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BOOK IV


Lectio 1 Lecture 1
Place, its existence
Chapter 1
Ὁμοίως δ' ἀνάγκη καὶ περὶ τόπου τὸν φυσικὸν ὥσπερ καὶ περὶ ἀπείρου γνωρίζειν, εἰ ἔστιν ἢ μή, καὶ πῶς ἔστι, καὶ τί ἐστιν. The physicist must have a knowledge of Place, too, as well as of the infinite—namely, whether there is such a thing or not, and the manner of its existence and what it is—
τά τε γὰρ ὄντα πάντες ὑπολαμβάνουσιν εἶναί που (τὸ γὰρ μὴ ὂν οὐδαμοῦ εἶναι· both because all suppose that things which exist are somewhere (the non-existent is nowhere—where is the goat-stag or the sphinx?),
ποῦ γάρ ἐστι τραγέλαφος ἢ σφίγξ;) καὶ τῆς κινήσεως ἡ κοινὴ μάλιστα καὶ κυριωτάτη κατὰ τόπον ἐστίν, ἣν καλοῦμεν φοράν. and because 'motion' in its most general and primary sense is change of place, which we call 'locomotion'.
ἔχει δὲ πολλὰς ἀπορίας τί ποτ' ἐστὶν ὁ τόπος· οὐ γὰρ ταὐτὸν φαίνεται θεωροῦσιν ἐξ ἁπάντων τῶν ὑπαρχόντων. ἔτι δ' οὐδ' ἔχομεν οὐδὲν παρὰ τῶν ἄλλων οὔτε προηπορημένον οὔτε προηυπορημένον περὶ (208b.) αὐτοῦ. The question, what is place? presents many difficulties. An examination of all the relevant facts seems to lead to divergent conclusions. Moreover, we have inherited nothing from previous thinkers, whether in the way of a statement of difficulties or of a solution.
ὅτι μὲν οὖν ἔστιν ὁ τόπος, δοκεῖ δῆλον εἶναι ἐκ τῆς ἀντιμεταστάσεως· ὅπου γὰρ ἔστι νῦν ὕδωρ, ἐνταῦθα ἐξελθόντος ὥσπερ ἐξ ἀγγείου πάλιν ἀὴρ ἔνεστιν, ὁτὲ δὲ τὸν αὐτὸν τόπον τοῦτον ἄλλο τι τῶν σωμάτων κατέχει· τοῦτο δὴ τῶν ἐγγιγνομένων καὶ μεταβαλλόντων ἕτερον πάντων εἶναι δοκεῖ· ἐν ᾧ γὰρ ἀὴρ ἔστι νῦν, ὕδωρ ἐν τούτῳ πρότερον ἦν, ὥστε δῆλον ὡς ἦν ὁ τόπος τι καὶ ἡ χώρα ἕτερον ἀμφοῖν, εἰς ἣν καὶ ἐξ ἧς μετέβαλον. The existence of place is held to be obvious from the fact of mutual replacement. Where water now is, there in turn, when the water has gone out as from a vessel, air is present. When therefore another body occupies this same place, the place is thought to be different from all the bodies which come to be in it and replace one another. What now contains air formerly contained water, so that clearly the place or space into which and out of which they passed was something different from both.
ἔτι δὲ αἱ φοραὶ τῶν φυσικῶν σωμάτων καὶ ἁπλῶν, οἷον πυρὸς καὶ γῆς καὶ τῶν τοιούτων, οὐ μόνον δηλοῦσιν ὅτι ἐστί τι ὁ τόπος, ἀλλ' ὅτι καὶ ἔχει τινὰ δύναμιν. φέρεται γὰρ ἕκαστον εἰς τὸν αὑτοῦ τόπον μὴ κωλυόμενον, τὸ μὲν ἄνω τὸ δὲ κάτω· ταῦτα δ' ἐστὶ τόπου μέρη καὶ εἴδη, τό τε ἄνω καὶ τὸ κάτω καὶ αἱ λοιπαὶ τῶν ἓξ διαστάσεων. ἔστι δὲ τὰ τοιαῦτα οὐ μόνον πρὸς ἡμᾶς, τὸ ἄνω καὶ κάτω καὶ δεξιὸν καὶ ἀριστερόν· ἡμῖν μὲν γὰρ οὐκ ἀεὶ τὸ αὐτό, ἀλλὰ κατὰ τὴν θέσιν, ὅπως ἂν στραφῶμεν, γίγνεται (διὸ καὶ ταὐτὸ πολλάκις δεξιὸν καὶ ἀριστερὸν καὶ ἄνω καὶ κάτω καὶ πρόσθεν καὶ ὄπισθεν), ἐν δὲ τῇ φύσει διώρισται χωρὶς ἕκαστον. οὐ γὰρ ὅ τι ἔτυχέν ἐστι τὸ ἄνω, ἀλλ' ὅπου φέρεται τὸ πῦρ καὶ τὸ κοῦφον· ὁμοίως δὲ καὶ τὸ κάτω οὐχ ὅ τι ἔτυχεν, ἀλλ' ὅπου τὰ ἔχοντα βάρος καὶ τὰ γεηρά, ὡς οὐ τῇ θέσει διαφέροντα μόνον ἀλλὰ καὶ τῇ δυνάμει. δηλοῖ δὲ καὶ τὰ μαθηματικά· οὐκ ὄντα γὰρ ἐν τόπῳ ὅμως κατὰ τὴν θέσιν τὴν πρὸς ἡμᾶς ἔχει δεξιὰ καὶ ἀριστερὰ ὡς τὰ μόνον λεγόμενα διὰ θέσιν, οὐκ ἔχοντα φύσει τούτων ἕκαστον. ἔτι οἱ τὸ κενὸν φάσκοντες εἶναι τόπον λέγουσιν· Further, the typical locomotions of the elementary natural bodies—namely, fire, earth, and the like—show not only that place is something, but also that it exerts a certain influence. Each is carried to its own place, if it is not hindered, the one up, the other down. Now these are regions or kinds of place—up and down and the rest of the six directions. Nor do such distinctions (up and down and right and left, etc.) hold only in relation to us. To us they are not always the same but change with the direction in which we are turned: that is why the same thing may be both right and left, up and down, before and behind. But in nature each is distinct, taken apart by itself. It is not every chance direction which is 'up', but where fire and what is light are carried; similarly, too, 'down' is not any chance direction but where what has weight and what is made of earth are carried—the implication being that these places do not differ merely in relative position, but also as possessing distinct potencies. This is made plain also by the objects studied by mathematics. Though they have no real place, they nevertheless, in respect of their position relatively to us, have a right and left as attributes ascribed to them only in consequence of their relative position, not having by nature these various characteristics.
