it is a part of the world, according to Alexander; but according to Simplicius because it is a simple body. Concerning the heaven, its condition according to nature has been stated, namely, that it is animated and spherical, and also that it is indestructible and ungenerated. Hence the task which remains is to speak of the other two bodies. For it was shown in the first book that there are three bodies: one, namely, which is in motion around the center — which has already been treated; another, which is moved away from the center; and a third which is moved toward the center. These [last] two still remain to be treated —for the earth was discussed not with respect to its nature, but in its relation to the heaven. |
| Secundo ibi: simul autem accidet etc., ostendit quid restet dicendum quantum ad opera et passiones. Et dicit quod simul cum his duobus, restat inquirendum de generatione et corruptione: quia vel generatio nihil est, sed est remota a natura totius universi; aut solum invenitur in his elementis quae moventur motu recto, et in corporibus quae ex eis componuntur. Haec autem consideratio locum non habebat, dum adhuc de rebus incorruptibilibus ageretur. Oportet autem hanc considerationem praemittere, quia multum valet ad considerandum naturas corporum. | 550. Secondly, at [406] he shows what remains to be said as to activities and passions [properties]. And he says that along with these two it remains to investigate generation and corruption, because either generation is nothing and has no connection with the nature of the entire universe, or it is found only in those elements that are moved with a straight motion and in bodies composed of them. But there was no place for this consideration so long as indestructible bodies were being considered. But this consideration must be taken up first, because it contributes a great deal to the consideration of the nature of bodies. |
Lecture 2:
Opinions of the ancients on the generation of thingsChapter 1 cont. Οἱ μὲν οὖν πρότερον φιλοσοφήσαντες περὶ τῆς ἀληθείας καὶ πρὸς οὓς νῦν λέγομεν ἡμεῖς λόγους καὶ πρὸς ἀλλήλους διηνέχθησαν. 407 Earlier speculation was at variance both with itself and with the views here put forward as to the true answer to this question. Οἱ μὲν γὰρ αὐτῶν ὅλως ἀνεῖλον γένεσιν καὶ φθοράν οὐθὲν γὰρ οὔτε γίγνεσθαί φασιν οὔτε φθείρεσθαι τῶν ὄντων, ἀλλὰ μόνον δοκεῖν ἡμῖν, οἷον οἱ περὶ Μέλισσόν τε καὶ Παρμενίδην, οὕς, εἰ καὶ τἆλλα λέγουσι καλῶς, ἀλλ' οὐ φυσικῶς γε δεῖ νομίσαι λέγειν τὸ γὰρ εἶναι ἄττα τῶν ὄντων ἀγένητα καὶ ὅλως ἀκίνητα μᾶλλόν ἐστιν ἑτέρας καὶ προτέρας ἢ τῆς φυσικῆς σκέψεως. Ἐκεῖνοι δὲ διὰ τὸ μηθὲν μὲν ἄλλο παρὰ τὴν τῶν αἰσθητῶν οὐσίαν ὑπολαμβάνειν εἶναι, τοιαύτας δέ τινας νοῆσαι πρῶτοι φύσεις, εἴπερ ἔσται τις γνῶσις ἢ φρόνησις, οὕτω μετήνεγκαν ἐπὶ ταῦτα τοὺς ἐκεῖθεν λόγους. 408 Some removed generation and destruction from the world altogether. Nothing that is, they said, is generated or destroyed, and our conviction to the contrary is an illusion. So maintained the school of Melissus and Parmenides. But however excellent their theories may otherwise be, anyhow they cannot be held to speak as students of nature. There may be things not subject to generation or any kind of movement, but if so they belong to another and a higher inquiry than the study of nature. They, however, had no idea of any form of being other than the substance of things perceived; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred what was true of them to things perceived. Ἕτεροι δέ τινες ὥσπερ ἐπίτηδες τὴν ἐναντίαν τούτοις ἔσχον δόξαν. Εἰσὶ γάρ τινες οἵ φασιν οὐθὲν ἀγένητον εἶναι τῶν πραγμάτων, ἀλλὰ πάντα γίγνεσθαι, γενόμενα δὲ τὰ μὲν ἄφθαρτα διαμένειν, τὰ δὲ πάλιν φθείρεσθαι, μάλιστα μὲν οἱ περὶ Ἡσίοδον, εἶτα καὶ τῶν ἄλλων οἱ πρῶτοι φυσιολογήσαντες. 409 Others, perhaps intentionally, maintain precisely the contrary opinion to this. It has been asserted that everything in the world was subject to generation and nothing was ungenerated, but that after being generated some things remained indestructible while the rest were again destroyed. This had been asserted in the first instance by Hesiod and his followers, Οἱ δὲ τὰ μὲν ἄλλα πάντα γίνεσθαί φασι καὶ ῥεῖν, εἶναι δὲ παγίως οὐθέν, ἓν δέ τι μόνον ὑπομένειν, ἐξ οὗ ταῦτα πάντα μετασχηματίζεσθαι πέφυκεν ὅπερ ἐοίκασι βούλεσθαι λέγειν ἄλλοι τε πολλοὶ καὶ Ἡράκλειτος ὁ Ἐφέσιος. 410 but afterwards outside his circle by the earliest natural philosophers. But what these thinkers maintained was that all else has been generated and, as they said, 'is flowing away, nothing having any solidity, except one single thing which persists as the basis of all these transformations. So we may interpret the statements of Heraclitus of Ephesus and many others. Εἰσὶ δέ τινες καὶ οἳ πᾶν σῶμα γενητὸν ποιοῦσι, συντιθέντες καὶ διαλύοντες εἰς (299a.) ἐπίπεδα καὶ ἐξ ἐπιπέδων. 411 And some subject all bodies whatever to generation, by means of the composition and separation of planes.
| Praemisso prooemio, in quo ostendit quid restet considerandum circa scientiam naturalem, hic incipit prosequi ea quae dicta sunt. | 551. Having presented an introduction in which he showed what remains to be considered in natural science, he now undertakes to pursue what has been said. |
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Et primo inquirendo de opinionibus philosophorum circa praedicta; secundo determinando veritatem, in quarto libro, ibi: de gravi autem et levi et cetera. |
First by inquiring into the opinions of philosophers on this matter; Secondly, by determining the truth, in Book IV. |
| Circa primum duo facit: | About the first he does two things: |
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primo inquirit de generatione et motu corporum naturalium, an sit; secundo quorum et propter quid sit, ibi: quod autem neque omnium est generatio et cetera. |
First he inquires into the generation and motion of natural bodies, as to whether it exists; Secondly, as to which things are generated and moved, and why (L. 8). |
| Circa primum duo facit: | Concerning the first he does two things:. |
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primo inquirit, secundum opiniones antiquorum philosophorum, an sit generatio; secundo inquirit an motus localis sit naturalis corporibus naturalibus, ibi: quod autem necessarium existere motum et cetera. |
First he inquires according to the opinions of early philosophers whether generation is a fact; Secondly, whether local motion is natural to natural bodies (L. 5). |
| Circa primum duo facit: | As to the first he does two things: |
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primo enumerat opiniones antiquorum circa generationem; secundo inquirit de veritate earum, ibi: de aliis quidem igitur alter sit sermo et cetera. |
First he cites the opinions of the ancients about generation; Secondly, he investigates the truth of these opinions (L. 3). |
| Circa primum tria facit: | Regarding the first he does three things: |
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primo ponit diversitatem philosophorum circa generationem; secundo ponit opiniones negantium generationem, ibi: hi quidem enim ipsorum etc.; tertio ponit opiniones attribuentium generationem corporibus, ibi: alteri autem quidam et cetera. |
First he shows the difference among philosophers as to generation; Secondly, he presents the opinions that deny generation, at 552; Thirdly, those that attribute generation to bodies, at 554. |
| Dicit ergo primo quod illi qui prius philosophati sunt de veritate, scilicet speculativa (quod dicit ad differentiam eorum qui philosophati sunt circa moralia et circa politica), diversificati sunt in suis opinionibus et contra se invicem, et contra ea quae nunc dicuntur de generatione. | He says therefore first [407] that those who previously philosophized about the truth, namely, speculative truth (which he says to distinguish them from those who philosophized on morals and on politics), are in their opinions both at variance with one another and with what will now be said about generation. |
| Deinde cum dicit: hi quidem enim ipsorum etc., ponit opiniones auferentium generationem. Et dicit quod quidam antiquorum philosophorum totaliter auferebant generationem et corruptionem a rebus: dicunt enim quod nihil entium fit aut corrumpitur, sed solum videtur nobis aliquid generari aut corrumpi. Et ista fuit opinio sequentium Melissum et Parmenidem. Quos quantum ad aliquid laudat, et quantum ad aliquid reprehendit. Laudat quidem quantum ad hoc, quod ipsi primi intellexerunt quod oportet esse aliquas naturas ingenitas et incorruptibiles et immobiles. Quod quidem hac ratione moti ponebant, quia de his quae subiiciuntur generationi et corruptioni, non potest esse certa cognitio aut scientia: si ergo est aliqua cognitio certa aut scientia, oportet esse aliquas naturas ingenitas et incorruptibiles. Etsi enim de his quae cadunt sub generatione et corruptione sit aliqua scientia, hoc non est nisi inquantum in eis est aliquid ingenitum et incorruptibile, secundum participationem illarum naturarum, quae secundum se sunt ingenitae et incorruptibiles: cognoscuntur enim secundum suas formas, forma autem est quoddam divinum in rebus, inquantum est quaedam participatio primi actus. | 552. Then at [408] he presents the opinions of those who remove generation. And he says that certain of the ancient philosophers totally removed generation and decay from things — for they said that nothing in beings comes to be or is destroyed, but something only seems to us to be generated or destroyed. This was the opinion of the followers of Melissus and Parmenides, whom Aristotle in one respect praises and in another condemns. He praises them for being the first to recognize that there have to be natures that are ungenerated and indestructible and immobile. This they were moved to assert for the reason that there cannot be sure knowledge or science about things that are subject to generation and decay. If, then, there is any certain knowledge or science, there must be certain natures which are ungenerated and indestructible. For even if there be some science of the things subject to generation and decay, it is only insofar as there is in them something ungenerated and indestructible, according to a participation in those natures that of themselves are ungenerated and indestructible. For they are known according to their forms, and form is something divine in things, insofar as it is a participation of the first act. |
| Reprehendit autem eos Aristoteles in hoc quod, quia nihil opinabantur esse praeter sensibilia, et tamen intelligebant quod oporteret esse quasdam substantias ingenitas et incorruptibiles, transtulerunt ea quae pertinent ad rationem supernaturalium substantiarum, ad haec sensibilia; dicentes haec sensibilia esse ingenita et incorruptibilia secundum veritatem, generari autem et corrumpi secundum opinionem. Manifestum est autem quod, si sunt quaedam entia ingenita et incorruptibilia et omnino immobilia, eorum consideratio non pertinet ad naturalem philosophiam, quae tota versatur circa mobilia; sed magis pertinet ad aliam priorem philosophiam, quae est metaphysica. Et ideo Parmenides et Melissus, licet quantum ad aliquid bene dicerent, ponentes quod oporteret esse aliquid ingenitum et immobile; non tamen quantum ad hoc bene dicebant, quod de rebus naturalibus non naturaliter loquebantur, attribuentes ea quae sunt substantiarum immobilium, substantiis naturalibus, quae sunt substantiae sensibiles. | But Aristotle reprehends them because, since they supposed that nothing beyond what can be sensed exists, and yet understood that there have to be certain ungenerated and indestructible substances, they transferred what belongs to the notion of the substances above nature to these sensible things, stating these sensible things to be in truth ungenerated and indestructible, but to be generated and destroyed according to opinion. But it is manifest that if there are certain ungenerated and indestructible and utterly immobile beings, their study does not pertain to natural philosophy, which is wholly concerned with changeable things, but pertains more to another prior philosophy, which is Metaphysics. And therefore Parmenides and Melissus, although they spoke well in one respect, by positing the need for something ungenerated and immobile to exist, nevertheless did not speak well in treating of natural things in a non-natural way, attributing the qualities of immobile substances to natural substances, which are sensible substances. |
| Dicit autem Simplicius in suo commento quod Aristoteles more suo reprehendit Parmenidem et Melissum, secundum ea quae exterius ex eorum verbis apparebant, ne aliqui, superficialiter intelligentes, deciperentur: secundum autem rei veritatem, intentio horum philosophorum erat quod ipsum ens, quod scilicet est per essentiam suam, est ingenitum et incorruptibile et omnino immobile. Quod autem dicebant generationem et corruptionem in rebus esse secundum opinionem, et non secundum veritatem, hoc ideo dicebant, quia opinabantur quod sensibilia, in quibus invenitur generatio et corruptio, non sunt vere entia, sed solum secundum opinionem. | 553. But Simplicius in his commentary says that Aristotle in his customary way reprehends Parmenides and Melissus for what externally appeared from their words lest anyone, understanding them superficially, should be deceived, but that in fact the intention of these philosophers was that being of itself, i.e., being that exists by its very essence, is ungenerated and indestructible and completely unchangeable. As to their statement that generation and decay are in things only according to opinion and not in reality, this they said because they believed that sensible things, in which generation and decay are found, are not truly beings but only according to opinion. |
| Deinde cum dicit: alteri autem quidam etc., ponit opinionem attribuentium generationem corporibus: et ponit tres opiniones. Et dicit quod quidam alii habebant contrariam opinionem praedictis, ac si studiose intenderent eis contradicere. Quidam enim dicunt quod nulla res est ingenita, sed omnia generantur: eorum tamen quae generantur, quaedam permanent incorruptibilia, quaedam autem corrumpuntur. Et hoc maxime dixerunt sectatores Hesiodi, qui fuit unus de theologis poetis, qui divina sub tegumentis quarundam fabularum tradiderunt. Unde Hesiodus dicitur posuisse etiam chaos, ex quo omnia generantur, esse generatum. Omne autem generatum ab aliquo generante generatur: unde dabant intelligere super omnia ista esse quandam causam primam, scilicet intellectum et divinitatem, a qua omnia processerunt. Et huiusmodi processum a primo principio generationem vocabant. | 554. Then at [409] he presents the opinion of those who attribute generation to bodies, and he gives three opinions. He says that certain others held an opinion contrary to the foregoing,, as though purposely intending to contradict them. For some maintain that nothing is ungenerated but that all things are generated, and that among these some remain indestructible and others are destroyed. Such was the doctrine especially of the followers of Hesiod, one of the Theologizing Poets, who treated divine matters under the guise of fables. Hence Hesiod is said to have posited even chaos, from which all things are generated, to have been generated. But whatever is generated is generated by some generator. Hence they gave it out that over all those things there is a certain first cause, namely, an intellect and a divinity, from which all things proceeded. Such a procession of all things from the first principle they called "generation." |
| Secundam opinionem ponit ibi: deinde et aliorum et cetera. Et dicit quod post praedictos poetas, inter alios, qui primitus de natura tractaverunt, quidam dixerunt quod omnia alia generantur et sunt in continuo fluxu, ita quod nihil in eis est fixum et permanens, praeter unum, materiale scilicet principium, quod subsistit omnibus quae fiunt et corrumpuntur. Et hoc idem dixerunt multi alii philosophi: sicut Thales, qui posuit hoc principium esse aquam; Anaximenes autem aerem; Anaximander autem medium inter utrumque, scilicet vaporem; Heraclitus autem Ephesius ignem (de quo specialiter mentionem facit, quia ipse magis asserebat omnia esse in continuo fluxu). | 555. The second opinion is given at [410]. And he says that after the afore-said poets, among others who first treated of nature, were those who maintained that all other things are generated and remain in a state of continuous flux, so that nothing is fixed and permanent in things except one, namely, the material principle which underlies all things that come to be and decay. This same thing was maintained by many other philosophers — such as Thales, who proposed that water is this first principle; and Anaxagoras, air; but Anaximander, an intermediate between the two, namely, vapor. Heraclitus of Ephesus proposed fire (and is specially mentioned because he more than others asserted all things to be in continual flux). |
| Tertiam opinionem ponit ibi: sunt autem quidam et cetera. Et dicit quod quidam sunt, qui posuerunt omne corpus esse generabile; quia ponunt quod omnia corpora componuntur ex superficiebus, et iterum resolvuntur in superficies. Et haec fuit opinio Platonis. | 556. The third opinion he gives at [411]. And he says that there are some who maintained every body is generable because they posit that all bodies are composed of surfaces and are reducible to surfaces. This was Plato's opinion. |
Lecture 3:
Bodies not generated from surfaces — proved mathematically and naturallyChapter 1 cont. Περὶ μὲν οὖν τῶν ἄλλων ἕτερος ἔστω λόγος τοῖς δὲ τοῦτον τὸν τρόπον λέγουσι καὶ πάντα τὰ σώματα συνιστᾶσιν ἐξ ἐπιπέδων ὅσα μὲν ἄλλα συμβαίνει λέγειν ὑπεναντία τοῖς μαθήμασιν, ἐπιπολῆς ἰδεῖν καίτοι δίκαιον ἢ μὴ κινεῖν ἢ πιστοτέροις αὐτὰ λόγοις κινεῖν τῶν ὑποθέσεων. 412 Discussion of the other views may be postponed. But this last theory which composes every body of planes is, as the most superficial observation shows, in many respects in plain contradiction with mathematics. It is, however, wrong to remove the foundations of a science unless you can replace them with others more convincing. Ἔπειτα δῆλον ὅτι τοῦ αὐτοῦ λόγου ἐστὶ στερεὰ μὲν ἐξ ἐπιπέδων συγκεῖσθαι, ἐπίπεδα δ' ἐκ γραμμῶν, ταύτας δ' ἐκ στιγμῶν οὕτω δ' ἐχόντων οὐκ ἀνάγκη τὸ τῆς γραμμῆς μέρος γραμμὴν εἶναι περὶ δὲ τούτων ἐπέσκεπται πρότερον ἐν τοῖς περὶ κινήσεως λόγοις, ὅτι οὐκ ἔστιν ἀδιαίρετα μήκη. 413 And, secondly, the same theory which composes solids of planes clearly composes planes of lines and lines of points, so that a part of a line need not be a line. This matter has been already considered in our discussion of movement, where we have shown that an indivisible length is impossible. Ὅσα δὲ περὶ τῶν φυσικῶν σωμάτων ἀδύνατα συμβαίνει λέγειν τοῖς ποιοῦσι τὰς ἀτόμους γραμμάς, ἐπὶ μικρὸν θεωρήσωμεν καὶ νῦν τὰ μὲν γὰρ ἐπ' ἐκείνων ἀδύνατα συμβαίνοντα καὶ τοῖς φυσικοῖς ἀκολουθήσει, τὰ δὲ τούτοις ἐπ' ἐκείνων οὐχ ἅπαντα διὰ τὸ τὰ μὲν ἐξ ἀφαιρέσεως λέγεσθαι, τὰ μαθηματικά, τὰ δὲ φυσικὰ ἐκ προσθέσεως. 414 But with respect to natural bodies there are impossibilities involved in the view which asserts indivisible lines, which we may briefly consider at this point. For the impossible consequences which result from this view in the mathematical sphere will reproduce themselves when it is applied to physical bodies, but there will be difficulties in physics which are not present in mathematics; for mathematics deals with an abstract and physics with a more concrete object. Πολλὰ δ' ἐστὶν ἃ τοῖς ἀδιαιρέτοις οὐχ οἷόν τε ὑπάρχειν, τοῖς δὲ φυσικοῖς ἀναγκαῖον. [Οἷον εἴ τί ἐστιν ἀδιαίρετον] ἐν ἀδιαιρέτῳ γὰρ διαιρετὸν ἀδύνατον ὑπάρχειν, τὰ δὲ πάθη διαιρετὰ πάντα διχῶς ἢ γὰρ κατ' εἶδος ἢ κατὰ συμβεβηκός, κατ' εἶδος μὲν οἷον χρώματος τὸ λευκὸν ἢ τὸ μέλαν, κατὰ συμβεβηκὸς δέ, ἂν ᾧ ὑπάρχει ᾖ διαιρετόν, ὥστε ὅσα ἁπλᾶ τῶν παθημάτων, πάντ' ἐστὶ διαιρετὰ τοῦτον τὸν τρόπον. Διὸ τὸ ἀδύνατον ἐν τοῖς τοιούτοις ἐπισκεπτέον. 415 There are many attributes necessarily present in physical bodies which are necessarily excluded by indivisibility; all attributes, in fact, which are divisible. There can be nothing divisible in an indivisible thing, but the attributes of bodies are all divisible in one of two ways. They are divisible into kinds, as colour is divided into white and black, and they are divisible per accidens when that which has them is divisible. In this latter sense attributes which are simple are nevertheless divisible. Attributes of this kind will serve, therefore, to illustrate the impossibility of the view. Εἰ δὴ τῶν ἀδυνάτων ἐστὶν ἑκατέρου μέρους μηδὲν ἔχοντος βάρος τὰ ἄμφω ἔχειν βάρος, τὰ δ' αἰσθητὰ σώματα ἢ πάντα ἢ ἔνια βάρος ἔχει, οἷον ἡ γῆ καὶ τὸ ὕδωρ, ὡς κἂν αὐτοὶ φαῖεν, εἰ ἡ στιγμὴ μηδὲν ἔχει βάρος, δῆλον ὅτι οὐδ' αἱ γραμμαί, εἰ δὲ μὴ αὗται, οὐδὲ τὰ ἐπίπεδα ὥστ' οὐδὲ τῶν σωμάτων οὐθέν. 416 It is impossible, if two parts of a thing have no weight, that the two together should have weight. But either all perceptible bodies or some, such as earth and water, have weight, as these thinkers would themselves admit. Now if the point has no weight, clearly the lines have not either, and, if they have not, neither have the planes. Therefore no body has weight. Ἀλλὰ μὴν ὅτι τὴν στιγμὴν οὐχ οἷόν τε βάρος ἔχειν, φανερόν. Τὸ μὲν γὰρ βαρὺ ἅπαν καὶ βαρύτερον καὶ τὸ κοῦφον καὶ κουφότερον ἐνδέχε(299b.) ταί τινος εἶναι. Τὸ δὲ βαρύτερον ἢ κουφότερον ἴσως οὐκ ἀνάγκη βαρὺ ἢ κοῦφον εἶναι, ὥσπερ καὶ τὸ μὲν μέγα μεῖζον, τὸ δὲ μεῖζον οὐ πᾶν μέγα πολλὰ γάρ ἐστιν ἃ μικρὰ ὄντα ἁπλῶς ὅμως μείζω ἑτέρων ἐστίν. Εἰ δὴ ὃ ἂν βαρὺ ὂν βαρύτερον ᾖ, ἀνάγκη βάρει μεῖζον εἶναι, τὸ βαρὺ ἅπαν διαιρετὸν ἂν εἴη. Ἡ δὲ στιγμὴ ἀδιαίρετον ὑπόκειται. 417 It is, further, manifest that their point cannot have weight. For while a heavy thing may always be heavier than something and a light thing lighter than something, a thing which is heavier or lighter than something need not be itself heavy or light, just as a large thing is larger than others, but what is larger is not always large. A thing which, judged absolutely, is small may none the less be larger than other things. Whatever, then, is heavy and also heavier than something else, must exceed this by something which is heavy. A heavy thing therefore is always divisible. But it is common ground that a point is indivisible. Ἔτι εἰ τὸ μὲν βαρὺ πυκνόν τι, τὸ δὲ κοῦφον μανόν, ἔστι δὲ πυκνὸν μανοῦ διαφέρον τῷ ἐν ἴσῳ ὄγκῳ πλεῖον ἐνυπάρχειν εἰ οὖν ἐστι στιγμὴ βαρεῖα καὶ κούφη, ἔστι καὶ πυκνὴ καὶ μανή. Ἀλλὰ τὸ μὲν πυκνὸν διαιρετόν, ἡ δὲ στιγμὴ ἀδιαίρετος. 418 Again, suppose that what is heavy or weight is a dense body, and what is light rare. Dense differs from rare in containing more matter in the same cubic area. A point, then, if it may be heavy or light, may be dense or rare. But the dense is divisible while a point is indivisible. Εἰ δὲ πᾶν τὸ βαρὺ ἢ μαλακὸν ἢ σκληρὸν ἀνάγκη εἶναι, ῥᾴδιον ἐκ τούτων ἀδύνατόν τι συναγαγεῖν. Μαλακὸν μὲν γὰρ τὸ εἰς ἑαυτὸ ὑπεῖκον, σκληρὸν δὲ τὸ μὴ ὑπεῖκον τὸ δὲ ὑπεῖκον διαιρετόν. 419 And if what is heavy must be either hard or soft, an impossible consequence is easy to draw. For a thing is soft if its surface can be pressed in, hard if it cannot; and if it can be pressed in it is divisible. Ἀλλὰ μὴν οὐδ' ἐκ μὴ ἐχόντων βάρος ἔσται βάρος. Καὶ γὰρ ἐπὶ πόσων συμβήσεται τοῦτο καὶ ἐπὶ ποίων; Ἢ πῶς διοριοῦσι μὴ βουλόμενοι πλάττειν; 420 Moreover, no weight can consist of parts not possessing weight. For how, except by the merest fiction, can they specify the number and character of the parts which will produce weight? καὶ εἰ πᾶν μεῖζον βάρος βάρους βάρει, συμβήσεται καὶ ἕκαστον τῶν ἀβαρῶν βάρος ἔχειν εἰ γὰρ αἱ τέτταρες στιγμαὶ βάρος ἔχουσι, τὸ δ' ἐκ πλειόνων ἢ τοδὶ βαρέος ὄντος βαρύτερον, τὸ δὲ βαρέος βαρύτερον ἀνάγκη βάρει εἶναι, ὥσπερ καὶ τὸ λευκοῦ λευκότερον λευκῷ, ἔσται τὸ μεῖζον μιᾷ στιγμῇ βαρύτερον, ὥστε, ἀφαιρεθέντος τοῦ ἴσου, [ὥστε] καὶ ἡ μία στιγμὴ βάρος ἕξει. 421 And, further, when one weight is greater than another, the difference is a third weight; from which it will follow that every indivisible part possesses weight. For suppose that a body of four points possesses weight. A body composed of more than four points will superior in weight to it, a thing which has weight. But the difference between weight and weight must be a weight, as the difference between white and whiter is white. Here the difference which makes the superior weight heavier is the single point which remains when the common number, four, is subtracted. A single point, therefore, has weight.
| Praemissis opinionibus de generatione rerum, hic inquirit de veritate praedictarum opinionum. Et praetermissis aliis opinionibus, de quibus in aliis locis inquirit, specialiter inquisitionem facit de ultima opinione, quae est Platonis; tum quia erat famosior, tum etiam quia ordine inquisitionis erat prior. Nam aliae opiniones ponebant vel auferebant specialium corporum generationem; haec autem opinio videbatur tradere generationem corporis, inquantum est corpus, ponendo corpus ex superficiebus generari. | 557. Having presented the opinions on the generation of things, he now inquires into the truth of the aforesaid opinions. And passing by the other opinions, which he discussed in other places, he makes inquiry especially about the last one, which is Plato's, both because it was more famous, and because in the order of inquiry it was prior. For the other opinions posited or removed generation of special bodies; but this opinion seemed to teach the generation of body insofar as it is body, since it posits body to be generated from surfaces. |
| Circa hoc autem duo facit: | In regard to this he does two things: |
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primo improbat hanc opinionem; secundo ostendit eisdem rationibus improbari posse opinionem Pythagoricorum, ponentium corpora generari ex numeris, ibi: idem autem accidit et cetera. |
First he disproves this opinion; Secondly, he shows that the same arguments can disprove the opinion of the Pythagoreans, who posit that bodies are generated from numbers, at 574. |
| Circa primum duo facit: | As to the first he does two things: |
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primo improbat praedictam opinionem rationibus mathematicis; secundo rationibus naturalibus, ibi: quaecumque autem de naturalibus et cetera. |
First he disproves the aforesaid opinion with mathematical arguments; Secondly, with natural arguments, at 560. |
| Circa primum ponit duas rationes. Circa quarum primam dicit quod de aliis praedictarum opinionum debet fieri alius sermo: partim quidem in I physicorum, partim autem in libro de generatione, partim autem inferius in hoc eodem libro. Sed quantum ad illos qui ponunt omnia corpora ex superficiebus constitui, in promptu est videre quod accidit eis dicere multa contraria disciplinis, idest scientiis mathematicis. Quae supponunt punctum esse indivisibile; et ita ex punctis non fit linea, quae est divisibilis: supponunt etiam lineam esse longitudinem sine latitudine; et ita ex lineis non fit superficies, quae habet longitudinem cum latitudine, sine profunditate: et ita ex superficiebus non fit corpus, quod cum longitudine et latitudine habet etiam profunditatem. Non est autem rectum quod aliquis removeat huiusmodi suppositiones mathematicorum, nisi aliquis afferat probabiliores rationes quam sint istae suppositiones. Et ideo videtur praedicta opinio Platonis esse improbanda, quae absque ratione cogente huiusmodi suppositiones removit. | 558. As to the first he gives two arguments. With respect to the first of these he says [412] that a discussion of the other opinions should be held elsewhere: partly, indeed in Physics I, partly in the book On Generation,, and partly in a later section of the present book, But as to those who posit that all bodies are constituted of surfaces, it is possible at once to see that they are found to hold many things contrary to the "disciplines," i.e., the mathematical sciences. These suppose that a point is indivisible, and that, consequently, a line, which is divisible, is not made of points. Mathematics supposes too, that a line is a length without breadth; consequently, a surface does not come to be from lines, because it has length and width without depth. Thus, too, neither does a body come from surfaces, since a body has length and width and depth. But it is not correct for anyone to reject these suppositions of the mathematicians, unless he can present arguments more probable than the suppositions. Consequently, the opinion of Plato seems to deserve to be disapproved, on the ground that he removes mathematical suppositions without a strong enough reason. |
| Secundam rationem ponit ibi: deinde palam et cetera. Et dicit eiusdem rationis esse quod solida, idest corpora, componantur ex superficiebus, et quod superficies componantur ex lineis, et linea ex punctis: quia sicut punctus est terminus et divisio lineae, ita linea superficiei, et superficies corporis. Si autem sic se habet sicut Plato posuit, quod corpora componantur ex superficiebus, sequetur quod superficies componantur ex lineis, et lineae ex punctis: et ita non erit necesse quod pars lineae sit linea. Et de hoc dicit esse prius consideratum in sermonibus de motu, idest in VI Physic., ubi probatum est quod lineae non sunt indivisibiles, neque ex indivisibilibus compositae. Invenitur autem quidam alius libellus, in quo probatur quod non sunt lineae indivisibiles: quem quidam dicunt esse Theophrasti. | 559. The second argument is at [4133. And he says the reason is the same for solids, i.e., bodies, to be composed of surfaces, and surfaces composed of lines, and lines of points, because, just as the point is the terminal and divider of the line, so the line is of the surface and the surface of the body. But if what Plato says is true, namely, that bodies are composed of surfaces, it will follow that a surface is composed of lines and lines of points. Consequently, it will not be necessary that a part of a line be a line. This matter, he says, was previously considered in "the discussions on motion," i.e., in Physics VI, where it was proved that lines are not indivisible, and are not composed of indivisibles. There is also found a certain other short book in which it is proved that lines are not indivisible, said by some to be by Theophrastus. |
| Deinde cum dicit: quaecumque autem de naturalibus etc., improbat praedictam positionem per rationes naturales. | 560. Then at [414] he disproves the aforesaid opinion with natural arguments. |
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Et primo assignat rationem quare necesse sit huiusmodi rationes inducere, non solum mathematicas, sed etiam naturales; secundo exequitur propositum, ibi: multa autem sunt et cetera. |
First he states why it is necessary to present such arguments, i.e., not only mathematical, but also natural; Secondly, he pursues his plan, at 561. |
| Dicit ergo primo quod, quia dictum est quod impossibile sequatur secundum mathematicam considerationem, ad id quod aliqui ponunt esse lineas indivisibiles, ex quibus componuntur superficies, et per consequens corpora; oportet quod etiam nunc consideremus breviter impossibilia quae sequuntur ad hanc opinionem, circa naturalia corpora. Et hoc necessarium est: quia quaecumque impossibilia accidunt circa mathematica corpora, necesse est quod consequantur ad corpora naturalia. Et hoc ideo, quia mathematica dicuntur per abstractionem a naturalibus; naturalia autem se habent per appositionem ad mathematica (superaddunt enim mathematicis naturam sensibilem et motum, a quibus mathematica abstrahunt); et sic patet quod ea quae sunt de ratione mathematicorum, salvantur in naturalibus, et non e converso. Et ideo quaecumque inconvenientia sunt contra mathematica, sunt etiam contra naturalia sed non convertitur. | He says therefore first [414] that, because we have said that an impossibility in mathematics follows upon the assumption by some of indivisible lines, from which surfaces are composed, and consequently bodies, it is also necessary to consider now briefly the impossibilities affecting natural bodies that will follow from this assumption. The reason this is necessary is that whatever impossibilities affect mathematical bodies must, as a consequence, extend to natural bodies. And this is so because mathematical things are obtained by abstraction from natural things, but natural things are by apposition to mathematical things — for they add to mathematical objects a sensible nature and motion, from which mathematics abstracts. Thus it is clear that mathematical properties are saved in natural things, but not conversely. Therefore, whatever impossibilities are against mathematical things are also against natural things, but not vice versa. |
| Deinde cum dicit: multa autem sunt etc., ostendit quae impossibilia ex praedicta positione sequantur circa corpora naturalia. | 561. Then at [415] he shows what impossibilities affecting natural bodies flow from the aforesaid position. |
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Et primo ponit quandam rationem generalem; secundo explicat eam per partes, ibi: si itaque impossibilium et cetera. |
First he presents a certain general argument; Secondly, he explains it part by part, at 562. |
| Dicit ergo primo quod multa sunt quae non possunt inesse indivisibilibus, quae tamen necesse est inesse naturalibus corporibus. Possumus autem indivisibilia hic accipere mathematica, eo quod per abstractionem dicuntur: et sic hoc quod hic dicitur, inducetur ad manifestandum quod immediate dictum est, scilicet quod naturalia se habent per additionem ad mathematica; quia multa necesse est inesse naturalibus, quae non possunt inesse mathematicis, sicut omnes passiones quae sunt divisibiles. Sed melius est ut indivisibilia accipiamus sicut superficies respectu corporum, et lineas respectu superficierum, et puncta respectu linearum; quae etiam sunt indivisibilia simpliciter. | He says therefore first [415] that there are many things which must exist in natural bodies but cannot exist in indivisibles. We could take "indivisibles" here as "mathematical things" on the ground that they are said by abstraction; thus what is said here will be adduced to show what was just said, namely, that natural things are by apposition to mathematical, since many things must be present in natural things that cannot be present in mathematical things, such as all the passions [properties] that are divisible. But it is better to take "indivisibles" as surfaces with respect to bodies, and lines with respect to surfaces, and points to lines — which latter are indivisible absolutely. |
| Dicit ergo quod multa necesse est inesse corporibus naturalibus, quae non possunt inesse rebus indivisibilibus; puta si aliquid est indivisibile, ut punctum vel linea vel superficies. Vel: puta si quid est divisibile; quia id quod est divisibile, ex necessitate inest corpori naturali, non autem rebus indivisibilibus. Divisibile enim non potest inesse rei indivisibili omnino: quia id quod inest alicui, quodammodo comprehenditur ab ipso; divisibile autem non potest comprehendi ab indivisibili secundum quantitatem. Omnes autem passiones dupliciter dividuntur: vel secundum speciem, vel secundum accidens. Quod non est sic intelligendum, quasi quaelibet passio utroque modo dividatur: sed quia quaelibet passio vel uno vel altero modo dividitur. | He says therefore that many things must be present in natural bodies that cannot be present in indivisible things: "For example, if something is indivisible," such as a point or line or surface; or, "for example, if something is divisible" — because what is divisible is of necessity in a natural body, but not in things that are indivisible. For something divisible cannot exist at all in an indivisible thing — since what is in something is in a certain way comprehended by it: but the divisible cannot be comprehended by the indivisible according to quantity. All passions are divided in two ways: either according to species, or according to accident. This of course does not mean that each and every passion is divided in both ways, but that each is divided in one way or the other. |
| Exponit autem utrumque modum divisionis. Et dicit quod secundum speciem dividitur passio, sicut species coloris sunt album et nigrum. Quod quidem potest intelligi dupliciter. Uno modo quod hoc commune quod est color, dividatur per album et nigrum sicut per suas species: sed hoc non facit ad propositum, quia nihil prohibet de aliquo indivisibili praedicari aliquid quod est commune ad multa. Unde oportet intelligere quod passio divisibilis secundum speciem intelligatur sicut color medius, qui componitur ex duabus speciebus coloris, quae sunt album et nigrum: talem autem passionem non videtur possibile inesse rei omnino simplici, quia, cum passiones propriae causentur a subiecto, necesse est quod passionis compositae sint diversa principia; quod repugnat simplicitati subiecti. | He then explains both ways of division. And he says that a passion is divided "according to species" in the way that the species of color are white and black. This can be understood in two senses. In one way, in the sense that this common thing which is color is divided into black and white, as though by its species; but this contributes nothing to our argument, because there is nothing to prevent something common to many from being predicated of some indivisible. Consequently, we must understand a passion divisible according to species in the sense of an intermediate color, which is a composite of two species of color, namely, black and white. Now it does not seem that such a passion can exist in a thing that is entirely simple: because, since the proper passions are caused by the subject, the principles of a composite passion must be diverse, and diversity is repugnant to the simplicity of a subject. |
| Exponit autem consequenter de divisibili secundum accidens. Et dicit quod passio dicitur secundum accidens divisibilis, si subiectum cui accidit sit divisibile; sicut dividitur albedo per divisionem subiecti. Unde omnes passiones quae sunt simplices secundum speciem, inveniuntur divisibiles hoc modo, scilicet secundum subiectum, inquantum scilicet insunt corpori naturali. | Then he explains what is divisible "according to accident." And he says that a passion is said to be divisible according to accident, if the subject of which it is an accident is divisible, as white is divided by dividing its subject. Hence all passions that are simple according to species are divisible in this way, i.e., according to subject, insofar, namely, as they exist in a natural subject. |
| Et ideo circa tales passiones, quae uno vel altero modo sunt divisibiles, est considerandum quod impossibile sequatur dicentibus lineas indivisibiles vel superficies, ex quibus componantur corpora naturalia, ex talibus quae non sunt susceptiva passionum corporum naturalium. | And therefore, regarding such passions which are divisible in one way or the other, it is to be understood that an impossibility follows upon those saying lines to be indivisible or surfaces, from which natural bodies are composed, namely, out of such things which cannot be the subject of the passions of natural bodies. |
| Deinde cum dicit: si itaque impossibilium etc., ponit speciales rationes ad improbandum positionem praedictam. Circa quarum primam duo facit: | 562. Then at [416] he gives special arguments which disprove the aforesaid position. In regard to the first argument he does two things: |
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primo proponit rationem; secundo probat ea quae supposuerat, ibi: sed et quod punctum et cetera. |
First he presents the argument; Secondly, he proves what he had supposed, at 563. |
| Dicit ergo primo impossibile esse, si utrumque eorum ex quibus aliquid componitur, nullam habeat gravitatem, quod compositum ex ambobus habeat gravitatem. Sed corpora sensibilia habent gravitatem; aut omnia, sicut dicebat Democritus, aut quaedam, scilicet terra et aqua, sicut ipsimet Platonici dicebant. Ergo corpus sensibile non potest componi ex rebus non habentibus gravitatem. Sed punctum nullam habet gravitatem: ergo ex punctis non potest componi aliquid habens gravitatem. Componitur autem ex eis secundum praedictam positionem linea: ergo etiam linea non potest habere gravitatem. Et per consequens neque superficies, quae componitur ex lineis: et ulterius neque corpus, quod componitur ex superficiebus: quod est contra praedicta. | He says therefore first [416] that it is impossible, if neither of the things out of which something is composed has heaviness, that the composite of both have heaviness. But sensible bodies have heaviness: either all of them, as Democritus says, or some, namely, earth and water, as the Platonists said. Therefore, a sensible body cannot be composed of things not having heaviness. But a point has no heaviness; therefore, a thing with heaviness cannot be composed of points. Yet according to the aforesaid opinion, a line is composed of points. Therefore, a line also cannot have heaviness. Consequently, neither can a surface, which is composed of lines; furthermore, neither can a body, which is composed of surfaces — which is against the aforesaid. |
| Est autem considerandum quod ista ratio tenet in partibus quantitativis, quae sunt eiusdem naturae et rationis et ad invicem et cum toto: non autem tenet in partibus essentialibus, quarum est alia ratio et ab invicem et a toto. Unde non sequitur, si materia non est gravis nec forma, quod compositum non sit grave: quia materia est gravis in potentia, per formam autem fit aliquid grave actu. | It should be noted that this argument holds for quantitative parts which are of the same nature and notion both in relation to one another and to the whole; but it does not hold in essential parts, which have a different notion with respect to one another and with respect to the whole. Hence it does not follow, if matter is not heavy and form is not heavy, that the composite is not heavy — because matter is heavy in potency, but through form something is made actually heavy. |
| Deinde cum dicit: sed et quod punctum etc., probat quae supposuerat in ratione praemissa. | 563. Then at [417] he proves what he had assumed in the preceding argument. |
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Et primo probat quod punctum non sit grave; secundo quod ex non gravibus non potest componi aliquid grave, ibi: sed adhuc neque ex non habentibus et cetera. |
First he proves that a point is not heavy; Secondly, that something heavy cannot be from non—heavy things, at 566. |
| Primum autem probat tribus rationibus. Quarum prima talis est. Omne grave potest esse aliquo alio gravius, et omne leve contingit esse aliquo levius: sed tamen non est necesse omne quod est gravius aut levius, esse grave aut leve. | The first he proves with three arguments, the first of which is this: Every heavy thing can be heavier than some other, and every light thing can be lighter than something else; but yet it is not necessary that everything heavier or lighter be heavy or light. |
| Videtur autem quod hic dicitur esse falsum: nam comparativum praesupponit positivum; omne enim albius est album. | But it seems that what is said here is false, for the comparative presupposes the positive — everything whiter is white. |
| Dicunt ergo quidam quod comparativum, si proprie accipiatur, praesupponit positivum, et infert ipsum: sed quandoque comparatio est abusiva, puta cum aliquid comparative dicitur respectu oppositi, sicut si dicatur cygnus albior corvo; vel etiam si aliquid dicatur comparative propter hoc quod minus participat de opposito, puta si dicatur aliquis Aethiops esse albior corvo, quia est minus niger; et sicut dicitur aliquod minus malum esse eligibilius magis malo, cum tamen malum non sit eligibile, nec Aethiops sit albus. Et per hunc modum hic philosophus dicit quod non omne gravius est grave, nec omne levius est leve: unde ad designandam abusivam comparationem, addidit forte. | Some therefore say that the comparative, if taken in its proper sense, does suppose and imply the positive; but that sometimes the comparison is "abusive." This occurs, for example, when a thing is said comparatively with respect to an opposite, as when a swan is said to be "whiter" than a raven, or even when a thing is described in the comparative degree because it possesses less of the opposite, as when an Ethiopian is said to be "whiter" than a raven because he is less black, or when it is said that some lesser evil is "more worthy of choice" than a greater evil — whereas evil is not worthy of choice, and an Ethiopian is not white. And it is in this way that the Philosopher here says that not everything heavier is heavy, nor everything lighter light. Hence, to designate an "abusive" comparison, he added, "perchance." |
| Sed quia non est consuetudo Aristotelis ut ex abusivis locutionibus argumentetur, ideo dicendum est quod quaedam sunt quae dicuntur tantum absolute, sicut album vel dulce; et in talibus comparativum praesupponit positivum, et infert ipsum. Quaedam autem sunt quae quandoque dicuntur absolute, quandoque autem relative, sicut grave et leve: nam, ut in quarto dicetur, ignis dicitur absolute levis, terra autem absolute gravis; aer autem ad ignem quidem gravis, ad aquam autem et terram levis. Sic et aqua ad terram quidem est levis, ad ignem autem et ad aerem gravis. Manifestum est autem quod id quod est absolute grave, est etiam grave per comparationem ad alia; et id quod est absolute leve, est etiam leve per comparationem ad alia; et per hunc modum omne grave est gravius, et omne leve est levius. Non tamen sequitur quod omne levius est leve, aut omne gravius sit grave: quia non sequitur, si est leve ad alia, quod sit leve absolute; et eadem ratio est de gravi. Et quod haec sit ratio dicti, patet ex exemplo quod ponit. | But since it is not Aristotle's custom to argue from "abusive" terms, it therefore should be stated that there are some things which are described only absolutely, as in the case of white or sweet; and in such cases the comparative presupposes the positive, and implies it. But there are other things which are sometimes said absolutely and sometimes relatively — as in the case of heavy and light: for, as will be said in Book IV, fire is said to be absolutely light and earth absolutely heavy; but air is heavy to fire, while light to water and earth. So too, water is light to earth but to air and fire heavy. Now it is evident that what is absolutely heavy, is also heavy when compared to other things; and that which is absolutely light, is light compared to other things. In this sense, everything heavy is heavier and everything light is lighter. But it does not follow that everything heavier is heavy, and everything lighter is light — since it does not follow that, if something is light in relation to other things, that it is light absolutely; and the same goes for the heavy. |
| Magnum enim, communiter acceptum, dicitur ad aliquid, ut patet in praedicamentis: sed applicatum alicui rei, dicitur absolute magnum quod pertingit ad quantitatem debitam illi rei; sicut homo dicitur magnus absolute, qui attingit ad perfectam hominis quantitatem. Et ita patet quod magnum dicitur absolute, et ad aliquid. Et inde est quod omne magnum absolute dicitur magnum ad aliquid, quod est esse maius: non autem omne maius est magnum absolute; multa enim sunt quae absolute considerata sunt parva, quae tamen aliis sunt maiora. | That this is the explanation of the statement is plain from the example he gives. For "large," taken commonly, is relative, as is evident in the Predicaments, but as applied to some thing, that is called "large" absolutely which attains to the quantity due it — as a man is called "large" absolutely, who attains to the perfect quantity of a man. Thus it is plain that "large" is said absolutely and relatively. Hence everything "large" absolutely is said to be large in relation to something, and this is to be "larger"; but not everything described as "larger" is large absolutely, for there are many things which, absolutely considered, are small, and yet are larger than other things. |
| Si igitur omne grave est gravius quodam alio, necesse est quod omne grave sit maius alio quodam in gravitate. Et ita sequitur quod sit divisibile: nam omne maius dividitur in aequale et plus. Sed punctum est indivisibile, ut supponitur ex eius definitione. Ergo punctum non est grave. | Therefore, if everything heavy is heavier than something else, then necessarily everything heavy must be greater in heaviness than something else. And so it follows that it is divisible: for everything that is greater is divided into what is equal and something more. But a point is indivisible, as is supposed from its definition. Therefore a point is not heavy. |
| Secundam rationem ponit ibi: adhuc si grave etc.; quae talis est. Grave et leve consequuntur ad rarum et spissum: videmus enim quod secundum differentiam raritatis et densitatis, elementa differunt in gravitate et levitate. Sed spissum in hoc differt a raro, quod in aequali mole, idest sub eisdem dimensionibus, plura continet, quia plus habet de materia, ut in IV Physic. habetur. Cum autem corpora quaedam sint gravia, quaedam levia, si punctum ponitur grave, pari ratione ponitur leve; et si ponitur spissum, pari ratione ponitur rarum. Sed illud quod ponitur spissum, oportet esse divisibile, inquantum plura continet sub minori mole: similiter id quod est rarum, oportet quod sit divisibile, inquantum aequale continet sub maiori mole. Punctum autem est indivisibile: ergo neque est spissum neque rarum; et per consequens neque grave neque leve. | 564. The second argument is given at [418], as follows: Heavy and light follow upon rare and dense — for we see that according to rarity and density, elements differ in heaviness and lightness. But the dense differs from what is rare in that, "in an equal mass," i.e., under the same dimensions, it contains more, because it has more matter, as is had in Physics IV. But since some bodies are heavy and some light, then if a point is posited as heavy, it is with equal reason posited as light; and if it is posited as dense, it is with equal reason posited as rare. But what is posited as dense must be divisible, insofar as it contains more under a smaller mass; similarly, what is rare must be divisible, insofar as it contains an equal amount under greater dimensions. But a point is indivisible. Therefore, it is neither thick nor rare and, consequently, neither heavy nor light. |
| Tertiam rationem ponit ibi: si autem omne grave etc.; quae talis est. Omne grave aut est molle aut durum: cuius ratio est, quia gravitas consequitur duo elementa, scilicet terram et aquam, quorum unum, scilicet aqua, cedit tangenti, et ideo est principium mollitiei; alterum autem, scilicet terra, non cedit, et ideo est principium duritiei. Manifestum est autem quod omne molle est divisibile: quia cedit tangenti infra seipsum; quod non posset esse nisi haberet plures partes, quarum una quodammodo resurgeret in locum alterius. Et eadem ratione oportet durum esse divisibile: non enim posset dici non cedens, nisi haberet quo cederet. Cum igitur punctum sit indivisibile, non erit durum neque molle: et ita non erit grave. | 565. The third argument is given at [419], as follows: Whatever is heavy is either soft or hard: the season being that heaviness follows on two elements, namely, earth and water, one of which, namely, water, yields to the touch and is, accordingly, a principle of softness, while the other, namely, earth, does not yield and is a principle of hardness. Now it is obvious that everything soft is divisible, because it yields within itself to what touches it. But this could not happen unless it had a number of parts, one of which is able in some way to move into the place of another. For the same reason, what is hard must be divisible, for it could not be said to be "unyielding," unless it had whence it could yield. Consequently, since a point is indivisible, it will be neither hard nor soft, and, therefore, not heavy. |
| Deinde cum dicit: sed adhuc neque ex non habentibus etc., ostendit quod nullum grave potest componi ex duobus vel pluribus, quorum nullum est grave. Sed hoc est intelligendum de compositione qua aliquid componitur ex partibus quantitativis: nam ex partibus essentialibus componitur aliquid grave, puta ex materia et forma, quorum neutrum est grave. | 566. Then at [420] he shows that nothing heavy can be composed of two or more things, none of which is heavy. But this must be understood of the composition by which something is composed of quantitative parts — for something heavy is composed of essential parts, for example, of matter and form, neither of which is heavy. |
| Ad hoc autem ostendendum inducit duas rationes. Quarum prima est quae procedit secundum quorundam opinionem, qui dicebant quod ex aliquibus non gravibus, quando multiplicabantur, componebatur aliquid grave: quando autem erant in minori numero, non constituebatur ex eis aliquid grave. Oportet igitur quod determinent quot existentibus constituatur gravitas: alioquin quod dicitur sine certa ratione, videtur esse fictitium. | To prove this he presents two arguments. The first of these proceeds in accordance with the opinion of some who said that from certain things not heavy, when they were multiplied, something heavy was composed, but that when they were in a lesser number, nothing heavy was made of them. But those who present this opinion must determine how many such things are required to form heaviness; otherwise what is said without a sure reason is seen as fictitious. |
| Secundam rationem ponit ibi: et si omnis gravitas etc.; quae talis est. Omnis gravitas maior alia gravitate, excedit minorem gravitatem per aliquam gravitatem: quia per additionem similium fit aliquid maius. Et ex hoc sequitur, secundum positionem praedictam, quod quodlibet indivisibile habeat gravitatem. Ponamus enim quod sit aliquod corpus ex quatuor punctis constitutum, gravitatem habens: sit aliud corpus constitutum ex pluribus punctis, puta ex quinque. Et sic erit gravius; ita scilicet quod oportebit id in quo excedit, esse grave. Et quamvis non omne gravius sit grave, ut supra dictum est, tamen omne quod est gravius gravi, oportet esse grave, sicut omne quod est albius albo, oportet esse album. Et ideo, cum illud quod est maius in uno puncto, sit gravius corpore quod est sibi aequale si auferatur ab eo unum punctum, sequetur quod unum punctum sit grave; quod est impossibile, ut ex praemissis patet. Ergo relinquitur impossibile esse quod ex non gravibus fiat aliquod grave. | 567. The second argument is presented at [421], as follows: Every heaviness greater than another heaviness exceeds the lesser by a certain heaviness, because something is made greater by the addition of like things. From this it follows, according to the aforesaid position, that every indivisible has heaviness. For let us suppose a body constituted of four points, having heaviness; let us take another body made of more points, say five. Thus it will be heavier — and in such a way that that by which it is heavier, must be heavy. And although not everything heavier is heavy, as was said above, yet whatever is heavier than something heavy must be heavy, just as everything which is whiter than something white must be white. And therefore, since what is greater by one point is heavier than a body which is equal to it if that point be removed, it will follow that one point is heavy. But that is impossible, as is clear from what has gone before. Therefore, it remains that it is impossible for something heavy to be made from things that are not heavy. |
Lecture 4:
Other natural arguments against Plato's opinion. Pythagorean opinion refutedChapter 1 cont. Ἔτι εἰ μὲν τὰ ἐπίπεδα μόνον κατὰ γραμμὴν ἐνδέχεται συντίθεσθαι, ἄτοπον ὥσπερ γὰρ γραμμὴ πρὸς γραμμὴν ἀμφοτέρως συντίθεται, καὶ κατὰ μῆκος καὶ κατὰ πλάτος, δεῖ καὶ ἐπίπεδον ἐπιπέδῳ τὸν αὐτὸν τρόπον. Γραμμὴ δὲ δύναται γραμμῇ συντίθεσθαι κατὰ γραμμὴν ἐπιτιθεμένη ἀλλ' οὐ προστιθεμένη. Ἀλλὰ μὴν εἴ γε καὶ κατὰ πλάτος ἐνδέχεται συντίθεσθαι, ἔσται τι σῶμα ὃ οὔτε στοιχεῖον οὔτε ἐκ στοιχείων, συντιθέμενον ἐκ τῶν οὕτω συντιθεμένων ἐπιπέδων. 422 Further, to assume, on the one hand, that the planes can only be put in linear contact would be ridiculous. For just as there are two ways of putting lines together, namely, end to and side by side, so there must be two ways of putting planes together. Lines can be put together so that contact is linear by laying one along the other, though not by putting them end to end. But if, similarly, in putting the lanes together, superficial contact is allowed as an alternative to linear, that method will give them bodies which are not any element nor composed of elements. Ἔτι εἰ μὲν πλήθει βαρύτερα τὰ σώματα τῶν ἐπιπέδων, ὥσπερ ἐν τῷ (300a.) Τιμαίῳ διώρισται, δῆλον ὡς ἕξει καὶ ἡ γραμμὴ καὶ ἡ στιγμὴ βάρος ἀνάλογον γὰρ πρὸς ἄλληλα ἔχουσιν, ὥσπερ καὶ πρότερον εἰρήκαμεν. Εἰ δὲ μὴ τοῦτον διαφέρει τὸν τρόπον ἀλλὰ τῷ τὴν μὲν γῆν εἶναι βαρὺ τὸ δὲ πῦρ κοῦφον, ἔσται καὶ τῶν ἐπιπέδων τὸ μὲν κοῦφον τὸ δὲ βαρύ. Καὶ τῶν γραμμῶν δὴ καὶ τῶν στιγμῶν ὡσαύτως τὸ γὰρ τῆς γῆς ἐπίπεδον ἔσται βαρύτερον ἢ τὸ τοῦ πυρός. 423 Again, if it is the number of planes in a body that makes one heavier than another, as the Timaeus explains, clearly the line and the point will have weight. For the three cases are, as we said before, analogous. But if the reason of differences of weight is not this, but rather the heaviness of earth and the lightness of fire, then some of the planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earthplane, I mean, will be heavier than the fire-plane. Ὅλως δὲ συμβαίνει ἢ μηδέν ποτ' εἶναι μέγεθος, ἢ δύνασθαί γε ἀναιρεθῆναι, εἴπερ ὁμοίως ἔχει στιγμὴ μὲν πρὸς γραμμήν, γραμμὴ δὲ πρὸς ἐπίπεδον, τοῦτο δὲ πρὸς σῶμα πάντα γὰρ εἰς ἄλληλα ἀναλυόμενα εἰς τὰ πρῶτα ἀναλυθήσεται ὥστ' ἐνδέχοιτ' ἂν στιγμὰς μόνον εἶναι, σῶμα δὲ μηθέν. 424 In general, the result is either that there is no magnitude at all, or that all magnitude could be done away with. For a point is to a line as a line is to a plane and as a plane is to a body. Now the various forms in passing into one another will each be resolved into its ultimate constituents. It might happen therefore that nothing existed except points, and that there was no body at all. Πρὸς δὲ τούτοις καὶ εἰ ὁ χρόνος ὁμοίως ἔχει, ἀναιροῖτ' ἄν ποτε ἢ ἐνδέχοιτ' ἂν ἀναιρεθῆναι τὸ γὰρ νῦν τὸ ἄτομον οἷον στιγμὴ γραμμῆς ἐστιν. 425 A further consideration is that if time is similarly constituted, there would be, or might be, a time at which it was done away with. For the indivisible now is like a point in a line. Τὸ δ' αὐτὸ συμβαίνει καὶ τοῖς ἐξ ἀριθμῶν συντιθεῖσι τὸν οὐρανόν ἔνιοι γὰρ τὴν φύσιν ἐξ ἀριθμῶν συνιστᾶσιν, ὥσπερ τῶν Πυθαγορείων τινές τὰ μὲν γὰρ φυσικὰ σώματα φαίνεται βάρος ἔχοντα καὶ κουφότητα, τὰς δὲ μονάδας οὔτε σώματα ποιεῖν οἷόν τε συντιθεμένας οὔτε βάρος ἔχειν. 426 The same consequences follow from composing the heaven of numbers, as some of the Pythagoreans do who make all nature out of numbers. For natural bodies are manifestly endowed with weight and lightness, but an assemblage of units can neither be composed to form a body nor possess weight. [not in Greek] Quod quidem igitur neque omnium generatio est neque simpliciter nullius, palam ex dictis. Therefore, it is clear from what has been said that generation neither applies to everything nor to nothing.
| Praemissa prima ratione quam Aristoteles posuit ad improbandum opinionem Platonis, ponentis corpora ex superficiebus generari, hic ponit secundam rationem. | 568. Having given a first argument against Plato's opinion that bodies are generated from surfaces, Aristotle here presents a second argument. |
| Ad cuius evidentiam sciendum est quod Plato, quia non distinguebat inter unum quod est principium numeri, et unum quod convertitur cum ente, quod significat substantiam rei, ponebat per consequens quod unum quod est principium numeri, esset substantia rei: et per consequens omnes res ponebat esse numeros. Unde et dimensiones quantitatis continuae dicebat esse quosdam numeros positionem habentes: et sic secundum ipsum punctus est unitas positionem habens, et sic de aliis. Et quia dualitatem attribuebat materiae, unitatem autem formae, aestimabat quod formae omnium corporum essent accipiendae secundum rationem figurarum, secundum quas corpora terminantur. Ultimi autem termini dimensionum sunt puncta, quae sunt unitates positae, ut dictum est. Et ideo diversas figuras corporeas diversis corporibus attribuebat: sicut figuram pyramidalem igni, figuram autem octo basium aeri, figuram autem viginti basium aquae, figuram autem cubicam terrae, figuram autem duodecim basium aetheri, idest caelo. Manifestum est autem figuras corporeas ex superficiebus constitui, inquantum ad invicem coniunguntur secundum tactum linearem: sic enim faciunt angulum corporalem. Et ideo, formalem compositionem corporum distribuens, Plato dicebat quod corpora componuntur ex superficiebus secundum lineam coniunctis. | To understand this argument it should be known that Plato, because he did not distinguish between the "one" which is the principle of number, and the "one" which is convertible with being, which signifies the substance of the thing, posited as a consequence that the "one" which is the principle of number is the substance of a thing, and consequently, that all things are numbers. Accordingly, he posited the dimensions of continuous quantity to be certain numbers "having position." According to him, therefore, a point is unity having position, and so for all the others. And because he attributed duality to matter and unity to form, he estimated that the forms of all bodies should be taken according to the notion of the figures according to which the bodies are terminated. Now the ultimate terminations of dimensions are points, which are "positioned unities," as has been said. Therefore he attributed the various bodily figures to the various bodies: such as that of the pyramid to fire, that of eight bases [faces, in this case, the octohedron] to air, a figure of 20 bases [the icosahedron] to water, the cube to earth, a 12-based figure [the dodecahedron] to the aether, i.e., to the heaven. Now it is clear that bodily figures are constituted of surfaces, insofar as they are conjoined according to contact along lines — thus constituting corporeal angles. And therefore, assigning the formal composition to bodies, Plato said that bodies are composed of surfaces joined along a line. |
| Contra hoc igitur obiicit Aristoteles, dicens inconveniens esse si ponatur superficies componi sive coniungi ad instituendum corpus, solum secundum linearem contactum. | 569. Against this, therefore, Aristotle objects [422], and says that an impossibility follows, if it is assumed that surfaces are composed or joined to form a body by mere linear contact. |
| Et hoc manifestat per exemplum lineae. Linea enim duobus modis potest alteri lineae coniungi: uno modo secundum longitudinem, quod est secundum punctualem contactum, inquantum scilicet longitudini unius lineae coniungitur in puncto longitudo alterius lineae, sive faciat angulum cum ea sive non; alio modo secundum latitudinem, quod est secundum appositionem totius lineae ad totam lineam in via latitudinis. Et similiter oportet quod superficies componatur superficiei dupliciter: scilicet secundum profunditatem, puta si tota una superficies supponatur alteri superficiei; et secundum linearem contactum, sive constituat angulum corporalem sive non. Et ad exponendum quod dixerat, subdit quod linea potest componi lineae secundum hoc quod supponatur alteri, et non solum secundum hoc quod apponatur ei secundum contactum linearem. | This he manifests with the example of a line. For a line can be joined to another line in two ways: One way is according to length, and which is according to contact by point, insofar, namely, as the length of one line is joined to the length of another at a point, whether it makes an angle with it or not. The other way is according to width, which consists in adding one whole line to another whole line in the direction of width. Similarly, surface must be joined to surface in two ways: namely, according to depth — for example, if one whole surface should be placed under another; and according to linear contact, whether they form a corporeal angle or not. To explain further what he says, he adds that line can be joined to line by being placed under it, and not only as being added to it according to linear contact [at a point]. |
| Quia igitur duplex est modus quo superficies coniungi possunt; et secundum alterum modum, scilicet secundum contactum linearem, compositae faciunt omnia elementa; sequetur quod, si componantur secundum latitudinem, idest supponendo superficiem superficiei, id quod componetur ex superficiebus sic compositis, erit corpus quod nec est elementum nec ex elementis. Quod autem non sit elementum patet, quia omnia elementa constituuntur secundum alium modum coniunctionis superficierum. Quod autem non sit ex elementis patet, quia ista compositio superficierum, quae est secundum superpositionem, videtur constituere ipsam profunditatem corporis, quae est eius substantia; alia vero compositio superficierum constituit corpus secundum figuram, quae est forma adveniens substantiae corporali. Unde compositio suppositionis erit prior: et id quod est constitutum ex tali modo compositionis, videtur comparari ad id quod est constitutum secundum alium modum compositionis, sicut materia ad formam. Ex superficiebus autem, secundum opinionem Platonis, natum est componi corpus. Sequitur igitur quod id quod praecedit omnia elementa, sicut elementorum materia suscipiens omnes figuras seu formas eorum, sit corpus. Et hoc reputabat Plato inconveniens: non enim primam materiam dicebat esse corpus, sicut quidam antiqui naturales posuerunt. | 570. Therefore, because there are two ways in which surfaces can be joined and because it is according to one way, namely, according to linear contact, that joined surfaces form all the elements, it will follow that, if they should be joined "in the direction of width," i.e., by placing one surface under another, the resultant of surfaces so composed will be a body that is neither an element nor composed from elements. That it is not an element is plain, since all the elements are constituted according to the other mode of conjunction of surfaces. That it is not made from elements is plain, since this combination of surfaces, resulting from superposition, seems to cause a body's depth, which is its substance, while the other combination of surfaces establishes the body with respect to figure, which is a form added to bodily substance. Hence the combination according to sub-position will be prior, and what results from this composition seems to be compared to what results from the other kind of composition, as matter is compared to form. But according to the opinion of Plato, a body's nature is to be composed of surfaces [in linear contact]. It follows, therefore, that what precedes all the elements, as though it were their matter receiving all their figures, or forms, is a body. And Plato regarded this as something unacceptable — for he did not state the first matter to he a body, as certain of the early natural philosophers did. |
| Deinde cum dicit: adhuc si quidem etc., ponit tertiam rationem; quae talis est. Cum ex superficiebus constituantur corpora, quorum quaedam sunt aliis graviora, hoc potest contingere dupliciter. Uno modo sic, quod corpus constituatur gravius ex hoc quod ex pluribus superficiebus componitur, sicut dicitur in Timaeo. Et ex hoc sequetur quod superficies sint graves: quia excessus in gravitate non fit nisi secundum aliquid grave, ut supra dictum est. Et ex hoc sequetur ulterius quod lineae et puncta habeant gravitatem: haec enim proportionaliter se habent, sicut prius dictum est; quia scilicet sicut superficies se habet ad corpus, ita linea ad superficiem, et punctum ad lineam. Puncta autem habere gravitatem, supra improbatum est. | 571. Then at [423] he presents a third argument, as follows: Since bodies are constituted out of surfaces, some of which bodies are heavier than others, this can come about in two ways. One way is that a body would be made heavier from the fact that it is composed of more surfaces, as is said in the Timaeus. And from this it will follow that surfaces are heavy — because an excess in heaviness cannot be produced except by something that is itself heavy, as was said above. And from this it will further follow that lines and points have heaviness — for these are proportionately related, that is, as surfaces are to bodies, so lines are to surfaces and points to lines. But that points should have heaviness has been disproved above. |
| Alius autem modus est, quod corpora gravia a levioribus non differant per hunc modum, idest per multitudinem superficierum; sed per hoc quod terra componitur ex gravibus, et ignis ex levibus. Et ita sequetur quod superficierum quaedam erunt leves, et quaedam graves, et similiter linearum et punctorum: quia superficies terrae erit gravior quam superficies ignis. Et ita redibit idem inconveniens ut prius. | The other way is that heavy bodies do not differ from light in this way, i.e., by the multiplication of surfaces, but on account of earth's being composed of heavy [surfaces] and fire of light. And thus it will follow that some surfaces are light and some heavy, and the same for lines and points — because a surface of earth will be heavier than one of fire. And so the same impossibility will arise as before. |
| Deinde cum dicit: totaliter autem accidit etc., ponit quartam rationem; dicens quod accidit secundum positionem Platonis, quod nulla sit magnitudo, vel quod omnis magnitudo possit auferri, idest esse desinere. Quia similiter se habet punctum ad lineam, et linea ad superficiem, et superficies ad corpus: et ita, si corpus componatur ex superficiebus, poterit in superficiem resolvi; et eadem ratione omnes magnitudines resolventur in prima, idest in puncta. Et sic sequeretur quod nullum sit corpus, sed solum puncta. Nec est simile si quis velit argumentari quod potest contingere nulla corpora mixta esse, quia possunt resolvi in elementa ex quibus componuntur: quia huiusmodi corpora supponuntur caelestibus corporibus, quae operantur in eis mixtionem; puncta autem non supponuntur aliquibus superioribus principiis, quae eis inferant necessitatem compositionis. | 572. Then at [424] he presents a fourth argument, saying that according to the position of Plato it follows that no magnitude exists, or that every magnitude can be "taken away" i.e., cease to exist. For point is to line as line is to surface and surface to body. Consequently, if a body is composed of surfaces, it will be able to be reduced to surface, and, by the same token, all magnitudes will be reduced to the "first things," i.e., to points. Thus it would follow that there would be no body but points only. Nor is it similar if one should wish to argue that it can occur that there be no mixed [composite] bodies, since they can be resolved into the elements out of which they are composed — since such bodies are subject to the heavenly bodies, which produce a mixture in them. But points are not subject to any higher principles which would induce in them the necessity of composition. |
| Deinde cum dicit: adhuc autem etc., ponit quintam rationem; dicens quod, si tempus hoc modo se habeat quod componatur ex instantibus, sicut corpus ex superficiebus vel linea ex punctis (quod totum est unius rationis, ut probatur in VI Physic.), sequitur quod etiam tempus continget totaliter tolli per resolutionem in sua indivisibilia: quia ipsum nunc est indivisibile temporis, sicut punctum est indivisibile lineae. | 573. Then at [425] he presents a fifth argument, saying that if time is such as to be composed of instants, in the same way as a body is of surfaces, or a line of points (all of which involve the same notion, as is proved in Physics VI), it follows that time too can be entirely destroyed by being reduced to its indivisibles — for the "now" is the indivisible of time, just as the point is the indivisible of line. |
| Deinde cum dicit: idem autem accidit etc., assimilat praedictam positionem positioni Pythagoricorum. Et dicit quod eadem inconvenientia accidunt illis qui ponunt caelum constitui ex numeris. Quidam enim Pythagoricorum posuerunt totam naturam ex numeris esse constitutam, ratione supra dicta, quos Plato secutus est. Hoc autem improbat philosophus hic: quia corpora naturalia habent gravitatem et levitatem; unitates autem ad invicem coniunctae, non possunt facere corpus quod sit continuum, sed aliquid discretum; nec etiam habent gravitatem, quia abstrahunt a situ, et per consequens a loco. | 574. Then at [426] he assimilates the foregoing position to that of the Pythagoreans. And he says that the same irreconcilable factors follow for those who claim that the heaven is constituted from numbers. For some Pythagoreans posited that all nature is constituted from numbers for the aforesaid reason, and Plato followed them. But now the Philosopher disproves this: For natural bodies have heaviness and lightness. But units joined one to another cannot form a body that is continuous; rather they form something discrete. Nor do they possess heaviness, because they abstract from position, and, consequently, from place. |
| Ultimo autem epilogando concludit quod neque omnium est generatio, neque nullius. Quod enim non sit nullius, sensu apparet. Quod autem non sit omnium, patet per hoc quod impossibile est omnis corporis esse generationem; quod quidem esset, si corpus ex superficiebus generaretur. | Finally, in summary he concludes [427] that there is neither generation of all things nor of none. That it is not of none is evident to sense. But that it is not of all things is plain from the fact that it is impossible for there to be generation of every body — which would indeed be the case if a body were generated from surfaces. |
Lecture 5:
Natural motion in natural bodies. Leucippus and DemocritusChapter 2 Ὅτι δ' ἀναγκαῖον ὑπάρχειν κίνησιν τοῖς ἁπλοῖς σώμασι φύσει τινὰ πᾶσιν, ἐκ τῶνδε δῆλον. 428 The necessity that each of the simple bodies should have a natural movement may be shown as follows. Ἐπεὶ γὰρ κινούμενα φαίνεται, κινεῖσθαί γε ἀναγκαῖον βίᾳ, εἰ μὴ οἰκείαν ἔχει κίνησιν τὸ δὲ βίᾳ καὶ παρὰ φύσιν ταὐτόν. Ἀλλὰ μὴν εἰ παρὰ φύσιν ἐστί τις κίνησις, ἀνάγκη εἶναι καὶ κατὰ φύσιν, παρ' ἣν αὕτη καὶ εἰ πολλαὶ αἱ παρὰ φύσιν, τὴν κατὰ φύσιν μίαν κατὰ φύσιν μὲν γὰρ ἁπλῶς, παρὰ φύσιν δ' ἔχει πολλὰς ἕκαστον. 429 They manifestly move, and if they have no proper movement they must move by constraint: and the constrained is the same as the unnatural. Now an unnatural movement presupposes a natural movement which it contravenes, and which, however many the unnatural movements, is always one. For naturally a thing moves in one way, while its unnatural movements are manifold. Ἔτι δὲ καὶ ἐκ τῆς ἠρεμίας δῆλον καὶ γὰρ ἠρεμεῖν ἀναγκαῖον ἢ βίᾳ ἢ κατὰ φύσιν βίᾳ δὲ μένει οὗ καὶ φέρεται βίᾳ, καὶ κατὰ φύσιν οὗ κατὰ φύσιν. Ἐπεὶ οὖν φαίνεταί τι μένον ἐπὶ τοῦ μέσου, εἰ μὲν κατὰ φύσιν, δῆλον ὅτι καὶ ἡ φορὰ ἡ ἐνταῦθα κατὰ φύσιν αὐτῷ εἰ δὲ βίᾳ, τί τὸ φέρεσθαι κωλῦον; Εἰ μὲν ἠρεμοῦν, τὸν αὐτὸν κυκλήσομεν λόγον ἀνάγκη γὰρ ἢ κατὰ φύσιν εἶναι τὸ (300b.) πρῶτον ἠρεμοῦν ἢ εἰς ἄπειρον ἰέναι, ὅπερ ἀδύνατον εἰ δὲ κινούμενον τὸ κωλῦον φέρεσθαι, καθάπερ φησὶν Ἐμπεδοκλῆς τὴν γῆν ὑπὸ τῆς δίνης ἠρεμεῖν, ποῦ ἂν ἐφέρετο, ἐπειδὴ εἰς ἄπειρον ἀδύνατον; Οὐθὲν γὰρ γίγνεται ἀδύνατον, τὸ δ' ἄπειρον διελθεῖν ἀδύνατον. Ὥστ' ἀνάγκη στῆναί που τὸ φερόμενον, κἀκεῖ μὴ βίᾳ μένειν ἀλλὰ κατὰ φύσιν. Εἰ δ' ἐστὶν ἠρεμία κατὰ φύσιν, ἔστι καὶ κίνησις κατὰ φύσιν, ἡ εἰς τοῦτον τὸν τόπον φορά. 430 The same may be shown, from the fact of rest. Rest, also, must either be constrained or natural, constrained in a place to which movement was constrained, natural in a place movement to which was natural. Now manifestly there is a body which is at rest at the centre. If then this rest is natural to it, clearly motion to this place is natural to it. If, on the other hand, its rest is constrained, what is hindering its motion? Something, which is at rest: but if so, we shall simply repeat the same argument; and either we shall come to an ultimate something to which rest where it is or we shall have an infinite process, which is impossible. The hindrance to its movement, then, we will suppose, is a moving thing—as Empedocles says that it is the vortex which keeps the earth still—: but in that case we ask, where would it have moved to but for the vortex? It could not move infinitely; for to traverse an infinite is impossible, and impossibilities do not happen. So the moving thing must stop somewhere, and there rest not by constraint but naturally. But a natural rest proves a natural movement to the place of rest. Διὸ καὶ Λευκίππῳ καὶ Δημοκρίτῳ, τοῖς λέγουσιν ἀεὶ κινεῖσθαι τὰ πρῶτα σώματα ἐν τῷ κενῷ καὶ τῷ ἀπείρῳ, λεκτέον τίνα κίνησιν καὶ τίς ἡ κατὰ φύσιν αὐτῶν κίνησις. 431 Hence Leucippus and Democritus, who say that the primary bodies are in perpetual movement in the void or infinite, may be asked to explain the manner of their motion and the kind of movement which is natural to them. Εἰ γὰρ ἄλλο ὑπ' ἄλλου κινεῖται βίᾳ τῶν στοιχείων, ἀλλὰ καὶ κατὰ φύσιν ἀνάγκη τινὰ εἶναι κίνησιν ἑκάστου, παρ' ἣν ἡ βίαιός ἐστιν καὶ δεῖ τὴν πρώτην κινοῦσαν μὴ βίᾳ κινεῖν, ἀλλὰ κατὰ φύσιν εἰς ἄπειρον γὰρ εἶσιν, εἰ μή τι ἔσται κατὰ φύσιν κινοῦν πρῶτον, ἀλλ' ἀεὶ τὸ πρότερον βίᾳ κινούμενον κινήσει. 432 For if the various elements are constrained by one another to move as they do, each must still have a natural movement which the constrained contravenes, and the prime mover must cause motion not by constraint but naturally. If there is no ultimate natural cause of movement and each preceding term in the series is always moved by constraint, we shall have an infinite process.