τὸ γὰρ κενὸν τόπος ἂν εἴη ἐστερημένος σώματος. ὅτι μὲν οὖν ἐστί τι ὁ τόπος παρὰ τὰ σώματα, καὶ πᾶν σῶμα αἰσθητὸν ἐν τόπῳ, διὰ τούτων ἄν τις ὑπολάβοι· Again, the theory that the void exists involves the existence of place: for one would define void as place bereft of body. These considerations then would lead us to suppose that place is something distinct from bodies, and that every sensible body is in place.
δόξειε δ' ἂν καὶ Ἡσίοδος ὀρθῶς λέγειν ποιήσας πρῶτον τὸ χάος. λέγει γοῦν "πάντων μὲν πρώτιστα χάος γένετ', αὐτὰρ ἔπειτα γαῖ' εὐρύστερνος," ὡς δέον πρῶτον ὑπάρξαι χώραν τοῖς οὖσι, διὰ τὸ νομίζειν, ὥσπερ οἱ πολλοί, πάντα εἶναί που καὶ ἐν τόπῳ. εἰ δ' ἐστὶ τοιοῦτο, θαυμαστή τις ἂν εἴη ἡ τοῦ τόπου δύναμις καὶ προτέρα πάντων· οὗ γὰρ ἄνευ τῶν ἄλλων οὐδὲν ἔστιν, ἐκεῖνο δ' (209a.) ἄνευ τῶν ἄλλων, ἀνάγκη πρῶτον εἶναι· οὐ γὰρ ἀπόλλυται ὁ τόπος τῶν ἐν αὐτῷ φθειρομένων. Hesiod too might be held to have given a correct account of it when he made chaos first. At least he says: 'First of all things came chaos to being, then broad-breasted earth,' implying that things need to have space first, because he thought, with most people, that everything is somewhere and in place. If this is its nature, the potency of place must be a marvellous thing, and take precedence of all other things. For that without which nothing else can exist, while it can exist without the others, must needs be first; for place does not pass out of existence when the things in it are annihilated.
Postquam philosophus determinavit in tertio de motu et infinito, quod competit motui intrinsece, secundum quod est de genere continuorum, nunc in quarto libro intendit determinare de iis quae adveniunt motui extrinsece. Et primo de iis quae adveniunt motui extrinsece quasi mensurae mobilis; secundo de tempore, quod est mensura ipsius motus, ibi: consequens autem dictis et cetera. 406. After treating in Book III of motion, and the infinite, which belongs intrinsically to motion insofar as it is in the genus of continuous things, the Philosopher now intends, in Book IV, to deal with the things that are extrinsically connected with motion. First, of things that are connected with motion extrinsically as measures of mobile things: Secondly, of time which is the measure of motion itself, at no.558 (L.15,1.
Circa primum duo facit: primo determinat de loco; secundo de vacuo, ibi: eodem autem modo accipiendum et cetera. As to the first he does two things: First, he studies place; Secondly, the void, at no. 494 (L.9).
Circa primum duo facit: primo ostendit quod determinandum est a naturali de loco; secundo prosequitur propositum, ibi: quod quidem igitur locus sit et cetera. About the first he does two things: First, he shows that it is the business of the natural philosopher to study place; Secondly, he carries out his proposition, at no. 411.
Circa primum duo facit. Primo proponit quod intendit: et dicit quod sicut ad naturalem pertinet determinare de infinito, si est vel non est, et quomodo sit, et quid sit, similiter etiam et de loco. Secundo ibi: et ea namque quae sunt etc., probat quod dixerat: et primo ex parte ipsius loci; secundo ex parte nostra, ibi: habet autem multas dubitationes et cetera. As to the first he does two things: First, [277] he proposes what he intends and says that just as it is the business of the natural philosopher to determine about the infinite; namely, whether it exists or not, and how it exists, and what it is, so also about place; Secondly, at no. 407, he proves what he had said: First from the viewpoint of place itself; Secondly, from our viewpoint [i.e., that of the ones studying place] at no. 409.
Circa primum ponit duas rationes: quarum prima talis est. Ea quae sunt communia omnibus naturalibus, pertinent maxime ad considerationem naturalis; sed locus est huiusmodi: omnes enim communiter opinantur omnia ea quae sunt, in aliquo loco esse. Et ad hoc probandum utuntur sophistico argumento a positione consequentis. Argumentantur enim sic. Quod non est, nusquam est, idest in nullo loco est: non enim est dare ubi sit Tragelaphus aut sphinx, quae sunt quaedam fictitia sicut Chimaera. Argumentatur ergo quod si id quod in nullo loco est, non sit; ergo omne quod est, est in loco. 407. About the first he gives two reasons, of which the following is the first [278]. Whatever things are common to all natural things pertain especially to the considerations of the natural philosopher; but place is such, for all generally maintain that whatever exists is in some place. They prove it by a sophistic argument consisting of positing the consequent. They argue thus: What does not exist is nowhere, i.e., in no place, for there is no place where the goat-stag or the sphinx exist, which are certain fictions after the manner of chimeras. They argue therefore that if what is found in no place does not exist, then whatever exists is in a place.
Sed si esse in loco convenit omnibus entibus, videtur quod locus magis pertineat ad considerationem metaphysici quam physici. But if to be in place belongs to all beings, it seems that place pertains rather to the consideration of metaphysics then that of physics.
Et dicendum est quod hic argumentatur ab opinione ponentium omnia entia esse sensibilia, propter hoc quod imaginationem corporum transcendere non possunt: et secundum hos naturalis scientia est philosophia prima, communis omnibus entibus, ut dicitur in IV Metaphys. And it must be said that Aristotle here argues from the opinion of those who posit that all beings are sensible, on account of their inability to go beyond their imaginations. According to them, natural science is first philosophy, common to all beings, as is mentioned in Metaphysics IV (L.5).
Secundam rationem ponit ibi: et de motu qui communis maxime est etc.: quae talis est. Ad philosophum naturalem pertinet considerare de motu; sed motus qui est secundum locum, quem dicimus loci mutationem, est maxime communis inter omnes motus: quaedam enim, scilicet corpora caelestia, moventur hoc motu tantum, cum tamen nihil moveatur aliis motibus quin moveatur hoc motu. Similiter etiam hic motus est magis proprius: quia hic solus motus est vere continuus et perfectus, ut in octavo probabitur. Motus autem secundum locum non potest cognosci nisi cognoscatur locus. Naturalis igitur debet considerare de loco. 408. Then [279] he gives the second reason: The consideration of motion belongs to the natural philosopher; but the motion which is according to place and is called “change of place” is the most general of all motions. For some things namely, the heavenly bodies, are moved solely according to this motion and nothing is moved with other motions without being moved by this one. Moreover, this motion is more properly so because it alone is truly continuous and perfect, as will be proved in Book VIII. But notion according to place cannot be known without knowing place. The natural philosopher therefore should consider place.
Deinde cum dicit: habet autem multas dubitationes etc., inducit ad idem rationem ex parte nostra. De illis enim a sapientibus determinandum est, de quibus dubitatio est; multae autem dubitationes sunt de loco, quid sit. Quarum quidem dubitationum duplex est causa. Una est ex parte ipsius loci: quia non omnes proprietates loci ducunt in eandem sententiam de loco; sed ex quibusdam proprietatibus loci videtur quod locus sit hoc, ex quibusdam autem videtur quod locus sit aliud. Alia vero causa est ex parte hominum: quia antiqui neque bene moverunt dubitationem circa locum, neque etiam bene exquisierunt veritatem. 409. Then [280] he arrives at the same conclusion from our viewpoint: Wise men should settle matters about which there is doubt; but there are many doubts about what place is. The cause of these doubts is twofold. One is based on place itself: because not all the properties of place lead to the same opinion about place, but from certain properties of place it seems that place is one thing and from other properties that it is something else. The other cause is based on men, for the ancients neither proposed their doubts about place well nor pursued the truth of the matter well.
Deinde cum dicit: quod quidem igitur locus sit etc., incipit determinare de loco: et primo per modum disputativum; secundo determinando veritatem, ibi: post haec autem accipiendum et cetera. 410. Then [281] he begins to determine about place. First in a dialectical manner; Secondly, by determining the truth, at no. 434.
Circa primum duo facit: primo inquirit disputative an sit locus; secundo quid sit, ibi: quoniam autem aliud et cetera. As to the first he does two things: First he discusses dialectically whether place exists; Secondly what it is at no. 422.
Circa primum duo facit: primo ponit rationes ad ostendendum locum esse; secundo ad ostendendum quod locus non sit, ibi: at vero habet defectum et cetera. About the first he does two things: First he gives reasons showing that place exists; Secondly, showing that it does not exist, at no. 415.
Circa primum duo facit: primo ostendit locum esse, rationibus acceptis a rei veritate; secundo ab opinionibus aliorum, ibi: amplius vacuum et cetera. As to the first he does two things: First he shows that place exists, by using reasons based on the truth of things; Secondly, by reasons based on the opinions of others, at no. 413.
Circa primum ponit duas rationes: in quarum prima sic procedit. Dicit enim quod ex ipsa transmutatione corporum quae moventur secundum locum, manifestum est quod locus aliquid sit. Sicut enim transmutatio quae est secundum formas, homines induxit ad cognitionem materiae, quia scilicet oportet esse aliquod subiectum in quo sibi formae succedant; ita transmutatio secundum locum induxit homines ad cognitionem loci; oportet enim esse aliquid ubi sibi corpora succedant. Et hoc est quod subdit, quod exeunte aqua inde ubi nunc est, sicut ex quodam vase, iterum subintrat aer. Cum igitur eundem locum quandoque aliud corpus detineat, ex hoc manifestum videtur esse quod locus sit aliud ab iis quae sunt in loco et transmutantur secundum locum: quia ubi nunc est aer, prius aqua ibi erat; quod non esset si locus non esset aliud et ab aere et ab aqua. Relinquitur igitur quod locus est aliquid; et est quoddam receptaculum, alterum ab utroque locatorum; et est terminus motus localis a quo et in quem. 411. In regard to the first, he gives two reasons. In the first of these he proceeds thus: That place is something, is clear from the very transmutation of bodies that are moved according to place. For just as the transmutation which is according to form led men to the knowledge of matter, because there had to be a subject in which the forms could succeed one another, so transmutation according to place led men to a knowledge of place, for there had to be something where bodies could succeed one another. And this is what he adds, namely, that when water goes out from where it now is, i.e., from some vessel, air re-enters. Since, therefore, another body sometimes occupies the same place, it is clear that place is something different from the things that are in place and which are moved according to place. For where air now is there was previously water, and this would not be if place were not something different from both the air and the water. Consequently, place is something: it is a sort of receptacle distinct from any of the things located in it, and it is the term “from which” and “unto which” of local motion.
Secundam rationem ponit ibi: amplius autem loci mutationes et cetera. Et dicit quod cum quorumcumque corporum motus ostendat locum esse, ut dictum est, motus localis corporum naturalium simplicium, ut ignis et terrae et aliorum huiusmodi gravium et levium, non solum ostendit quod locus sit aliquid, sed etiam quod locus habeat quandam potentiam et virtutem. 412. He gives the second reason [282], saying that since the motion of any body whatsoever shows that place exists, as has been said, then the local motion of natural simple bodies, such as fire and earth, and such like heavy and light bodies, not only shows that place is something, but also that place has a certain power and force.
Videmus enim quod unumquodque horum fertur in suum proprium locum quando non impeditur, grave quidem deorsum, leve autem sursum. Ex quo patet quod locus habet quandam virtutem conservandi locatum: et propter hoc locatum tendit in suum locum desiderio suae conservationis. Non autem ex hoc ostenditur quod locus habeat virtutem attractivam, nisi sicut finis dicitur attrahere. For we observe that each of these bodies is carried to its proper place when it is not prevented, i.e., the heavy are carried down and the light upward. This shows that place has a certain power of pre-serving the thing that is in place. For this reason, an object tends to its own place by a desire of self-preservation. This, however, does not prove that place has the power to attract, except in the sense in which the end is said to attract.
Sursum autem et deorsum, et alia de numero sex distantiarum, scilicet ante et retro, dextrorsum et sinistrorsum, sunt partes et species loci. Huiusmodi autem distantiae determinantur in universo secundum naturam, et non solum quoad nos. Et hoc patet, quia in his in quibus ista dicuntur quoad nos, non semper idem est sursum vel deorsum vel dextrorsum vel sinistrorsum; sed variatur secundum quod diversimode nos convertimur ad ipsum; unde multoties aliquid immobile manens, quod prius erat dextrum, fit sinistrum, et similiter de aliis, prout nos diversimode ad illa convertimur. “Up” and “down” and the other directions, namely, “before” and “behind,” “right” and “left,” are the parts and species of place. These directions are determined in the universe according to nature and not merely in relation to ourselves. This is clear from the fact that when we speak of them in relation to ourselves, the same thing is not always “up” or “down,” “right” or “left,” but varies according to our various relations to it. Hence it frequently happens that an immobile object which was “on the right” comes to be “on the left.” The same is true of the other directions, depending on our different relations to them.