| Postquam philosophus improbavit positionem ponentium omnia corpora generari ex superficiebus, hic incipit inquirere utrum corpora naturalia habeant motus naturales. Et circa hoc duo facit: primo ostendit quod corpora naturalia habent motus naturales; secundo ostendit quomodo motus violenti corporum perficiantur diversimode a motibus naturalibus, ibi: quoniam autem natura et cetera. Circa primum duo facit: | 575. After disproving the position of those who posit that all bodies are generated from surfaces, the Philosopher here begins to inquire whether natural bodies have natural motions. Concerning this he does two things: |
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primo ostendit quod corpora naturalia habent motus naturales; secundo ostendit quod habent gravitatem et levitatem, quibus inclinantur ad suos motus naturales, ibi: quod autem quaedam habere et cetera. |
First he shows that natural bodies have natural motions; Secondly, how compulsory motions of bodies take place in ways other than those of natural motions, at 590 (L. 7). |
| Circa primum duo facit: | Regarding the first he does two things: |
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primo probat quod corpora naturalia habent motus naturales; secundo improbat quorundam philosophorum opiniones, circa hoc errantium, ibi: propter quod et Leucippo et cetera. |
First he proves that natural bodies have natural motions; Secondly, he refutes the opinions of certain philosophers, in error on this matter, at 578. |
| Circa primum duo facit. | In regard to the first he does two things: |
| Primo proponit quod intendit: et dicit quod, quia supra dictum est quod operationes et passiones corporum sunt generationes et motus eorum, et de generatione corporum inquisitum est, restat dicendum de motibus eorum. Et dicit quod manifestum est ex his quae dicentur, quod necesse est omnibus corporibus simplicibus inesse aliquem motum naturalem. Corpora vero mixta sequuntur motum corporis simplicis praedominantis in eis. Ergo omnibus corporibus naturalibus inest aliquis motus naturalis. | First he proposes what he intends [428] and says that because it was said above that the operations and passions of bodies are their generations and motions, and we have already inquired about the generation of bodies, it remains to discuss their motions. And he says it is manifest from what will be said that there must be some natural motion in all simple bodies, whereas mixed bodies follow the motion of the simple body that is predominant in it. Therefore, some natural motion is in every natural body. |
| Secundo ibi: quoniam enim mota etc., probat propositum duabus rationibus. Quarum prima sumitur ex parte motus. Videmus enim ad sensum corpora simplicia moveri: si ergo non habent proprium motum sibi naturalem, necesse est quod moveantur per violentiam. Idem autem est moveri per violentiam, et moveri praeter naturam: quod enim est secundum naturam, non est violentum, quia violentum est in quo nil confert vim patiens, ut dicitur in III Ethic. | 576. Secondly, at [429] he proves his proposition with two arguments, the first of which is based on motion. For we see by the senses that simple bodies are moved; if, therefore, they do not have a proper motion natural to them, then they must be being moved by violence. But to be moved by violence is the same as to be moved beside nature — for what is according to nature is not violent, because the violent is that in which what undergoes the force contributes nothing, as is said in Ethics III. |
| Ex eo autem quod est aliquis motus praeter naturam, sequitur quod sit aliquis motus secundum naturam, respectu cuius dicitur motus violentus praeter naturam: non enim aegritudo esset dispositio praeter naturam, nisi esset sanitas dispositio secundum naturam; omnis enim privatio praesupponit habitum. Et licet sequatur ex hoc quod est motus praeter naturam, quod sit motus aliquis secundum naturam; tamen, quamvis sint multi motus praeter naturam, motus tamen secundum naturam est unus (unius scilicet corporis): quia natura unius rei est determinata ad unum, a qua contingit multipliciter deviare; sicut est sanitas una, aegritudines vero multae. Et hoc ideo, quia unumquodque secundum suam naturam est simpliciter, idest uno modo, eo quod natura unius rei est una: sed unumquodque habet non solum multos motus, sed etiam multas dispositiones, praeter naturam. | Now from the fact that there are motions beside nature, it follows that there is motion according to nature in respect to which a violent motion is called "beside nature" [praeter naturam]; for sickness would not be a disposition beside nature, unless health were a disposition according to nature, because every privation presupposes something positive. And although from the fact that there is a motion beside nature, it follows that there is a motion according to nature, yet, while there are many motions beside nature, the motion according to nature is one, i.e., for one body, because the nature of one thing is determined to one, from which many deviations are possible, just as health is one but sicknesses many. The reason for this is that each thing is "absolutely" according to its nature, i.e., in one way, because the nature of one thing is one; but each thing has not only many motions, but also many dispositions, beside nature. |
| Sed contra hoc videtur esse quod in principio libri dictum est, quod motui secundum naturam contrariatur motus praeter naturam, et quod unum uni est contrarium. | But against this seems to be the statement made in the beginning of this book, namely, that to a motion according to nature there is contrary to it one beside nature, and that one thing is contrary to one. |
| Ad quod dici potest quod philosophus ibi loquitur de motibus simplicibus: unum enim corpus non potest moveri pluribus motibus simplicibus praeter naturam; potest tamen moveri pluribus motibus compositis praeter naturam. Vel potest dici quod etsi unum uni sit contrarium, tamen contrarium quod est ut privatio, potest se habere multipliciter; sicut sanitas simpliciter est, aegritudo autem multipliciter. Et similiter motus secundum naturam est uno modo, motus autem praeter naturam multis modis. | To this it can be said that the Philosopher is speaking there of simple motions: for one body cannot be moved beside nature with several simple motions, although it can be moved beside its nature by several composite motions. Or it can be said that even though one thing is contrary to one, yet the contrary which is as privation can occur in many ways, just as health is something absolutely, but sickness can occur in many ways. Similarly, motion according to nature occurs in one way, but beside nature in many ways. |
| Secundam rationem ponit ibi: adhuc autem etc.: et sumitur ex parte quietis. Et praesupponit duo. Quorum primum est, quod necesse est omne quod quiescit, quiescere aut violenter aut secundum naturam. Secundum est, quod ibi quiescit aliquid per violentiam, quo movetur per violentiam; et ibi quiescit aliquid secundum naturam, quo movetur secundum naturam. | 577. The second argument is presented at [430] and is based on rest. It presupposes two things. First of all, that whatever is at rest must be resting either according to violence or according to nature. Secondly, a thing rests through violence in a place whither it is moved through violence; but wherever it is moved according to nature, it rests according to nature. |
| Ex his autem argumentatur sic. Videmus ad sensum aliquod corpus quiescere in medio, puta terram aut lapidem: ergo, secundum praemissa, aut quiescit per violentiam, aut secundum naturam. Et si quidem secundum naturam, sequitur secundum praemissa quod etiam motus talis corporis ad hunc locum sit naturalis. Si autem quiescit per violentiam, oportet quod sit aliquid inferens ei violentiam, quod prohibeat ipsum moveri. Illud ergo quod prohibet ipsum moveri, aut movetur aut quiescit. | From these suppositions he argues thus: It is evident to our senses that some body, for example, earth or a stone, is at rest in the middle. Therefore, according to what has been premised, it is resting either through violence or according to nature. If according to nature, then, according to the suppositions, it follows that the motion of such a body to this place is natural. But if it is resting through violence, then something must be present exerting violence upon it and preventing it from being moved. But what is so preventing it from being moved is itself either in motion or at rest. |
| Si quiescit, sicut columna quiescens prohibet lapidem superpositum moveri, redibit eadem quaestio de hoc prohibente, utrum quiescat naturaliter vel violenter. Et si naturaliter, concludetur quod etiam naturaliter movetur: si autem violenter, iterum indigebit alio prohibente. Et sic necesse est vel quod deveniatur ad aliquod primum quiescens secundum naturam, quod etiam ex consequenti naturaliter movebitur; aut quod in infinitum procedatur in corporibus, quod est impossibile, ut in primo ostensum est. | If it is at rest, as a pillar at rest prevents a stone upon it from being moved, the same question returns about this impediment: Is it at rest naturally or violently? If naturally, it will be concluded that it is also moved naturally; but if violently, it will in turn need something preventing it. Consequently, it is necessary either to arrive at some first thing at rest according to nature, which will consequently be moved according to nature, or to go on infinitely in bodies — which is impossible, as was shown in Book I. |
| Si vero dicatur quod quiescens violenter in medio prohibetur moveri ab aliquo quod movetur (sicut Empedocles dixit quod terra quiescit per violentiam prohibita a gyratione caeli), remota tali prohibitione, consequens est quod corpus prohibitum prius moveri, feretur ad aliquem locum determinatum: quia impossibile est quod feratur in infinitum, quia impossibile est infinitum pertransire, nihil autem est in fieri, quod est impossibile factum esse. Si ergo ad aliquem locum determinatum movetur, quando illuc devenerit, stabit et quiescet non violenter, sed naturaliter: et ita, secundum praemissa, si quiescit naturaliter in hoc loco, sequitur quod naturaliter ad hunc locum moveatur. Et sic erit aliquis motus naturalis. | But if it be said that a thing at rest by violence in the middle is prevented from being moved by something in motion (as Empedocles said that the earth is at rest, being prevented by violence from moving by the gyration of the heaven) then, if that obstacle were removed, the consequence would be that the previously impeded body would be carried to some definite place — it being impossible for it to be carried ad infinitum, since it is impossible for the infinite to be traversed, and nothing can be in the process of becoming which cannot come to be. If then it is being moved to some definite place, then, when it shall have arrived there, it will stop or rest there not violently but naturally. And so, according to the premises, if it rests naturally in this place, it follows that it is moved naturally to this place. Consequently, there will exist some natural motion. |
| Deinde cum dicit: propter quod et Leucippo etc., improbat quorundam philosophorum opiniones circa praedicta. | 578. Then at [431] he disproves the opinions of certain philosophers on this matter. |
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Et primo opinionem Democriti; secundo opinionem Platonis, ibi: idem autem hoc accidere et cetera. |
First the opinion of Democritus; Secondly, the opinion of Plato (L. 6). |
| Circa primum duo facit. Primo ex praemissis concludit insufficientiam dictorum Democriti. Ponebat enim corpora indivisibilia, quae dicebat esse principia, semper moveri in spatio infinito et vacuo. Ostensum est autem quod corporum simplicium est aliquis naturalis motus: ergo debebant determinare qua specie motus huiusmodi corpora moventur, et quis est motus naturalis eorum. Cum autem hoc non determinaverint, insufficienter posuerunt. | In regard to the first he does two things. First, from the premises he concludes to the inadequacy of Democritus' sayings. For he posited that the indivisible bodies which he said to be principles are always being moved in an infinite and empty space. But it has been shown that simple bodies have some natural motion. Therefore they should decide by what kind of motion such bodies are being moved and what their natural motion is. However, since they have not determined this, their doctrine is incomplete. |
| Secundo ibi: si enim aliud ab alio etc., ponit quandam excusationem: quia ipsi dicebant quod unum istorum corporum indivisibilium, quae ponebant elementa, moveatur ab alio per violentiam. Sed hoc excludit dupliciter. | 579. Secondly, at [432] he presents a certain excuse, because they said that one of those indivisible bodies which they posited as elements is moved violently by another. |
| Primo quidem quia, si ponitur motus violentus, necesse est quod ponatur motus secundum naturam, praeter quem est motus violentus, ut supra dictum est. Secundo quia oportet quod saltem primum movens non moveat per violentiam, sed secundum naturam. Quod enim movet per violentiam, habet principium suae motionis extra, et ita non movet nisi motum. Si ergo non ponatur aliquod primum movens secundum naturam, sed semper moveat per violentiam prius motum ab aliquo alio, procedetur in infinitum in moventibus; quod est impossibile, ut probatum est in VIII Physic. Et ita non excusantur quin oportuerit eos assignare motum naturalem. | But he rejects this on two grounds. First, because if violent motion is posited, then natural motion must be posited, beside which the violent motion is, as was said above. Secondly, because at least the first mover must not cause motion through violence but according to nature. For whatever causes motion through violence has the principle of its motion without, and thus does not move except as moved. If then a first thing causing motion by nature is not posited, but always one that is acting through violence being previously moved by something else, there will be an infinite process in movers — which is impossible, as was proved in Physics VIII. Therefore they are not excused from the need for positing natural motion. |
Lecture 6:
Refutation of Plato's opinion of disordered motion before the worldChapter 2 cont. Τὸ αὐτὸ δὲ τοῦτο συμβαίνειν ἀναγκαῖον κἂν εἰ καθάπερ ἐν τῷ Τιμαίῳ γέγραπται, πρὶν γενέσθαι τὸν κόσμον ἐκινεῖτο τὰ στοιχεῖα ἀτάκτως. Ἀνάγκη γὰρ ἢ βίαιον εἶναι τὴν κίνησιν ἢ κατὰ φύσιν. Εἰ δὲ κατὰ φύσιν ἐκινεῖτο, ἀνάγκη κόσμον εἶναι, ἐάν τις βούληται θεωρεῖν ἐπιστήσας τό τε γὰρ πρῶτον κινοῦν ἀνάγκη κινεῖν ἑαυτὸ κινούμενον κατὰ φύσιν, καὶ τὰ κινούμενα μὴ βίᾳ, ἐν τοῖς οἰκείοις ἠρεμοῦντα τόποις, ποιεῖν ἥνπερ ἔχουσι νῦν τάξιν, τὰ μὲν βάρος ἔχοντα ἐπὶ τὸ μέσον, τὰ δὲ κουφότητα ἔχοντα ἀπὸ τοῦ μέσου ταύτην δ' ὁ κόσμος ἔχει τὴν διάταξιν. 433 The same difficulty is involved even if it is supposed, as we read in the Timaeus, that before the ordered world was made the elements moved without order. Their movement must have been due either to constraint or to their nature. And if their movement was natural, a moment's consideration shows that there was already an ordered world. For the prime mover must cause motion in virtue of its own natural movement, and the other bodies, moving without constraint, as they came to rest in their proper places, would fall into the order in which they now stand, the heavy bodies moving towards the centre and the light bodies away from it. But that is the order of their distribution in our world. Ἔτι δὲ τοσοῦτον ἐπανέροιτ' ἄν τις, πότερον οὐχ οἷόν τ' ἦν κινούμενα ἀτάκτως καὶ μίγνυσθαι τοιαύτας μίξεις ἔνια, ἐξ ὧν συνίσταται τὰ κατὰ φύσιν συνιστάμενα σώματα, λέγω δ' οἷον ὀστᾶ καὶ σάρκας, καθάπερ Ἐμπεδοκλῆς φησὶ γίνεσθαι ἐπὶ τῆς φιλότητος λέγει γὰρ ὡς πολλαὶ μὲν κόρσαι ἀναύχενες ἐβλάστησαν. 434 There is a further question, too, which might be asked. Is it possible or impossible that bodies in unordered movement should combine in some cases into combinations like those of which bodies of nature's composing are composed, such, I mean, as bones and flesh? Yet this is what Empedocles asserts to have occurred under Love. 'Many a head', says he, 'came to birth without a neck.' Τοῖς δ' ἄπειρα ἐν ἀπείρῳ τὰ κινούμενα ποιοῦσιν, εἰ μὲν ἓν τὸ κινοῦν, ἀνάγκη μίαν φέρεσθαι φοράν, ὥστ' οὐκ ἀτάκτως κινηθήσεται, εἰ δ' ἄπειρα τὰ (301a.) κινοῦντα, καὶ τὰς φορὰς ἀναγκαῖον ἀπείρους εἶναι εἰ γὰρ πεπερασμέναι, τάξις τις ἔσται οὐ γὰρ τῷ μὴ φέρεσθαι εἰς τὸ αὐτὸ ἡ ἀταξία συμβαίνει οὐδὲ γὰρ νῦν εἰς τὸ αὐτὸ φέρεται πάντα, ἀλλὰ τὰ συγγενῆ μόνον. 435 The answer to the view that there are infinite bodies moving in an infinite is that, if the cause of movement is single, they must move with a single motion, and therefore not without order; and if, on the other hand, the causes are of infinite variety, their motions too must be infinitely varied. For a finite number of causes would produce a kind of order, since absence of order is not proved by diversity of direction in motions: indeed, in the world we know, not all bodies, but only bodies of the same kind, have a common goal of movement. Ἔτι τὸ ἀτάκτως οὐθέν ἐστιν ἕτερον ἢ τὸ παρὰ φύσιν ἡ γὰρ τάξις ἡ οἰκεία τῶν αἰσθητῶν φύσις ἐστίν. Ἀλλὰ μὴν καὶ τοῦτο ἄτοπον καὶ ἀδύνατον, τὸ ἄπειρον ἄτακτον ἔχειν κίνησιν ἔστι γὰρ φύσις ἐκείνη τῶν πραγμάτων οἵαν ἔχει τὰ πλείω καὶ τὸν πλείω χρόνον συμβαίνει οὖν αὐτοῖς τοὐναντίον τὴν μὲν ἀταξίαν εἶναι κατὰ φύσιν, τὴν δὲ τάξιν καὶ τὸν κόσμον παρὰ φύσιν καίτοι οὐδὲν ὡς ἔτυχε γίγνεται τῶν κατὰ φύσιν. 436 Again, disorderly movement means in reality unnatural movement, since the order proper to perceptible things is their nature. And there is also absurdity and impossibility in the notion that the disorderly movement is infinitely continued. For the nature of things is the nature which most of them possess for most of the time. Thus their view brings them into the contrary position that disorder is natural, and order or system unnatural. But no natural fact can originate in chance. Ἔοικε δὲ τοῦτό γε αὐτὸ καλῶς Ἀναξαγόρας λαβεῖν ἐξ ἀκινήτων γὰρ ἄρχεται κοσμοποιεῖν. Πειρῶνται δὲ καὶ οἱ ἄλλοι συγκρίνοντές πως πάλιν κινεῖν καὶ διακρίνειν. Ἐκ διεστώτων δὲ καὶ κινουμένων οὐκ εὔλογον ποιεῖν τὴν γένεσιν. Διὸ καὶ Ἐμπεδοκλῆς παραλείπει τὴν ἐπὶ τῆς φιλότητος οὐ γὰρ ἂν ἠδύνατο συστῆσαι τὸν οὐρανὸν ἐκ κεχωρισμένων μὲν κατασκευάζων, σύγκρισιν δὲ ποιῶν διὰ τὴν φιλότητα ἐκ διακεκριμένων γὰρ συνέστηκεν ὁ κόσμος τῶν στοιχείων ὥστ' ἀναγκαῖον γίνεσθαι ἐξ ἑνὸς καὶ συγκεκριμένου. 437 This is a point which Anaxagoras seems to have thoroughly grasped; for he starts his cosmogony from unmoved things. The others, it is true, make things collect together somehow before they try to produce motion and separation. But there is no sense in starting generation from an original state in which bodies are separated and in movement. Hence Empedocles begins after the process ruled by Love: for he could not have constructed the heaven by building it up out of bodies in separation, making them to combine by the power of Love, since our world has its constituent elements in separation, and therefore presupposes a previous state of unity and combination. Ὅτι μὲν οὖν ἐστι φυσική τις κίνησις ἑκάστου τῶν σωμάτων, ἣν οὐ βίᾳ κινοῦνται οὐδὲ παρὰ φύσιν, φανερὸν ἐκ τούτων. 438 These arguments make it plain that every body has its natural movement, which is not constrained or contrary to its nature.
| Postquam philosophus improbavit opinionem Democriti et Leucippi circa motus corporum naturalium, hic improbat opinionem Platonis circa idem. | 580. After disproving the opinion of Democritus and Leucippus on the motions of natural bodies, the Philosopher here disproves Plato's opinion on the same matter. |
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Et primo per rationes; secundo per dicta aliorum philosophorum, qui circa hoc melius sensisse videntur, ibi: videtur autem hoc ipsum et cetera. |
First with arguments; Secondly, with the saying of other philosophers, who are seen to have had better perception on this matter, at 585. |
| Circa primum ponit quatuor rationes. Circa quarum primam dicit quod idem inconveniens quod accidit Democrito et Leucippo, necesse est accidere si quis ponat quod antequam mundus esset factus, elementa ex quibus mundus constituitur, movebantur motu inordinato, sicut in Timaeo scribitur a Platone, narrante quod antequam mundus a Deo fieret, materia inordinate fluctuabat. | 581. Regarding the first he presents four arguments, with respect to the first of which he says [433] that the same impossibility that happens to Democritus and Leucippus must recur, if anyone posits that before the world was made the elements out of which it is formed were being moved with a disorderly motion, as Plato writes in the Timaeus, recounting that, before the world was made by God, matter fluctuated without order. |
| Quod autem idem accidat ex hac positione, ostendit subdens quod necesse est dicere, quod motus inordinatus quo movebantur elementa, aut esset violentus aut secundum naturam. Et si quidem esset violentus, reditur in primam positionem: unde accidit idem inconveniens. Si autem esset secundum naturam, hoc est contrarium posito. Ponitur enim quod mundus nondum erat: si vero elementa movebantur secundum naturam, necesse est dicere quod tunc mundus erat, si quis attente velit considerare. Nam cum omnis motus, etiam secundum Platonem, reducatur sicut in causam in primum movens, si elementa quocunque modo movebantur, necesse est dicere quod primum movens movebat seipsum secundum naturam. | That the same impossibility recurs when this is posited he proves by adding that the disorderly motion by which the elements were being moved was either violent or according to nature, If violent, we are led back to the first position: hence the same impossibility recurs. But if the motion were according to nature, then we are contradicting our assumption. For it is assumed that the world was not yet existing, whereas, if the elements were being moved according to nature, then it is necessary to say the world was already existing, if one wishes to consider attentively. For since every motion, even according to Plato, is reduced to a first mover as to its cause, then, if the elements were in some way moved, it must be said that the first mover was moving himself according to nature. |
| Primum autem movens hic intelligitur non simpliciter primum, quia hoc est omnino immobile, ut probatur in VIII Physic. et in XII Metaphys., sed primum movens in genere naturalium moventium, quod movet seipsum, tanquam compositum ex motore et moto, ut probatum est in VIII Physic. Alia tamen littera habet: primum movens necesse movere ipsum motum (scilicet primum) secundum naturam; et tunc intelligitur de primo motore movente simpliciter, quod est omnino immobile, quod movet primum mobile. | By first mover is here understood, not the absolutely first mover, which is utterly immobile, as. is proved in Physics VIII and in Metaphysics XII, but the first mover in the genus of natural movers, i.e., one that moves itself and is composed of mover and moved, as was proved in Physics VIII. But if we follow another reading, namely, "the first mover must move the (first) moved according to nature," then it refers to the first mover moving absolutely, which is wholly immobile, which moves the first mobile. |
| Quocumque autem modo accipiatur primum movens, necesse est quod moveat secundum naturam: non enim est possibile ut id quod est praeter naturam, sit prius eo quod est secundum naturam, ut ex praemissis patet. Si autem primum movens naturaliter movet, necesse est quod corpora mota, quae sequuntur motionem primi moventis, non moveantur per violentiam, neque quiescant per violentiam in propriis locis, sed servent eundem ordinem quem nunc tenent; ita scilicet quod corpora gravia cedant ad medium et ibi quiescant, corpora autem levia ferantur a medio et sursum maneant. Haec autem est dispositio mundi existentis: sequitur ergo quod mundus esset antequam fieret. Non ergo est consonum ponere quod elementa, priusquam mundus fieret, moverentur secundum naturam, sed secundum violentiam. Et sic sequitur idem inconveniens quod Democrito et Leucippo. | But no matter how "first mover" is understood, it must move according to nature, for it is not possible that what is beside nature precede what is according to nature, as is clear from the premises. Now if the first mover moves naturally, necessarily the bodies which follow the motion of the first mover are not being moved by violence nor rest by violence in their appropriate places, but maintain the same order as now prevails, i.e., such that heavy bodies fall to the middle and rest there, but light bodies are borne from the middle and remain above. But this is the situation of the world as it now is; it follows, therefore, that the world would have been before it came into existence. It is not sound, therefore, to posit that the elements, before the world came to be, were being moved according to nature, but according to violence. And thus there follows the same impossibility as for Democritus and Leucippus. |
| Secundam rationem ponit ibi: adhuc autem et cetera. Quae quidem quantum ad aliquid in idem tendit quod prima, scilicet quod mundus esset antequam fieret: sed prima hoc concludebat ex parte corporum simplicium, haec autem ratio concludit ex parte corporum mixtorum (utrorumque enim dispositio attenditur etiam in consistentia mundi). | 582. The second argument he presents at [434] and in one sense it leads to the same thing as the first, namely, that the world would exist before it came to be. But the first argument came to this conclusion by considering simple bodies; the present argument concludes to it by considering mixed bodies (for the disposition of both arises in the make-up of the world. |
| Dicit ergo: si elementa, antequam mundus fieret, movebantur inordinate, potest aliquis quaerere utrum elementa quae inordinate movebantur, possent misceri talibus mixtionibus, ut ex eis constituerentur corpora quae secundum naturam consistunt, scilicet carnes et ossa et alia huiusmodi. Si quis enim dicat hoc non fuisse possibile, sequitur quod elementa non omnino inordinate movebantur, cum scilicet non possent indifferenter quibuslibet motibus moveri. Nam Empedocles, ponens elementa moveri ab amicitia, dixit quod huiusmodi corpora per motum quo amicitia ea movebat, constituebantur; ita scilicet quod ex solis motibus elementorum per amicitiam, alicui generabatur caro, alicui os, alicui caput, alicui manus; unde dixit quod ex tali coniunctione elementorum per amicitiam, sunt producta multa capita sine cervice. Si ergo dicatur non fuisse possibile haec produci, elementa non omnino inordinate movebantur. Si vero possibile erat haec produci, iam erat completa mundi dispositio, non solum quantum ad corpora simplicia, sed etiam quantum ad mixta. Est autem attendendum quod germinatio capitum sine cervice, secundum Empedoclem, causatur ex amicitia, non secundum ultimum terminum suae motionis, in quo ex omnibus facit unum; sed secundum processum quo paulatim plura in unum redigit, ex elementis corpora mixta constituens. | He says therefore: If the elements, before the world was made, were being moved haphazardly, someone can ask whether the elements so moved were able to be mixed in such mixtures that natural bodies such as flesh and bones and so on, would result. If anyone should declare this not possible, it follows that the elements were not in utterly disorderly motion, since, namely, they could not be moved by any and all motions. For Empedocles, in positing that the elements are moved by friendship, said that such bodies were formed by the motion produced by friendship, in such a way, namely, that by the sole motion of the elements by friendship, for one there was generated flesh, for another, bone, for another a head, for another, hands. He further said that as a result of such a combination of elements through friendship, many heads were produced without a neck. If, therefore, it is maintained that it was impossible for these things to be produced, then the elements were not moved wholly without order. But if it were possible for these to be produced, then the disposition of the world was already completed, not only regarding simple bodies, but mixed bodies as well. — It should be noted that the generation of heads without necks is, according to Empedocles, caused by friendship not in terms of a final product of its activity, but as part of the process whereby it gradually reduces the many to one, constituting mixed bodies from the elements. |
| Tertiam rationem ponit ibi: his autem qui infinita et cetera. Inducitur autem haec ratio non absolute contra Platonem, sed coassumendo opinionem Democriti et Leucippi, qui ponebant infinita corpora indivisibilia moveri in spatio infinito. | 583. The third argument he sets down at [435]. It is not directed absolutely against Plato but in combination with the opinions of Democritus and Leucippus, who held that infinite indivisible bodies are being moved in infinite space. |
| Dicit ergo quod illis qui ponunt infinita corpora moveri in spatio infinito, si hanc positionem Platonis susciperent, quod ante mundum elementa moverentur motu inordinato, sequeretur inconveniens. Aut enim omnia illa infinita moverentur ab uno movente (scilicet secundum speciem, puta a gravitate vel levitate), aut ab infinitis. Et si quidem ab uno, necesse esset ea ferri una specie motus localis, puta motu qui est sursum vel motu qui est deorsum: et ita non moverentur inordinate; iam enim in hoc attenditur aliqua ordinatio motus, quod omnia feruntur in idem. Si vero essent infinita principia motus specie differentia, sequeretur quod etiam essent infinitae species motus: quod est impossibile, secundum praemissa, in quibus ostensum est non esse infinitas et indeterminatas species motus. | He says, therefore, that if those who posit infinite bodies being moved in infinite space accept Plato's position that before the world the elements were in haphazard motion, an impossibility would follow. For either all those infinite bodies would be being moved by one mover (i.e., according to species, e.g., by heaviness or lightness), or by an infinitude of movers. If by one, then they would have to be moved by one kind of local motion, for example, by upward motion or downward. Consequently they would not be in haphazard motion, since there is already a certain order in the fact that all things are being moved to the same place. But if there were an infinitude of principles, all specifically different, it would follow that the species of motion would also be infinite. But this is impossible, according to things previously set down, in which it was shown that the species of motion are not infinite and indeterminate. |
| Idem autem dicendum est de finitis principiis motuum et finitis motibus: quia si essent finitae species motus, causatae a finitis principiis, iam attenderetur in eis aliquis ordo. Non enim inordinatio motuum provenit ex hoc quod non omnia corpora feruntur in idem, quod est esse plures species motus: quia etiam nunc, quando, mundo iam facto, est ordinatus motus corporum, non omnia corpora feruntur in idem, sed solum ea quae sunt unius generis, sicut omnia gravia deorsum. | Likewise the same must be said if the principles of the motions are finite and the motions themselves finite — for, if there were finite species of motion, caused by finite principles, there would already be implied in them a certain order. For the disorder of motions does not arise from the fact that not all bodies are being moved to the same place, which is for there to be several species of motion, since even now, when, with the world existing, there is an ordered motion of bodies, not all bodies are being moved to one and the same place, but only those that are of the same genus, as all heavy bodies downward, |
| Addit ergo per hanc rationem quod necesse est ponere motus infinitos, si antequam mundus fieret, corpora movebantur inordinate. | He adds therefore by this argument that it is necessary to posit infinite motions if before the world was made bodies were being moved haphazardly. |
| Quartam rationem ponit ibi: adhuc autem inordinate etc.; per quam ostenditur quod praedicta positio sibi ipsi contradicit. Nihil enim aliud est esse aliquid inordinate, quam esse praeter naturam. In rebus enim sensibilibus apparet quod ordo est propria natura eorum: quia scilicet per propriam naturam unumquodque eorum inclinatur ad aliquid certum; haec autem inclinatio est ordo qui attenditur in sensibilibus rebus; tunc enim unumquodque dicitur inordinate agere aut moveri, quando hoc accidit non secundum inclinationem naturae propriae. | 584. He sets down the fourth argument at [436], and shows that the position in question contradicts itself. For to exist in disorder is nothing other than to exist beside nature. In sensible things it appears that order is their proper nature, since, namely, through its proper nature each of them is inclined to something definite. But this inclination is the order discerned in sensible things — for things are said to act or to move in a disorderly fashion when this happens contrary to the inclination of a thing's proper nature. |
| Ex quo adhuc apparet hoc esse inconveniens et impossibile, quod res sensibilis habeat motum inordinatum infinitum, idest infinito tempore durantem: quia sicut dictum est, motus inordinatus est, qui est contra naturam; apparet autem hoc ad rationem naturae cuiuscumque rei pertinere, quod inveniatur in pluribus quae sunt unius generis, et plurimo tempore. Non enim dicitur esse naturale homini quod aliquibus paucis convenit, puta esse ambidextrum; neque etiam quod convenit aliquibus secundum aliquod modicum tempus, puta esse febricitantem; sed quod in pluribus et frequentius invenitur. | From this it also appears that it is unfitting and impossible for a sensible thing to have a disorderly motion that is "infinite," i.e., enduring for an infinite time, because, as has been said, a disordered motion is one contrary to nature. Now it appears that it belongs to the nature of each thing that it be found in many members of the same genus and most of the time. For what is found in just a few men is not said to be natural to man — for example, to be ambidextrous; nor what is true of some for just a short time — for example, to have a fever. But the natural is that which is found in the greater number and more frequently. |
| Sic igitur accidit ipsis Platonicis ponere simul contraria: scilicet quod inordinatio motus sit secundum naturam, eo quod fuit tempore infinito ante mundum; et quod ordinatio motus, et mundus constitutus motu iam ordinato, sit praeter naturam, eo quod pauciori tempore fuit; quamvis nihil eorum quae sunt secundum naturam, sit ut contingit, idest absque certo ordine. | Consequently, the Platonists come to assume two contraries at the same time, namely, that disorderly motion is according to nature, since it existed for an infinite time before the world, and that ordered motion, as well as the world constituted after the ordering of motion, are contrary to nature, since they have existed for a shorter time, even though nothing according to nature is "as it happens," i.e., without a definite order. |
| Est autem attendendum quod rationes Aristotelis directe contra positionem Platonis procedunt, si ex verbis eius intelligatur quod prius tempore erat inordinatio motus elementorum, quam fieret mundus. Sectatores autem Platonis dicunt eum hoc non intellexisse; sed quod omnis ordinatio motus sensibilium est a primo principio, ita quod alia, in se considerata, praeter influentiam primi principii, sunt inordinata. Et secundum hoc Aristoteles non obiicit hic contra sensum Platonis, sed contra Platonicorum verba, ne ab eis aliquis in errorem inducatur. | It should be noted that the arguments of Aristotle go directly against the position of Plato, if the latter's words mean that there was a disorderly motion of the elements prior to the time that the world was made. But Plato's adherents say that this was not what he understood, but that all order in the motion of sensible things comes from the first principle, so that other things, considered in themselves, outside the influence of the first principle, are disordered. And according to this, Aristotle is not here objecting against Plato's sense, but against the words of the Platonists, lest they lead anyone into error. |
| Deinde cum dicit: videtur autem hoc ipsum etc., improbat praedictam positionem ex dictis aliorum philosophorum, qui super hoc melius sensisse videntur. Circa quod considerandum est quod tam Democritus et Leucippus, quam etiam Plato, duo videbantur posuisse circa corpora existentia ante mundum: primo quidem quia ponebant ea moveri; secundo quia ponebant ea segregata. | 585. Then at [437] he uses the saying of other philosophers to disprove the position in question, because they are seen to have had a better understanding of the matter. Concerning this, it should be noted that Democritus and Leucippus, as well as Plato, seem to have maintained two things in regard to bodies existing before the world: that they are in motion, and that they are segregated. |
| Quantum ergo ad primum, dicit quod hoc ipsum quod consideratur circa constitutionem mundi, videtur Anaxagoras bene sumere. Posuit enim quod mundus incoeperit ex corporibus non prius motis. Quod quidem rationabilius est quam dicere mundum fieri ex corporibus prius motis. Nam motus actus quidam est in potentia existentis, et ita medium est inter primam potentiam et primum actum; in his autem quae fiunt, principium sumitur ab his quae sunt omnino in potentia; et ideo rationabilius est principium mundi constituere ex his quae omnino non moventur, quam ex rebus motis. | As to the first, therefore, he says that, with regard to the constitution of the world, Anaxagoras seems to have surmised well. For he posited that the world began from bodies not previously moved. And this is more reasonable than to say that the world was made from bodies previously moved, because motion is a certain act of a thing existing in potency, and, consequently, is intermediate between first potency and first act. But in things that are being brought about, the beginning is taken from what is entirely in potency. Therefore it is more reasonable to fashion the beginning of the world from things wholly not in motion than from things moved. |
| Quantum autem ad secundum, dicit quod etiam alii philosophi ponentes principium mundi, congregantes aliqualiter (idest dicentes quod antequam mundus fieret, erant omnia aliqualiter congregata in unum) tentaverunt assignare modum, quomodo res iterum moverentur et ad invicem segregarentur, in ipsa mundi constitutione; sicut posuit Anaximander, et etiam Empedocles. Non est enim rationabile quod aliquis faciat generationem mundi ex rebus prius distantibus et motis. Sicut enim motus est actus quidam, ita etiam discretio seu distantia rerum est per proprias formas, secundum quod res sunt in actu (secundum enim quod sunt in potentia res, non discernuntur); et quia generatio proprie fit ex eo quod est in potentia, ideo non est rationabile generare mundum ex rebus discretis et motis. | As to the second he says that even those other philosophers who, in positing the beginning of the world, "gathered together to some extent," (i.e., by saying that before the world came to be, all things were to some extent assembled into one) attempted to explain how things would then be set in motion and separated, in the founding of the world, as did Anaxagoras and also Empedocles. For it is not reasonable to produce the generation of the world out of things previously distant and in motion. For just as motion is a certain act, so also the distinction, or distance, between things results from their proper forms, according to which things are in act (for insofar as things are in potency they are not distinguished); and since generation strictly comes to be from what is in potency, it is therefore not reasonable to generate the world out of distinct and moved things. |
| Et inde est quod Empedocles in prima generatione mundi praetermisit amicitiam, ad quam pertinet congregare disgregata. Non enim poterat Empedocles tradere constitutionem caeli, idest mundi, ita quod constitueret ipsum ex rebus prius segregatis, faciendo congregationem prius disgregatorum, per amicitiam: sic enim sequeretur quod mundus esset constitutus ex elementis prius disgregatis, quod est contra praedicta. Unde, quia in constitutione mundi utebatur solum lite, ad quam pertinet disgregare coniuncta, consequens est quod mundus, secundum ipsum, fieret ex aliquo uno et congregato ex multis. | For this reason Empedocles, in explaining the first generation of the world, made no mention of friendship whose function is to assemble the scattered. For Empedocles could not explain the constitution of the "heaven," i.e., of the world, by friendship, in such a way as to constitute it out of things previously separated, by making a gathering together of the previously scattered. For then it would follow that the world was constituted of things previously scattered, which is against the foregoing. Hence, because he used only strife in constituting the world, and strife's role is to scatter the assembled, the consequence is that the world, according to him, came from something one and gathered together out of many things. |
| Ultimo autem epilogando concludit manifestum esse ex praedictis quod est quidam naturalis motus uniuscuiusque corporis, quo non movetur per violentiam, neque praeter naturam. | Finally, in summary, he concludes [438) that it is plain from the foregoing that there is for each body a certain natural motion by which it is moved neither by violence nor beside its nature. |
Lecture 7:
Every body moving naturally in a straight line has either gravity or lightness, Natural and violent motionsChapter 2 cont. Ὅτι δ' ἔχειν ἔνια ἀναγκαῖον ῥοπὴν βάρους καὶ κουφότητος, ἐκ τῶνδε δῆλον. 439 We go on to show that there are certain bodies whose necessary impetus is that of weight and lightness. Κινεῖσθαι μὲν γάρ φαμεν ἀναγκαῖον εἶναι εἰ δὲ μὴ ἕξει φύσει ῥοπὴν τὸ κινούμενον, ἀδύνατον κινεῖσθαι ἢ πρὸς τὸ μέσον ἢ ἀπὸ τοῦ μέσου. 440 Of necessity, we assert, they must move, and a moved thing which has no natural impetus cannot move either towards or away from the centre. Ἔστω γὰρ τὸ μὲν ἐφ' οὗ Α ἀβαρές, τὸ δ' ἐφ' οὗ Β βάρος ἔχον, ἐνηνέχθω δὲ τὸ ἀβαρὲς τὴν ΓΔ, τὸ δὲ Β ἐν τῷ ἴσῳ χρόνῳ τὴν ΓΕ μείζω γὰρ οἰσθήσεται τὸ βάρος ἔχον. Ἐὰν δὴ διαιρεθῇ τὸ σῶμα τὸ ἔχον βάρος ὡς ἡ ΓΕ πρὸς τὴν ΓΔ (δυνατὸν γὰρ οὕτως ἔχειν πρός τι τῶν ἐν αὐτῷ μορίων), εἰ τὸ ὅλον φέρεται τὴν ὅλην τὴν ΓΕ, τὸ μόριον ἀνάγκη ἐν τῷ αὐτῷ χρόνῳ τὴν ΓΔ φέρεσθαι, ὥστε ἴσον οἰσθήσεται τὸ ἀβαρὲς καὶ τὸ βάρος ἔχον ὅπερ ἀδύνα(301b.) τον. Ὁ δ' αὐτὸς λόγος καὶ ἐπὶ κουφότητος. 441 Suppose a body A without weight, and a body B endowed with weight. Suppose the weightless body to move the distance CD, while B in the same time moves the distance CE, which will be greater since the heavy thing must move further. Let the heavy body then be divided in the proportion CE: CD (for there is no reason why a part of B should not stand in this relation to the whole). Now if the whole moves the whole distance CE, the part must in the same time move the distance CD. A weightless body, therefore, and one which has weight will move the same distance, which is impossible. And the same argument would fit the case of lightness. Ἔτι δ' εἰ ἔσται τι σῶμα κινούμενον μήτε κουφότητα μήτε βάρος ἔχον, ἀνάγκη τοῦτο βίᾳ κινεῖσθαι, βίᾳ δὲ κινούμενον ἄπειρον ποιεῖ τὴν κίνησιν. Ἐπεὶ γὰρ δύναμίς τις ἡ κινοῦσα, τὸ δ' ἔλαττον καὶ τὸ κουφότερον ὑπὸ τῆς αὐτῆς δυνάμεως πλεῖον κινηθήσεται, κεκινήσθω τὸ μὲν ἐφ' ᾧ τὸ Α, τὸ ἀβαρές, τὴν ΓΕ, τὸ δ' ἐφ' ᾧ τὸ Β, τὸ βάρος ἔχον, ἐν τῷ ἴσῳ χρόνῳ τὴν ΓΔ. Διαιρεθέντος δὴ τοῦ βάρος ἔχοντος σώματος ὡς ἡ ΓΕ πρὸς τὴν ΓΔ, συμβήσεται τὸ ἀφαιρούμενον ἀπὸ τοῦ βάρος ἔχοντος σώματος τὴν ΓΕ φέρεσθαι ἐν τῷ ἴσῳ χρόνῳ, ἐπείπερ τὸ ὅλον ἐφέρετο τὴν ΓΔ. Τὸ γὰρ τάχος ἕξει τὸ τοῦ ἐλάττονος πρὸς τὸ τοῦ μείζονος ὡς τὸ μεῖζον σῶμα πρὸς τὸ ἔλαττον. Ἴσον ἄρα τὸ ἀβαρὲς οἰσθήσεται σῶμα καὶ τὸ βάρος ἔχον ἐν τῷ αὐτῷ χρόνῳ. Τοῦτο δ' ἀδύνατον. 442 Again, a body which is in motion but has neither weight nor lightness, must be moved by constraint, and must continue its constrained movement infinitely. For there will be a force which moves it, and the smaller and lighter a body is the further will a given force move it. Now let A, the weightless body, be moved the distance CE, and B, which has weight, be moved in the same time the distance CD. Dividing the heavy body in the proportion CE:CD, we subtract from the heavy body a part which will in the same time move the distance CE, since the whole moved CD: for the relative speeds of the two bodies will be in inverse ratio to their respective sizes. Thus the weightless body will move the same distance as the heavy in the same time. But this is impossible. Hence, since the motion of the weightless body will cover a greater distance than any that is suggested, it will continue infinitely. Ὥστ' ἐπεὶ παντὸς τοῦ προτεθέντος μεῖζον κινηθήσεται διάστημα τὸ ἀβαρές, ἄπειρον ἂν φέροιτο. Φανερὸν οὖν ὅτι ἀνάγκη σῶμα πᾶν βάρος ἔχειν ἢ κουφότητα διωρισμένον. 443 It is therefore obvious that every body must have a definite weight or lightness. Ἐπεὶ δὲ φύσις μέν ἐστιν ἡ ἐν αὐτῷ ὑπάρχουσα κινήσεως ἀρχή, δύναμις δ' ἡ ἐν ἄλλῳ ἢ ᾗ ἄλλο, κίνησις δὲ ἡ μὲν κατὰ φύσιν ἡ δὲ βίᾳ πᾶσα, 444 But since 'nature' means a source of movement within the thing itself, while a force is a source of movement in something other than it or in itself qua other, and since movement is always due either to nature or to constraint, τὴν μὲν κατὰ φύσιν, οἷον τῷ λίθῳ τὴν κάτω, θάττω ποιήσει τὸ κατὰ δύναμιν, τὴν δὲ παρὰ φύσιν ὅλως αὐτή. 445 movement which is natural, as downward movement is to a stone, will be merely accelerated by an external force, while an unnatural movement will be due to the force alone. Πρὸς ἀμφότερα δὲ ὥσπερ ὀργάνῳ χρῆται τῷ ἀέρι (πέφυκε γὰρ οὗτος καὶ κοῦφος εἶναι καὶ βαρύς) τὴν μὲν οὖν ἄνω ποιήσει φορὰν ᾗ κοῦφος, ὅταν ὠσθῇ καὶ λάβῃ τὴν ἀρχὴν ἀπὸ τῆς δυνάμεως, τὴν δὲ κάτω πάλιν ᾗ βαρύς ὥσπερ γὰρ ἐναφάψασα παραδίδωσιν ἑκατέρῳ. Διὸ καὶ οὐ παρακολουθοῦντος τοῦ κινήσαντος φέρεται τὸ βίᾳ κινηθέν. Εἰ γὰρ μὴ τοιοῦτόν τι σῶμα ὑπῆρχεν, οὐκ ἂν ἦν βίᾳ κίνησις. 446 In either case the air is as it were instrumental to the force. For air is both light and heavy, and thus qua light produces upward motion, being propelled and set in motion by the force, and qua heavy produces a downward motion. In either case the force transmits the movement to the body by first, as it were, impregnating the air. That is why a body moved by constraint continues to move when that which gave the impulse ceases to accompany it. Otherwise, i.e. if the air were not endowed with this function, constrained movement would be impossible. Καὶ τὴν κατὰ φύσιν δ' ἑκάστου κίνησιν συνεπουρίζει τὸν αὐτὸν τρόπον. 447 And the natural movement of a body may be helped on in the same way. Ὅτι μὲν οὖν ἅπαν ἢ κοῦφον ἢ βαρύ, καὶ πῶς αἱ παρὰ φύσιν κινήσεις ἔχουσι ἐν τούτοις, φανερόν. 448 This discussion suffices to show (1) that all bodies are either light or heavy, and (2) how unnatural movement takes place.