Sed in natura aliquid determinatum est sursum et deorsum secundum motum gravium et levium: et aliae positiones secundum motum caeli, ut in tertio dictum est. Non enim indifferenter quaecumque pars mundi est sursum vel deorsum: sed semper sursum est quo feruntur levia, deorsum autem quo feruntur gravia. Quaecumque autem secundum se habent determinatas positiones, necesse est quod habeant potentias quibus determinentur: alia enim est in animali potentia dextri, et alia sinistri. Unde relinquitur quod locus sit, et habeat aliquam potentiam. But in nature there is a definite “up” and “down” according to the motion of heavy and light bodies, and the other [four] directions are determined by the movements of the heavens, as was said in Book III. It is not just any part of the universe that is “up” and just any part that is “down,” but “up” is always whether light bodies are carried and “down” is whether heavy bodies tend. Now whatever things have according to themselves definite positions must have powers by which they are determined, for in an animal the power of the right is distinct from the power of the left. Accordingly, place exists and has definite powers.
Quod autem in aliquibus dicatur positio solum quoad nos, ostendit per mathematica; quae quidem, licet non sint in loco, tamen attribuitur eis positio solum per respectum ad nos. Unde in eis non est positio secundum naturam; sed solum secundum intellectum, secundum quod intelliguntur in aliquo ordine ad nos, vel supra vel subtus vel dextrorsum vel sinistrorsum. Now, that in certain things the position is assigned only in relation to us is shown in mathematical objects, which, although they are not in place, yet have a position attributed to them solely in relation to ourselves. Hence they have no position according to nature but only according to the intellect, inasmuch as they are understood in some relation to ourselves, either as above or below, or to the right or left.
Deinde cum dicit: amplius vacuum affirmantes etc., ostendit locum esse, ex opinionibus aliorum. Et primo ex opinione ponentium vacuum. Quia quicumque affirmant vacuum esse, necesse est quod dicant esse locum, cum vacuum nihil aliud sit quam locus privatus corpore. Et sic ex hoc et ex praemissis rationibus potest aliquis concipere quod locus sit aliquid praeter corpora, et quod omnia corpora sensibilia sint in loco. 413. Then [283] he appeals to the opinions of others to show that place exists. First, to the opinion of those who posit a void. For whoever asserts that the void exists must admit that place exists, since the void is nothing more than a place devoid of body. And so from this and from the reasons given above, it is possible to conceive that place is something other than bodies and that all sensible bodies exist in place.
Secundo ibi: videbitur autem utique etc., inducit ad idem opinionem Hesiodi, qui fuit unus de antiquis poetis theologis; qui posuit primo factum esse chaos. Dixit enim quod primo inter omnia factum est chaos, quasi quaedam confusio et receptaculum corporum; et postea facta est terra lata ad recipiendum diversa corpora: ac si primo necesse esset esse receptaculum rerum quam ipsas res. Et hoc ideo posuerunt quia crediderunt, sicut et multi alii, quod omnia quae sunt, sint in loco. Quod si verum est, sequitur quod locus non solum sit, sed quod habeat mirabilem potentiam, quae sit prima omnium entium. Illud enim quod potest esse sine aliis, et alia non possunt esse sine eo, videtur esse primum. Locus autem secundum eos potest esse sine corporibus: quod exinde coniiciebant, quia videmus locum remanere destructis locatis. Res autem non possunt esse sine loco. Relinquitur igitur secundum eos, quod locus sit primum inter omnia entia. 414. Secondly, [284] to confirm the same point he uses the opinion of Hesiod, who was one of the ancient theological poets. It was he who taught that the first thing made was chaos. For he said that the first of all things made was chaos, it being a sort of confusion and a receptacle for bodies; later the extended earth was made to receive various bodies—as if first a receptacle of things had to exist before the things themselves could exist. And he and others posited this because, with many others, they believed that all things that exist are in place. And if this is true, it follows that place not only exists but that it has a remarkable power in that it is the first of all beings. For that can exist without other things but they not without it, seems to be first. But according to them place can exist without bodies—a conjecture they made by observing that place remains even when the things occupying it are destroyed. But things cannot exist without place. It follows, therefore, according to them, that place is the first among all beings.

Lecture 2
Six dialectical reasons showing place does not exist
Lectio 2
Chapter 1 cont.
οὐ μὴν ἀλλ' ἔχει γε ἀπορίαν, εἰ ἔστι, τί ἐστι, πότερον ὄγκος τις σώματος ἤ τις ἑτέρα φύσις· ζητητέον γὰρ τὸ γένος αὐτοῦ πρῶτον. διαστήματα μὲν οὖν ἔχει τρία, μῆκος καὶ πλάτος καὶ βάθος, οἷς ὁρίζεται σῶμα πᾶν. ἀδύνατον δὲ σῶμα εἶναι τὸν τόπον· ἐν ταὐτῷ γὰρ ἂν εἴη δύο σώματα. True, but even if we suppose its existence settled, the question of its nature presents difficulty—whether it is some sort of 'bulk' of body or some entity other than that, for we must first determine its genus. (1) Now it has three dimensions, length, breadth, depth, the dimensions by which all body also is bounded. But the place cannot be body; for if it were there would be two bodies in the same place.
ἔτι εἴπερ ἔστι σώματος τόπος καὶ χώρα, δῆλον ὅτι καὶ ἐπιφανείας καὶ τῶν λοιπῶν περάτων· ὁ γὰρ αὐτὸς ἁρμόσει λόγος· ὅπου γὰρ ἦν πρότερον τὰ τοῦ ὕδατος ἐπίπεδα, ἔσται πάλιν τὰ τοῦ ἀέρος. ἀλλὰ μὴν οὐδεμίαν διαφορὰν ἔχομεν στιγμῆς καὶ τόπου στιγμῆς, ὥστ' εἰ μηδὲ ταύτης ἕτερόν ἐστιν ὁ τόπος, οὐδὲ τῶν ἄλλων οὐδενός, οὐδ' ἐστί τι παρ' ἕκαστον τούτων ὁ τόπος. (2) Further, if body has a place and space, clearly so too have surface and the other limits of body; for the same statement will apply to them: where the bounding planes of the water were, there in turn will be those of the air. But when we come to a point we cannot make a distinction between it and its place. Hence if the place of a point is not different from the point, no more will that of any of the others be different, and place will not be something different from each of them.