| Postquam philosophus ostendit quod corpora naturalia habent motus naturales, et improbavit positiones philosophorum qui circa hoc erraverunt, hic ostendit quod corpora quae moventur naturaliter motu recto, habent gravitatem et levitatem: principia enim motus naturalis in dictis corporibus attenduntur secundum gravitatem et levitatem. | 586. After showing that natural bodies have natural motions, and disproving the positions of philosophers who erred on this matter, the Philosopher here shows that bodies naturally moved with a straight motion have heaviness and lightness; for the principles of natural motion in such bodies are reckoned with respect to heaviness and lightness. |
| Primo ergo proponit quod intendit; dicens manifestum esse ex his quae sequuntur, quod quaedam corpora, quae scilicet moventur naturaliter motu recto, necesse est habere gravitatem et levitatem, quibus inclinantur ad propria loca. Dicit autem quaedam, ad differentiam eorum quae circulariter moventur. | Therefore, first, he proposes what he intends [439] and says that it will be plain from what follows that certain bodies, namely, those naturally moved with a straight motion must have heaviness and lightness by which they are inclined to their appropriate places. He says "certain" bodies, in order to distinguish them from those that are circularly moved. |
| Secundo ibi: moveri quidem enim etc., inducit probationem ad propositum, dicens: hic dicimus communiter quod necesse est corpora naturalia moveri: ex hoc enim dicuntur naturalia, quod habent in seipsis principium motus, ut ex II Physic. apparet. Sed si illud quod movetur non habet naturalem inclinationem, qua tendit in aliquem locum determinatum, impossibile est quod moveatur vel ad medium, quod fit per inclinationem gravitatis, vel a medio, quod fit per inclinationem levitatis. Ergo necesse est corpora quae moventur motu recto, habere gravitatem et levitatem. | 587. Secondly, at [440] he presents a proof of his proposition, saying: Here we say in a general way that it is necessary for natural bodies to be moved, for they are called "natural" from having within themselves the principle of motion, as is plain from Physics II. But if what is moved does not have a natural inclination by which it tends to some determinate place, it cannot be moved either to the center, which comes about through the inclination of heaviness, or from the center, which is due to the inclination of lightness. Therefore it is necessary that bodies which are moved in a straight motion have heaviness and lightness. |
| Tertio ibi: sit enim quod quidem in quo etc., probat quod supposuerat; scilicet quod, si praedicta corpora non habeant gravitatem et levitatem, quod non moverentur. | 588. Thirdly at [441] he proves what he had presupposed, namely, that if the bodies in question did not have heaviness and lightness, they would not be moved. |
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Et primo ostendit quod non moverentur naturaliter; secundo ostendit quod non moverentur per violentiam, ibi: adhuc autem si erit aliquod corpus et cetera. |
First he shows that they would not be moved naturally; Secondly, that they would not be moved by violence, at 589. |
| Dicit ergo primo quod, si aliquod inferiorum corporum non habet gravitatem vel levitatem, sint duo corpora, quorum unum sit a, non habens gravitatem, aliud autem sit b, habens gravitatem. Moveatur autem a, quod est corpus non grave, aliquo determinatio tempore, puta per spatium unius horae, per magnitudinem quae est gd, motu scilicet qui est ad medium. Corpus autem quod est b, gravitatem habens, feretur in eodem tempore, eadem specie motus, per maiorem magnitudinem, quae sit ge: necesse est enim quod corpus habens gravitatem, feratur aequali tempore per maius spatium quam corpus non habens gravitatem; sicut et corpus gravius velocius fertur deorsum quam corpus minus grave. Dividatur autem corpus b, habens gravitatem, secundum proportionem quae est ge ad gd, ut scilicet se habeat totum b ad partem eius, puta quae sit c, sicut se habet totum ge ad gd: nihil enim prohibet talem divisionem fieri corporis b, cum omne corpus finitum possit dividi secundum quamcumque proportionem datam. Procedatur ergo sic. Sicut se habet ge ad gd, ita se habet b ad partem eius; ergo permutatim, sicut se habet totum b ad totum ge, ita se habet pars divisa ad gd. Si ergo totum b fertur tempore determinato per totum ge, necesse est quod pars ipsius b in eodem tempore feratur per magnitudinem gd. In eodem autem tempore corpus a, non habens gravitatem, ferebatur super eandem magnitudinem. Ergo sequetur quod corpus habens gravitatem, et corpus non habens gravitatem, in aequali tempore ferantur super eandem magnitudinem. Et eadem ratio est, si alterum corpus ponatur habere levitatem. Sic ergo manifestum est quod sequitur inconveniens, si aliquod inferiorum corporum ponatur non habere gravitatem neque levitatem. | He says therefore first [441] that if any of the lower bodies does not possess heaviness or lightness, let there be two bodies, and let A be the body lacking heaviness and B the body having heaviness. Now let A, which is the non-heavy body, be moved for a certain period of time, say for the space of one hour, over a magnitude GD, with a motion directed to the center. Then B, which has heaviness, will, during the same time be moved with the same type of motion over a larger magnitude GE; for a body having heaviness must in an equal time traverse a greater distance than a body not having heaviness, just as a heavier body is carried downward more swiftly than a less heavy. Now let B which has heaviness be divided in the ratio of GE to GD so that the whole of B is related to a part, say C, as the whole GE is to GD; for there is nothing to prevent such a division of body B, since every finite body can be divided according to any given ratio. Therefore, let us go on thus. As GE is to GD, so B is to its part C; therefore, by commutative proportion, B is to GE as C (which is part of B) is to GD. If, therefore, the whole B traverses in a given time the entire magnitude GE, then the part of B must traverse the magnitude GD in the same time. But body A (the one having no heaviness) traversed the same magnitude in the same amount of time. Therefore, it will follow that a body having heaviness, and one not having heaviness, will traverse the same magnitude in equal time. And the same argument is valid if the other body is assumed to have lightness. Consequently, it is plain that something irreconcilable follows, if any of the lower bodies is assumed to have neither heaviness nor lightness. |
| Deinde cum dicit: adhuc autem si erit aliquod corpus etc., ostendit quod, si sit aliquod inferiorum corporum non habens gravitatem vel levitatem, quod non possit per violentiam moveri. Et dicit: ex quo ostensum est per rationem praedictam quod corpus carens gravitate vel levitate non potest moveri naturaliter motu recto, necesse est, si movetur, quod moveatur per violentiam: nam omnis motus huiusmodi corporum aut est naturalis aut violentus. Sed nec per violentiam moveri poterit: quia si moveatur per violentiam, necesse est quod sit motus infinitus, idest infinitae velocitatis; quod est impossibile. Et quod hoc sequatur, probat, praemisso hoc principio, quod si aliqua virtus, idest violentia, sit movens aliquod corpus, minus et levius ab eadem virtute, idest ab eadem violentia, plus, idest velocius, movebitur in motu, scilicet sursum: nam corpus maius et gravius magis violentiae resistet. | 589. Then at [442] he shows that if any of the lower bodies lacks heaviness or lightness, it cannot be moved by violence. And he says: From the fact that it was shown by the foregoing argument that a body lacking heaviness or lightness cannot be moved naturally with a straight motion, then, if it is moved at all, it must be through violence, for every motion of such bodies is either natural or compulsory. But it cannot be moved by violence either, because, if it were moved by violence, its motion would have to be "infinite," i.e., of infinite speed, which is impossible. And that this would follow he proves by using the principle that if any "power," i.e., violence, moves a body, a lesser and lighter will be moved by the same "power," i.e., by the same violence, "more," i.e., more swiftly, in motion, namely, upward — for a larger and heavier body offers more resistance to violence. |
| Sit igitur a corpus non habens gravitatem, quod violenter moveatur sursum per magnitudinem quae est ge; aliud autem corpus sit b, gravitatem habens, quod ab eadem virtute in aequali tempore moveatur per magnitudinem quae est gd, minorem utique quam ge. Sicut gravius minus movetur ab eadem virtute, ita grave minus quam non grave. Dividatur ergo corpus b, habens gravitatem, secundum proportionem quae est magnitudinis ge ad gd. Sequetur ergo, sicut et prius, quod id quod aufertur per divisionem a corpore b gravitatem habente, feratur per magnitudinem ge in aequali tempore, in quo ferebatur per ipsam corpus a non habens gravitatem: quia totum corpus b in eodem tempore ferebatur per magnitudinem gd, quae est minor. Oportet enim esse proportionem velocitatis minoris magnitudinis ad maiorem, sicut se habet maius corpus ad minus; ita scilicet quod in eodem tempore maius corpus moveatur per minorem magnitudinem, et minus per maiorem; quia minus corpus ab eadem virtute velocius movetur. Sequetur igitur quod per aequale spatium feratur corpus non grave, et corpus habens gravitatem, in eodem tempore; quod est impossibile. Quodcumque autem corpus grave proponatur, quantumcumque velociter moveatur, adhuc corpus non grave movebitur in eodem tempore per maius spatium. Sic igitur sequetur quod corpus non grave moveatur infinita velocitate per violentiam; quod est impossibile. Et eadem ratio est de corpore non levi. | Therefore let A be a body not having heaviness and let it be moved upward violently through the magnitude GE; but let B be a body having heaviness which by the same force in an equal time is moved through the magnitude GD, which is of course less than GE. Just as the heavier is moved less by the same force, so the heavy is moved less than the non-heavy. Let then the body B, having heaviness, be divided in the ratio which is that of the ratio of magnitude GE to GD. It will follow, therefore, just as it did before, that what is taken away through division from body B which has heaviness, will be moved through magnitude GE in a time equal to that in which body A, which lacks heaviness, was moved through it, because the whole body B in the same time was moved through magnitude GE which is less. For the ratio of the speed of the lesser magnitude to the greater must be as the ratio of the greater body to the lesser, so that, in the same time, the greater body is moved a smaller distance, and the lesser body a greater distance, because a lesser body is moved more swiftly by an equal power. It will follow, therefore, that in the same period of time a non-heavy body and one having heaviness are moved an equal distance — which is impossible. But no matter what heavy body is taken and no matter how swiftly it is moved, a non-heavy body will be moved a greater distance in the same time. Accordingly, it will follow that a body lacking heaviness would be moved with an infinite speed through violence — which is impossible. And the same argument holds for a non-light body. |
| Sic ergo epilogando concludit manifestum esse quod omne corpus quod determinatum est, scilicet quod movetur motu recto, habet gravitatem vel levitatem. Dicitur autem corpus quod movetur motu recto determinatum, vel quia hic determinate de ipso loquitur; vel quia huiusmodi corpora moventur motu recto prout sunt segregata et divisa, non autem secundum se tota. | Therefore, in summary, he concludes [443] that plainly every body which is "determinate," i.e., which is moved with a straight motion has heaviness or lightness. He calls the body which is moved with a straight motion "determinate," either because he is here speaking determinately of it, or because such bodies are moved with a straight motion insofar as they are segregated and divided and not insofar as they are taken all together. |
| Deinde cum dicit: quoniam autem natura etc., quia fecerat mentionem de motu naturali et violento, hic ostendit qualiter uterque motus perficiatur. Et circa hoc duo facit: | 590. Then at [444], because he had mentioned both natural and violent motion, he now shows how both types are produced. Regarding this he does two things: |
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primo ostendit differentiam motus naturalis et violenti; secundo ostendit quomodo uterque motus invenitur in aere, ibi: ad ambo autem et cetera. |
First he shows the difference between natural and violent motion; Secondly, how both are found in air, at 591. |
| Circa primum duo facit: | About the first he does two things: |
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primo ostendit differentiam motus naturalis et violenti; secundo ostendit quomodo violenta admiscentur etiam motui naturali, ibi: eum quidem et cetera. |
First he shows the difference between natural and violent motion; Secondly, how violence enters in even to natural motion, at 590. |
| Differunt autem motus naturalis et violentus secundum sua principia; et ideo primo definit principia utriusque motus. Et dicit quod natura est principium motus existens in eo quod movetur, ut manifestum est in II Physic.: virtus autem, idest potentia movens per violentiam, est principium motus existens in alio, secundum quod est aliud. Quod quidem dicit quia potest per accidens principium motus violenti esse in eodem, non tamen secundum quod est idem, sed secundum quod est aliud; sicut etiam medicus sanat seipsum non sicut medicum, sed sicut infirmum. Et ex hoc patet quod quidam motus est secundum naturam, quidam autem motus est violentus. Est enim motus secundum naturam, cuius principium est in ipso quod movetur: non solum autem principium activum, sed etiam passivum, quod quidem est potentia per quam aliquid est naturaliter susceptivum motionis alterius. Et ideo, cum corpora inferiora moventur a corporibus superioribus, non est motus violentus, sed naturalis: quia in corporibus inferioribus est naturalis aptitudo ut sequantur motiones superiorum corporum. Motus autem violentus est quando nullum principium motus est ab intrinseco, sed solum ab extrinseco; sicut cum homo proiicit corpus grave sursum, in quo nulla est naturalis aptitudo ad talem motum. | Now, natural and violent motions differ with respect to their principles, and therefore he first defines the principles of each of these motions [444]. And he says that nature is a principle of a motion existing in that which is moved, as is plain in Physics IIe "force", however, i.e., a power that causes motion violently, is a principle existing in another, as it is other. He says this because it could accidentally happen that a principle of violent motion exist in one and the same thing, but not insofar as it is one and the same, but insofar as it is other, as when a doctor heals himself not as doctor but as sick. And from this it is plain that there is a motion that is natural and a motion that is violent. For a motion is according to nature whose principle is in what is moved, not only as active principle, but also as passive, which, indeed, is the potency by which something is naturally capable of undergoing motion from another. Consequently, when lower bodies are moved by the higher bodies, the motion is not violent but natural, because in the lower bodies there is a natural aptitude to follow the motions of the higher bodies. But a motion is violent when no principle of the motion is from within but only from without, as when a man throws a heavy body upward, in which body there is no natural aptitude for such motion. |
| Ostendit autem consequenter quomodo violentia admisceatur motui naturali. Eum enim motum qui est alicui corpori naturalis, sicut lapidi est motus naturalis deorsum, potentia violenter movens facit quandoque velociorem: et sic talis motus quodammodo est commixtus, dum speciem habet a natura, additionem autem velocitatis a motore violento. | Then at [445] he shows as a consequence how violence enters into natural motion. For in the case of a motion which is natural to some body, as for a stone to be moved downward naturally, a force that acts violently sometimes quickens that motion. Consequently, such a motion is in a certain sense mixed, since the kind of motion it is is due to nature, but the addition in speed is due to the violent mover. |
| Sed motum violentum totaliter perficit ipsa violentia, quia dat ei et speciem motus et mensuram velocitatis: quocumque enim modo esset ibi aliquid a natura, non esset praeter naturam. | But in the case of a violent motion, it is violence that entirely produces it and makes it the type of motion it is, and accounts for the amount of its speed — for to the extent that something from nature should happen to be present in it, to that extent it would not be beside nature. |
| Deinde cum dicit: ad ambo autem etc., ostendit quomodo aer deservit utrique motui. | 591. Then at [446] he explains the role that air plays in both these motions. |
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Et primo quomodo deservit motui violento; secundo quomodo deservit motui naturali, ibi: et eum autem qui secundum naturam et cetera. |
First, the part it plays in violent motion; Secondly, how it serves natural motion, at 592. |
| Dicit ergo primo quod virtus motoris violenti utitur aere tanquam quodam instrumento ad ambo, idest ad motum sursum et ad motum deorsum. Aer autem natus est esse levis et gravis: sicut enim supra dictum est, et infra in quarto plenius dicetur, ignis est simpliciter levis, terra autem simpliciter gravis, aer autem et aqua medio modo se habent inter utrumque: nam aer ad ignem quidem est gravis, ad aquam autem et terram est levis; aqua autem ad terram quidem est levis, ad ignem autem et aerem est gravis. Sic igitur aer, secundum quod est levis, perficiet motum violentum qui est sursum (ita tamen prout movetur, et fuerit principium talis motionis potentia violenti motoris): motum autem qui est deorsum perficit secundum quod est gravis. Virtus enim violenti motoris, per modum cuiusdam impressionis, tradit motum utrique, idest vel aeri sursum moto et deorsum moto, vel etiam aeri et corpori gravi, puta lapidi. | He says therefore first [446] that the force of a violent mover uses the air as an instrument "for both," i.e., for upward and downward motion. For air is apt by nature to be light and heavy: for, as was said above, and as will be explained at greater length in Book IV, fire is absolutely light and earth absolutely heavy, but air and water are intermediate between these two, since air is heavy compared to fire, but light compared to water and earth; but water is light compared to earth, while compared to fire and air it is heavy. Accordingly, air, insofar as it is light, will perfect a violent motion that is upward (but only insofar as it is moved and insofar as the principle of such a motion is the power of the violent mover); and insofar as it is heavy, it will perfect a motion that is downward.. For the force of the violent mover, by a kind of impression, imparts a motion "to both," i.e., either to the air moved upwards and moved downwards, or to the air and to the heavy body, such as a stone. |
| Non est autem intelligendum quod virtus violenti motoris imprimat lapidi qui per violentiam movetur, aliquam virtutem per quam moveatur, sicut virtus generantis imprimit genito formam, quam consequitur motus naturalis: nam sic motus violentus esset a principio intrinseco, quod est contra rationem motus violenti. Sequeretur etiam quod lapis, ex hoc ipso quod movetur localiter per violentiam, alteraretur: quod est contra sensum. Imprimit ergo motor violentus lapidi solum motum: quod quidem fit dum tangit ipsum. Sed quia aer est susceptibilior talis impressionis, tum quia est subtilior, tum quia est quodammodo levis, velocius movetur per impressionem violenti motoris, quam lapis: et sic, desistente violento motore, aer ab eo motus ulterius propellit lapidem, et etiam aerem coniunctum; qui etiam movet lapidem ulterius, et hoc fit quousque durat impressio primi motoris violenti, ut dicitur in VIII Physic. Et inde est quod, quamvis motor violentus non sequatur ipsum mobile quod per violentiam fertur, puta lapidem, ut praesentialiter ipsum moveat, tamen movet per impressionem aeris: si enim non esset tale corpus quale est aer, non esset motus violentus. | This does not mean that the force of the violent mover impresses upon the stone which is moved by violence some force by which it might be moved, in the way that the power of the generator impresses on the thing generated a form upon which natural motion follows — for then the violent motion would proceed from an intrinsic principle, and that is contrary to the notion of a violent motion. It would also follow that a stone, by the very fact that it is in local motion through violence, would be altered — and this is contrary to what we sense. Therefore, the violent mover impresses motion alone upon the stone, and this it does while it touches it. But because air is more susceptible to such an impression (both because it is more subtle and because it is in a sense light), it is moved more swiftly through the impression of the violent mover than the stone. Consequently, when the violent mover desists, the air moved by it continues to propel the stone and also the adjoining air, which likewise moves the stone farther, and this continues so long as the impression of the first violent mover endures, as is said in Physics VIII. Hence it is that the violent mover, even though it does not follow the mobile that is being carried along through violence, e.g., a stone, so as to move it by being present to it, yet it moves it through the impression of the air —if there were no body such as is the air, there would not be violent motion. |
| Ex quo patet quod aer est instrumentum motus violenti necessarium, et non solum propter bene esse. | From this it is plain that air is a necessary instrument of violent motion and not simply an improving one. |
| Deinde cum dicit: et eum autem qui secundum naturam etc., ostendit quomodo aer deserviat motui naturali. Et dicit quod aer eodem modo promovet motum naturalem uniuscuiusque corporum, sicut et motum violentum: inquantum scilicet per suam levitatem coadiuvat ad motum qui est sursum, per suam autem gravitatem ad motum qui est deorsum. | 592. Then at [447] he shows what role air plays in natural motion. And he says that air promotes the natural motion of each body in the same way as its violent motion, namely, insofar as by its lightness it helps an upward motion, and by its heaviness a downward motion. |
| Potest autem esse dubium utrum aer deserviat motui naturali corporum gravium et levium ex necessitate, vel solum propter bene esse. | 593. But the question can be raised whether the air serves the natural motion of heavy bodies and light bodies so as to be necessary or merely helpful. |
| Determinat autem Averroes quod etiam motui naturali deserviat ex necessitate: et hoc duplici ratione. Primo quidem quia, sicut ipse dicit in commento suo in hoc loco, motor gravium et levium est generans, qui, dum dat formam, ex consequenti dat motum naturalem, sicut et omnia accidentia naturalia quae consequuntur formam: et sic generans causat motum naturalem mediante forma. Motus autem naturalis debet immediate sequi a suo motore. Unde, cum motus naturalis non immediate sequatur a generante, sed a forma, videtur quod forma sit proprius motor in motu naturali. Unde videtur quod corpora gravia et levia quodammodo moveant seipsa. Non autem per se: quia movens seipsum dividitur in movens et motum, ut probatur in VIII Physic.; quod non invenitur in corporibus gravibus et levibus, quae non dividuntur nisi in formam et materiam, cuius non est moveri, ut probatur in V Physic. Unde relinquitur quod corpus grave vel leve moveat seipsum per accidens, sicut nauta qui movet navem, ad cuius motum ipse movetur: et similiter corpus grave et leve per suam formam movet aerem, ad cuius motum ipsum corpus grave et leve movetur. Et sic concludit quod aer sit de necessitate motus naturalis. Secundo quia, ut ipse dicit in commento IV Physic., oportet esse aliquam resistentiam inter movens et mobile. Nulla autem est resistentia materiae corporis gravis vel levis ad eius formam, quae est principium motus. Et ideo necesse est quod sit aliqua resistentia ex parte medii, quod est aer vel aqua: et sic aer est de necessitate motus naturalis. | Averroes says that it also serves natural motion of necessity, and for two reasons. First, because, as he says in his commentary on this passage, the mover of heavy and of light things is their generator which, in giving the form, gives as a consequence the natural motion, just as it gives all the natural accidents which follow the form. Consequently, the generator causes natural motion through the form. Now a natural motion should follow from its mover immediately. Hence, since the natural motion does not follow immediately from the generator but from the form, it seems that the form is the proper mover in natural motion. Accordingly, it seems that heavy and light bodies in a sense move themselves. But not by themselves, because a thing that moves itself is distinguished into mover and moved, as was proved in Physics VIII — a distinction not found in heavy and light bodies, which are divided only into form and matter, the latter of which is not apt to be moved, as is proved in Physics, V. Hence it remains that a heavy or light body moves itself ear accidens, in the way that a sailor moves a ship through whose movement he himself is moved. Similarly, the light and the heavy body through their form move the air, upon whose motion the heavy and the light body are moved. And thus he concludes that air is necessary for natural motion. Secondly, because, as he says in his commentary on Physics IV, there must be some resistance between mover and mobile. But the matter of a heavy or a light body does not resist its form, which is the principle of motion. Therefore it is necessary that there be some resistance from the medium, which is air or water. Thus air is necessary for natural motion. |
| Utrumque autem ex eadem radice erroris procedit. Existimavit enim quod forma corporis gravis et levis sit principium activum motus per modum moventis, ut sic oporteat esse aliquam resistentiam ad inclinationem formae; et quod motus non procedat immediate a generante qui dat formam. Sed hoc est omnino falsum. Nam forma gravis et levis non est principium motus sicut agens motum, sed sicut quo movens movet; sicut color est principium visionis, quo aliquid videtur. Unde et Aristoteles dicit in VIII Physic., post ea quae dixerat de motu gravium et levium: quod quidem igitur nihil horum movet seipsum manifestum est: sed motus habent principium, non movendi neque faciendi, sed patiendi. | 594. But both of these arguments proceed from the source of error. For he believed the form of a heavy and of a light body to be an active principle of motion after the manner of a mover, in such a way that resistance would be required to the form's inclination, and also that motion does not proceed immediately from the generator which gives the form. But this is completely false. For the form of a heavy and of a light body is not a principle of motion as though it were an agent itself moved, but as that by which the mover causes motion, just as color is a principle of seeing, by which something is seen. That is why Aristotle in Physics III, after discussing the motion of the heavy and light, says: "It is plain that neither of these moves itself but that they have a principle of motion, not indeed of moving something or making something, but of being acted upon." |
| Sic igitur motus gravium et levium non procedit a generante mediante alio principio movente; neque etiam oportet aliam resistentiam quaerere in hoc motu, quam illam quae est inter generans et genitum. Et sic relinquitur quod aer non requiratur ad motum naturalem ex necessitate, sicut in motu violento. Quia id quod naturaliter movetur, habet sibi inditam virtutem, quae est principium motus: unde non oportet quod ab alio impellente moveatur, sicut id quod per violentiam movetur, quia nullam virtutem inditam habet, ad quam sequatur talis motus. | Consequently, the motion of the heavy and the light does not come from the generator through the medium of some moving principle; nor is it necessary to look for any other resistance in this motion than that which prevails between the generator and the thing generated. Consequently it remains that air is not required for natural motion of necessity as it is in violent motion. For what is moved naturally has been endowed with a power which is a principle of motion. Hence it does not need to be moved by something else impelling it, as in the case of a thing violently moved, since the latter has no inherent power, upon which such a motion follows. |
| Et hanc etiam differentiam designant verba Aristotelis: nam de motu violento loquens, dicit quod nisi esset aliquod tale corpus, non esset qui vi motus; de motu autem naturali dicit quod aer promovet eum qui secundum naturam uniuscuiusque motum. | The very words of Aristotle point up this difference: For when speaking of violent motion he says, "Unless there were such a body, there would not be motion by constraint"; but in speaking of natural motion he says, "Air helps that motion of each thing which is according to nature. |
| Ultimo autem epilogando concludit manifestum esse ex praedictis quod omne corpus aut est leve aut grave, et qualiter se habeant motus qui sunt praeter naturam. | Finally, in summary, he concludes [448] that it is plain from the aforesaid that all bodies are either light or heavy, and how unnatural movement takes place. |
Lecture 8:
Everything not generated. Elements and their existenceChapter 2 cont. Ὅτι δ' οὔτε πάντων ἐστὶ γένεσις οὔθ' ἁπλῶς οὐθενός, δῆλον ἐκ τῶν προειρημένων 449 From what has been said earlier it is plain that there cannot be generation either of everything or in an absolute sense of anything. ἀδύνατον γὰρ παντὸς σώματος εἶναι γένεσιν, (302a.) εἰ μὴ καὶ κενὸν εἶναί τι δυνατὸν κεχωρισμένον ἐν ᾧ γὰρ ἔσται τόπῳ τὸ νῦν γιγνόμενον εἰ ἐγίγνετο, ἐν τούτῳ πρότερον τὸ κενὸν ἀναγκαῖον εἶναι σώματος μηθενὸς ὄντος. 450 It is impossible that everything should be generated, unless an extra-corporeal void is possible. For, assuming generation, the place which is to be occupied by that which is coming to be, must have been previously occupied by void in which no body was. Ἄλλο μὲν γὰρ ἐξ ἄλλου σῶμα γίγνεσθαι δυνατόν, οἷον ἐξ ἀέρος πῦρ, ὅλως δ' ἐκ μηδενὸς ἄλλου προϋπάρχοντος μεγέθους ἀδύνατον μάλιστα γὰρ ἂν ἐκ δυνάμει τινὸς ὄντος σώματος ἐνεργείᾳ γένοιτ' ἂν σῶμα. Ἀλλ' εἰ τὸ δυνάμει ὂν σῶμα μηθέν ἐστιν ἄλλο σῶμα ἐνεργείᾳ πρότερον, κενὸν ἔσται κεχωρισμένον. 451 Now it is quite possible for one body to be generated out of another, air for instance out of fire, but in the absence of any pre-existing mass generation is impossible. That which is potentially a certain kind of body may, it is true, become such in actuality, But if the potential body was not already in actuality some other kind of body, the existence of an extra-corporeal void must be admitted. Chapter 3 Λοιπὸν δ' εἰπεῖν τίνων τέ ἐστι γένεσις [σωμάτων], καὶ διὰ τί ἐστιν. Ἐπεὶ οὖν ἐν ἅπασιν ἡ γνῶσις διὰ τῶν πρώτων, πρῶτα δὲ τῶν ἐνυπαρχόντων τὰ στοιχεῖα, σκεπτέον ποῖα τῶν τοιούτων σωμάτων ἐστὶ στοιχεῖα, καὶ διὰ τί ἐστιν, ἔπειτα μετὰ ταῦτα πόσα καὶ ποῖ' ἄττα. Τοῦτο δ' ἔσται φανερὸν ὑποθεμένοις τίς ἐστιν ἡ τοῦ στοιχείου φύσις. 452 It remains to say what bodies are subject to generation, and why. Since in every case knowledge depends on what is primary, and the elements are the primary constituents of bodies, we must ask which of such bodies are elements, and why; and after that what is their number and character. The answer will be plain if we first explain what kind of substance an element is. Ἔστω δὴ στοιχεῖον τῶν σωμάτων, εἰς ὃ τἆλλα σώματα διαιρεῖται, ἐνυπάρχον δυνάμει ἢ ἐνεργείᾳ (τοῦτο γὰρ ποτέρως, ἔτι ἀμφισβητήσιμον), αὐτὸ δ' ἐστὶν ἀδιαίρετον εἰς ἕτερα τῷ εἴδει 453 An element, we take it, is a body into which other bodies may be analysed, present in them potentially or in actuality (which of these, is still disputable), and not itself divisible into bodies different in form. τοιοῦτον γάρ τι τὸ στοιχεῖον ἅπαντες καὶ ἐν ἅπασι βούλονται λέγειν. 454 That, or something like it, is what all men in every case mean by element. Εἰ δὴ τὸ εἰρημένον ἐστὶ στοιχεῖον, ἀνάγκη εἶναι ἄττα τοιαῦτα τῶν σωμάτων. Ἐν μὲν γὰρ σαρκὶ καὶ ξύλῳ καὶ ἑκάστῳ τῶν τοιούτων ἔνεστι δυνάμει πῦρ καὶ γῆ φανερὰ γὰρ ταῦτα ἐξ ἐκείνων ἐκκρινόμενα. Ἐν δὲ πυρὶ σὰρξ ἢ ξύλον οὐκ ἐνυπάρχουσιν, οὔτε κατὰ δύναμιν οὔτε κατ' ἐνέργειαν ἐξεκρίνετο γὰρ ἄν. Ὁμοίως δ' οὐδ' εἰ ἕν τι μόνον εἴη τοιοῦτον, οὐδ' ἐν ἐκείνῳ οὐ γὰρ εἰ ἔσται σὰρξ ἢ ὀστοῦν ἢ τῶν ἄλλων ὁτιοῦν, οὔπω φατέον ἐνυπάρχειν δυνάμει, ἀλλὰ προσθεωρητέον τίς ὁ τρόπος τῆς γενέσεως. 455 Now if what we have described is an element, clearly there must be such bodies. For flesh and wood and all other similar bodies contain potentially fire and earth, since one sees these elements exuded from them; and, on the other hand, neither in potentiality nor in actuality does fire contain flesh or wood, or it would exude them. Similarly, even if there were only one elementary body, it would not contain them. For though it will be either flesh or bone or something else, that does not at once show that it contained these in potentiality: the further question remains, in what manner it becomes them. Ἀναξαγόρας δ' ἐναντίως Ἐμπεδοκλεῖ λέγει περὶ τῶν στοιχείων. Ὁ μὲν γὰρ πῦρ καὶ γῆν καὶ τὰ σύστοιχα τούτοις στοιχεῖά φησιν εἶναι τῶν σωμάτων καὶ συγκεῖσθαι πάντ' ἐκ τούτων, Ἀναξαγόρας δὲ τοὐναντίον τὰ γὰρ ὁμοιομερῆ στοιχεῖα (λέγω δ' οἷον σάρκα καὶ ὀστοῦν καὶ τῶν τοι(302b.) ούτων ἕκαστον), ἀέρα δὲ καὶ πῦρ μίγματα τούτων καὶ τῶν ἄλλων σπερμάτων πάντων εἶναι γὰρ ἑκάτερον αὐτῶν ἐξ ἀοράτων τῶν ὁμοιομερῶν πάντων ἠθροισμένον. Διὸ καὶ γίγνεσθαι πάντ' ἐκ τούτων τὸ γὰρ πῦρ καὶ τὸν αἰθέρα προσαγορεύει ταὐτό. 456 Now Anaxagoras opposes Empedocles' view of the elements. Empedocles says that fire and earth and the related bodies are elementary bodies of which all things are composed; but this Anaxagoras denies. His elements are the homoeomerous things, viz. flesh, bone, and the like. Earth and fire are mixtures, composed of them and all the other seeds, each consisting of a collection of all the homoeomerous bodies, separately invisible; and that explains why from these two bodies all others are generated. (To him fire and aither are the same thing.) Ἐπεὶ δ' ἐστὶ παντὸς φυσικοῦ σώματος κίνησις οἰκεία, τῶν δὲ κινήσεων αἱ μὲν ἁπλαῖ αἱ δὲ μικταί, καὶ αἱ μὲν μικταὶ τῶν μικτῶν, αἱ δὲ ἁπλαῖ τῶν ἁπλῶν εἰσι, φανερὸν ὅτι ἔσται ἄττα σώματα ἁπλᾶ. Εἰσὶ γὰρ καὶ κινήσεις ἁπλαῖ. 457 But since every natural body has it proper movement, and movements are either simple or mixed, mixed in mixed bodies and simple in simple, there must obviously be simple bodies; for there are simple movements. Ὥστε δῆλον καὶ ὅτι ἐστὶ στοιχεῖα καὶ διὰ τί ἐστιν. 458 It is plain, then, that there are elements, and why.
| Postquam philosophus inquisivit de generatione et motu, utrum insit corporibus naturalibus vel non; supposito ex praemissis quod sit in corporibus generatio et motus, hic incipit inquirere quomodo hoc sit. Et circa hoc duo facit: | 595. After inquiring whether generation and motion are present in natural bodies, and supposing from the previous discussion that they are, the Philosopher here begins to inquire how this is. In regard to this he does two things: |
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primo resumit quoddam improbandum, quod supra improbaverat, sed imperfecte; secundo prosequitur propositum, ibi: reliquum autem dicere et cetera. |
First he takes up again, in order to disprove it, something he had previously disproved incompletely; Secondly, he pursues his proposition, at 599. |
| Circa primum tria facit: | About the first he does three things: |
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primo proponit id quod supra probatum est; secundo perficit probationem, ibi: impossibile enim etc.; tertio excludit quandam obviationem, ibi: aliud quidem enim et cetera. |
First he states what was proved above; Secondly, he completes the proof, at 596; Thirdly, he excludes an objection, at 597. |
| Dicit ergo primo manifestum esse ex supra dictis quod neque generatio est omnium, sicut ponebant illi qui dicebant corpora componi ex superficiebus; neque etiam generatio est nullius, sicut posuerant Parmenides et Melissus. | 596. He says therefore first [449] that it is plain, from what was stated above, that there is neither generation of all things, as those claimed who posited that all things are composed from surfaces, nor no generation at all, as Parmenides and Melissus supposed. |
| Deinde cum dicit: impossibile enim etc., perficit improbationem ponentium quod omnium est generatio. Hoc enim supra improbavit ostendendo quod corpora non componuntur ex superficiebus: posset autem aliquis dicere omnium corporum esse generationem multis aliis modis; et ideo philosophus inducit hanc probationem universaliorem. Et dicit quod ex hoc potest confirmari quod non est omnium generatio, quia impossibile est quod sit generatio omnis corporis, nisi ponatur aliquod vacuum separatum a corporibus (quod quidem dicit, quia quidam philosophi ponebant vacuum corporibus inditum, sicut Democritus et Leucippus). Vacuum autem separatum dicitur locus qui non est repletus aliquo corpore, possibilis repleri, ut habetur in IV Physic. Ideo autem sequitur vacuum esse separatum, si omne corpus generatur, quia in loco in quo est corpus quod modo generatur, si locus ille fuisset prius isto corpore, necessarium erat quod esset ibi vacuum, cum nullum corpus esset ibi. Nullum autem corpus esset ibi prius, si omne corpus generatur. Unde ex hoc quod ponitur omne corpus generari, sequitur vacuum separatum esse. | Then at [450] he completes the refutation of those who posited that there is generation of all things. For he had disproved this previously by showing that bodies are not composed of surfaces. But someone could say that there is generation of all bodies in many other ways. Consequently, the Philosopher presents this more universal proof. And he says that we can get confirmation of the fact that there is not generation of all things from this, namely, because it is impossible for there to be generation of every body, unless a void separated from bodies be posited — which he says because certain philosophers, as Democritus and Leucippus, posited a void inherent in bodies. Now by a separated void is meant a place that is not filled with any body, but which can be filled, as was had in Physics IV. The reason why a separated void follows if every body is generated is that, in the place in which a newly generated body exists, if that place existed prior to that body, there would have to be a void there, because no body existed there. But no body would have existed there previously, if every body is generated. Hence the assumption that every body is generated requires the existence of a separated void. |
| Deinde cum dicit: aliud quidem enim etc., excludit quandam obviationem. Posset enim aliquis dicere quod videmus unumquodque corporum generari, nullo vacuo existente. Sed ad hoc ipse respondet quod, cum fit quoddam corpus particulare, generatur ex alio corpore, puta ignis ex aere; et ita ante generationem ignis, aer erat in eodem loco; et sic non est vacuum. Sed si omne corpus generetur, non potest poni aliud corpus quod prius repleverit locum, quia praeter omne corpus non est aliud corpus: et ita oportebit quod corpus fieret ex non corpore. Impossibile est autem quod corpus fiat totaliter ex nulla praeexistente magnitudine corporali. Maxime enim fieret corpus actu, ex eo quod est potentia corpus. Et si quidem ita sit potentia hoc corpus, quod sit actu aliud corpus, non sequitur inconveniens: sic enim ponimus fieri ignem ex materia quae est potentia ignis, actu autem aer. Sed si esset ita potentia corpus, quod non esset actu aliquod aliud corpus, sicut oporteret ponere eos qui ponunt omne corpus generari, sequeretur quod ante generationem omnis corporis esset vacuum separatum. | 597. Then at [451] he excludes an objection, for someone could say that we see each body being generated, even though no void exists. But to this he answers that when a certain particular body comes to be, it is generated from some other body, for example, fire from air — and thus., before the generation of the fire, air was in the same place, and so it is not void. But if every body should be generated, we cannot posit another body that previously filled the place, because there is no other body outside of every body. Hence, the body would have to be made from non-body. But it is impossible that a body be made entirely from no pre-existing bodily magnitude. For there would be produced a body in act, above all from that which is body in potency. And if that which is that body in potency is so in such a way as to be actually another body, nothing impossible follows, for that is the way we explain fire as coming to be from matter that is potentially fire, but actually air. But if it were a body in potency in such a way as not to be in act some other body, as those who posit that every body is generated would be forced to assume, it would follow that, before the generation of every body, there would be a separated void. |
| Est autem attendendum quod Aristoteles intendit hic probare non esse generationem omnis corporis, ita scilicet quod tota universitas corporum simul generetur: non autem intendit probare quod aliquod particulare corpus non generetur ex non corpore. Sic enim contra probationem Aristotelis haberet locum obviatio quam ponit Simplicius in commento suo, scilicet quod non esset necesse esse vacuum, vel propter rarefactionem et condensationem, vel propter hoc quod, hoc corpore generato, aliud corrumpitur. Unde etiam non esset haec sufficiens probatio quam ipse aestimat, scilicet quod communium non est generatio, sed particularium (non enim est generatio hominis simpliciter, sed huius hominis): quia tota universitas corporis est sicut unum corpus completum in una specie existens, sicut in primo habitum est; nihil autem prohibet individuum quod est unum tantum in una specie, generari et corrumpi, sicut de Phoenice dicunt. Unde et per hoc non excluderetur generatio omnis corporis, quam philosophus removere intendit. | 598. It should be noted that Aristotle intends to prove here that there is not generation of every body, in the sense of the whole universality of bodies being generated simultaneously. But it is not his intention to prove that some particular body is not generated from non-body. For then there would arise against Aristotle's proof the objection mentioned by Simplicius in his commentary, namely, that a void would not be necessary, either on account of rarefaction and condensation, or because, when this body is generated, another is corrupted. Whence, too, this would not be, as he thought, a sufficient proof that there is not generation of things in common, but of particulars (for there is not generation of man absolutely, but of this man), for the whole universality of body is as one complete body existing in one species, as was had previously. But there is nothing to prevent an individual alone in its species from being generated and corrupted, as they say of the Phoenix. Hence there would not be excluded by this the generation of every body, which the Philosopher intends to reject. |
| Nec etiam probatio philosophi est contra sententiam fidei nostrae, qua ponimus totam universitatem corporum de novo incoepisse: quia non ponimus praeexistere locum, quod hic philosophus supponit; neque ponimus generationem corporum ex eo quod est in potentia, sed per creationem. | Nor is the Philosopher's proof against the doctrine of our faith which teaches that the sum total of bodies at some time began to exist, because we do not posit a pre-existent place, as the Philosopher here supposes; nor do we posit that bodies were generated from what is in potency, but through creation. |
| Deinde cum dicit: reliquum autem dicere etc., ostendit quomodo sit generatio et motus corporum. Et circa hoc duo facit: | 599. Then at [452] he explains how there is generation and motion of bodies. And about this he does two things: |
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primo dicit de quo est intentio, et quo ordine id sit agendum; secundo exequitur propositum, ibi: sit itaque elementum et cetera. |
First he states his intention and the order to be followed; Secondly, he executes his plan, at 600. |
| Dicit ergo primo quod, cum non sint omnia corpora generabilia, neque nulla, ut supra dictum est, reliquum est manifestare quorum corporum est generatio, et propter quid est, idest quae est causa generationis. Quae quidem consideratio inchoatur in hoc libro, sed perficitur in libro de generatione. Sed quia omnis cognitio est per aliqua prima, ex quibus definitiones et demonstrationes procedunt; manifestum est autem quod elementa quarumlibet rerum sunt prima inter ea quae insunt rebus (licet aliqua extrinseca principia possent esse priora, puta agens et finis); oportet quod ad cognoscendum generationem corporum, prius cognoscatur quae sunt elementa corporum generabilium et corruptibilium, et qua ratione sunt elementa, et ulterius quot sunt elementa, et qualia corpora. | He says therefore first [452] that, since neither is it true that all bodies can be generated, nor that none can, as was said, we are left with the task of showing which bodies are involved in generation, and "because of what this is," i.e., what is the cause of generation. This consideration begins in this book but is completed in the book On Generation. But because all knowledge is through certain first things, from which definitions and demonstrations proceed, and it is plain that the elements of any things are first among what is present in the things (although certain extrinsic principles could be prior, e.g., the agent and end), the consequence is that, if we are to understand the generation of bodies, we must first know what are the elements of bodies that can be generated and destroyed, and why they are elements, and how many elements there are, and how many kinds of bodies there are. |
| Ad hoc autem manifestandum, oportet accipere quasi suppositionem et principium, quae sit natura elementi; quod manifestatur per eius definitionem. | Now in order to elucidate all this, it is necessary to take as a supposition and principle what the nature of an element is. And this is revealed by its definition. |
| Deinde cum dicit: sit itaque elementum etc., exequitur propositum ordine praedicto. | 600. Then at [453] he carries out his plan according to the aforesaid order. |
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Primo enim ostendit quae sit elementi natura, quam significat definitio; secundo quae et qualia sint corporum elementa, ibi: si itaque quod dictum est etc.; tertio inquirit quomodo sit corporum generatio, ibi: quoniam autem neque infinita et cetera. |
First he shows what is the nature of an element, as signified by its definition; Secondly, what are the elements of bodies and their condition, at 601. |
| Circa primum duo facit: | As to the first he does two things: |
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primo ponit partes definitionis elementi; secundo probat hanc elementi definitionem, ibi: tale enim et cetera. |
First he sets down the parts of the definition of element; Secondly, he proves this definition of element, at 600. |
| Circa primum, ponit tres partes definitionis elementi. Quarum prima est, quod elementum aliorum corporum est, in quod alia corpora dividuntur seu resolvuntur. Non enim quaelibet causa potest dici elementum, sed solum illa quae intrat rei compositionem. Unde universalia elementa sunt materia et forma, ut patet in I Physic. Quae tamen non sunt corpora: hic autem intendit philosophus de elementis quae sunt corpora. | In regard to the first he presents three parts of the definition of element. The first of these is that the element is of other bodies, that into which other bodies are divided or resolved. Not every cause can be called an "element," but only one that enters into the composition of the thing. Hence the universal elements are matter and form, as is plain in Physics I. But these are not bodies, whereas the Philosopher is here treating of the elements that are bodies. |
| Secunda particula est, quod elementum existit in eo cuius est elementum, potentia aut actu. Adhuc autem sub dubitatione existit quomodo sunt elementa in elementatis, utrum scilicet in actu vel in potentia. Si enim generatio et corruptio corporum fit per congregationem et segregationem, sicut Empedocles et Anaxagoras posuerunt, consequens est quod elementa sint actu in mixto. Si autem generatio et corruptio corporum est per alterationem, necesse est dicere quod elementa sint potentia in mixto. | The second particle is that an element exists in that of which it is an element, and does so either potentially or actually. (The question of how elements are present in the products of elements, i.e., whether they are present actually or potentially, is for the moment left open). For if the generation and corruption of bodies takes place through assembling and dispersing, as Empedocles and Anaxagoras supposed, then the elements are actually in the compound. But if generation and corruption of bodies are the results of alteration, it is necessary to say that the elements are in potency in the compound. |
| Tertia particula est, quod elementum non dividitur in alia, scilicet diversa secundum speciem. Oportet enim omne corpus divisibile esse: quaedam tamen corpora dividuntur in diversa secundum speciem, sicut manus in carnem et ossa, ex quibus quadam compositione compaginatur, vel sicut caro resolvitur in aerem, ignem, aquam et terram, per quandam alterationem; ignis autem et aer, aqua et terra neutro modo resolvuntur in diversa secundum speciem. Quod quidem complet rationem elementi; sicut etiam elementa locutionis dicuntur litterae, quae non dividuntur in diversa secundum speciem. | The third particle is that an element is not divided into other things, namely, things diverse in species. For every body has to be divisible: but some bodies are divided into things that are specifically diverse, as the hand into flesh and bones, out of which it is compacted by a certain composition, or as flesh is resolved into air, fire, water and earth, by a certain alteration. But fire and air, water and earth, are in neither way resolved into things specifically diverse. This particle completes the notion of element; just as letters are called the "elements" of a word, not being divided into things specifically diverse. |
| Deinde cum dicit: tale enim etc., probat praedictam definitionem ex communi usu loquentium: nominibus enim utendum est ut plures, ut dicitur in II Topic. Et hoc est quod dicit, quod omnes volunt dicere esse elementum aliquid tale quale descriptum est, etiam in omnibus generibus, puta in corporalibus locutionibus et demonstrationibus, in quibus principia dicuntur elementa, quae non resolvuntur in alia principia. | Then at [454] he proves the aforesaid definition by appealing to the way people generally speak — for words are to be used as they are generally accepted, as is said in Topics II. And this is what he says, namely, that every one intends to mean by "element" something such as has been described, no matter what the field, for example, in corporal speech, and in demonstrations, in which the principles are called "elements" that are not resolved into other principles. |
| Deinde cum dicit: si itaque quod dictum est etc., ostendit quae et quot sint elementa. Et circa hoc tria facit: | 601. Then at [455] he shows which things are elements and how many there are. In regard to this he does three things: |
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primo ostendit quod necesse est quaedam esse elementa corporum; secundo inquirit utrum sint finita vel infinita, ibi: utrum autem finita vel infinita etc.; tertio inquirit utrum sit unum tantum, ibi: quoniam autem necesse finita et cetera. |
First he shows that it is necessary for there to be elements of bodies; Secondly, he inquires into whether they are finite or infinite (Chap. IV); Thirdly, whether there is but one element (Chapter V). |
| Circa primum duo facit: | Concerning the first he does two things: |
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primo concludit ex praemissa definitione elementi, quod necesse est ponere quaedam elementa corporum; secundo ostendit quomodo haec diversimode ponebant Anaxagoras et Empedocles, ibi: Anaxagoras autem et cetera. |
First he concludes from the foregoing definition that it is necessary to posit certain elements of bodies; Secondly, he shows how these were diversely posited by Anaxagoras and Empedocles, at 602. |
| Dicit ergo primo quod, si praedicta est definitio elementi, necesse est dicere quod sint quaedam elementa corporum: inveniuntur enim quaedam corpora, quibus praedictae conditiones conveniunt. In carne enim et ligno, et in quolibet talium corporum, scilicet mixtorum, ignis et terra sunt in potentia; quia scilicet per quandam alterationem ex igne et terra et aliis huiusmodi praedicta corpora componuntur. Et hoc manifestum est ex ipsa segregatione, qua corpora mixta in huiusmodi simplicia resolvuntur; sicut patet in resolutione corporis animalis, quod in pulverem et quandam humorositatem et quosdam vapores resolvitur; et ita etiam est de aliis corporibus mixtis. Utitur autem hic large segregatione, quae proprie fit in ea quae insunt actu. | He says therefore first [455] that, if the foregoing is the definition of element, it is necessary to say that there are certain elements of bodies, for there exist certain bodies in which the foregoing conditions are verified. For in flesh and wood and all such bodies, i.e., compounds, fire and earth are present in potency, since it is from fire and earth and the like that, by a certain alteration, the above-mentioned bodies are composed. And this is evident by the segregation by which mixed [compound] bodies are resolved into such simple bodies, as is evident when an animal body is resolved, which breaks down into dust and a certain moistness and certain vapors — and similar things happen to other mixed bodies. |
| Quod autem huiusmodi corpora in quae alia resolvuntur, ipsa non resolvantur in alia, quod etiam pertinet ad definitionem elementi, ostendit, subdens quod in igne neque caro neque lignum inest, sive secundum potentiam sive secundum actum. Cuius signum assumit ex hoc quod, si caro et lignum essent in igne, ignis resolveretur in ista: quod nullo modo apparet. Generatur enim ex igne caro aut lignum, non per resolutionem, sed per adiunctionem aliorum corporum simplicium, simul ad mixtionem coalteratorum. Quia vero aliqui posuerunt unum tantum elementum, sicut Thales Milesius aquam, subiungit quod similis ratio est si ponatur unum tantum elementum aut plura, quod in elemento uno non inerunt alia corpora. Licet enim inveniantur alia corpora praeter illud elementum, puta caro aut os aut aliquod aliud huiusmodi, non tamen est dicendum quod aliquod horum insit potentia vel actu in corpore quod ponitur elementum. | That such bodies into which other bodies are resolved are themselves not resolved into others, which also belongs to the definition of element, he shows when he adds that in fire neither flesh nor wood is present, either potentially or actually. A sign of this he takes to be the fact that if flesh and wood existed in fire, fire would be resolved into them, and that never is seen to happen. For flesh or wood are generated from fire, not by resolution, but by the addition of other simple bodies altered at the same time for the composite. But because some philosophers posited but one element, as Thales of Miletus water, he adds that whether one element is posited or many, it is still true that in one element there will not exist other bodies. For although other bodies besides the element may be found, for example, flesh or bone or something of this kind, it must not be said that any of them is present either actually or potentially in the body taken as an element. |
| Et cum ita sit quod quaedam sint elementa corporum, considerandum est quis modus generationis est, quo vel alia corpora generantur ex elementis, scilicet per mixtionem, vel elementa ex aliis corporibus per resolutionem. Et hoc secundum veritatem determinabit in libro de generatione. | Since it is true that there are certain elements of bodies, one must consider what the manner of generation is, by which either other bodies are generated from elements, namely, by compounding, or elements from other bodies, namely, by resolution. And he will settle this as to truth in the book On Generation. |
| Deinde cum dicit: Anaxagoras autem etc., ostendit diversitatem Anaxagorae et Empedoclis circa corporalia elementa. | 602. Then at [456] he shows how Anaxagoras differed from Empedocles on the question of bodily elements. |
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Et primo ponit opinionem utriusque; secundo ostendit quae earum sit praeferenda, ibi: quoniam autem est omnis et cetera. |
First he presents the opinions of each; Secondly, he shows which opinion is to be preferred, at 603. |
| Dicit ergo primo quod de elementis corporalibus contrarie locuti sunt Anaxagoras et Empedocles. Empedocles enim posuit quod ignis et terra et alia media, quae sunt simul elementa cum istis, sunt corpora elementaria corporum, ex quibus omnia alia corpora componuntur. Sed Anaxagoras dicit contrarium, scilicet quod alia corpora homoeomera, idest similium partium, puta caro et os et alia huiusmodi, sunt elementa corporum: aerem vero et ignem et terram et aquam dicebat esse commixta ex praemissis, scilicet carne et osse, et ex omnibus aliis seminibus corporum naturalium. Ponebat enim Anaxagoras quod partes corporum similium infinitae et indivisibiles erant semina omnium quae apparent in natura; ita scilicet quod per extractionem eorum ab aliquo mixto, generantur omnia corpora naturalia sensibilia. Quia igitur ex igne et terra et aliis huiusmodi videntur omnia alia corpora generari, aestimavit quod tam ignis quam terra et alia intermedia essent constituta ex omnibus indivisibilibus partibus similibus simul congregatis. Et secundum hoc partes consimiles ponebat esse elementa horum quatuor corporum; ex quibus tamen dicebat omnia fieri propter semina inexistentia. Et quia de igne mentionem non faciebat, ne ex hoc aliquod dubium oriretur, subdit quod ipse appellabat ignem aetherem. | He says therefore first [456] that Anaxagoras and Empedocles held contrary opinions on elements. For Empedocles posited that fire and earth, and other intermediates, which are elements with these, are the elemental bodies of bodies, from which all other bodies are composed. But Anaxagoras says the contrary, namely, that other "homoemeric" bodies, i.e., of similar parts, for example, flesh and bone and the like, are the elements of bodies, while air and fire and earth and water he said to be compounded out of the foregoing, i.e., out of flesh and bone and all the other seeds of natural bodies. For Anaxagoras posited that infinite and indivisible parts of similar bodies were the seeds of all things that appear in nature, in the sense that, by their extraction from some compound, all natural sensible bodies are generated. Therefore, because all other bodies seem to be generated from fire and earth and the like, he estimated that fire and earth and other intermediate things resulted from all the indivisible similar parts assembled together. And according to this, he posited the consimilar parts to be the elements of these four bodies, from which he nevertheless said all things come to be on account of the seeds existing therein. And since he did not mention fire, therefore, lest any doubt arise concerning this, he adds that he [Anaxagoras] called fire "aether." |
| Deinde cum dicit: quoniam autem est omnis etc., ostendit quod opinio Empedoclis est praeferenda. Sicut enim patet ex his quae in primo habita sunt, omnis corporis naturalis est aliquis proprius motus; et cum sint quidam motus simplices, quidam mixti, manifestum quod mixti motus sunt mixtorum corporum, simplices autem sunt simplicium corporum. Et ex hoc manifestum est quod sunt quaedam corpora simplicia, cum sint quidam motus simplices. Et quia motus simplices, qui sunt a medio et ad medium, magis appropriantur elementis quae ponit Empedocles, manifestum est eius opinionem esse praeferendam. | 603. Then at [457] he shows that the opinion of Empedocles is to be preferred. For as is plain from the discussion in Book I, every natural body possesses some proper motion, and since some motions are simple and some mixed, it is clear that mixed motions belong to mixed bodies, and simple motions to simple bodies. And from this it is evident that there are certain simple bodies, since [458] there are certain simple motions. And since the simple motions, which are from the middle and to the middle, belong more to the elements posited by Empedocles, it is plain that his opinion should be preferred. |
| Quamvis posset dici hanc esse secundam rationem ad principalem conclusionem, quam epilogando infert, dicens manifestum esse quod sint elementa, et propter quid sint. | However, this could be called a second argument in support of the principal conclusion which he draws as a summary, saying that it is plain that elements exist and for what purpose they exist. |
* * * * * * *
Here ends Thomas Aquinas' Commentary
The following is the remainder of Aristotle's text:
| 4 | 4 |
| Πότερον δὲ πεπερασμένα ἢ ἄπειρα, καὶ εἰ πεπερασμένα, πόσα τὸν ἀριθμόν, ἑπόμενον ἂν εἴη σκοπεῖν. | The next question to consider is whether the elements are finite or infinite in number, and, if finite, what their number is. |
| Πρῶτον μὲν οὖν ὅτι οὐκ ἔστιν ἄπειρα, καθάπερ οἴονταί τινες, θεωρητέον, καὶ πρῶτον τοὺς πάντα τὰ ὁμοιομερῆ στοιχεῖα ποιοῦντας, καθάπερ καὶ Ἀναξαγόρας. Οὐθεὶς γὰρ τῶν οὕτως ἀξιούντων ὀρθῶς λαμβάνει τὸ στοιχεῖον ὁρῶμεν γὰρ πολλὰ καὶ τῶν μικτῶν σωμάτων εἰς ὁμοιομερῆ διαιρούμενα, λέγω δ' οἷον σάρκα καὶ ὀστοῦν καὶ ξύλον καὶ λίθον. Ὥστ' εἴπερ τὸ σύνθετον οὐκ ἔστι στοιχεῖον, οὐχ ἅπαν ἔσται τὸ ὁμοιομερὲς στοιχεῖον, ἀλλὰ τὸ ἀδιαίρετον εἰς ἕτερα τῷ εἴδει, καθάπερ εἴρηται πρότερον. | Let us first show reason or denying that their number is infinite, as some suppose. We begin with the view of Anaxagoras that all the homoeomerous bodies are elements. Any one who adopts this view misapprehends the meaning of element. Observation shows that even mixed bodies are often divisible into homoeomerous parts; examples are flesh, bone, wood, and stone. Since then the composite cannot be an element, not every homoeomerous body can be an element; only, as we said before, that which is not divisible into bodies different in form. |
| Ἔτι δ' οὐδ' οὕτως λαμβάνοντας τὸ στοιχεῖον ἀνάγκη ποιεῖν ἄπειρα πάντα γὰρ ταὐτὰ ἀποδοθήσεται καὶ πεπερασμένων ὄντων, ἐάν τις λάβῃ τὸ αὐτὸ γὰρ ποιήσει, κἂν δύο ἢ τρία μόνον ᾖ τοιαῦτα, καθάπερ ἐγχειρεῖ καὶ Ἐμπεδοκλῆς. Ἐπεὶ γὰρ καὶ ὣς αὐτοῖς συμβαίνει μὴ πάντα ποιεῖν ἐξ ὁμοιομερῶν (πρόσωπον γὰρ οὐκ ἐκ προσώπων ποιοῦσιν, οὐδ' ἄλλο τῶν κατὰ φύσιν ἐσχηματισμένων οὐθέν), φανερὸν ὅτι πολλῷ βέλτιον πεπερασμένας ποιεῖν τὰς ἀρχάς, καὶ ταύτας ὡς ἐλαχίστας πάντων γε τῶν αὐτῶν μελλόντων δείκνυσθαι, καθάπερ ἀξιοῦσι καὶ οἱ ἐν τοῖς μαθήμασιν ἀεὶ γὰρ πεπερασμένας λαμβάνουσιν ἀρχὰς ἢ τῷ εἴδει ἢ τῷ ποσῷ. | But even taking 'element' as they do, they need not assert an infinity of elements, since the hypothesis of a finite number will give identical results. Indeed even two or three such bodies serve the purpose as well, as Empedocles' attempt shows. Again, even on their view it turns out that all things are not composed of homocomerous bodies. They do not pretend that a face is composed of faces, or that any other natural conformation is composed of parts like itself. Obviously then it would be better to assume a finite number of principles. They should, in fact, be as few as possible, consistently with proving what has to be proved. This is the common demand of mathematicians, who always assume as principles things finite either in kind or in number. |
| Ἔτι εἰ σῶμα σώματος ἕτερον λέγεται κατὰ τὰς οἰκείας διαφοράς, αἱ δὲ τῶν σωμάτων διαφοραὶ πεπερασμέναι (δια(303a.) φέρουσι γὰρ τοῖς αἰσθητοῖς, ταῦτα δὲ πεπέρανται δεῖ δὲ τοῦτο δειχθῆναι), φανερὸν ὅτι καὶ τὰ στοιχεῖα ἀνάγκη πεπερασμένα εἶναι. | Again, if body is distinguished from body by the appropriate qualitative difference, and there is a limit to the number of differences (for the difference lies in qualities apprehended by sense, which are in fact finite in number, though this requires proof), then manifestly there is necessarily a limit to the number of elements. |
| Ἀλλὰ μὴν οὐδ' ὡς ἕτεροί τινες λέγουσιν, οἷον Λεύκιππός τε καὶ Δημόκριτος ὁ Ἀβδηρίτης, εὔλογα τὰ συμβαίνοντα φασὶ γὰρ εἶναι τὰ πρῶτα μεγέθη πλήθει μὲν ἄπειρα, μεγέθει δὲ ἀδιαίρετα, καὶ οὔτ' ἐξ ἑνὸς πολλὰ γίγνεσθαι οὔτε ἐκ πολλῶν ἕν, ἀλλὰ τῇ τούτων συμπλοκῇ καὶ περιπαλάξει πάντα γεννᾶσθαι. Τρόπον γάρ τινα καὶ οὗτοι πάντα τὰ ὄντα ποιοῦσιν ἀριθμοὺς καὶ ἐξ ἀριθμῶν καὶ γὰρ εἰ μὴ σαφῶς δηλοῦσιν, ὅμως τοῦτο βούλονται λέγειν. | There is, further, another view—that of Leucippus and Democritus of Abdera—the implications of which are also unacceptable. The primary masses, according to them, are infinite in number and indivisible in mass: one cannot turn into many nor many into one; and all things are generated by their combination and involution. Now this view in a sense makes things out to be numbers or composed of numbers. The exposition is not clear, but this is its real meaning. |