τί γὰρ ἄν ποτε καὶ θείημεν εἶναι τὸν τόπον; οὔτε γὰρ στοιχεῖον οὔτ' ἐκ στοιχείων οἷόν τε εἶναι τοιαύτην ἔχοντα φύσιν, οὔτε τῶν σω ματικῶν οὔτε τῶν ἀσωμάτων· μέγεθος μὲν γὰρ ἔχει, σῶμα δ' οὐδέν· ἔστι δὲ τὰ μὲν τῶν αἰσθητῶν στοιχεῖα σώματα, ἐκ δὲ τῶν νοητῶν οὐδὲν γίγνεται μέγεθος. (3) What in the world then are we to suppose place to be? If it has the sort of nature described, it cannot be an element or composed of elements, whether these be corporeal or incorporeal: for while it has size, it has not body. But the elements of sensible bodies are bodies, while nothing that has size results from a combination of intelligible elements.
ἔτι δὲ καὶ τίνος ἄν τις θείη τοῖς οὖσιν αἴτιον εἶναι τὸν τόπον; οὐδεμία γὰρ αὐτῷ ὑπάρχει αἰτία τῶν τεττάρων· οὔτε γὰρ ὡς ὕλη τῶν ὄντων (οὐδὲν γὰρ ἐξ αὐτοῦ συνέστηκεν) οὔτε ὡς εἶδος καὶ λόγος τῶν πραγμάτων οὔθ' ὡς τέλος, οὔτε κινεῖ τὰ ὄντα. (4) Also we may ask: of what in things is space the cause? None of the four modes of causation can be ascribed to it. It is neither in the sense of the matter of existents (for nothing is composed of it), nor as the form and definition of things, nor as end, nor does it move existents.
ἔτι δὲ καὶ αὐτὸς εἰ ἔστι τι τῶν ὄντων, ποὺ ἔσται. ἡ γὰρ Ζήνωνος ἀπορία ζητεῖ τινὰ λόγον· εἰ γὰρ πᾶν τὸ ὂν ἐν τόπῳ, δῆλον ὅτι καὶ τοῦ τόπου τόπος ἔσται, καὶ τοῦτο εἰς ἄπειρον. (5) Further, too, if it is itself an existent, where will it be? Zeno's difficulty demands an explanation: for if everything that exists has a place, place too will have a place, and so on ad infinitum.
ἔτι ὥσπερ ἅπαν σῶμα ἐν τόπῳ, οὕτω καὶ ἐν τόπῳ ἅπαντι σῶμα· πῶς οὖν ἐροῦμεν περὶ τῶν αὐξανομένων; ἀνάγκη γὰρ ἐκ τούτων συναύξεσθαι αὐτοῖς τὸν τόπον, εἰ μήτ' ἐλάττων μήτε μείζων ὁ τόπος ἑκάστου. διὰ μὲν οὖν τούτων οὐ μόνον τί ἐστιν, ἀλλὰ καὶ εἰ ἔστιν, ἀπορεῖν ἀναγκαῖον. (6) Again, just as every body is in place, so, too, every place has a body in it. What then shall we say about growing things? It follows from these premisses that their place must grow with them, if their place is neither less nor greater than they are. By asking these questions, then, we must raise the whole problem about place—not only as to what it is, but even whether there is such a thing.
Postquam philosophus posuit rationes ad ostendendum quod locus sit, hic ponit sex rationes ad ostendendum quod locus non sit. Principium autem ad investigandum de aliquo an sit, oportet accipere quid sit, saltem quid significetur per nomen. Et ideo dicit quod quamvis ostensum sit quod locus sit, tamen habet defectum, idest dubitationem, quid est, etsi est: utrum scilicet sit quaedam moles corporea, aut aliqua natura alterius generis. 415. After giving reasons to show that place exists, the Philosopher now gives six reasons showing that place does not exist. Now the way to begin investigating the question “whether a thing exists” is to settle on “what it is,” at least as to what its name means. Therefore he says [285] that although it has been shown that place exists, there is a difficulty, i.e., a question, about what it is, even if it does exist: Is it a bodily mass or a nature of some other kind?
Et ex hoc sic argumentatur. Si locus est aliquid, oportet quod sit corpus: quia locus habet tres dimensiones, scilicet longitudinis, latitudinis et profunditatis: his autem determinatur corpus; quia omne quod habet tres dimensiones, est corpus. Sed impossibile est locum esse corpus: quia cum locus et locatum sint simul, sequeretur duo corpora esse simul; quod est inconveniens. Ergo impossibile est locum aliquid esse. 416. Hence, he argues thus: If place is anything it must be a body; for place has three dimensions, namely, length, width and depth; and such things determine a body because whatever has three dimensions is body. But place cannot be a body, because, since place and the body in it are together, there would be two bodies together, which is unacceptable. Therefore, it is impossible for place to be anything.
Secundam rationem ponit ibi: amplius, si vere corporis locus est etc.: quae talis est. Si locus corporis vere est quoddam receptaculum corporis aliud a corpore, oportet quod etiam superficiei sit aliquod receptaculum aliud ab ipsa: et similiter est de aliis terminis quantitatis, quae sunt linea et punctus. Et hanc conditionalem sic probat. Propter hoc enim ostendebatur locus esse alius a corporibus, quia ubi nunc est corpus aeris, ibi prius erat corpus aquae: sed similiter ubi prius erat superficies aquae, nunc est superficies aeris: ergo locus superficiei est aliud a superficie. Et similis ratio est de linea et puncto. 417. He gives a second reason [286]: If the place of a body is a receptacle distinct from the body, then the place of its surface must be a receptacle distinct from this surface, and similarly for the other limits of quantity, such as the line and the point. He proves this conditional proposition in the following manner: Place was proved to be distinct from bodies on the ground that where the body of air now is, there was the body of water previously; but similarly where the surface of the water was, there is now the surface of the air; therefore the place of the surface is distinct from the surface and the same holds for the line and the point.