| Καὶ πρὸς τούτοις, ἐπεὶ διαφέρει τὰ σώματα σχήμασιν, ἄπειρα δὲ τὰ σχήματα, ἄπειρα καὶ τὰ ἁπλᾶ σώματά φασιν εἶναι. Ποῖον δὲ καὶ τί ἑκάστου τὸ σχῆμα τῶν στοιχείων, οὐθὲν ἐπιδιώρισαν, ἀλλὰ μόνον τῷ πυρὶ τὴν σφαῖραν ἀπέδωκαν ἀέρα δὲ καὶ ὕδωρ καὶ τἆλλα μεγέθει καὶ μικρότητι διεῖλον, ὡς οὖσαν αὐτῶν τὴν φύσιν οἷον πανσπερμίαν πάντων τῶν στοιχείων. | And further, they say that since the atomic bodies differ in shape, and there is an infinity of shapes, there is an infinity of simple bodies. But they have never explained in detail the shapes of the various elements, except so far to allot the sphere to fire. Air, water, and the rest they distinguished by the relative size of the atom, assuming that the atomic substance was a sort of master-seed for each and every element. |
| Πρῶτον μὲν οὖν ταὐτὸν καὶ τούτοις ἁμάρτημα τὸ μὴ πεπερασμένας λαβεῖν τὰς ἀρχάς, ἐξὸν ἅπαντα ταὐτὰ λέγειν. | Now, in the first place, they make the mistake already noticed. The principles which they assume are not limited in number, though such limitation would necessitate no other alteration in their theory. |
| Ἔτι δ' εἰ μὴ ἄπειροι τῶν σχημάτων αἱ διαφοραί, δῆλον ὅτι οὐκ ἔσται τὰ στοιχεῖα ἄπειρα. | Further, if the differences of bodies are not infinite, plainly the elements will not be an infinity. |
| Πρὸς δὲ τούτοις ἀνάγκη μάχεσθαι ταῖς μαθηματικαῖς ἐπιστήμαις ἄτομα σώματα λέγοντας, καὶ πολλὰ τῶν ἐνδόξων καὶ τῶν φαινομένων κατὰ τὴν αἴσθησιν ἀναιρεῖν, περὶ ὧν εἴρηται πρότερον ἐν τοῖς περὶ χρόνου καὶ κινήσεως. | Besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. But of these things we have already spoken in our discussion of time and movement. |
| Ἅμα δὲ καὶ ἐναντία λέγειν αὐτοὺς αὑτοῖς ἀνάγκη ἀδύνατον γὰρ ἀτόμων ὄντων τῶν στοιχείων μεγέθει καὶ μικρότητι διαφέρειν ἀέρα καὶ γῆν καὶ ὕδωρ οὐ γὰρ οἷόν τ' ἐξ ἀλλήλων γίγνεσθαι ὑπολείψει γὰρ ἀεὶ τὰ μέγιστα σώματα ἐκκρινόμενα, φασὶ δ' οὕτω γίγνεσθαι ὕδωρ καὶ ἀέρα καὶ γῆν ἐξ ἀλλήλων. | They are also bound to contradict themselves. For if the elements are atomic, air, earth, and water cannot be differentiated by the relative sizes of their atoms, since then they could not be generated out of one another. The extrusion of the largest atoms is a process that will in time exhaust the supply; and it is by such a process that they account for the generation of water, air, and earth from one another. |
| Ἔτι οὐδὲ κατὰ τὴν τούτων ὑπόληψιν δόξειεν ἂν ἄπειρα γίγνεσθαι τὰ στοιχεῖα, εἴπερ τὰ μὲν σώματα διαφέρει σχήμασι, τὰ δὲ σχήματα πάντα σύγκειται ἐκ πυραμίδων, τὰ μὲν εὐθύγραμμα ἐξ εὐθυ(303b.) γράμμων, ἡ δὲ σφαῖρα ἐξ ὀκτὼ μορίων. Ἀνάγκη γὰρ εἶναί τινας ἀρχὰς τῶν σχημάτων. Ὥστε εἴτε μία εἴτε δύο εἴτε πλείους, καὶ τὰ ἁπλᾶ σώματα τοσαῦτα ἔσται τὸ πλῆθος. | Again, even on their own presuppositions it does not seem as if the clements would be infinite in number. The atoms differ in figure, and all figures are composed of pyramids, rectilinear the case of rectilinear figures, while the sphere has eight pyramidal parts. The figures must have their principles, and, whether these are one or two or more, the simple bodies must be the same in number as they. |
| Ἔτι δ' εἰ ἑκάστῳ μὲν τῶν στοιχείων ἐστί τις οἰκεία κίνησις, καὶ ἡ τοῦ ἁπλοῦ σώματος ἁπλῆ, μή εἰσι δ' αἱ ἁπλαῖ κινήσεις ἄπειροι διὰ τὸ μήτε τὰς ἁπλᾶς φορὰς πλείους εἶναι δυοῖν μήτε τοὺς τόπους ἀπείρους, οὐκ ἂν εἴη οὐδ' οὕτως ἄπειρα τὰ στοιχεῖα. | Again, if every element has its proper movement, and a simple body has a simple movement, and the number of simple movements is not infinite, because the simple motions are only two and the number of places is not infinite, on these grounds also we should have to deny that the number of elements is infinite. |
| 5 | 5 |
| Ἐπεὶ δ' ἀνάγκη πεπεράνθαι τὰ στοιχεῖα, λοιπὸν σκέψασθαι πότερον πλείω ἔσται ἢ ἕν. Ἔνιοι γὰρ ἓν μόνον ὑποτίθενται, καὶ τοῦτο οἱ μὲν ὕδωρ, οἱ δ' ἀέρα, οἱ δὲ πῦρ, οἱ δ' ὕδατος μὲν λεπτότερον, ἀέρος δὲ πυκνότερον, ὃ περιέχειν φασὶ πάντας τοὺς οὐρανοὺς ἄπειρον ὄν. | Since the number of the elements must be limited, it remains to inquire whether there is more than one element. Some assume one only, which is according to some water, to others air, to others fire, to others again something finer than water and denser than air, an infinite body—so they say—bracing all the heavens. |
| Ὅσοι μὲν οὖν τὸ ἓν τοῦτο ποιοῦσιν ὕδωρ ἢ ἀέρα ἢ ὕδατος μὲν λεπτότερον, ἀέρος δὲ πυκνότερον, εἶτ' ἐκ τούτου μανότητι καὶ πυκνότητι τἆλλα γεννῶσιν, οὗτοι λανθάνουσιν αὐτοὶ αὑτοὺς ἄλλο τι πρότερον τοῦ στοιχείου ποιοῦντες ἔστι γὰρ ἡ μὲν ἐκ τῶν στοιχείων γένεσις σύνθεσις, ὥς φασιν, ἡ δ' εἰς τὰ στοιχεῖα διάλυσις, ὥστ' ἀνάγκη πρότερον εἶναι τῇ φύσει τὸ λεπτομερέστερον. Ἐπεὶ οὖν φασὶ πάντων τῶν σωμάτων τὸ πῦρ λεπτότατον εἶναι, πρῶτον ἂν εἴη τῇ φύσει τὸ πῦρ διαφέρει δ' οὐθέν, ἀνάγκη γὰρ ἕν τι τῶν ἄλλων εἶναι πρῶτον, καὶ μὴ τὸ μέσον. | Now those who decide for a single element, which is either water or air or a body finer than water and denser than air, and proceed to generate other things out of it by use of the attributes density and rarity, all alike fail to observe the fact that they are depriving the element of its priority. Generation out of the elements is, as they say, synthesis, and generation into the elements is analysis, so that the body with the finer parts must have priority in the order of nature. But they say that fire is of all bodies the finest. Hence fire will be first in the natural order. And whether the finest body is fire or not makes no difference; anyhow it must be one of the other bodies that is primary and not that which is intermediate. |
| Ἔτι δὲ τὸ μὲν πυκνότητι καὶ μανότητι τἆλλα γεννᾶν οὐθὲν διαφέρει ἢ λεπτότητι καὶ παχύτητι τὸ μὲν γὰρ λεπτὸν μανόν, τὸ δὲ παχὺ βούλονται εἶναι πυκνόν. Πάλιν δὲ τὸ λεπτότητι καὶ παχύτητι ταὐτὸν καὶ τὸ μεγέθει καὶ μικρότητι λεπτὸν μὲν γὰρ τὸ μικρομερές, παχὺ δὲ τὸ μεγαλομερές τὸ γὰρ ἐπεκτεινόμενον ἐπὶ πολὺ λεπτόν, τοιοῦτον δὲ τὸ ἐκ μικρῶν μερῶν συνεστός, ὥστ' αὐτοῖς συμβαίνει μεγέθει καὶ μικρότητι διαιρεῖν τὴν τῶν ἄλλων οὐσίαν. Οὕτω δὲ διοριζομένοις ἅπαντα συμβήσεται λέγειν πρός τι, καὶ οὐκ ἔσται ἁπλῶς τὸ μὲν πῦρ τὸ δ' ὕδωρ τὸ δ' ἀήρ, ἀλλὰ τὸ αὐτὸ πρὸς μὲν τόδε (304a.) πῦρ, πρὸς δέ τι ἄλλο ἀήρ, ὅπερ συμβαίνει καὶ τοῖς πλείω μὲν τὰ στοιχεῖα λέγουσι, μεγέθει δὲ καὶ μικρότητι διαφέρειν φάσκουσιν ἐπεὶ γὰρ τῷ ποσῷ διώρισται ἕκαστον, ἔσται τις λόγος πρὸς ἄλληλα τῶν μεγεθῶν, ὥστε τὰ τοῦτον ἔχοντα τὸν λόγον πρὸς ἄλληλα ἀνάγκη τὸ μὲν ἀέρα εἶναι τὸ δὲ πῦρ τὸ δὲ γῆν τὸ δ' ὕδωρ, διὰ τὸ ἐνυπάρχειν ἐν τοῖς μείζοσι τοὺς τῶν ἐλαττόνων λόγους. | Again, density and rarity, as instruments of generation, are equivalent to fineness and coarseness, since the fine is rare, and coarse in their use means dense. But fineness and coarseness, again, are equivalent to greatness and smallness, since a thing with small parts is fine and a thing with large parts coarse. For that which spreads itself out widely is fine, and a thing composed of small parts is so spread out. In the end, then, they distinguish the various other substances from the element by the greatness and smallness of their parts. This method of distinction makes all judgement relative. There will be no absolute distinction between fire, water, and air, but one and the same body will be relatively to this fire, relatively to something else air. The same difficulty is involved equally in the view elements and distinguishes them by their greatness and smallness. The principle of distinction between bodies being quantity, the various sizes will be in a definite ratio, and whatever bodies are in this ratio to one another must be air, fire, earth, and water respectively. For the ratios of smaller bodies may be repeated among greater bodies. |
| Ὅσοι δὲ πῦρ ὑποτίθενται τὸ στοιχεῖον, τοῦτο μὲν διαφεύγουσιν, ἄλλα δ' αὐτοῖς ἀναγκαῖον ἄλογα συμβαίνειν. | Those who start from fire as the single element, while avoiding this difficulty, involve themselves in many others. |
| Οἱ μὲν γὰρ αὐτῶν σχῆμα περιάπτουσι τῷ πυρί, καθάπερ οἱ τὴν πυραμίδα ποιοῦντες, καὶ τούτων οἱ μὲν ἁπλουστέρως λέγοντες ὅτι τῶν μὲν σχημάτων τμητικώτατον ἡ πυραμίς, τῶν δὲ σωμάτων τὸ πῦρ, οἱ δὲ κομψοτέρως τῷ λόγῳ προσάγοντες ὅτι τὰ μὲν σώματα πάντα σύγκειται ἐκ τοῦ λεπτομερεστάτου, τὰ δὲ σχήματα τὰ στερεὰ ἐκ πυραμίδων, ὥστ' ἐπεὶ τῶν μὲν σωμάτων τὸ πῦρ λεπτότατον, τῶν δὲ σχημάτων ἡ πυραμὶς μικρομερέστατον καὶ πρῶτον, τὸ δὲ πρῶτον σχῆμα τοῦ πρώτου σώματος, πυραμὶς ἂν εἴη τὸ πῦρ. | Some of them give fire a particular shape, like those who make it a pyramid, and this on one of two grounds. The reason given may be—more crudely—that the pyramid is the most piercing of figures as fire is of bodies, or—more ingeniously—the position may be supported by the following argument. As all bodies are composed of that which has the finest parts, so all solid figures are composed of pryamids: but the finest body is fire, while among figures the pyramid is primary and has the smallest parts; and the primary body must have the primary figure: therefore fire will be a pyramid. |
| Οἱ δὲ περὶ μὲν σχήματος οὐδὲν ἀποφαίνονται, λεπτομερέστατον δὲ μόνον ποιοῦσιν, ἔπειτ' ἐκ τούτου συντιθεμένου φασὶ γίγνεσθαι τἆλλα καθάπερ ἂν εἰ συμφυσωμένου ψήγματος. | Others, again, express no opinion on the subject of its figure, but simply regard it as the of the finest parts, which in combination will form other bodies, as the fusing of gold-dust produces solid gold. |
| Ἀμφοτέροις δὲ ταὐτὰ συμβαίνει δυσχερῆ εἰ μὲν γὰρ ἄτομον τὸ πρῶτον σῶμα ποιοῦσι, πάλιν ἥξουσιν οἱ πρότερον εἰρημένοι λόγοι πρὸς ταύτην τὴν ὑπόθεσιν. | Both of these views involve the same difficulties. For (1) if, on the one hand, they make the primary body an atom, the view will be open to the objections already advanced against the atomic theory. |
| Ἔτι οὐκ ἐνδέχεται τοῦτο λέγειν φυσικῶς βουλομένοις θεωρεῖν. Εἰ γὰρ ἅπαν σῶμα σώματι συμβλητὸν κατὰ τὸ ποσόν, ἔχει δ' ἀνάλογον τὰ μεγέθη τά τε τῶν ὁμοιομερῶν πρὸς ἄλληλα καὶ τὰ τῶν στοιχείων (οἷον τὰ τοῦ παντὸς ὕδατος πρὸς τὸν ἅπαντα ἀέρα καὶ τοῦ στοιχείου πρὸς τὸ στοιχεῖον, ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων), ὁ δ' ἀὴρ πλείων τοῦ ὕδατος καὶ ὅλως τὸ λεπτομερέστερον τοῦ παχυμερεστέρου, φανερὸν ὅτι καὶ τὸ στοιχεῖον ἔλαττον ἔσται τὸ τοῦ ὕδατος ἢ τὸ τοῦ ἀέρος. Εἰ οὖν τὸ ἔλαττον μέγεθος ἐνυπάρχει τῷ μείζονι, διαιρετὸν ἂν εἴη τὸ τοῦ ἀέρος (304b.) στοιχεῖον. Ὡσαύτως δὲ καὶ τὸ τοῦ πυρὸς καὶ ὅλως τῶν λεπτομερεστέρων. | And further the theory is inconsistent with a regard for the facts of nature. For if all bodies are quantitatively commensurable, and the relative size of the various homoeomerous masses and of their several elements are in the same ratio, so that the total mass of water, for instance, is related to the total mass of air as the elements of each are to one another, and so on, and if there is more air than water and, generally, more of the finer body than of the coarser, obviously the element of water will be smaller than that of air. But the lesser quantity is contained in the greater. Therefore the air element is divisible. And the same could be shown of fire and of all bodies whose parts are relatively fine. |
| Εἰ δὲ διαιρετόν, τοῖς μὲν σχηματίζουσι τὸ πῦρ συμβήσεται μὴ εἶναι τὸ τοῦ πυρὸς μέρος πῦρ διὰ τὸ μὴ συγκεῖσθαι τὴν πυραμίδα ἐκ πυραμίδων, ἔτι δὲ μὴ πᾶν σῶμα εἶναι ἢ στοιχεῖον ἢ ἐκ στοιχείων (τὸ γὰρ μέρος τοῦ πυρὸς οὔτε πῦρ οὔθ' ἕτερον στοιχεῖον οὐδέν) τοῖς δὲ τῷ μεγέθει διορίζουσι πρότερόν τι τοῦ στοιχείου στοιχεῖον εἶναι, καὶ τοῦτ' εἰς ἄπειρον βαδίζειν, εἴπερ ἅπαν σῶμα διαιρετὸν καὶ τὸ μικρομερέστατον στοιχεῖον. | (2) If, on the other hand, the primary body is divisible, then (a) those who give fire a special shape will have to say that a part of fire is not fire, because a pyramid is not composed of pyramids, and also that not every body is either an element or composed of elements, since a part of fire will be neither fire nor any other element. And (b) those whose ground of distinction is size will have to recognize an element prior to the element, a regress which continues infinitely, since every body is divisible and that which has the smallest parts is the element. |
| Ἔτι δὲ καὶ τούτοις συμβαίνει λέγειν ὡς ταὐτὸν πρὸς μὲν τόδε πῦρ ἐστι, πρὸς ἄλλο δ' ἀήρ, καὶ πάλιν ὕδωρ καὶ γῆ. | Further, they too will have to say that the same body is relatively to this fire and relatively to that air, to others again water and earth. |
| Κοινὸν δὲ πᾶσιν ἁμάρτημα τοῖς ἓν τὸ στοιχεῖον ὑποτιθεμένοις τὸ μίαν μόνην κίνησιν ποιεῖν φυσικήν, καὶ πάντων τὴν αὐτήν. Ὁρῶμεν γὰρ πᾶν τὸ φυσικὸν σῶμα κινήσεως ἔχον ἀρχήν. Εἰ οὖν ἅπαντα τὰ σώματα ἕν τί ἐστι, πάντων ἂν εἴη μία κίνησις καὶ ταύτην ἀναγκαῖον ὥσῳπερ ἂν πλείω γίγνηται, κινεῖσθαι μᾶλλον, ὥσπερ καὶ τὸ πῦρ ὅσῳ ἂν πλεῖον γίγνηται, φέρεται θᾶττον ἄνω τὴν αὑτοῦ φοράν. Συμβαίνει δὲ πολλὰ κάτω φέρεσθαι θᾶττον. | The common error of all views which assume a single element is that they allow only one natural movement, which is the same for every body. For it is a matter of observation that a natural body possesses a principle of movement. If then all bodies are one, all will have one movement. With this motion the greater their quantity the more they will move, just as fire, in proportion as its quantity is greater, moves faster with the upward motion which belongs to it. But the fact is that increase of quantity makes many things move the faster downward. |
| Ὥστε διά τε ταῦτα καὶ πρὸς τούτοις ἐπεὶ διώρισται πρότερον ὅτι πλείους αἱ φυσικαὶ κινήσεις, δῆλον ὅτι ἀδύνατον ἓν εἶναι τὸ στοιχεῖον. Ἐπειδὴ δὲ οὔτε ἄπειρα οὔτε ἕν, ἀνάγκη πλείω εἶναι καὶ πεπερασμένα. | For these reasons, then, as well as from the distinction already established of a plurality of natural movements, it is impossible that there should be only one element. But if the elements are not an infinity and not reducible to one, they must be several and finite in number. |
| 6 | 6 |
| Ἐπισκεπτέον δὲ πρῶτον πότερον ἀΐδιά ἐστιν ἢ γινόμενα φθείρεται τούτου γὰρ δειχθέντος φανερὸν ἔσται καὶ πόσ' ἄττα καὶ ποῖά ἐστιν. Ἀΐδια μὲν οὖν εἶναι ἀδύνατον ὁρῶμεν γὰρ καὶ πῦρ καὶ ὕδωρ καὶ ἕκαστον τῶν ἁπλῶν σωμάτων διαλυόμενον. Ἀνάγκη δὲ ἢ ἄπειρον εἶναι ἢ ἵστασθαι τὴν διάλυσιν. Εἰ μὲν οὖν ἄπειρος, ἔσται καὶ ὁ χρόνος ὁ τῆς διαλύσεως ἄπειρος, καὶ πάλιν ὁ τῆς συνθέσεως ἕκαστον γὰρ ἐν ἄλλῳ χρόνῳ διαλύεται καὶ συντίθεται τῶν μορίων. | First we must inquire whether the elements are eternal or subject to generation and destruction; for when this question has been answered their number and character will be manifest. In the first place, they cannot be eternal. It is a matter of observation that fire, water, and every simple body undergo a process of analysis, which must either continue infinitely or stop somewhere. (1) Suppose it infinite. Then the time occupied by the process will be infinite, and also that occupied by the reverse process of synthesis. For the processes of analysis and synthesis succeed one another in the various parts. |
| Ὥστε συμβήσεται ἔξω τοῦ ἀπείρου χρόνου ἄλλον εἶναι ἄπειρον, ὅταν ὅ τε τῆς συνθέσεως ἄπειρος ᾖ καὶ ἔτι πρότερος τούτου ὁ τῆς διαλύσεως. Ὥστε τοῦ ἀπείρου ἔξω γίγνεται ἄπειρον (305a.) ὅπερ ἀδύνατον. | It will follow that there are two infinite times which are mutually exclusive, the time occupied by the synthesis, which is infinite, being preceded by the period of analysis. There are thus two mutually exclusive infinites, which is impossible. |
| Εἰ δὲ στήσεταί που ἡ διάλυσις, ἤτοι ἄτομον ἔσται τὸ σῶμα ἐν ᾧ ἵσταται, ἢ διαιρετὸν μὲν οὐ μέντοι διαιρεθησόμενον οὐδέποτε, καθάπερ ἔοικεν Ἐμπεδοκλῆς βούλεσθαι λέγειν. | (2) Suppose, on the other hand, that the analysis stops somewhere. Then the body at which it stops will be either atomic or, as Empedocles seems to have intended, a divisible body which will yet never be divided. |
| Ἄτομον μὲν οὖν οὐκ ἔσται διὰ τοὺς πρότερον εἰρημένους λόγους ἀλλὰ μὴν οὐδὲ διαιρετὸν μὲν οὐδέποτε δὲ διαλυθησόμενον. Τὸ γὰρ ἔλαττον σῶμα τοῦ μείζονος εὐφθαρτότερόν ἐστιν. Εἴπερ οὖν καὶ τὸ πολὺ φθείρεται κατὰ ταύτην τὴν φθοράν, ὥστε διαλύεσθαι εἰς ἐλάττω, ἔτι μᾶλλον τοῦτο πάσχειν εὔλογον τὸ ἔλαττον. Δύο δὲ τρόπους ὁρῶμεν φθειρόμενον τὸ πῦρ ὑπό τε γὰρ τοῦ ἐναντίου φθείρεται σβεννύμενον, καὶ αὐτὸ ὑφ' αὑτοῦ μαραινόμενον. Τοῦτο δὲ πάσχει τὸ ἔλαττον ὑπὸ τοῦ πλείονος, καὶ θᾶττον, ὅσῳ ἂν ᾖ ἔλαττον. Ὥστ' ἀνάγκη φθαρτὰ καὶ γενητὰ εἶναι τὰ στοιχεῖα τῶν σωμάτων. | The foregoing arguments show that it cannot be an atom; but neither can it be a divisible body which analysis will never reach. For a smaller body is more easily destroyed than a larger; and a destructive process which succeeds in destroying, that is, in resolving into smaller bodies, a body of some size, cannot reasonably be expected to fail with the smaller body. Now in fire we observe a destruction of two kinds: it is destroyed by its contrary when it is quenched, and by itself when it dies out. But the effect is produced by a greater quantity upon a lesser, and the more quickly the smaller it is. The elements of bodies must therefore be subject to destruction and generation. |
| Ἐπεὶ δ' ἐστὶ γενητά, ἤτοι ἐξ ἀσωμάτου ἢ ἐκ σώματος ἔσται ἡ γένεσις, καὶ εἰ ἐκ σώματος, ἤτοι ἐξ ἄλλου ἢ ἐξ ἀλλήλων. | Since they are generated, they must be generated either from something incorporeal or from a body, and if from a body, either from one another or from something else. |
| Ὁ μὲν οὖν ἐξ ἀσωμάτου γεννῶν λόγος ποιεῖ κεχωρισμένον κενόν. Πᾶν γὰρ τὸ γινόμενον <�ἔν τινι γίγνεται καὶ> ἤτοι ἀσώματον ἔσται ἐν ᾧ ἡ γένεσις, ἢ ἕξει σῶμα καὶ εἰ μὲν ἕξει σῶμα, δύο ἅμα ἔσται σώματα ἐν τῷ αὐτῷ, τό τε γιγνόμενον καὶ τὸ προϋπάρχον εἰ δ' ἀσώματον, ἀνάγκη κενὸν εἶναι ἀφωρισμένον τοῦτο δ' ὅτι ἀδύνατον, δέδεικται πρότερον. | The theory which generates them from something incorporeal requires an extra-corporeal void. For everything that comes to be comes to be in something, and that in which the generation takes place must either be incorporeal or possess body; and if it has body, there will be two bodies in the same place at the same time, viz. that which is coming to be and that which was previously there, while if it is incorporeal, there must be an extra-corporeal void. But we have already shown that this is impossible. |
| Ἀλλὰ μὴν οὐδ' ἐκ σώματός τινος ἐγχωρεῖ γίνεσθαι τὰ στοιχεῖα συμβήσεται γὰρ ἄλλο σῶμα πρότερον εἶναι τῶν στοιχείων. Τοῦτο δ' εἰ μὲν ἕξει βάρος ἢ κουφότητα, τῶν στοιχείων ἔσται τι, μηδεμίαν δ' ἔχον ῥοπὴν ἀκίνητον ἔσται καὶ μαθηματικόν τοιοῦτον δὲ ὂν οὐκ ἔσται ἐν τόπῳ. Ἐν ᾧ γὰρ ἠρεμεῖ, ἐν τούτῳ καὶ κινεῖσθαι δυνατόν. Καὶ εἰ μὲν βίᾳ, παρὰ φύσιν, εἰ δὲ μὴ βίᾳ, κατὰ φύσιν. Εἰ μὲν οὖν ἔσται ἐν τόπῳ καί που, ἔσται τι τῶν στοιχείων εἰ δὲ μὴ ἐν τόπῳ, οὐδὲν ἐξ αὐτοῦ ἔσται τὸ γὰρ γινόμενον, καὶ ἐξ οὗ γίγνεται, ἀνάγκη ἅμα εἶναι. | But, on the other hand, it is equally impossible that the elements should be generated from some kind of body. That would involve a body distinct from the elements and prior to them. But if this body possesses weight or lightness, it will be one of the elements; and if it has no tendency to movement, it will be an immovable or mathematical entity, and therefore not in a place at all. A place in which a thing is at rest is a place in which it might move, either by constraint, i.e. unnaturally, or in the absence of constraint, i.e. naturally. If, then, it is in a place and somewhere, it will be one of the elements; and if it is not in a place, nothing can come from it, since that which comes into being and that out of which it comes must needs be together. |
| Ἐπεὶ δ' οὔτε ἐξ ἀσωμάτου γίγνεσθαι δυνατὸν οὔτ' ἐξ ἄλλου σώματος, λείπεται ἐξ ἀλλήλων γίγνεσθαι. | The elements therefore cannot be generated from something incorporeal nor from a body which is not an element, and the only remaining alternative is that they are generated from one another. |
| 7 | 7 |
| Πάλιν οὖν ἐπισκεπτέον τίς ὁ τρόπος τῆς ἐξ ἀλλήλων γενέσεως, πότερον ὡς Ἐμπεδοκλῆς λέγει καὶ Δημόκριτος, ἢ ὡς οἱ εἰς τὰ ἐπίπεδα διαλύοντες, ἢ ἔστιν ἄλλος τις τρόπος (305b.) παρὰ τούτους. | We must, therefore, turn to the question, what is the manner of their generation from one another? Is it as Empedocles and Democritus say, or as those who resolve bodies into planes say, or is there yet another possibility? |
| Οἱ μὲν οὖν περὶ Ἐμπεδοκλέα καὶ Δημόκριτον λανθάνουσιν αὐτοὶ αὑτοὺς οὐ γένεσιν ἐξ ἀλλήλων ποιοῦντες, ἀλλὰ φαινομένην γένεσιν ἐνυπάρχον γὰρ ἕκαστον ἐκκρίνεσθαί φασιν, ὥσπερ ἐξ ἀγγείου τῆς γενέσεως οὔσης, ἀλλ' οὐκ ἔκ τινος ὕλης, οὐδὲ γίγνεσθαι μεταβάλλοντος. | (1) What the followers of Empedocles do, though without observing it themselves, is to reduce the generation of elements out of one another to an illusion. They make it a process of excretion from a body of what was in it all the time—as though generation required a vessel rather than a material—so that it involves no change of anything. |
| Ἔπειτα κἂν οὕτως οὐδὲν ἧττον ἄλογα τὰ συμβαίνοντα. Τὸ γὰρ αὐτὸ μέγεθος οὐ δοκεῖ συμπιληθὲν γίνεσθαι βαρύτερον. Ἀνάγκη δὲ τοῦτο λέγειν τοῖς φάσκουσιν ἐκκρίνεσθαι τὸ ὕδωρ ἐκ τοῦ ἀέρος ἐνυπάρχον ὅταν γὰρ ὕδωρ ἐξ ἀέρος γένηται, βαρύτερόν ἐστιν. | And even if this were accepted, there are other implications equally unsatisfactory. We do not expect a mass of matter to be made heavier by compression. But they will be bound to maintain this, if they say that water is a body present in air and excreted from air, since air becomes heavier when it turns into water. |
| Ἔτι δὲ τῶν μεμιγμένων σωμάτων οὐκ ἀνάγκη χωρισθὲν θάτερον ἀεὶ πλείω τόπον ἐπέχειν ὅταν δ' ἐξ ὕδατος ἀὴρ γένηται, πλείω καταλαμβάνει τόπον τὸ γὰρ λεπτομερέστερον ἐν πλείονι τόπῳ γίγνεται. Φανερὸν δὲ τοῦτό γε καὶ ἐν τῇ μεταβάσει διατμιζομένου γὰρ καὶ πνευματουμένου τοῦ ὑγροῦ ῥήγνυται τὰ περιέχοντα τοὺς ὄγκους ἀγγεῖα διὰ τὴν στενοχωρίαν. Ὥστ' εἰ μὲν ὅλως μή ἐστι κενὸν μηδ' ἐπεκτείνεται τὰ σώματα, καθάπερ φασὶν οἱ ταῦτα λέγοντες, φανερὸν τὸ ἀδύνατον εἰ δ' ἔστι κενὸν καὶ ἐπέκτασις, ἄλογον τὸ ἐξ ἀνάγκης ἀεὶ πλείω τόπον ἐπιλαμβάνειν τὸ χωριζόμενον. | Again, when the mixed body is divided, they can show no reason why one of the constituents must by itself take up more room than the body did: but when water turns into air, the room occupied is increased. The fact is that the finer body takes up more room, as is obvious in any case of transformation. As the liquid is converted into vapour or air the vessel which contains it is often burst because it does not contain room enough. Now, if there is no void at all, and if, as those who take this view say, there is no expansion of bodies, the impossibility of this is manifest: and if there is void and expansion, there is no accounting for the fact that the body which results from division cfpies of necessity a greater space. |
| Ἀνάγκη δὲ καὶ ὑπολείπειν τὴν ἐξ ἀλλήλων γένεσιν, εἴπερ ἐν τῷ πεπερασμένῳ μεγέθει μὴ ἐνυπάρχει ἄπειρα πεπερασμένα. Ὅταν γὰρ ἐκ γῆς ὕδωρ γένηται, ἀφῄρηταί τι τῆς γῆς, εἴπερ ἐκκρίσει ἡ γένεσις καὶ πάλιν ὅταν ἐκ τῆς ὑπολειπομένης, ὡσαύτως. Εἰ μὲν οὖν ἀεὶ τοῦτ' ἔσται, συμβήσεται ἐν τῷ πεπερασμένῳ ἄπειρα ἐνυπάρχειν ἐπεὶ δὲ τοῦτ' ἀδύνατον, οὐκ ἂν ἀεὶ γίγνοιτο ἐξ ἀλλήλων. Ὅτι μὲν οὖν οὐκ ἔστι τῇ ἐκκρίσει ἡ εἰς ἄλληλα μετάβασις, εἴρηται. | It is inevitable, too, that generation of one out of another should come to a stop, since a finite quantum cannot contain an infinity of finite quanta. When earth produces water something is taken away from the earth, for the process is one of excretion. The same thing happens again when the residue produces water. But this can only go on for ever, if the finite body contains an infinity, which is impossible. Therefore the generation of elements out of one another will not always continue. We have now explained that the mutual transformations of the elements cannot take place by means of excretion. |
| Λείπεται δ' εἰς ἄλληλα μεταβάλλοντα γίγνεσθαι. Τοῦτο δὲ διχῶς ἢ γὰρ τῇ μετασχηματίσει, καθάπερ ἐκ τοῦ αὐτοῦ κηροῦ γίγνοιτ' ἂν σφαῖρα καὶ κύβος, ἢ τῇ διαλύσει τῇ εἰς τὰ ἐπίπεδα, ὥσπερ ἔνιοί φασιν. | (2) The remaining alternative is that they should be generated by changing into one another. And this in one of two ways, either by change of shape, as the same wax takes the shape both of a sphere and of a cube, or, as some assert, by resolution into planes. |
| Εἰ μὲν οὖν τῇ μετασχηματίσει γίνεται, συμβαίνει ἐξ ἀνάγκης ἄτομα λέγειν τὰ σώματα διαιρετῶν γὰρ ὄντων οὐκ ἔσται τὸ τοῦ πυρὸς μέρος πῦρ, οὐδὲ τὸ τῆς γῆς γῆ, διὰ τὸ μὴ εἶναι μήτε τὸ τῆς πυραμίδος μέρος πάντως πυραμίδα μήτε τὸ τοῦ κύβου (306a.) κύβον. | (a) Generation by change of shape would necessarily involve the assertion of atomic bodies. For if the particles were divisible there would be a part of fire which was not fire and a part of earth which was not earth, for the reason that not every part of a pyramid is a pyramid nor of a cube a cube. |
| Εἰ δὲ τῇ τῶν ἐπιπέδων διαλύσει, πρῶτον μὲν ἄτοπον τὸ μὴ πάντα γεννᾶν ἐξ ἀλλήλων, ὅπερ ἀνάγκη λέγειν αὐτοῖς, καὶ λέγουσιν. Οὔτε γὰρ εὔλογον ἓν μόνον ἄμοιρον γενέσθαι τῆς μεταβάσεως, οὔτε φαίνεται κατὰ τὴν αἴσθησιν, ἀλλ' ὁμοίως πάντα μεταβάλλειν εἰς ἄλληλα. Συμβαίνει δὲ περὶ τῶν φαινομένων λέγουσι μὴ ὁμολογούμενα λέγειν τοῖς φαινομένοις. Τούτου δ' αἴτιον τὸ μὴ καλῶς λαβεῖν τὰς πρώτας ἀρχάς, ἀλλὰ πάντα βούλεσθαι πρός τινας δόξας ὡρισμένας ἀνάγειν. Δεῖ γὰρ ἴσως τῶν μὲν αἰσθητῶν αἰσθητάς, τῶν δὲ ἀϊδίων ἀϊδίους, τῶν δὲ φθαρτῶν φθαρτὰς εἶναι τὰς ἀρχάς, ὅλως δ' ὁμογενεῖς τοῖς ὑποκειμένοις. Οἱ δὲ διὰ τὴν τούτων φιλίαν ταὐτὸ ποιεῖν ἐοίκασι τοῖς τὰς θέσεις ἐν τοῖς λόγοις διαφυλάττουσιν ἅπαν γὰρ ὑπομένουσι τὸ συμβαῖνον ὡς ἀληθεῖς ἔχοντες ἀρχάς, ὥσπερ οὐκ ἐνίας δέον κρίνειν ἐκ τῶν ἀποβαινόντων, καὶ μάλιστα ἐκ τοῦ τέλους. | But if (b) the process is resolution into planes, the first difficulty is that the elements cannot all be generated out of one another. This they are obliged to assert, and do assert. It is absurd, because it is unreasonable that one element alone should have no part in the transformations, and also contrary to the observed data of sense, according to which all alike change into one another. In fact their explanation of the observations is not consistent with the observations. And the reason is that their ultimate principles are wrongly assumed: they had certain predetermined views, and were resolved to bring everything into line with them. It seems that perceptible things require perceptible principles, eternal things eternal principles, corruptible things corruptible principles; and, in general, every subject matter principles homogeneous with itself. But they, owing to their love for their principles, fall into the attitude of men who undertake the defence of a position in argument. In the confidence that the principles are true they are ready to accept any consequence of their application. As though some principles did not require to be judged from their results, and particularly from their final issue! |
| Τέλος δὲ τῆς μὲν ποιητικῆς ἐπιστήμης τὸ ἔργον, τῆς δὲ φυσικῆς τὸ φαινόμενον ἀεὶ κυρίως κατὰ τὴν αἴσθησιν. Συμβαίνει δ' αὐτοῖς μάλιστα τὴν γῆν εἶναι στοιχεῖον, καὶ μόνην ἄφθαρτον, εἴπερ τὸ ἀδιάλυτον ἄφθαρτόν τ' ἐστὶ καὶ στοιχεῖον ἡ γὰρ γῆ μόνη ἀδιάλυτος εἰς ἄλλο σῶμα. | And that issue, which in the case of productive knowledge is the product, in the knowledge of nature is the unimpeachable evidence of the senses as to each fact. The result of their view is that earth has the best right to the name element, and is alone indestructible; for that which is indissoluble is indestructible and elementary, and earth alone cannot be dissolved into any body but itself. |
| Ἀλλὰ μὴν οὐδ' ἐν τοῖς διαλυομένοις ἡ τῶν τριγώνων παραιώρησις εὔλογος. Συμβαίνει δὲ καὶ τοῦτο ἐν τῇ εἰς ἄλληλα μεταβάσει διὰ τὸ ἐξ ἀνίσων τῷ πλήθει συνεστάναι τριγώνων. | Again, in the case of those elements which do suffer dissolution, the 'suspension' of the triangles is unsatisfactory. But this takes place whenever one is dissolved into another, because of the numerical inequality of the triangles which compose them. |
| Ἔτι δ' ἀνάγκη τοῖς ταῦτα λέγουσιν οὐκ ἐκ σώματος ποιεῖν γένεσιν ὅταν γὰρ ἐξ ἐπιπέδων γένηται, οὐκ ἐκ σώματος ἔσται γεγονός. | Further, those who hold these views must needs suppose that generation does not start from a body. For what is generated out of planes cannot be said to have been generated from a body. |
| Πρὸς δὲ τούτοις ἀνάγκη μὴ πᾶν σῶμα λέγειν διαιρετόν, ἀλλὰ μάχεσθαι ταῖς ἀκριβεστάταις ἐπιστήμαις αἱ μὲν γὰρ καὶ τὸ νοητὸν λαμβάνουσι διαιρετόν, αἱ μαθηματικαί, οἱ δὲ οὐδὲ τὸ αἰσθητὸν ἅπαν συγχωροῦσι διὰ τὸ βούλεσθαι σῴζειν τὴν ὑπόθεσιν. Ἀνάγκη γὰρ ὅσοι σχῆμα ποιοῦσιν ἑκάστου τῶν στοιχείων καὶ τούτῳ διορίζουσι τὰς οὐσίας αὐτῶν, ἀδιαίρετα ποιεῖν αὐτά τῆς γὰρ πυραμίδος ἢ τῆς σφαίρας διαιρεθείσης πως οὐκ ἔσται τὸ λειπόμενον σφαῖρα ἢ πυραμίς. | And they must also assert that not all bodies are divisible, coming thus into conflict with our most accurate sciences, namely the mathematical, which assume that even the intelligible is divisible, while they, in their anxiety to save their hypothesis, cannot even admit this of every perceptible thing. For any one who gives each element a shape of its own, and makes this the ground of distinction between the substances, has to attribute to them indivisibility; since division of a pyramid or a sphere must leave somewhere at least a residue which is not sphere or a pyramid. |
| Ὥστε ἢ τὸ τοῦ πυρὸς μέρος οὐ πῦρ, ἀλλ' ἔσται τι πρότερον τοῦ (306b.) στοιχείου, διὰ τὸ πᾶν εἶναι ἢ στοιχεῖον ἢ ἐκστοιχείων ἢ οὐχ ἅπαν σῶμα διαιρετόν. | Either, then, a part of fire is not fire, so that there is a body prior to the element—for every body is either an element or composed of elements—or not every body is divisible. |
| 8 | 8 |
| Ὅλως δὲ τὸ πειρᾶσθαι τὰ ἁπλᾶ σώματα σχηματίζειν ἄλογόν ἐστι, πρῶτον μὲν ὅτι συμβήσεται μὴ ἀναπληροῦσθαι τὸ ὅλον ἐν μὲν γὰρ τοῖς ἐπιπέδοις τρία σχήματα δοκεῖ συμπληροῦν τὸν τόπον, τρίγωνον καὶ τετράγωνον καὶ ἑξάγωνον, ἐν δὲ τοῖς στερεοῖς δύο μόνον, πυραμὶς καὶ κύβος ἀνάγκη δὲ πλείω τούτων λαμβάνειν διὰ τὸ πλείω τὰ στοιχεῖα ποιεῖν. | In general, the attempt to give a shape to each of the simple bodies is unsound, for the reason, first, that they will not succeed in filling the whole. It is agreed that there are only three plane figures which can fill a space, the triangle, the square, and the hexagon, and only two solids, the pyramid and the cube. But the theory needs more than these because the elements which it recognizes are more in number. |
| Ἔπειτα φαίνεται πάντα μὲν τὰ ἁπλᾶ σώματα σχηματιζόμενα τῷ περιέχοντι τόπῳ, μάλιστα δὲ τὸ ὕδωρ καὶ ὁ ἀήρ. Διαμένειν μὲν οὖν τὸ τοῦ στοιχείου σχῆμα ἀδύνατον οὐ γὰρ ἂν ἥπτετο πανταχῇ τοῦ περιέχοντος τὸ ὅλον. Ἀλλὰ μὴν εἰ μεταρρυθμισθήσεται, οὐκέτι ἔσται ὕδωρ, εἴπερ τῷ σχήματι διέφερεν. Ὥστε φανερὸν ὅτι οὐκ ἔστιν ὡρισμένα τὰ σχήματα αὐτῶν. | Secondly, it is manifest that the simple bodies are often given a shape by the place in which they are included, particularly water and air. In such a case the shape of the element cannot persist; for, if it did, the contained mass would not be in continuous contact with the containing body; while, if its shape is changed, it will cease to be water, since the distinctive quality is shape. Clearly, then, their shapes are not fixed. |
| Ἀλλ' ἔοικεν ἡ φύσις αὐτὴ τοῦτο σημαίνειν ἡμῖν, ὃ καὶ κατὰ λόγον ἐστίν ὥσπερ γὰρ ἐν τοῖς ἄλλοις ἀειδὲς καὶ ἄμορφον δεῖ τὸ ὑποκείμενον εἶναι (μάλιστα γὰρ ἂν οὕτω δύναιτο ῥυθμίζεσθαι, καθάπερ ἐν τῷ Τιμαίῳ γέγραπται, τὸ πανδεχές), οὕτω καὶ τὰ στοιχεῖα δεῖ νομίζειν ὥσπερ ὕλην εἶναι τοῖς συνθέτοις διὸ καὶ δύναται μεταβάλλειν εἰς ἄλληλα χωριζομένων τῶν κατὰ τὰ πάθη διαφορῶν. | Indeed, nature itself seems to offer corroboration of this theoretical conclusion. Just as in other cases the substratum must be formless and unshapen—for thus the 'all-receptive', as we read in the Timaeus, will be best for modelling—so the elements should be conceived as a material for composite things; and that is why they can put off their qualitative distinctions and pass into one another. |
| Πρὸς δὲ τούτοις πῶς ἐνδέχεται γίγνεσθαι σάρκα καὶ ὀστοῦν ἢ ὁτιοῦν τῶν συνεχῶν σωμάτων; οὔτε γὰρ ἐξ αὐτῶν τῶν στοιχείων ἐγχωρεῖ διὰ τὸ μὴ γίγνεσθαι συνεχὲς ἐκ τῆς συνθέσεως, οὔτ' ἐκ τῶν ἐπιπέδων συντιθεμένων τὰ γὰρ στοιχεῖα γεννᾶται τῇ συνθέσει καὶ οὐ τὰ ἐκ τῶν στοιχείων. Ὥστ' ἐάν τις ἀκριβολογεῖσθαι βούληται καὶ μὴ ἐκ παρόδου τοὺς λόγους ἀποδέχεσθαι τοὺς τοιούτους, ἀναιροῦντας ὄψεται τὴν γένεσιν ἐκ τῶν ὄντων. | Further, how can they account for the generation of flesh and bone or any other continuous body? The elements alone cannot produce them because their collocation cannot produce a continuum. Nor can the composition of planes; for this produces the elements themselves, not bodies made up of them. Any one then who insists upon an exact statement of this kind of theory, instead of assenting after a passing glance at it, will see that it removes generation from the world. |
| Ἀλλὰ μὴν καὶ πρὸς τὰ πάθη τε καὶ τὰς δυνάμεις καὶ τὰς κινήσεις ἀσύμφωνα τὰ σχήματα τοῖς σώμασιν, εἰς ἃ μάλιστα βλέψαντες οὕτω διένειμαν. Οἷον ἐπεὶ τὸ πῦρ εὐκίνητόν ἐστι καὶ θερμαντικὸν καὶ καυστικόν, οἱ μὲν ἐποίησαν αὐτὸ σφαῖραν, οἱ δὲ πυραμίδα ταῦτα γὰρ εὐκινητότατα μὲν διὰ τὸ ἐλαχίστων ἅπτεσθαι καὶ ἥκι(307a.) στα βεβηκέναι, θερμαντικώτατα δὲ καὶ καυστικώτατα, διότι τὸ μὲν ὅλον ἐστὶ γωνία, τὸ δὲ ὀξυγωνιώτατον, καίει δὲ καὶ θερμαίνει ταῖς γωνίαις, ὥς φασιν. | Further, the very properties, powers, and motions, to which they paid particular attention in allotting shapes, show the shapes not to be in accord with the bodies. Because fire is mobile and productive of heat and combustion, some made it a sphere, others a pyramid. These shapes, they thought, were the most mobile because they offer the fewest points of contact and are the least stable of any; they were also the most apt to produce warmth and combustion, because the one is angular throughout while the other has the most acute angles, and the angles, they say, produce warmth and combustion. |
| Πρῶτον μὲν οὖν κατὰ τὴν κίνησιν ἀμφότεροι διημαρτήκασιν εἰ γὰρ καὶ ἔστιν εὐκινητότατα ταῦτα τῶν σχημάτων, ἀλλ' οὐ τὴν τοῦ πυρὸς κίνησιν εὐκίνητα ἡ μὲν γὰρ τοῦ πυρὸς ἄνω καὶ κατ' εὐθεῖαν, ταῦτα δ' εὐκίνητα κύκλῳ, τὴν καλουμένην κύλισιν. Ἔπειτ' εἰ ἔστιν ἡ γῆ κύβος διὰ τὸ βεβηκέναι καὶ μένειν, μένει δ' οὐχ οὗ ἔτυχεν ἀλλ' ἐν τῷ αὑτῆς τόπῳ, ἐκ δὲ τοῦ ἀλλοτρίου φέρεται μὴ κωλυομένη, καὶ τὸ πῦρ δὲ καὶ τὰ ἄλλα ὡσαύτως, δῆλον ὅτι καὶ τὸ πῦρ καὶ ἕκαστον τῶν στοιχείων ἐν μὲν τῷ ἀλλοτρίῳ τόπῳ σφαῖρα ἔσται ἢ πυραμίς, ἐν δὲ τῷ οἰκείῳ κύβος. | Now, in the first place, with regard to movement both are in error. These may be the figures best adapted to movement; they are not, however, well adapted to the movement of fire, which is an upward and rectilinear movement, but rather to that form of circular movement which we call rolling. Earth, again, they call a cube because it is stable and at rest. But it rests only in its own place, not anywhere; from any other it moves if nothing hinders, and fire and the other bodies do the same. The obvious inference, therefore, is that fire and each several element is in a foreign place a sphere or a pyramid, but in its own a cube. |
| Ἔτι δ' εἰ θερμαίνει καὶ καίει τὸ πῦρ διὰ τὰς γωνίας, ἅπαντα ἔσται τὰ στοιχεῖα θερμαντικά, μᾶλλον δ' ἴσως ἕτερον ἑτέρου πάντα γὰρ ἔχει γωνίας, οἷον τό τε ὀκτάεδρον καὶ τὸ δωδεκάεδρον. (Δημοκρίτῳ δὲ καὶ ἡ σφαῖρα, ὡς γωνία τις οὖσα, τέμνει ὡς εὐκίνητον). | Again, if the possession of angles makes a body produce heat and combustion, every element produces heat, though one may do so more than another. For they all possess angles, the octahedron and dodecahedron as well as the pyramid; and Democritus makes even the sphere a kind of angle, which cuts things because of its mobility. |
| Ὥστε διοίσει τῷ μᾶλλον καὶ ἧττον. Τοῦτο δ' ὅτι ψεῦδος, φανερόν. Ἅμα δὲ συμβήσεται καὶ τὰ μαθηματικὰ σώματα καίειν καὶ θερμαίνειν ἔχει γὰρ κἀκεῖνα γωνίας, καὶ ἔνεισιν ἐν αὐτοῖς ἄτομοι καὶ σφαῖραι καὶ πυραμίδες, ἄλλως τε καὶ εἰ ἔστιν ἄτομα μεγέθη, καθάπερ φασίν. Εἰ γὰρ τὰ μὲν τὰ δὲ μή, λεκτέον τὴν διαφοράν, ἀλλ' οὐχ ἁπλῶς οὕτω λεκτέον ὡς λέγουσιν. | The difference, then, will be one of degree: and this is plainly false. They must also accept the inference that the mathematical produce heat and combustion, since they too possess angles and contain atomic spheres and pyramids, especially if there are, as they allege, atomic figures. Anyhow if these functions belong to some of these things and not to others, they should explain the difference, instead of speaking in quite general terms as they do. |
| Ἔτι εἰ τὸ καιόμενον πυροῦται, τὸ δὲ πῦρ ἐστι σφαῖρα ἢ πυραμίς, ἀνάγκη τὸ καιόμενον γίγνεσθαι σφαίρας ἢ πυραμίδας. Τὸ μὲν οὖν τέμνειν καὶ διαιρεῖν ἔστω κατὰ λόγον συμβαῖνον τῷ σχήματι τὸ δ' ἐξ ἀνάγκης τὴν πυραμίδα ποιεῖν πυραμίδας ἢ τὴν σφαῖραν σφαίρας παντελῶς ἄλογον, καὶ ὅμοιον ὥσπερ εἴ τις ἀξιοίη τὴν μάχαιραν εἰς μαχαίρας διαιρεῖν ἢ τὸν πρίονα εἰς πρίονας. | Again, combustion of a body produces fire, and fire is a sphere or a pyramid. The body, then, is turned into spheres or pyramids. Let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does; still it remains quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. One might as well postulate that a knife or a saw divides things into knives or saws. |
| Ἔτι δὲ γελοῖον πρὸς τὸ διαιρεῖν μόνον ἀποδοῦναι τὸ σχῆμα τῷ πυρί δοκεῖ γὰρ μᾶλλον συγκρίνειν καὶ συνορίζειν ἢ διακρίνειν. Διακρίνει μὲν γὰρ τὰ μὴ (307b.) ὁμόφυλα, συγκρίνει δὲ τὰ ὁμόφυλα καὶ ἡ μὲν σύγκρισις καθ' αὑτό ἐστι (τὸ γὰρ συνορίζειν καὶ ἑνοῦν τοῦ πυρός), ἡ δὲ διάκρισις κατὰ συμβεβηκός (συγκρῖνον γὰρ τὸ ὁμόφυλον ἐξαιρεῖ τὸ ἀλλότριον). Ὥστ' ἢ πρὸς ἄμφω ἐχρῆν ἀποδοῦναι ἢ μᾶλλον ἐπὶ τὸ συγκρίνειν. | It is also ridiculous to think only of division when allotting fire its shape. Fire is generally thought of as combining and connecting rather than as separating. For though it separates bodies different in kind, it combines those which are the same; and the combining is essential to it, the functions of connecting and uniting being a mark of fire, while the separating is incidental. For the expulsion of the foreign body is an incident in the compacting of the homogeneous. In choosing the shape, then, they should have thought either of both functions or preferably of the combining function. |
| Πρὸς δὲ τούτοις, ἐπεὶ τὸ θερμὸν καὶ τὸ ψυχρὸν ἐναντία τῇ δυνάμει, ἀδύνατον ἀποδοῦναι τῷ ψυχρῷ σχῆμά τι δεῖ γὰρ ἐναντίον εἶναι τὸ ἀποδιδόμενον, οὐθὲν δ' ἐναντίον ἐστὶ σχῆμα σχήματι. Διὸ καὶ πάντες ἀπολελοίπασι τοῦτο καίτοι προσῆκεν ἢ πάντα ἀφορίσαι σχήμασιν ἢ μηδέν. Ἔνιοι δὲ περὶ τῆς δυνάμεως αὐτοῦ πειραθέντες εἰπεῖν ἐναντία λέγουσιν αὐτοὶ αὑτοῖς. | In addition, since hot and cold are contrary powers, it is impossible to allot any shape to the cold. For the shape given must be the contrary of that given to the hot, but there is no contrariety between figures. That is why they have all left the cold out, though properly either all or none should have their distinguishing figures. Some of them, however, do attempt to explain this power, and they contradict themselves. A body of large particles, they say, is cold because instead of penetrating through the passages it crushes. |
| Φασὶ γὰρ εἶναι ψυχρὸν τὸ μεγαλομερὲς διὰ τὸ συνθλίβειν καὶ μὴ διιέναι διὰ τῶν πόρων. Δῆλον τοίνυν ὅτι καὶ τὸ θερμὸν ἂν εἴη τὸ διιόν τοιοῦτον δ' ἀεὶ τὸ λεπτομερές. Ὥστε συμβαίνει μικρότητι καὶ μεγέθει διαφέρειν τὸ θερμὸν καὶ τὸ ψυχρόν, ἀλλ' οὐ τοῖς σχήμασιν. Ἔτι δ' εἰ ἄνισοι αἱ πυραμίδες, αἱ μεγάλαι ἂν εἶεν οὐ πῦρ οὐδ' αἴτιον τὸ σχῆμα τοῦ καίειν, ἀλλὰ τοὐναντίον. | Clearly, then, that which is hot is that which penetrates these passages, or in other words that which has fine particles. It results that hot and cold are distinguished not by the figure but by the size of the particles. Again, if the pyramids are unequal in size, the large ones will not be fire, and that figure will produce not combustion but its contrary. |
| Ὅτι μὲν οὖν οὐ τοῖς σχήμασι διαφέρει τὰ στοιχεῖα, φανερὸν ἐκ τῶν εἰρημένων ἐπεὶ δὲ κυριώταται διαφοραὶ τῶν σωμάτων αἵ τε κατὰ τὰ πάθη καὶ τὰ ἔργα καὶ τὰς δυνάμεις (ἑκάστου γὰρ εἶναί φαμεν τῶν φύσει καὶ ἔργα καὶ πάθη καὶ δυνάμεις), πρῶτον ἂν εἴη περὶ τούτων λεκτέον, ὅπως θεωρήσαντες ταῦτα λάβωμεν τὰς ἑκάστου πρὸς ἕκαστον διαφοράς. | From what has been said it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function, and power; for every natural body has, we maintain, its own functions, properties, and powers. Our first business, then, will be to speak of these, and that inquiry will enable us to explain the differences of each from each. |
Δ |
BOOK 4 |
| 1 | 1 |
| Περὶ δὲ βαρέος καὶ κούφου, τί τ' ἐστὶν ἑκάτερον καὶ τίς ἡ φύσις αὐτῶν, σκεπτέον, καὶ διὰ τίν' αἰτίαν ἔχουσι τὰς δυνάμεις ταύτας. Ἔστι γὰρ ἡ περὶ αὐτῶν θεωρία τοῖς περὶ κινήσεως λόγοις οἰκεία βαρὺ γὰρ καὶ κοῦφον τῷ δύνασθαι κινεῖσθαι φυσικῶς πως λέγομεν. (Ταῖς δὲ ἐνεργείαις ὀνόματ' αὐτῶν οὐ κεῖται, πλὴν εἴ τις οἴοιτο τὴν ῥοπὴν εἶναι τοιοῦτον.) (308a.) Διὰ δὲ τὸ τὴν φυσικὴν μὲν εἶναι πραγματείαν περὶ κίνησιν, ταῦτα δ' ἔχειν ἐν ἑαυτοῖς οἷον ζώπυρ' ἄττα κινήσεως, πάντες μὲν χρῶνται ταῖς δυνάμεσιν αὐτῶν, οὐ μὴν διωρίκασί γε, πλὴν ὀλίγων. | WE have now to consider the terms 'heavy' and 'light'. We must ask what the bodies so called are, how they are constituted, and what is the reason of their possessing these powers. The consideration of these questions is a proper part of the theory of movement, since we call things heavy and light because they have the power of being moved naturally in a certain way. The activities corresponding to these powers have not been given any name, unless it is thought that 'impetus' is such a name. But because the inquiry into nature is concerned with movement, and these things have in themselves some spark (as it were) of movement, all inquirers avail themselves of these powers, though in all but a few cases without exact discrimination. |
| Ἰδόντες οὖν πρῶτον τὰ παρὰ τῶν ἄλλων εἰρημένα, καὶ διαπορήσαντες ὅσα πρὸς τὴν σκέψιν ταύτην διελεῖν ἀναγκαῖον, οὕτω καὶ τὸ φαινόμενον ἡμῖν εἴπωμεν περὶ αὐτῶν. | We must then first look at whatever others have said, and formulate the questions which require settlement in the interests of this inquiry, before we go on to state our own view of the matter. |
| Λέγεται δὴ τὸ μὲν ἁπλῶς βαρὺ καὶ κοῦφον, τὸ δὲ πρὸς ἕτερον τῶν γὰρ ἐχόντων βάρος φαμὲν τὸ μὲν εἶναι κουφότερον, τὸ δὲ βαρύτερον, οἷον ξύλου χαλκόν. Περὶ μὲν οὖν τῶν ἁπλῶς λεγομένων οὐδὲν εἴρηται παρὰ τῶν πρότερον, περὶ δὲ τῶν πρὸς ἕτερον οὐ γὰρ λέγουσι τί ἐστι τὸ βαρὺ καὶ τί τὸ κοῦφον, ἀλλὰ τί τὸ βαρύτερον καὶ κουφότερον ἐν τοῖς ἔχουσι βάρος. Μᾶλλον δ' ἔσται δῆλον ὃ λέγομεν ὧδε. Τὰ μὲν γὰρ ἀεὶ πέφυκεν ἀπὸ τοῦ μέσου φέρεσθαι, τὰ δ' ἀεὶ πρὸς τὸ μέσον. Τούτων δὲ τὸ μὲν ἀπὸ τοῦ μέσου φερόμενον ἄνω λέγω φέρεσθαι, κάτω δὲ τὸ πρὸς τὸ μέσον. | Language recognizes (a) an absolute, (b) a relative heavy and light. Of two heavy things, such as wood and bronze, we say that the one is relatively light, the other relatively heavy. Our predecessors have not dealt at all with the absolute use, of the terms, but only with the relative. I mean, they do not explain what the heavy is or what the light is, but only the relative heaviness and lightness of things possessing weight. This can be made clearer as follows. There are things whose constant nature it is to move away from the centre, while others move constantly towards the centre; and of these movements that which is away from the centre I call upward movement and that which is towards it I call downward movement. |
| Ἄτοπον γὰρ τὸ μὴ νομίζειν εἶναί τι ἐν τῷ οὐρανῷ τὸ μὲν ἄνω τὸ δὲ κάτω, καθάπερ τινὲς ἀξιοῦσιν οὐ γὰρ εἶναι τὸ μὲν ἄνω τὸ δὲ κάτω φασίν, εἴπερ πάντῃ ὅμοιός ἐστι, καὶ πανταχόθεν ἀντίπους ἔσται πορευόμενος ἕκαστος αὐτὸς αὑτῷ. Ἡμεῖς δὲ τὸ τοῦ παντὸς ἔσχατον ἄνω λέγομεν, ὃ καὶ κατὰ τὴν θέσιν ἐστὶν ἄνω καὶ τῇ φύσει πρῶτον ἐπεὶ δ' ἐστί τι τοῦ οὐρανοῦ ἔσχατον καὶ μέσον, δῆλον ὅτι ἔσται καὶ ἄνω καὶ κάτω, ὥσπερ καὶ οἱ πολλοὶ λέγουσι, πλὴν οὐχ ἱκανῶς. | (The view, urged by some, that there is no up and no down in the heaven, is absurd. There can be, they say, no up and no down, since the universe is similar every way, and from any point on the earth's surface a man by advancing far enough will come to stand foot to foot with himself. But the extremity of the whole, which we call 'above', is in position above and in nature primary. And since the universe has an extremity and a centre, it must clearly have an up and down. Common usage is thus correct, though inadequate. |
| Τούτου δ' αἴτιον ὅτι νομίζουσιν οὐχ ὅμοιον εἶναι πάντῃ τὸν οὐρανόν, ἀλλ' ἓν εἶναι μόνον τὸ ὑπὲρ ἡμᾶς ἡμισφαίριον, ἐπεὶ προσυπολαβόντες καὶ κύκλῳ τοιοῦτον, καὶ τὸ μέσον ὁμοίως ἔχειν πρὸς ἅπαν, τὸ μὲν ἄνω φήσουσιν εἶναι, τὸ δὲ μέσον κάτω. | And the reason of its inadequacy is that men think that the universe is not similar every way. They recognize only the hemisphere which is over us. But if they went on to think of the world as formed on this pattern all round, with a centre identically related to each point on the extremity, they would have to admit that the extremity was above and the centre below.) |
| Ἁπλῶς μὲν οὖν κοῦφον λέγομεν τὸ ἄνω φερόμενον καὶ πρὸς τὸ ἔσχατον, βαρὺ δὲ ἁπλῶς τὸ κάτω καὶ πρὸς τὸ μέσον πρὸς ἄλλο δὲ κοῦφον καὶ κουφότερον, ὅτε, δυοῖν ἐχόντων βάρος καὶ τὸν ὄγκον ἴσον, κάτω φέρεται θάτερον φύσει θᾶττον. | By absolutely light, then, we mean that which moves upward or to the extremity, and by absolutely heavy that which moves downward or to the centre. By lighter or relatively light we mean that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its natural downward movement. |
| 2 | 2 |
| Τῶν δὴ πρότερον ἐλθόντων ἐπὶ τὴν περὶ τούτων σκέψιν σχεδὸν οἱ πλεῖστοι περὶ τῶν οὕτω βαρέων καὶ κούφων εἰρήκασι μόνον, ὅσων ἀμφοτέρων ἐχόντων βάρος θάτερόν ἐστι (308b.) κουφότερον οὕτω δὲ διελθόντες οἴονται διωρίσθαι καὶ περὶ τοῦ ἁπλῶς κούφου καὶ βαρέος ὁ δὲ λόγος αὐτοῖς οὐκ ἐφαρμόττει. Δῆλον δ' ἔσται τοῦτο μᾶλλον προελθοῦσιν. | Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter. And this treatment they consider a sufficient analysis also of the notions of absolute heaviness, to which their account does not apply. This, however, will become clearer as we advance. |
| Λέγουσι γὰρ τὸ κουφότερον καὶ βαρύτερον οἱ μὲν ὥσπερ ἐν τῷ Τιμαίῳ τυγχάνει γεγραμμένον, βαρύτερον μὲν τὸ ἐκ πλειόνων τῶν αὐτῶν συνεστός, κουφότερον δὲ τὸ ἐξ ἐλαττόνων, ὥσπερ μολίβδου μόλιβδος ὁ πλείων βαρύτερος καὶ χαλκοῦ χαλκός. Ὁμοίως δὲ καὶ τῶν ἄλλων τῶν ὁμοειδῶν ἕκαστον ἐν ὑπεροχῇ γὰρ τῶν ἴσων μορίων βαρύτερον ἕκαστόν ἐστιν. Τὸν αὐτὸν δὲ τρόπον καὶ ξύλου μόλιβδόν φασιν ἔκ τινων γὰρ τῶν αὐτῶν εἶναι πάντα τὰ σώματα καὶ μιᾶς ὕλης, ἀλλ' οὐ δοκεῖν. | One use of the terms 'lighter' and 'heavier' is that which is set forth in writing in the Timaeus, that the body which is composed of the greater number of identical parts is relatively heavy, while that which is composed of a smaller number is relatively light. As a larger quantity of lead or of bronze is heavier than a smaller—and this holds good of all homogeneous masses, the superior weight always depending upon a numerical superiority of equal parts—in precisely the same way, they assert, lead is heavier than wood. For all bodies, in spite of the general opinion to the contrary, are composed of identical parts and of a single material. |
| Οὕτω δὴ διωρισμένων οὐκ εἴρηται περὶ τοῦ ἁπλῶς κούφου καὶ βαρέος νῦν γὰρ τὸ μὲν πῦρ ἀεὶ κοῦφον καὶ ἄνω φέρεται, ἡ δὲ γῆ καὶ τὰ γεηρὰ πάντα κάτω καὶ πρὸς τὸ μέσον. Ὥστ' οὐ δι' ὀλιγότητα τῶν τριγώνων, ἐξ ὧν συνεστάναι φασὶν ἕκαστον αὐτῶν, τὸ πῦρ ἄνω φέρεσθαι πέφυκεν τό τε γὰρ πλεῖον ἧττον ἂν ἐφέρετο καὶ βαρύτερον ἦν ἐκ πλειόνων ὂν τριγώνων. Νῦν δὲ φαίνεται τοὐναντίον ὅσῳ γὰρ ἂν ᾖ πλεῖον, κουφότερόν ἐστι καὶ ἄνω φέρεται θᾶττον. Καὶ ἄνωθεν δὲ κάτω τὸ ὀλίγον οἰσθήσεται θᾶττον πῦρ, τὸ δὲ πολὺ βραδύτερον. | But this analysis says nothing of the absolutely heavy and light. The facts are that fire is always light and moves upward, while earth and all earthy things move downwards or towards the centre. It cannot then be the fewness of the triangles (of which, in their view, all these bodies are composed) which disposes fire to move upward. If it were, the greater the quantity of fire the slower it would move, owing to the increase of weight due to the increased number of triangles. But the palpable fact, on the contrary, is that the greater the quantity, the lighter the mass is and the quicker its upward movement: and, similarly, in the reverse movement from above downward, the small mass will move quicker and the large slower. |
| Πρὸς δὲ τούτοις, ἐπεὶ τὸ μὲν ἐλάσσω ἔχον τὰ ὁμογενῆ κουφότερον εἶναί φασι, τὸ δὲ πλείω βαρύτερον, ἀέρα δὲ καὶ ὕδωρ καὶ πῦρ ἐκ τῶν αὐτῶν εἶναι τριγώνων, ἀλλὰ διαφέρειν ὀλιγότητι καὶ πλήθει, διὸ τὸ μὲν αὐτῶν εἶναι κουφότερον τὸ δὲ βαρύτερον, ἔσται τι πλῆθος ἀέρος ὃ βαρύτερον ὕδατος ἔσται. Συμβαίνει δὲ πᾶν τοὐναντίον ἀεί τε γὰρ ὁ πλείων ἀὴρ ἄνω φέρεται μᾶλλον, καὶ ὅλως ὁτιοῦν μέρος ἀέρος ἄνω φέρεται ἐκ τοῦ ὕδατος. | Further, since to be lighter is to have fewer of these homogeneous parts and to be heavier is to have more, and air, water, and fire are composed of the same triangles, the only difference being in the number of such parts, which must therefore explain any distinction of relatively light and heavy between these bodies, it follows that there must be a certain quantum of air which is heavier than water. But the facts are directly opposed to this. The larger the quantity of air the more readily it moves upward, and any portion of air without exception will rise up out of the water. |
| Οἱ μὲν οὖν τοῦτον τὸν τρόπον περὶ κούφου καὶ βαρέος διώρισαν τοῖς δ' οὐχ ἱκανὸν ἔδοξεν οὕτω διελεῖν, ἀλλὰ καίπερ ὄντες ἀρχαιότεροι ταῖς ἡλικίαις καινοτέρως ἐνόησαν περὶ τῶν νῦν λεχθέντων. Φαίνεται γὰρ ἔνια τὸν ὄγκον μὲν ἐλάττω τῶν σωμάτων, ὄντα δὲ βαρύτερα. Δῆλον οὖν ὡς οὐχ ἱκανὸν τὸ φάσκειν ἐξ ἴσων συγκεῖσθαι τῶν πρώτων τὰ ἰσοβαρῆ ἴσα γὰρ ἂν ἦν τὸν ὄγκον. Τὰ δὲ πρῶτα καὶ ἄτομα τοῖς μὲν ἐπίπεδα λέγουσιν ἐξ ὧν συνέστηκε τὰ βάρος ἔχοντα (309a.) τῶν σωμάτων, ἄτοπον τὸ φάναι τοῖς δὲ στερεὰ μᾶλλον ἐνδέχεται λέγειν τὸ μεῖζον εἶναι βαρύτερον αὐτῶν. Τῶν δὲ συνθέτων, ἐπειδήπερ οὐ φαίνεται τοῦτον ἕκαστον ἔχειν τὸν τρόπον, ἀλλὰ πολλὰ βαρύτερα ὁρῶμεν ἐλάττω τὸν ὄγκον ὄντα, καθάπερ ἐρίου χαλκόν, ἕτερον τὸ αἴτιον οἴονταί τε καὶ λέγουσιν ἔνιοι τὸ γὰρ κενὸν ἐμπεριλαμβανόμενον κουφίζειν τὰ σώματά φασι καὶ ποιεῖν ἔστιν ὅτε τὰ μείζω κουφότερα πλεῖον γὰρ ἔχειν κενόν. Διὰ τοῦτο γὰρ καὶ τὸν ὄγκον εἶναι μείζω συγκείμενα πολλάκις ἐξ ἴσων στερεῶν ἢ καὶ ἐλαττόνων. Ὅλως δὲ καὶ παντὸς αἴτιον εἶναι τοῦ κουφοτέρου τὸ πλεῖον ἐνυπάρχειν κενόν. | So much for one view of the distinction between light and heavy. To others the analysis seems insufficient; and their views on the subject, though they belong to an older generation than ours, have an air of novelty. It is apparent that there are bodies which, when smaller in bulk than others, yet exceed them in weight. It is therefore obviously insufficient to say that bodies of equal weight are composed of an equal number of primary parts: for that would give equality of bulk. Those who maintain that the primary or atomic parts, of which bodies endowed with weight are composed, are planes, cannot so speak without absurdity; but those who regard them as solids are in a better position to assert that of such bodies the larger is the heavier. But since in composite bodies the weight obviously does not correspond in this way to the bulk, the lesser bulk being often superior in weight (as, for instance, if one be wool and the other bronze), there are some who think and say that the cause is to be found elsewhere. The void, they say, which is imprisoned in bodies, lightens them and sometimes makes the larger body the lighter. The reason is that there is more void. And this would also account for the fact that a body composed of a number of solid parts equal to, or even smaller than, that of another is sometimes larger in bulk than it. In short, generally and in every case a body is relatively light when it contains a relatively large amount of void. |
| Λέγουσι μὲν οὖν τοῦτον τὸν τρόπον, ἀνάγκη δὲ προσθεῖναι τοῖς οὕτω διορίζουσι μὴ μόνον τὸ κενὸν ἔχειν πλεῖον, ἂν ᾖ κουφότερον, ἀλλὰ καὶ τὸ στερεὸν ἔλαττον εἰ γὰρ ὑπερέξει τῆς τοιαύτης ἀναλογίας, οὐκ ἔσται κουφότερον. Διὰ γὰρ τοῦτο καὶ τὸ πῦρ εἶναί φασι κουφότατον, ὅτι πλεῖστον ἔχει κενόν. Συμβήσεται οὖν μικροῦ πυρὸς πολὺν χρυσὸν πλεῖον ἔχοντα τὸ κενὸν εἶναι κουφότερον, εἰ μὴ καὶ στερεὸν ἕξει πολλαπλάσιον ὥστε τοῦτο λεκτέον. | This is the way they put it themselves, but their account requires an addition. Relative lightness must depend not only on an excess of void, but also an a defect of solid: for if the ratio of solid to void exceeds a certain proportion, the relative lightness will disappear. Thus fire, they say, is the lightest of things just for this reason that it has the most void. But it would follow that a large mass of gold, as containing more void than a small mass of fire, is lighter than it, unless it also contains many times as much solid. The addition is therefore necessary. |
| Ἔνιοι μὲν οὖν τῶν μὴ φασκόντων εἶναι κενὸν οὐδὲν διώρισαν περὶ κούφου καὶ βαρέος, οἷον Ἀναξαγόρας καὶ Ἐμπεδοκλῆς οἱ δὲ διορίσαντες μέν, οὐ φάσκοντες δὲ εἶναι κενόν, οὐδὲν εἶπον διὰ τί τὰ μὲν ἁπλῶς κοῦφα τὰ δὲ βαρέα τῶν σωμάτων, καὶ φέρεται τὰ μὲν ἀεὶ ἄνω τὰ δὲ κάτω, οὐδὲ περὶ τοῦ ἔνια μείζω τὸν ὄγκον ὄντα κουφότερα τῶν ἐλαττόνων εἶναι σωμάτων οὐδὲν ἐπεμνήσθησαν, οὐδὲ δῆλον πῶς ἐκ τῶν εἰρημένων ὁμολογούμενα τοῖς φαινομένοις συμβήσεται λέγειν αὐτοῖς. | Of those who deny the existence of a void some, like Anaxagoras and Empedocles, have not tried to analyse the notions of light and heavy at all; and those who, while still denying the existence of a void, have attempted this, have failed to explain why there are bodies which are absolutely heavy and light, or in other words why some move upward and others downward. The fact, again, that the body of greater bulk is sometimes lighter than smaller bodies is one which they have passed over in silence, and what they have said gives no obvious suggestion for reconciling their views with the observed facts. |
| Ἀναγκαῖον δὲ καὶ τοῖς περὶ τῆς τοῦ πυρὸς κουφότητος αἰτιωμένοις τὸ πολὺ κενὸν ἔχειν σχεδὸν ἐν ταῖς αὐταῖς ἐνέχεσθαι δυσχερείαις. Ἔλαττον μὲν γὰρ ἕξει στερεὸν τῶν ἄλλων σωμάτων, καὶ τὸ κενὸν πλεῖον ἀλλ' ὅμως ἔσται τι πυρὸς πλῆθος ἐν ᾧ τὸ στερεὸν καὶ τὸ πλῆρες ὑπερβάλλει τῶν περιεχομένων στερεῶν ἔν τινι μικρῷ πλήθει γῆς. Ἐὰν δὲ φῶσι καὶ τὸ κενόν, πῶς διοριοῦσι τὸ ἁπλῶς βαρύ; Ἢ γὰρ τῷ πλεῖον στερεὸν ἔχειν ἢ τῷ ἔλαττον κενόν. Εἰ μὲν οὖν τοῦτο (309b.) φήσουσιν, ἔσται τι πλῆθος γῆς οὕτως ὀλίγον ἐν ᾧ στερεὸν ἔσται ἔλαττον ἢ ἐν πολλῷ πλήθει πυρός. Ὁμοίως δὲ κἂν τῷ κενῷ διορίσωσιν, ἔσται τι κουφότερον τοῦ ἁπλῶς κούφου καὶ φερομένου ἀεὶ ἄνω αὐτὸ φερόμενον ἀεὶ κάτω. Τοῦτο δὲ ἀδύνατον τὸ γὰρ ἁπλῶς κοῦφον ἀεὶ κουφότερον τῶν ἐχόντων βάρος καὶ κάτω φερομένων, τὸ δὲ κουφότερον οὐκ ἀεὶ κοῦφον διὰ τὸ λέγεσθαι καὶ ἐν τοῖς ἔχουσι βάρος ἕτερον ἑτέρου κουφότερον, οἷον γῆς ὕδωρ. | But those who attribute the lightness of fire to its containing so much void are necessarily involved in practically the same difficulties. For though fire be supposed to contain less solid than any other body, as well as more void, yet there will be a certain quantum of fire in which the amount of solid or plenum is in excess of the solids contained in some small quantity of earth. They may reply that there is an excess of void also. But the question is, how will they discriminate the absolutely heavy? Presumably, either by its excess of solid or by its defect of void. On the former view there could be an amount of earth so small as to contain less solid than a large mass of fire. And similarly, if the distinction rests on the amount of void, there will be a body, lighter than the absolutely light, which nevertheless moves downward as constantly as the other moves upward. But that cannot be so, since the absolutely light is always lighter than bodies which have weight and move downward, while, on the other hand, that which is lighter need not be light, because in common speech we distinguish a lighter and a heavier (viz. water and earth) among bodies endowed with weight. |
| Ἀλλὰ μὴν οὐδὲ τῷ τὸ κενὸν ἀνάλογον ἔχειν πρὸς τὸ πλῆρες ἱκανὸν λῦσαι τὴν λεγομένην νῦν ἀπορίαν. Συμβήσεται γὰρ καὶ τοῦτον τὸν τρόπον λέγουσιν ὡσαύτως τὸ ἀδύνατον. Ἐν γὰρ τῷ πλείονι πυρὶ καὶ ἐν τῷ ἐλάττονι τὸν αὐτὸν ἕξει λόγον τὸ στερεὸν πρὸς τὸ κενόν. Φέρεται δέ γε θᾶττον τὸ πλεῖον ἄνω πῦρ τοῦ ἐλάττονος, καὶ κάτω δὲ πάλιν ὡσαύτως ὁ πλείων χρυσὸς καὶ ὁ μόλιβδος ὁμοίως δὲ καὶ τῶν ἄλλων ἕκαστον τῶν ἐχόντων βάρος. Οὐκ ἔδει δὲ τοῦτο συμβαίνειν, εἴπερ τούτῳ διώρισται τὸ βαρὺ καὶ κοῦφον. | Again, the suggestion of a certain ratio between the void and the solid in a body is no more equal to solving the problem before us. The manner of speaking will issue in a similar impossibility. For any two portions of fire, small or great, will exhibit the same ratio of solid to void, but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size. This, however, should not be the case if the ratio is the ground of distinction between heavy things and light. There is also an absurdity in attributing the upward movement of bodies to a void which does not itself move. |
| Ἄτοπον δὲ καὶ εἰ διὰ τὸ κενὸν μὲν ἄνω φέρονται, τὸ δὲ κενὸν αὐτὸ μή. Ἀλλὰ μὴν εἴ γε τὸ μὲν κενὸν ἄνω πέφυκε φέρεσθαι, κάτω δὲ τὸ πλῆρες, καὶ διὰ τοῦτο τοῖς ἄλλοις αἴτια τῆς φορᾶς ἑκατέρας, οὐθὲν περὶ τῶν συνθέτων ἔδει σκοπεῖν διὰ τί τὰ μὲν κοῦφα τὰ δὲ βαρέα τῶν σωμάτων, ἀλλὰ περὶ τούτων αὐτῶν εἰπεῖν διὰ τί τὸ μὲν κοῦφον, τὸ δ' ἔχει βάρος, ἔτι δὲ τί τὸ αἴτιον τοῦ μὴ διεστάναι τὸ πλῆρες καὶ τὸ κενόν. | If, however, it is the nature of a void to move upward and of a plenum to move downward, and therefore each causes a like movement in other things, there was no need to raise the question why composite bodies are some light and some heavy; they had only to explain why these two things are themselves light and heavy respectively, and to give, further, the reason why the plenum and the void are not eternally separated. |
| Ἄλογον δὲ καὶ τὸ χώραν τῷ κενῷ ποιεῖν, ὥσπερ οὐκ αὐτὸ χώραν τινὰ οὖσαν ἀναγκαῖον δ', εἴπερ κινεῖται τὸ κενόν, εἶναι αὐτοῦ τινα τόπον, ἐξ οὗ μεταβάλλει καὶ εἰς ὅν. | It is also unreasonable to imagine a place for the void, as if the void were not itself a kind of place. But if the void is to move, it must have a place out of which and into which the change carries it. |
| Πρὸς δὲ τούτοις τί τῆς κινήσεως αἴτιον; Οὐ γὰρ δὴ τό γε κενόν οὐ γὰρ αὐτὸ κινεῖται μόνον, ἀλλὰ καὶ τὸ στερεόν. | Also what is the cause of its movement? Not, surely, its voidness: for it is not the void only which is moved, but also the solid. |
| Ὡσαύτως δὲ συμβαίνει κἄν τις ἄλλως διορίζῃ, μεγέθει καὶ σμικρότητι ποιῶν βαρύτερα καὶ κουφότερα ρων, κἂν ἄλλον ὁντινοῦν τρόπον κατασκευάζων, μόνον δὲ τὴν αὐτὴν ὕλην ἅπασιν ἀποδιδούς, ἢ πλείους μὲν ὑπεναντίας δὲ μόνον. | Similar difficulties are involved in all other methods of distinction, whether they account for the relative lightness and heaviness of bodies by distinctions of size, or proceed on any other principle, so long as they attribute to each the same matter, or even if they recognize more than one matter, so long as that means only a pair of contraries. |
| Μιᾶς μὲν γὰρ οὔσης οὐκ ἔσται τὸ ἁπλῶς βαρὺ καὶ κοῦφον, ὥσπερ τοῖς ἐκ τῶν τριγώνων συνιστᾶσιν ἐναντίας δέ, (310a.) καθάπερ οἱ τὸ κενὸν καὶ πλῆρες, οὐκ ἔσται τὰ μεταξὺ τῶν ἁπλῶς βαρέων καὶ κούφων διὰ τίν' αἰτίαν βαρύτερα καὶ κουφότερα ἀλλήλων καὶ τῶν ἁπλῶν ἐστιν. | If there is a single matter, as with those who compose things of triangles, nothing can be absolutely heavy or light: and if there is one matter and its contrary—the void, for instance, and the plenum—no reason can be given for the relative lightness and heaviness of the bodies intermediate between the absolutely light and heavy when compared either with one another or with these themselves. |
| Τὸ δὲ μεγέθει καὶ μικρότητι διορίζειν πεπλασμένῳ μὲν ἔοικε μᾶλλον τῶν πρότερον, ὅτι δ' ἐνδέχεται καθ' ἕκαστον ποιεῖν διαφορὰς τῶν τεττάρων στοιχείων, ἀσφαλεστέρως ἔχει πρὸς τὰς ἔμπροσθεν ἀπορίας. | The view which bases the distinction upon differences of size is more like a mere fiction than those previously mentioned, but, in that it is able to make distinctions between the four elements, it is in a stronger position for meeting the foregoing difficulties. |
| Τῷ δὲ μίαν ποιεῖν φύσιν τῶν τῷ μεγέθει διαφερόντων ἀναγκαῖον ταὐτὸν συμβαίνειν τοῖς μίαν ποιοῦσιν ὕλην, καὶ μήθ' ἁπλῶς εἶναι μηθὲν κοῦφον μήτε φερόμενον ἄνω, ἀλλ' ἢ ὑστερίζον ἢ ἐκθλιβόμενον, καὶ πολλὰ μικρὰ ὀλίγων μεγάλων βαρύτερα εἶναι. Εἰ δὲ τοῦτο ἔσται, συμβήσεται πολὺν ἀέρα καὶ πολὺ πῦρ ὕδατος εἶναι βαρύτερα καὶ γῆς ὀλίγης. Τοῦτο δ' ἐστὶν ἀδύνατον. | Since, however, it imagines that these bodies which differ in size are all made of one substance, it implies, equally with the view that there is but one matter, that there is nothing absolutely light and nothing which moves upward (except as being passed by other things or forced up by them); and since a multitude of small atoms are heavier than a few large ones, it will follow that much air or fire is heavier than a little water or earth, which is impossible. |
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| Τὰ μὲν οὖν παρὰ τῶν ἄλλων εἰρημένα ταῦτα, καὶ τοῦτον λέγεται τὸν τρόπον. | These, then, are the views which have been advanced by others and the terms in which they state them. |
| Ἡμεῖς δὲ λέγωμεν πρῶτον διορίσαντες περὶ οὗ μάλιστα ἀποροῦσί τινες, διὰ τί τὰ μὲν ἄνω φέρεται τὰ δὲ κάτω τῶν σωμάτων ἀεὶ κατὰ φύσιν, τὰ δὲ καὶ ἄνω καὶ κάτω, μετὰ δὲ ταῦτα περὶ βαρέος καὶ κούφου καὶ τῶν συμβαινόντων περὶ αὐτὰ παθημάτων, διὰ τίν' αἰτίαν ἕκαστον γίνεται. | We may begin our own statement by settling a question which to some has been the main difficulty—the question why some bodies move always and naturally upward and others downward, while others again move both upward and downward. After that we will inquire into light and heavy and of the various phenomena connected with them. |