Argumentatur ergo a destructione consequentis, per hoc quod non potest esse aliqua differentia loci puncti a puncto: quia, cum locus non excedat locatum, locus puncti non potest esse nisi aliquod indivisibile. Duo autem indivisibilia quantitatis, ut duo puncta simul coniuncta, non sunt nisi unum: ergo eadem ratione neque locus superficiei erit aliud a superficie, neque locus corporis erit aliud a corpore. He argues therefore by the destruction of the consequent, starting from the fact that there can be no difference between the place of this point itself. For, since a place is not greater than the thing in place, the place of a point can be only an indivisible. Now two quantitative indivisibles, e.g., two points joined together, are just one point. For the same reason, therefore, neither the place of the surface will be different from the surface itself, nor the place of the body different from the body itself.
Tertiam rationem ponit ibi: quid enim forte ponemus esse locum? et cetera: quae talis est. Omne quod est, vel est elementum, vel est ex elementis; sed locus neutrum horum est; ergo locus non est. Mediam probat sic. Omne quod est elementum vel ex elementis, est de numero corporeorum vel incorporeorum; sed locus non est de numero incorporeorum, quia habet magnitudinem; nec de numero corporeorum quia non est corpus, ut probatum est; ergo neque est elementum, neque ex elementis. 418. He gives a third reason [287]: whatever is, either in an element or composed of elements; but place is neither of these; therefore place does not exist. The middle [minor] premise he proves thus: Whatever is an element or composed of elements is either corporeal or incorporeal; but place is not incorporeal, for it has magnitude, nor is it corporeal, because it is not a body, as we have already shown. Therefore it is neither an element nor composed of elements.
Et quia posset aliquis dicere quod, licet non sit corpus, est tamen elementum corporeum; ad hoc excludendum subiungit quod sensibilium corporum sunt elementa corporea: quia elementa non sunt extra genus elementatorum. Nam ex intelligibilibus principiis, quae sunt incorporea, non constituitur aliqua magnitudo. Unde si locus non sit corpus, non potest esse elementum corporeum. Now since someone might say that even though it is not a body, it is nevertheless a bodily element, he excludes this by adding that all sensible bodies have corporeal elements, because the elements are not outside the genus of their compounds. For no magnitude results from intelligible principles which are incorporeal. Hence if place is not a body, it cannot be a corporeal element.
Quartam rationem ponit ibi: amplius et cuius utique etc.: quae talis est. Omne quod est, aliquo modo est causa respectu alicuius; sed locus non potest esse causa secundum aliquem quatuor modorum. Neque enim est causa sicut materia, quia ea quae sunt non constituuntur ex loco, quod est de ratione materiae; neque sicut causa formalis, quia tunc omnia quae habent unum locum, essent unius speciei, cum principium speciei sit forma; neque iterum sicut causa finalis rerum, quia magis videntur esse loca propter locata, quam locata propter loca; neque iterum est causa efficiens vel motiva, cum sit terminus motus. Videtur igitur quod locus nihil sit. 419. He gives the fourth reason [288]: Everything that exists is somehow a cause in relation to something else; but place cannot be a cause in any of the four ways. It is not a cause as matter, because things that exist are not composed out of place and that is implied in the very notion of matter, nor is it a formal cause, for then all things that have the same place would be of the same species, since the principle of the species is the form. It is not like the final cause in things, since places seem to be for the sake of the things in place rather than they for the sake of the places. Finally, it is not an efficient or moving cause, since place is the terminus of a motion. Therefore it seems place is nothing.
Quintam rationem ponit ibi: amplius et ipse, si est aliquid eorum etc., quae est ratio Zenonis: et est talis. Omne quod est, est in loco; si igitur locus est aliquid, sequitur quod sit in loco, et ille locus in alio loco, et sic in infinitum: quod est impossibile; ergo locus non est aliquid. 420. He gives the fifth reason [289], which is Zeno’s reason: Whatever exists is in place; hence if place is anything it follows that it is itself in place and that place in another place and so on ad infinitum. But this is impossible; consequently, place is not anything.
Sextam rationem ponit ibi: amplius, sicut omne corpus etc.: quae talis est. Omne corpus est in loco, et in omni loco est corpus, ut a multis probabiliter existimatur: ex quo accipitur quod locus non sit minor neque maior quam locatum. Cum ergo locatum crescit, oportet quod crescat et locus; sed hoc videtur impossibile, cum locus sit quoddam immobile; non ergo locus aliquid est. 421. He gives the sixth reason [290]: Every body is in a place and in every place is a body (according to the opinion of many). From this it is taken that place is neither smaller nor larger than the thing in place. When therefore a thing in place grows, its place also should grow. However, this seems impossible, for place is an immobile something. Therefore place is not anything.
Et ultimo epilogat quod per huiusmodi rationes non solum dubitatur quid sit locus, sed etiam an sit. Huiusmodi autem rationes solventur per ea quae sequuntur. In summary he says that for reasons of this sort doubts are raised not only as to the nature of place, but also as to its very existence. However, these reasons will be answered by what follows.

Lecture 3
Is place matter or form?
Lectio 3
Chapter
Ἐπεὶ δὲ τὸ μὲν καθ' αὑτὸ τὸ δὲ κατ' ἄλλο λέγεται, καὶ τόπος ὁ μὲν κοινός, ἐν ᾧ ἅπαντα τὰ σώματά ἐστιν, ὁ δ' ἴδιος, ἐν ᾧ πρώτῳ (λέγω δὲ οἷον σὺ νῦν ἐν τῷ οὐρανῷ ὅτι ἐν τῷ ἀέρι οὗτος δ' ἐν τῷ οὐρανῷ, καὶ ἐν τῷ ἀέρι δὲ ὅτι ἐν τῇ γῇ, ὁμοίως δὲ καὶ ἐν ταύτῃ ὅτι ἐν τῷδε τῷ τόπῳ, (209b.) ὃς περιέχει οὐδὲν πλέον ἢ σέ), εἰ δή ἐστιν ὁ τόπος τὸ πρῶτον περιέχον ἕκαστον τῶν σωμάτων, πέρας τι ἂν εἴη, ὥστε δόξειεν ἂν τὸ εἶδος καὶ ἡ μορφὴ ἑκάστου ὁ τόπος εἶναι, ᾧ ὁρίζεται τὸ μέγεθος καὶ ἡ ὕλη ἡ τοῦ μεγέθους· τοῦτο γὰρ ἑκάστου πέρας. οὕτω μὲν οὖν σκοποῦσιν ὁ τόπος τὸ ἑκάστου εἶδός ἐστιν· We may distinguish generally between predicating B of A because it (A) is itself, and because it is something else; and particularly between place which is common and in which all bodies are, and the special place occupied primarily by each. I mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens; and you are in the air because you are on the earth; and similarly on the earth because you are in this place which contains no more than you. Now if place is what primarily contains each body, it would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined: for this is the limit of each body. If, then, we look at the question in this way the place of a thing is its form.
ᾗ δὲ δοκεῖ ὁ τόπος εἶναι τὸ διάστημα τοῦ μεγέθους, ἡ ὕλη· τοῦτο γὰρ ἕτερον τοῦ μεγέθους, τοῦτο δ' ἐστὶ τὸ περιεχόμενον ὑπὸ τοῦ εἴδους καὶ ὡρισμένον, οἷον ὑπὸ ἐπιπέδου καὶ πέρατος, ἔστι δὲ τοιοῦτον ἡ ὕλη καὶ τὸ ἀόριστον· ὅταν γὰρ ἀφαιρεθῇ τὸ πέρας καὶ τὰ πάθη τῆς σφαίρας, λείπεται οὐδὲν παρὰ τὴν ὕλην. διὸ καὶ Πλάτων τὴν ὕλην καὶ τὴν χώραν ταὐτό φησιν εἶναι ἐν τῷ Τιμαίῳ· τὸ γὰρ μεταληπτικὸν καὶ τὴν χώραν ἓν καὶ ταὐτόν. ἄλλον δὲ τρόπον ἐκεῖ τε λέγων τὸ μεταληπτικὸν καὶ ἐν τοῖς λεγομένοις ἀγράφοις δόγμασιν, ὅμως τὸν τόπον καὶ τὴν χώραν τὸ αὐτὸ ἀπεφήνατο. λέγουσι μὲν γὰρ πάντες εἶναί τι τὸν τόπον, τί δ' ἐστίν, οὗτος μόνος ἐπεχείρησεν εἰπεῖν. But, if we regard the place as the extension of the magnitude, it is the matter. For this is different from the magnitude: it is what is contained and defined by the form, as by a bounding plane. Matter or the indeterminate is of this nature; when the boundary and attributes of a sphere are taken away, nothing but the matter is left. This is why Plato in the Timaeus says that matter and space are the same; for the 'participant' and space are identical. (It is true, indeed, that the account he gives there of the 'participant' is different from what he says in his so-called 'unwritten teaching'. Nevertheless, he did identify place and space.) I mention Plato because, while all hold place to be something, he alone tried to say what it is.
εἰκότως δ' ἐκ τούτων σκοπουμένοις δόξειεν ἂν εἶναι χαλεπὸν γνωρίσαι τί ἐστιν ὁ τόπος, εἴπερ τούτων ὁποτερονοῦν ἐστίν, εἴτε ἡ ὕλη εἴτε τὸ εἶδος· ἄλλως τε γὰρ τὴν ἀκροτάτην ἔχει θέαν, καὶ χω ρὶς ἀλλήλων οὐ ῥᾴδιον γνωρίζειν. In view of these facts we should naturally expect to find difficulty in determining what place is, if indeed it is one of these two things, matter or form. They demand a very close scrutiny, especially as it is not easy to recognize them apart.
ἀλλὰ μὴν ὅτι γε ἀδύνα τον ὁποτερονοῦν τούτων εἶναι τὸν τόπον, οὐ χαλεπὸν ἰδεῖν. τὸ μὲν γὰρ εἶδος καὶ ἡ ὕλη οὐ χωρίζεται τοῦ πράγματος, τὸν δὲ τόπον ἐνδέχεται· ἐν ᾧ γὰρ ἀὴρ ἦν, ἐν τούτῳ πάλιν ὕδωρ, ὥσπερ ἔφαμεν, γίγνεται, ἀντιμεθισταμένων ἀλλήλοις τοῦ τε ὕδατος καὶ τοῦ ἀέρος, καὶ τῶν ἄλλων σωμάτων ὁμοίως, ὥστε οὔτε μόριον οὔθ' ἕξις ἀλλὰ χωριστὸς ὁ τόπος ἑκάστου ἐστί. καὶ γὰρ δοκεῖ τοιοῦτό τι εἶναι ὁ τόπος οἷον τὸ ἀγγεῖον (ἔστι γὰρ τὸ ἀγγεῖον τόπος μεταφορητός)· τὸ δ' ἀγγεῖον οὐδὲν τοῦ πράγματός ἐστιν. But it is at any rate not difficult to see that place cannot be either of them. The form and the matter are not separate from the thing, whereas the place can be separated. As we pointed out, where air was, water in turn comes to be, the one replacing the other; and similarly with other bodies. Hence the place of a thing is neither a part nor a state of it, but is separable from it. For place is supposed to be something like a vessel—the vessel being a transportable place. But the vessel is no part of the thing.
ᾗ μὲν οὖν χωριστὸς [ἐστι] τοῦ πράγματος, ταύτῃ μὲν οὐκ ἔστι τὸ εἶδος· ᾗ δὲ περιέχει, ταύτῃ δ' ἕτερος τῆς ὕλης. In so far then as it is separable from the thing, it is not the form: qua containing, it is different from the matter.
δοκεῖ δὲ ἀεὶ τὸ ὄν που αὐτό τε εἶναί τι καὶ ἕτερόν τι ἐκτὸς αὐτοῦ. Also it is held that what is anywhere is both itself something and that there is a different thing outside it.
(Πλάτωνι μέντοι λεκτέον, εἰ δεῖ παρεκβάντας εἰπεῖν, διὰ τί οὐκ ἐν τόπῳ τὰ εἴδη καὶ οἱ ἀριθμοί, εἴπερ τὸ μεθεκτικὸν ὁ τόπος, εἴτε τοῦ μεγάλου (210a.) καὶ τοῦ μικροῦ ὄντος τοῦ μεθεκτικοῦ εἴτε τῆς ὕλης, ὥσπερ ἐν τῷ Τιμαίῳ γέγραφεν.) (Plato of course, if we may digress, ought to tell us why the form and the numbers are not in place, if 'what participates' is place—whether what participates is the Great and the Small or the matter, as he called it in writing in the Timaeus.)