| Περὶ μὲν οὖν τοῦ φέρεσθαι εἰς τὸν αὑτοῦ τόπον ἕκαστον ὁμοίως ὑποτῶν ἑτέληπτέον ὥσπερ καὶ περὶ τὰς ἄλλας γενέσεις καὶ μεταβολάς. Ἐπεὶ γάρ εἰσι τρεῖς αἱ κινήσεις (ἡ μὲν κατὰ μέγεθος, ἡ δὲ κατ' εἶδος, ἡ δὲ κατὰ τόπον), ἐν ἑκάστῃ τούτων τὴν μεταβολὴν ὁρῶμεν γινομένην ἐκ τῶν ἐναντίων εἰς τὰ ἐναντία καὶ τὰ μεταξύ, καὶ οὐκ εἰς τὸ τυχὸν τῷ τυχόντι μεταβολὴν οὖσαν ὁμοίως δὲ οὐδὲ κινητικὸν τὸ τυχὸν τοῦ τυχόντος ἀλλ' ὥσπερ τὸ ἀλλοιωτὸν καὶ τὸ αὐξητὸν ἕτερον, οὕτω καὶ τὸ ἀλλοιωτικὸν καὶ τὸ αὐξητικόν. Τὸν αὐτὸν δὴ τρόπον ὑποληπτέον καὶ τὸ κατὰ τόπον κινητικὸν καὶ κινητὸν οὐ τὸ τυχὸν εἶναι τοῦ τυχόντος. | The local movement of each body into its own place must be regarded as similar to what happens in connexion with other forms of generation and change. There are, in fact, three kinds of movement, affecting respectively the size, the form, and the place of a thing, and in each it is observable that change proceeds from a contrary to a contrary or to something intermediate: it is never the change of any chance subject in any chance direction, nor, similarly, is the relation of the mover to its object fortuitous: the thing altered is different from the thing increased, and precisely the same difference holds between that which produces alteration and that which produces increase. In the same manner it must be thought that produces local motion and that which is so moved are not fortuitously related. |
| Εἰ οὖν εἰς τὸ ἄνω καὶ τὸ κάτω κινητικὸν μὲν τὸ βαρυντικὸν καὶ τὸ κουφιστικόν, κινητὸν δὲ τὸ δυνάμει βαρὺ καὶ κοῦφον, τὸ δ' εἰς τὸν αὑτοῦ τόπον φέρεσθαι ἕκαστον τὸ εἰς τὸ αὑτοῦ εἶδός ἐστι φέρε(310b.) σθαι (καὶ ταύτῃ μᾶλλον ἄν τις ὑπολάβοι ὃ ἔλεγον οἱ ἀρχαῖοι, ὅτι τὸ ὅμοιον φέροιτο πρὸς τὸ ὅμοιον. Τοῦτο γὰρ οὐ συμβαίνει πάντως οὐ γὰρ ἐάν τις μεταθῇ τὴν γῆν οὗ νῦν ἡ σελήνη, οἰσθήσεται τῶν μορίων ἕκαστον πρὸς αὐτήν, ἀλλ' ὅπου περ καὶ νῦν. Ὅλως μὲν οὖν τοῖς ὁμοίοις καὶ ἀδιαφόροις ὑπὸ τῆς αὐτῆς κινήσεως ἀνάγκη τοῦτο συμβαίνειν, ὥσθ' ὅπου πέφυκεν ἕν τι φέρεσθαι μόριον, καὶ τὸ πᾶν. Ἐπεὶ δ' ὁ τόπος ἐστὶ τὸ τοῦ περιέχοντος πέρας, περιέχει δὲ πάντα τὰ κινούμενα ἄνω καὶ κάτω τό τε ἔσχατον καὶ τὸ μέσον, τοῦτο δὲ τρόπον τινὰ γίγνεται τὸ εἶδος τοῦ περιεχομένου, τὸ εἰς τὸν αὑτοῦ τόπον φέρεσθαι πρὸς τὸ ὅμοιόν ἐστι φέρεσθαι τὰ γὰρ ἐφεξῆς ὅμοιά ἐστιν ἀλλήλοις, οἷον ὕδωρ ἀέρι καὶ ἀὴρ πυρί. Ἀνάπαλιν δὲ λέγειν τοῖς μέσοις ἔστι, τοῖς δ' ἄκροις οὔ, οἷον ἀέρα μὲν ὕδατι, ὕδωρ δὲ γῇ ἀεὶ γὰρ τὸ ἀνώτερον πρὸς τὸ ὑφ' αὑτὸ, ὡς εἶδος πρὸς ὕλην, οὕτως ἔχει πρὸς ἄλληλα), τὸ δὲ ζητεῖν διὰ τί φέρεται τὸ πῦρ ἄνω καὶ ἡ γῆ κάτω, τὸ αὐτό ἐστι καὶ διὰ τί τὸ ὑγιαστὸν ἂν κινῆται καὶ μεταβάλλῃ ᾗ ὑγιαστόν, εἰς ὑγίειαν ἔρχεται ἀλλ' οὐκ εἰς λευκότητα. Ὁμοίως δὲ καὶ τἆλλα πάντα τὰ ἀλλοιωτά. Ἀλλὰ μὴν καὶ τὸ αὐξητὸν ὅταν μεταβάλλῃ ᾗ αὐξητόν, οὐκ εἰς ὑγίειαν ἔρχεται ἀλλ' εἰς μεγέθους ὑπεροχήν. Ὁμοίως δὲ καὶ τούτων ἕκαστον τὸ μὲν ἐν τῷ ποιῷ, τὸ δ' ἐν τῷ ποσῷ μεταβάλλει, καὶ ἐν τόπῳ τὰ μὲν κοῦφα ἄνω, τὰ δὲ βαρέα κάτω. | Now, that which produces upward and downward movement is that which produces weight and lightness, and that which is moved is that which is potentially heavy or light, and the movement of each body to its own place is motion towards its own form. (It is best to interpret in this sense the common statement of the older writers that 'like moves to like'. For the words are not in every sense true to fact. If one were to remove the earth to where the moon now is, the various fragments of earth would each move not towards it but to the place in which it now is. In general, when a number of similar and undifferentiated bodies are moved with the same motion this result is necessarily produced, viz. that the place which is the natural goal of the movement of each single part is also that of the whole. But since the place of a thing is the boundary of that which contains it, and the continent of all things that move upward or downward is the extremity and the centre, and this boundary comes to be, in a sense, the form of that which is contained, it is to its like that a body moves when it moves to its own place. For the successive members of the scries are like one another: water, I mean, is like air and air like fire, and between intermediates the relation may be converted, though not between them and the extremes; thus air is like water, but water is like earth: for the relation of each outer body to that which is next within it is that of form to matter.) Thus to ask why fire moves upward and earth downward is the same as to ask why the healable, when moved and changed qua healable, attains health and not whiteness; and similar questions might be asked concerning any other subject of aletion. Of course the subject of increase, when changed qua increasable, attains not health but a superior size. The same applies in the other cases. One thing changes in quality, another in quantity: and so in place, a light thing goes upward, a heavy thing downward. |
| Πλὴν ὅτι τὰ μὲν ἐν αὑτοῖς δοκεῖ ἔχειν ἀρχὴν τῆς μεταβολῆς (λέγω δὲ τὸ βαρὺ καὶ τὸ κοῦφον), τὰ δ' οὔ, ἀλλ' ἔξωθεν, οἷον τὸ ὑγιαστὸν καὶ τὸ αὐξητόν. Καίτοι ἐνίοτε καὶ ταῦτα ἐξ αὑτῶν μεταβάλλει, καὶ μικρᾶς γενομένης ἐν τοῖς ἔξω κινήσεως τὸ μὲν εἰς ὑγίειαν ἔρχεται, τὸ δ' εἰς αὔξην καὶ ἐπεὶ ταὐτὸν τὸ ὑγιαστὸν καὶ τὸ νόσου δεκτικόν, ἐὰν μὲν κινηθῇ ᾗ ὑγιαστόν, εἰς ὑγίειαν φέρεται, ἐὰν δ' ᾗ νοσερόν, εἰς νόσον. | The only difference is that in the last case, viz. that of the heavy and the light, the bodies are thought to have a spring of change within themselves, while the subjects of healing and increase are thought to be moved purely from without. Sometimes, however, even they change of themselves, ie. in response to a slight external movement reach health or increase, as the case may be. And since the same thing which is healable is also receptive of disease, it depends on whether it is moved qua healable or qua liable to disease whether the motion is towards health or towards disease. |
| Μᾶλλον δὲ τὸ βαρὺ καὶ τὸ κοῦφον τούτων ἐν ἑαυτοῖς ἔχειν φαίνεται τὴν ἀρχὴν διὰ τὸ ἐγγύτατα τῆς οὐσίας εἶναι τὴν τούτων ὕλην σημεῖον δ' ὅτι ἡ φορὰ ἀπολελυμένων ἐστί, καὶ γενέσει ὑστάτη τῶν κινήσεων, ὥστε πρώτη (311a.) ἂν εἴη κατὰ τὴν οὐσίαν αὕτη ἡ κίνησις. Ὅταν μὲν οὖν γίγνηται ἐξ ὕδατος ἀὴρ καὶ ἐκ βαρέος κοῦφον, ἔρχεται εἰς τὸ ἄνω. | But the reason why the heavy and the light appear more than these things to contain within themselves the source of their movements is that their matter is nearest to being. This is indicated by the fact that locomotion belongs to bodies only when isolated from other bodies, and is generated last of the several kinds of movement; in order of being then it will be first. Now whenever air comes into being out of water, light out of heavy, it goes to the upper place. |
| Ἅμα δ' ἐστὶ κοῦφον, καὶ οὐκέτι γίνεται, ἀλλ' ἐκεῖ ἐστιν. Φανερὸν δὴ ὅτι δυνάμει ὄν, εἰς ἐντελέχειαν ἰὸν ἔρχεται ἐκεῖ καὶ εἰς τὸ τοσοῦτον καὶ τὸ τοιοῦτον, οὗ ἡ ἐντελέχεια καὶ ὅσου καὶ οἵου [καὶ ὅπου]. Τὸ δ' αὐτὸ αἴτιον καὶ τοῦ ἤδη ὑπάρχοντα καὶ ὄντα γῆν καὶ πῦρ κινεῖσθαι εἰς τοὺς αὑτῶν τόπους μηδενὸς ἐμποδίζοντος. Καὶ γὰρ ἡ τροφή, ὅταν τὸ κωλῦον, καὶ τὸ ὑγιαστόν, ὅταν τὸ ἐπίσχον μὴ ᾖ, φέρεται εὐθύς. Κινεῖ δὲ τό τε ἐξ ἀρχῆς ποιῆσαν καὶ τὸ ὑποσπάσαν ἢ ὅθεν ἀπεπήδησεν, καθάπερ εἴρηται ἐν τοῖς πρώτοις λόγοις, ἐν οἷς διωρίζομεν ὅτι οὐθὲν τούτων αὐτὸ ἑαυτὸ κινεῖ. | It is forthwith light: becoming is at an end, and in that place it has being. Obviously, then, it is a potentiality, which, in its passage to actuality, comes into that place and quantity and quality which belong to its actuality. And the same fact explains why what is already actually fire or earth moves, when nothing obstructs it, towards its own place. For motion is equally immediate in the case of nutriment, when nothing hinders, and in the case of the thing healed, when nothing stays the healing. But the movement is also due to the original creative force and to that which removes the hindrance or off which the moving thing rebounded, as was explained in our opening discussions, where we tried to show how none of these things moves itself. |
| Διὰ τίνα μὲν οὖν αἰτίαν φέρεται τῶν φερομένων ἕκαστον, καὶ τὸ φέρεσθαι εἰς τὸν αὑτοῦ τόπον τί ἐστιν, εἴρηται. | The reason of the various motions of the various bodies, and the meaning of the motion of a body to its own place, have now been explained. |
| 4 | 4 |
| Τὰς δὲ διαφορὰς καὶ τὰ συμβαίνοντα περὶ αὐτὰ νῦν λέγωμεν. Πρῶτον μὲν οὖν διωρίσθω, καθάπερ φαίνεται πᾶσι, βαρὺ μὲν ἁπλῶς τὸ πᾶσιν ὑφιστάμενον, κοῦφον δὲ τὸ πᾶσιν ἐπιπολάζον. Ἁπλῶς δὲ λέγω εἴς τε τὸ γένος βλέπων, καὶ ὅσοις μὴ ἀμφότερα ὑπάρχει οἷον φαίνεται πυρὸς μὲν τὸ τυχὸν μέγεθος ἄνω φερόμενον, ἐὰν μή τι τύχῃ κωλῦον ἕτερον, γῆς δὲ κάτω τὸν αὐτὸν δὲ τρόπον καὶ θᾶττον τὸ πλεῖον. | We have now to speak of the distinctive properties of these bodies and of the various phenomena connected with them. In accordance with general conviction we may distinguish the absolutely heavy, as that which sinks to the bottom of all things, from the absolutely light, which is that which rises to the surface of all things. I use the term 'absolutely', in view of the generic character of 'light' and 'heavy', in order to confine the application to bodies which do not combine lightness and heaviness. It is apparent, I mean, that fire, in whatever quantity, so long as there is no external obstacle moves upward, and earth downward; and, if the quantity is increased, the movement is the same, though swifter. |
| Ἄλλως δὲ βαρὺ καὶ κοῦφον, οἷς ἀμφότερα ὑπάρχει καὶ γὰρ ἐπιπολάζουσί τισι καὶ ὑφίστανται, καθάπερ ἀὴρ καὶ ὕδωρ ἁπλῶς μὲν γὰρ οὐδέτερον τούτων κοῦφον ἢ βαρύ γῆς μὲν γὰρ ἄμφω κουφότερα (ἐπιπολάζει γὰρ αὐτῇ τὸ τυχὸν αὐτῶν μόριον), πυρὸς δὲ βαρύτερα (ὑφίσταται γὰρ αὐτῶν ὁπόσον ἂν ᾖ μόριον), πρὸς ἑαυτὰ δὲ ἁπλῶς τὸ μὲν βαρὺ τὸ δὲ κοῦφον ἀὴρ μὲν γὰρ ὁπόσος ἂν ᾖ, ἐπιπολάζει ὕδατι, ὕδωρ δὲ ὁπόσον ἂν ᾖ, ἀέρι ὑφίσταται. | But the heaviness and lightness of bodies which combine these qualities is different from this, since while they rise to the surface of some bodies they sink to the bottom of others. Such are air and water. Neither of them is absolutely either light or heavy. Both are lighter than earth—for any portion of either rises to the surface of it—but heavier than fire, since a portion of either, whatever its quantity, sinks to the bottom of fire; compared together, however, the one has absolute weight, the other absolute lightness, since air in any quantity rises to the surface of water, while water in any quantity sinks to the bottom of air. |
| Ἐπεὶ δὲ καὶ τῶν ἄλλων τὰ μὲν ἔχει βάρος τὰ δὲ κουφότητα, δῆλον ὅτι τούτων μὲν αἰτία πάντων ἡ ἐν τοῖς ἀσυνθέτοις διαφορά κατὰ γὰρ τὸ ἐκείνων τετυχηκέναι τοῦ μὲν πλεῖον τοῦ δ' ἔλαττον, ἔσται τὰ μὲν κοῦφα τὰ δὲ βαρέα τῶν σωμάτων. Ὥστε περὶ ἐκείνων λεκτέον τἆλλα γὰρ ἀκολουθεῖ τοῖς πρώτοις, ὅπερ ἔφαμεν χρῆναι ποιεῖν καὶ τοὺς διὰ τὸ πλῆρες τὸ βαρὺ λέγοντας (311b.) καὶ διὰ τὸ κενὸν τὸ κοῦφον. | Now other bodies are severally light and heavy, and evidently in them the attributes are due to the difference of their uncompounded parts: that is to say, according as the one or the other happens to preponderate the bodies will be heavy and light respectively. Therefore we need only speak of these parts, since they are primary and all else consequential: and in so doing we shall be following the advice which we gave to those whose attribute heaviness to the presence of plenum and lightness to that of void. |
| Συμβαίνει δὴ μὴ πανταχοῦ ταὐτὰ βαρέα δοκεῖν εἶναι καὶ κοῦφα διὰ τὴν τῶν πρώτων διαφοράν λέγω δ' οἷον ἐν μὲν ἀέρι βαρύτερον ἔσται ταλαντιαῖον ξύλον μολίβδου μναϊαίου, ἐν δὲ ὕδατι κουφότερον αἴτιον δ' ὅτι πάντα βάρος ἔχει πλὴν πυρὸς καὶ κουφότητα πλὴν γῆς. | It is due to the properties of the elementary bodies that a body which is regarded as light in one place is regarded as heavy in another, and vice versa. In air, for instance, a talent's weight of wood is heavier than a mina of lead, but in water the wood is the lighter. The reason is that all the elements except fire have weight and all but earth lightness. |
| Γῆν μὲν οὖν καὶ ὅσα γῆς ἔχει πλεῖστον, πανταχοῦ βάρος ἔχειν ἀναγκαῖον, ὕδωρ δὲ πανταχοῦ πλὴν ἐν γῇ, ἀέρα δὲ πλὴν ἐν ὕδατι καὶ γῇ ἐν τῇ αὑτοῦ γὰρ χώρᾳ πάντα βάρος ἔχει πλὴν πυρός, καὶ ὁ ἀήρ. Σημεῖον δ' ὅτι ἕλκει πλεῖον ὁ πεφυσημένος ἀσκὸς τοῦ κενοῦ. Ὥστ' εἴ τι ἀέρος ἔχει πλεῖον ἢ γῆς καὶ ὕδατος, ἐν μὲν ὕδατι ἐνδέχεται κουφότερον εἶναί τινος, ἐν δὲ ἀέρι βαρύτερον ἀέρι μὲν γὰρ οὐκ ἐπιπολάζει, τῷ δὲ ὕδατι ἐπιπολάζει. | Earth, then, and bodies in which earth preponderates, must needs have weight everywhere, while water is heavy anywhere but in earth, and air is heavy when not in water or earth. In its own place each of these bodies has weight except fire, even air. Of this we have evidence in the fact that a bladder when inflated weighs more than when empty. A body, then, in which air preponderates over earth and water, may well be lighter than something in water and yet heavier than it in air, since such a body does not rise in air but rises to the surface in water. |
| Ὅτι δ' ἐστί τι ἁπλῶς κοῦφον καὶ ἁπλῶς βαρύ, ἐκ τῶνδ' ἐστὶ φανερόν. Λέγω δ' ἁπλῶς κοῦφον ὃ ἀεὶ ἄνω καὶ βαρὺ ὃ ἀεὶ κάτω πέφυκε φέρεσθαι μὴ κωλυόμενον τοιαῦτα γάρ ἐστί τινα, καὶ οὐχ ὥσπερ οἴονταί τινες πάντ' ἔχειν βάρος βαρὺ μὲν γὰρ δοκεῖ τισιν εἶναι καὶ ἑτέροις, καὶ ἀεὶ φέρεσθαι πρὸς τὸ μέσον. Ἔστι δ' ὁμοίως καὶ τὸ κοῦφον. Ὁρῶμεν γάρ, καθάπερ εἴρηται πρότερον, ὅτι τὰ γεηρὰ πᾶσιν ὑφίσταται καὶ φέρεται πρὸς τὸ μέσον. Ἀλλὰ μὴν ὥρισται τὸ μέσον. Εἰ τοίνυν ἐστί τι ὃ πᾶσιν ἐπιπολάζει, καθάπερ φαίνεται τὸ πῦρ καὶ ἐν αὐτῷ τῷ ἀέρι ἄνω φερόμενον, ὁ δ' ἀὴρ ἡσυχάζων, δῆλον ὅτι τοῦτο φέρεται πρὸς τὸ ἔσχατον. Ὥστε βάρος οὐδὲν οἷόν τ' ἔχειν αὐτό ὑφίστατο γὰρ ἂν ἄλλῳ εἰ δὲ τοῦτο, εἴη ἄν τι ἄλλο, ὃ φέρεται ἐπὶ τὸ ἔσχατον, ὃ πᾶσι τοῖς φερομένοις ἐπιπολάζει. Νῦν δ' οὐδὲν φαίνεται. Τὸ ἄρα πῦρ οὐδὲν ἔχει βάρος, οὐδὲ ἡ γῆ κουφότητα οὐδεμίαν, εἴπερ ὑφίσταται πᾶσι καὶ τὸ ὑφιστάμενον φέρεται ἐπὶ τὸ μέσον. | The following account will make it plain that there is an absolutely light and an absolutely heavy body. And by absolutely light I mean one which of its own nature always moves upward, by absolutely heavy one which of its own nature always moves downward, if no obstacle is in the way. There are, I say, these two kinds of body, and it is not the case, as some maintain, that all bodies have weight. Different views are in fact agreed that there is a heavy body, which moves uniformly towards the centre. But is also similarly a light body. For we see with our eyes, as we said before, that earthy things sink to the bottom of all things and move towards the centre. But the centre is a fixed point. If therefore there is some body which rises to the surface of all things—and we observe fire to move upward even in air itself, while the air remains at rest—clearly this body is moving towards the extremity. It cannot then have any weight. If it had, there would be another body in which it sank: and if that had weight, there would be yet another which moved to the extremity and thus rose to the surface of all moving things. In fact, however, we have no evidence of such a body. Fire, then, has no weight. Neither has earth any lightness, since it sinks to the bottom of all things, and that which sinks moves to the centre. |
| Ἀλλὰ μὴν ὅτι γ' ἐστὶ μέσον πρὸς ὃ ἡ φορὰ τοῖς ἔχουσι βάρος καὶ ἀφ' οὗ τοῖς κούφοις, δῆλον πολλαχόθεν. | That there is a centre towards which the motion of heavy things, and away from which that of light things is directed, is manifest in many ways. |
| Πρῶτον μὲν τῷ εἰς ἄπειρον μὴ ἐνδέχεσθαι φέρεσθαι μηθέν. Ὥσπερ γὰρ οὐκ ἔστιν οὐθὲν ἀδύνατον, οὕτως οὐδὲ γίγνεται ἡ δὲ φορὰ γένεσίς ποθέν ποι. | First, because no movement can continue to infinity. For what cannot be can no more come-to-be than be, and movement is a coming to-be in one place from another. |
| Ἔπειτα πρὸς ὁμοίας φαίνεται γωνίας τὸ μὲν πῦρ ἄνω φερόμενον, ἡ δὲ γῆ κάτω καὶ πᾶν τὸ βάρος ἔχον. Ὥστ' ἀνάγκη φέρεσθαι (312a.) πρὸς τὸ μέσον. (Τοῦτο δὲ πότερον συμβαίνει πρὸς τὸ τῆς γῆς μέσον ἢ πρὸς τὸ τοῦ παντός, ἐπεὶ ταὐτὸν αὐτῶν ἐστιν, ἄλλος λόγος.) Ἐπεὶ δὲ τὸ πᾶσιν ὑφιστάμενον φέρεται πρὸς τὸ μέσον, ἀνάγκη τὸ πᾶσιν ἐπιπολάζον φέρεσθαι πρὸς τὸ ἔσχατον τῆς χώρας, ἐν ᾗ ποιοῦνται τὴν κίνησιν ἐναντίον γὰρ τὸ μὲν μέσον τῷ ἐσχάτῳ, τὸ δὲ ὑφιστάμενον ἀεὶ τῷ ἐπιπολάζοντι. | Secondly, like the upward movement of fire, the downward movement of earth and all heavy things makes equal angles on every side with the earth's surface: it must therefore be directed towards the centre. Whether it is really the centre of the earth and not rather that of the whole to which it moves, may be left to another inquiry, since these are coincident. But since that which sinks to the bottom of all things moves to the centre, necessarily that which rises to the surface moves to the extremity of the region in which the movement of these bodies takes place. For the centre is opposed as contrary to the extremity, as that which sinks is opposed to that which rises to the surface. |
| Διὸ καὶ εὐλόγως τὸ βαρὺ καὶ κοῦφον δύο ἐστίν καὶ γὰρ οἱ τόποι δύο, τὸ μέσον καὶ τὸ ἔσχατον. | This also gives a reasonable ground for the duality of heavy and light in the spatial duality centre and extremity. |
| Ἔστι δὲ δή τι καὶ μεταξὺ τούτων, ὃ πρὸς ἑκάτερον αὐτῶν λέγεται θάτερον ἔστι γὰρ ὡς ἔσχατον καὶ μέσον ἀμφοτέρων ἐστὶ τὸ μεταξύ διὰ τοῦτό ἐστί τι καὶ ἄλλο βαρὺ καὶ κοῦφον, οἷον ὕδωρ καὶ ἀήρ. | Now there is also the intermediate region to which each name is given in opposition to the other extreme. For that which is intermediate between the two is in a sense both extremity and centre. For this reason there is another heavy and light; namely, water and air. |
| Φαμὲν δὲ τὸ μὲν περιέχον τοῦ εἴδους εἶναι, τὸ δὲ περιεχόμενον τῆς ὕλης. Ἔστι δ' ἐν πᾶσι τοῖς γένεσιν αὕτη ἡ διάστασις καὶ γὰρ ἐν τῷ ποιῷ καὶ ἐν τῷ ποσῷ ἐστι τὸ μὲν ὡς εἶδος μᾶλλον, τὸ δ' ὡς ὕλη. Καὶ ἐν τοῖς κατὰ τόπον ὡσαύτως τὸ μὲν ἄνω τοῦ ὡρισμένου, τὸ δὲ κάτω τῆς ὕλης. | But in our view the continent pertains to form and the contained to matter: and this distinction is present in every genus. Alike in the sphere of quality and in that of quantity there is that which corresponds rather to form and that which corresponds to matter. In the same way, among spatial distinctions, the above belongs to the determinate, the below to matter. |
| Ὥστε καὶ ἐν αὐτῇ τῇ ὕλῃ τῇ τοῦ βαρέος καὶ κούφου, ᾗ μὲν τοιοῦτον δυνάμει, βαρέος ὕλη, ᾗ δὲ τοιοῦτον, κούφου καὶ ἔστι μὲν ἡ αὐτή, τὸ δ' εἶναι οὐ ταὐτόν, ὥσπερ καὶ τὸ νοσερὸν καὶ τὸ ὑγιαστόν. Τὸ γὰρ εἶναι οὐ ταὐτόν διόπερ οὐδὲ τὸ νοσώδει εἶναι ἢ ὑγιεινῷ. | The same holds, consequently, also of the matter itself of that which is heavy and light: as potentially possessing the one character, it is matter for the heavy, and as potentially possessing the other, for the light. It is the same matter, but its being is different, as that which is receptive of disease is the same as that which is receptive of health, though in being different from it, and therefore diseasedness is different from healthiness. |
| 5 | 5 |
| Τὸ μὲν οὖν ἔχον τοιαύτην ὕλην κοῦφον καὶ ἀεὶ ἄνω, τὸ δὲ τὴν ἐναντίαν βαρὺ καὶ ἀεὶ κάτω τὸ δ' ἑτέρας μὲν τούτων, ἐχούσας δ' οὕτω πρὸς ἀλλήλας ὡς αὗται ἁπλῶς, καὶ ἄνω καὶ κάτω [φερομένας] διὸ ἀὴρ καὶ ὕδωρ ἔχουσι καὶ κουφότητα καὶ βάρος ἑκάτερον, καὶ ὕδωρ μὲν πλὴν γῆς πᾶσιν ὑφίσταται, ἀὴρ δὲ πλὴν πυρὸς πᾶσιν ἐπιπολάζει. | A thing then which has the one kind of matter is light and always moves upward, while a thing which has the opposite matter is heavy and always moves downward. Bodies composed of kinds of matter different from these but having relatively to each other the character which these have absolutely, possess both the upward and the downward motion. Hence air and water each have both lightness and weight, and water sinks to the bottom of all things except earth, while air rises to the surface of all things except fire. |
| Ἐπεὶ δ' ἐστὶν ἓν μόνον ὃ πᾶσιν ἐπιπολάζει καὶ ἓν ὃ πᾶσιν ὑφίσταται, ἀνάγκη δύο ἄλλα εἶναι ἃ καὶ ὑφίσταταί τινι καὶ ἐπιπολάζει τινί. | But since there is one body only which rises to the surface of all things and one only which sinks to the bottom of all things, there must needs be two other bodies which sink in some bodies and rise to the surface of others. |
| Ὥστε ἀνάγκη καὶ τὰς ὕλας τοσαύτας εἶναι ὅσαπερ ταῦτα, τέτταρας, οὕτω δὲ τέτταρας ὡς μίαν μὲν ἁπάντων τὴν κοινήν, ἄλλως τε καὶ εἰ γίγνονται ἐξ ἀλλήλων, ἀλλὰ τὸ εἶναι ἕτερον. Οὐδὲν γὰρ κωλύει τῶν (312b.) ἐναντίων εἶναι μεταξὺ καὶ ἓν καὶ πλείω, ὥσπερ ἐν χρώμασιν πολλαχῶς γὰρ λέγεται τὸ μεταξὺ καὶ τὸ μέσον. | The kinds of matter, then, must be as numerous as these bodies, i.e. four, but though they are four there must be a common matter of all—particularly if they pass into one another—which in each is in being different. There is no reason why there should not be one or more intermediates between the contraries, as in the case of colour; for 'intermediate' and 'mean' are capable of more than one application. |
| Ἐν μὲν οὖν τῇ αὑτοῦ χώρᾳ τῶν ἐχόντων καὶ βάρος καὶ κουφότητα ἕκαστον ἔχει βάρος (ἡ δὲ γῆ ἐν ἅπασιν) κουφότητα δ' οὐκ ἔχει, ἀλλ' ἢ ἐν οἷς ἐπιπολάζει. | Now in its own place every body endowed with both weight and lightness has weightwhereas earth has weight everywhere—but they only have lightness among bodies to whose surface they rise. |
| Διὸ καὶ ὑποσπωμένων μὲν φέρεται εἰς τὰ ἐφεξῆς κάτω, ἀὴρ μὲν εἰς τὴν τοῦ ὕδατος χώραν, ὕδωρ δὲ εἰς τὴν τῆς γῆς. Ἄνω δ' εἰς τὴν τοῦ πυρός, ἀναιρουμένου τοῦ πυρός, οὐκ οἰσθήσεται ὁ ἀήρ, εἰ μὴ βίᾳ, ὥσπερ καὶ τὸ ὕδωρ σπᾶται, ὅταν γένηται τὸ ἐπίπεδον ἓν καὶ θᾶττον σπάσῃ τις ἄνω τῆς φορᾶς, ἣν φέρεται τὸ ὕδωρ κάτω. Οὐδὲ τὸ ὕδωρ εἰς τὴν τοῦ ἀέρος, ἀλλ' ἢ ὡς νῦν εἴρηται. Ἡ γῆ δὲ τοῦτο οὐ πάσχει, ὅτι οὐχ ἓν τὸ ἐπίπεδον. Διὸ τὸ μὲν ὕδωρ εἰς τὸ ἀγγεῖον πυρωθὲν σπᾶται, γῆ δ' οὔ. Ὥσπερ δὲ οὐδ' ἡ γῆ ἄνω, οὐδὲ τὸ πῦρ κάτω εἶσιν ὑφαιρουμένου τοῦ ἀέρος οὐδὲν γὰρ ἔχει βάρος οὐδ' ἐν τῇ αὑτοῦ χώρᾳ, ὥσπερ οὐδ' ἡ γῆ κουφότητα. Φέρεται δὲ κάτω τὰ δύο ὑποσπωμένων, ὅτι τὸ μὲν ἁπλῶς βαρύ ἐστιν ὃ πᾶσιν ὑφίσταται, τὸ δὲ πρός τι βαρὺ ὂν εἰς τὴν αὑτοῦ χώραν ἢ οἷς ἐπιπολάζει, δι' ὁμοιότητα τῆς ὕλης. | Hence when a support is withdrawn such a body moves downward until it reaches the body next below it, air to the place of water and water to that of earth. But if the fire above air is removed, it will not move upward to the place of fire, except by constraint; and in that way water also may be drawn up, when the upward movement of air which has had a common surface with it is swift enough to overpower the downward impulse of the water. Nor does water move upward to the place of air, except in the manner just described. Earth is not so affected at all, because a common surface is not possible to it. Hence water is drawn up into the vessel to which fire is applied, but not earth. As earth fails to move upward, so fire fails to move downward when air is withdrawn from beneath it: for fire has no weight even in its own place, as earth has no lightness. The other two move downward when the body beneath is withdrawn because, while the absolutely heavy is that which sinks to the bottom of all things, the relatively heavy sinks to its own place or to the surface of the body in which it rises, since it is similar in matter to it. |
| Ὅτι δ' ἀναγκαῖον ποιεῖν ἴσας τὰς διαφορὰς αὐτοῖς, δῆλον. Εἰ μὲν γὰρ μία ὕλη πάντων, οἷον ἢ τὸ κενὸν ἢ τὸ πλῆρες ἢ τὸ μέγεθος ἢ τὰ τρίγωνα, ἢ πάντα ἄνω ἢ πάντα κάτω οἰσθήσεται, ἡ δὲ ἑτέρα φορὰ οὐκέτι ἔσται ὥστ' ἢ κοῦφον οὐδὲν ἔσται ἁπλῶς, εἰ πάντα ῥέπει μᾶλλον τῷ ἐκ μειζόνων εἶναι σωμάτων ἢ ἐκ πλειόνων ἢ ὅτι πλήρη (τοῦτο δὲ ὁρῶμέν τε, καὶ δέδεικται ὅτι ὁμοίως κάτω τε ἀεὶ καὶ πανταχοῦ φέρεται καὶ ἄνω) ἐὰν δὲ τὸ κενὸν ἤ τι τοιοῦτον ὃ ἀεὶ ἄνω, οὐκ ἔσται ὃ ἀεὶ κάτω. Καὶ τῶν μεταξὺ δὴ ἔνια ἔσται κάτω θᾶττον γῆς ἐν γὰρ τῷ πολλῷ ἀέρι τρίγωνα πλείω ἢ τὰ στερεὰ ἢ τὰ μικρὰ ἔσται. Οὐ φαίνεται δ' οὐδὲ ἓν μόριον ἀέρος κάτω φερόμενον. Ὁμοίως δὲ καὶ ἐπὶ τοῦ κούφου, ἐὰν ἐκεῖνο ποιῇ τις ὑπερέχειν τῇ ὕλῃ. | It is plain that one must suppose as many distinct species of matter as there are bodies. For if, first, there is a single matter of all things, as, for instance, the void or the plenum or extension or the triangles, either all things will move upward or all things will move downward, and the second motion will be abolished. And so, either there will be no absolutely light body, if superiority of weight is due to superior size or number of the constituent bodies or to the fullness of the body: but the contrary is a matter of observation, and it has been shown that the downward and upward movements are equally constant and universal: or, if the matter in question is the void or something similar, which moves uniformly upward, there will be nothing to move uniformly downward. Further, it will follow that the intermediate bodies move downward in some cases quicker than earth: for air in sufficiently large quantity will contain a larger number of triangles or solids or particles. It is, however, manifest that no portion of air whatever moves downward. And the same reasoning applies to lightness, if that is supposed to depend on superiority of quantity of matter. |
| Ἐὰν δὲ δύο, τὰ μεταξὺ πῶς ἔσται ποιοῦντα ἃ ποιεῖ ἀήρ τε καὶ ὕδωρ; (Οἷον εἴ τις (313a.) φαίη εἶναι τὸ κενὸν καὶ πλῆρες τὸ μὲν οὖν πῦρ κενόν, διὸ ἄνω, τὴν δὲ γῆν πλῆρες, διὸ κάτω ἀέρα δὲ πλεῖον πυρὸς ἔχειν, ὕδωρ δὲ γῆς). Ἔσται γάρ τι ὕδωρ ὃ πλεῖον ἕξει πῦρ ὀλίγου ἀέρος, καὶ ἀὴρ πολὺς ὀλίγου ὕδατος γῆν πλείω, ὥστε δεήσει ἀέρος τι πλῆθος θᾶττον φέρεσθαι κάτω ὕδατος ὀλίγου. Τοῦτο δ' οὐ φαίνεται οὐδαμοῦ οὐδέποτε. | But if, secondly, the kinds of matter are two, it will be difficult to make the intermediate bodies behave as air and water behave. Suppose, for example, that the two asserted are void and plenum. Fire, then, as moving upward, will be void, earth, as moving downward, plenum; and in air, it will be said, fire preponderates, in water, earth. There will then be a quantity of water containing more fire than a little air, and a large amount of air will contain more earth than a little water: consequently we shall have to say that air in a certain quantity moves downward more quickly than a little water. But such a thing has never been observed anywhere. |
| Ἀνάγκη τοίνυν, ὥσπερ καὶ τὸ πῦρ ἄνω, ὅτι τοδὶ ἔχει, οἷον τὸ κενόν, τὰ δ' ἄλλα οὔ, καὶ τὴν γῆν κάτω, ὅτι τὸ πλῆρες ἔχει, καὶ τὸν ἀέρα εἰς τὴν αὑτοῦ καὶ ἀνώτερον τοῦ ὕδατος, ὅτι τοδί τι ἔχει, καὶ τὸ ὕδωρ κάτω, ὅτι τοιόνδε τι. | Necessarily, then, as fire goes up because it has something, e.g. void, which other things do not have, and earth goes downward because it has plenum, so air goes to its own place above water because it has something else, and water goes downward because of some special kind of body. |
| Εἰ δὲ ἦν ἕν τι ἄμφω ἢ δύο, ἄμφω δ' ὑπάρξει ταῦτα ἑκατέρῳ, ἔσται τι πλῆθος ἑκατέρου ὃ ὑπερέξει ὕδωρ τε ἀέρος ὀλίγου τῷ ἄνω καὶ ἀὴρ ὕδατος τῷ κάτω, καθάπερ εἴρηται πολλάκις. | But if the two bodies are one matter, or two matters both present in each, there will be a certain quantity of each at which water will excel a little air in the upward movement and air excel water in the downward movement, as we have already often said. |
| 6 | 6 |
| Τὰ δὲ σχήματα οὐκ αἴτια τοῦ φέρεσθαι ἁπλῶς ἢ κάτω ἢ ἄνω, ἀλλὰ τοῦ θᾶττον ἢ βραδύτερον. Δι' ἃς δ' αἰτίας, οὐ χαλεπὸν ἰδεῖν ἀπορεῖται γὰρ νῦν διὰ τί τὰ πλατέα σιδήρια καὶ μόλιβδος ἐπιπλεῖ ἐπὶ τοῦ ὕδατος, ἄλλα δὲ ἐλάττω καὶ ἧττον βαρέα, ἂν ᾖ στρογγύλα ἢ μακρά, οἷον βελόνη, κάτω φέρεται, καὶ ὅτι ἔνια διὰ μικρότητα ἐπιπλεῖ, οἷον τὸ ψῆγμα καὶ ἄλλα γεώδη καὶ κονιορτώδη ἐπὶ τοῦ ἀέρος. | The shape of bodies will not account for their moving upward or downward in general, though it will account for their moving faster or slower. The reasons for this are not difficult to see. For the problem thus raised is why a flat piece of iron or lead floats upon water, while smaller and less heavy things, so long as they are round or long—a needle, for instance—sink down; and sometimes a thing floats because it is small, as with gold dust and the various earthy and dusty materials which throng the air. |
| Περὶ δὴ τούτων ἁπάντων τὸ μὲν νομίζειν αἴτιον εἶναι ὥσπερ Δημόκριτος οὐκ ὀρθῶς ἔχει. Ἐκεῖνος γάρ φησι τὰ ἀναφερόμενα θερμὰ ἐκ τοῦ ὕδατος ἀνακωχεύειν (313b.) τὰ πλατέα τῶν ἐχόντων βάρος, τὰ δὲ στενὰ διαπίπτειν ὀλίγα γὰρ εἶναι τὰ ἀντικρούοντα αὐτοῖς. | With regard to these questions, it is wrong to accept the explanation offered by Democritus. He says that the warm bodies moving up out of the water hold up heavy bodies which are broad, while the narrow ones fall through, because the bodies which offer this resistance are not numerous. |
| Ἔδει δ' ἐν τῷ ἀέρι ἔτι μᾶλλον τοῦτο ποιεῖν, ὥσπερ ἐνίσταται κἀκεῖνος αὐτός. | But this would be even more likely to happen in air—an objection which he himself raises. |
| Ἀλλ' ἐνστὰς λύει μαλακῶς φησὶ γὰρ οὐκ εἰς ἓν ὁρμᾶν τὸν σοῦν, λέγων τὸν σοῦν τὴν κίνησιν τῶν ἄνω φερομένων σωμάτων. | His reply to the objection is feeble. In the air, he says, the 'drive' (meaning by drive the movement of the upward moving bodies) is not uniform in direction. |
| Ἐπεὶ δ' ἐστὶ τὰ μὲν εὐδιαίρετα τῶν συνεχῶν τὰ δ' ἧττον, καὶ διαιρετικὰ δὴ τὸν αὐτὸν τρόπον τὰ μὲν μᾶλλον τὰ δ' ἧττον, ταύτας εἶναι νομιστέον αἰτίας. Εὐδιαίρετον μὲν οὖν τὸ εὐόριστον, καὶ μᾶλλον τὸ μᾶλλον ἀὴρ δὲ μᾶλλον ὕδατος τοιοῦτον, ὕδωρ δὲ γῆς. Καὶ τὸ ἔλαττον δὴ ἐν ἑκάστῳ γένει εὐδιαιρετώτερον καὶ διασπᾶται ῥᾷον. Τὰ μὲν οὖν ἔχοντα πλάτος διὰ τὸ πολὺ περιλαμβάνειν ἐπιμένει, διὰ τὸ μὴ διασπᾶσθαι τὸ πλεῖον ῥᾳδίως τὰ δ' ἐναντίως ἔχοντα τοῖς σχήμασι διὰ τὸ ὀλίγον περιλαμβάνειν φέρεται κάτω, διὰ τὸ διαιρεῖν ῥᾳδίως. Καὶ ἐν ἀέρι πολὺ μᾶλλον, ὅσῳ εὐδιαιρετώτερος ὕδατός ἐστιν. | But since some continua are easily divided and others less easily, and things which produce division differ similarly in the case with which they produce it, the explanation must be found in this fact. It is the easily bounded, in proportion as it is easily bounded, which is easily divided; and air is more so than water, water than earth. Further, the smaller the quantity in each kind, the more easily it is divided and disrupted. Thus the reason why broad things keep their place is because they cover so wide a surface and the greater quantity is less easily disrupted. Bodies of the opposite shape sink down because they occupy so little of the surface, which is therefore easily parted. And these considerations apply with far greater force to air, since it is so much more easily divided than water. |
| Ἐπεὶ δὲ τό τε βάρος ἔχει τινὰ ἰσχὺν καθ' ἣν φέρεται κάτω, καὶ τὰ συνεχῆ πρὸς τὸ μὴ διασπᾶσθαι, ταῦτα δεῖ πρὸς ἄλληλα συμβάλλειν ἐὰν γὰρ ὑπερβάλλῃ ἡ ἰσχὺς ἡ τοῦ βάρους τῆς ἐν τῷ συνεχεῖ πρὸς τὴν διάσπασιν καὶ διαίρεσιν, βιάσεται κάτω θᾶττον, ἐὰν δὲ ἀσθενεστέρα ᾖ, ἐπιπολάσει. | But since there are two factors, the force responsible for the downward motion of the heavy body and the disruption—resisting force of the continuous surface, there must be some ratio between the two. For in proportion as the force applied by the heavy thing towards disruption and division exceeds that which resides in the continuum, the quicker will it force its way down; only if the force of the heavy thing is the weaker, will it ride upon the surface. |
| Περὶ μὲν οὖν βαρέος καὶ κούφου καὶ τῶν περὶ αὐτὰ συμβεβηκότων διωρίσθω τοῦτον ἡμῖν τὸν τρόπον. | We have now finished our examination of the heavy and the light and of the phenomena connected with them. |