ἔτι πῶς ἂν φέροιτο εἰς τὸν αὑτοῦ τόπον, εἰ ὁ τόπος ἡ ὕλη ἢ τὸ εἶδος; ἀδύνατον γὰρ οὗ μὴ κίνησις μηδὲ τὸ ἄνω ἢ κάτω ἐστί, τόπον εἶναι. ὥστε ζητητέος ἐν τοῖς τοιούτοις ὁ τόπος. εἰ δ' ἐν αὐτῷ ὁ τόπος (δεῖ γάρ, εἴπερ ἢ μορφὴ ἢ ὕλη), ἔσται ὁ τόπος ἐν τόπῳ· μεταβάλλει γὰρ ἅμα τῷ πράγματι καὶ κινεῖται καὶ τὸ εἶδος καὶ τὸ ἀόριστον, οὐκ ἀεὶ ἐν τῷ αὐτῷ ἀλλ' οὗπερ καὶ τὸ πρᾶγμα· ὥστε τοῦ τόπου ἔσται τόπος. Further, how could a body be carried to its own place, if place was the matter or the form? It is impossible that what has no reference to motion or the distinction of up and down can be place. So place must be looked for among things which have these characteristics. If the place is in the thing (it must be if it is either shape or matter) place will have a place: for both the form and the indeterminate undergo change and motion along with the thing, and are not always in the same place, but are where the thing is. Hence the place will have a place.
ἔτι ὅταν ἐξ ἀέρος ὕδωρ γένηται, ἀπόλωλεν ὁ τόπος· οὐ γὰρ ἐν τῷ αὐτῷ τόπῳ τὸ γενόμενον σῶμα· τίς οὖν ἡ φθορά; ἐξ ὧν μὲν τοίνυν ἀναγκαῖον εἶναί τι τὸν τόπον, καὶ πάλιν ἐξ ὧν ἀπορήσειεν ἄν τις αὐτοῦ περὶ τῆς οὐσίας, εἴρηται. Further, when water is produced from air, the place has been destroyed, for the resulting body is not in the same place. What sort of destruction then is that? This concludes my statement of the reasons why space must be something, and again of the difficulties that may be raised about its essential nature.
Postquam philosophus inquisivit disputative an locus sit, hic inquirit quid sit. Et primo ponit rationes disputativas ad ostendendum locum esse formam vel materiam; secundo ponit rationes in contrarium, ibi: at vero quod impossibile sit et cetera. 422. Having inquired dialectically into the question of place’s existence, the Philosopher now attacks the question: what is place? First he gives dialectical reasons showing that place is form or matter; Secondly, he gives reasons to the contrary, at no. 429.
Circa primum tria facit: primo ponit rationem ad ostendendum locum esse formam; secundo ad ostendendum locum esse materiam, ibi: secundum autem quod videtur esse locus etc.; tertio inducit corollarium ex his, ibi: merito autem ex his et cetera. As to the first he does three things: First he gives a reason showing that place is form; Secondly, that place is matter, at no. 425. Thirdly, from these he draws a corollary, at no. 428.
Dicit ergo primo: quod sicut in entibus quoddam est per se ens, et aliquod dicitur ens per accidens; similiter considerandum est circa locum, quod quidam locus est communis, in quo omnia corpora sunt, et alius est locus proprius, qui primo et per se dicitur locus. Locus autem communis non dicitur locus nisi per accidens et per posterius. Quod sic manifestat. Possum enim dicere quod tu es in caelo, quia es in aere, qui est in caelo; et quod tu es in aere et in caelo, quia es in terra; et in terra diceris esse, quia es in loco, qui nihil continet plus quam te. 423. He says therefore first 52917 that just as in beings some are per se beings and others per accidens, so in regard to place, one place is common, in which all bodies exist, and another is proper and is called “place”, primarily and per se. Now common place is so called only per accidens and in relation to a previous place. He explains this thus: “I can say that you are in the heavens, because you are in the air which is in the heavens, and that you are in the air and in the heavens, because you are on earth and you are said to be on earth, because you are in a place containing nothing but you.”
Sic ergo illud quod primo et per se continet unumquodque, est per se locus eius; huiusmodi autem est terminus ad quem res terminatur; sequitur ergo quod locus proprie et per se sit terminus rei. Forma autem est terminus uniuscuiusque: quia per formam terminatur materia uniuscuiusque ad proprium esse, et magnitudo ad determinatam mensuram: quantitates enim rerum consequuntur formas earum. Videtur igitur secundum hanc considerationem, quod locus sit forma. 424. Consequently, what contains a thing primarily and per se is its per se place. Now such a place is the boundary at which a thing is terminated. Therefore, place is properly and per se a boundary of a thing. But the boundary of each thing is its form, because it is through the form that the matter of anything is limited to its own existence and magnitude to a determinate measure. For the quantities of things follow upon their forms. According to this, therefore, it seems that place is the form.
Sed sciendum est quod in hac ratione est sophisma consequentis: syllogizatur enim in secunda figura ex duabus affirmativis. However, it should be noted that in this argument there is the fallacy of consequent; for it is a syllogism in the second figure with two affirmative premises.
Deinde cum dicit: secundum autem quod videtur esse locus etc., ponit rationem Platonis, per quam sibi videbatur quod locus esset materia. Ad cuius evidentiam sciendum est quod antiqui putaverunt locum esse spatium quod est inter terminos rei continentis, quod quidem habet dimensiones longitudinis, latitudinis et profunditatis. Non tamen huiusmodi spatium videbatur esse idem cum aliquo corporum sensibilium: quia recedentibus et advenientibus diversis corporibus sensibilibus, remanet idem spatium. Secundum hoc ergo sequitur quod locus sit dimensiones separatae. 425. Then [292] he gives a reason of Plato through which it seemed to him that place is matter. To see this, one must note that the ancients thought that place was the space enveloped by the boundaries of the container, which has the dimensions of length, breadth, and depth. But this space did not seem to be the same as any sensible body, because the space remained the same even when various bodies successively entered it and left. Thus it follows that place is a set of separate dimensions.
Et ex hoc volebat syllogizare Plato quod locus esset materia. Et hoc est quod dicit, quod secundum quod locus videtur aliquibus esse distantia magnitudinis spatii, separata a quolibet corpore sensibili, videbatur quod locus esset materia. Ipsa namque distantia vel dimensio magnitudinis, altera est a magnitudine. Nam magnitudo significat aliquid terminatum aliqua specie, sicut linea terminatur punctis, et superficies linea, et corpus superficie, quae sunt species magnitudinis: sed dimensio spatii est contenta sub forma et determinata, sicut corpus determinatur plano, idest superficie, ut quodam termino. Id autem quod continetur sub terminis, videtur esse in se non determinatum. Quod autem est in se non determinatum, sed determinatur per formam et terminum, est materia, quae habet rationem infiniti: quia si ab aliquo corpore sphaerico removeantur passiones sensibiles et termini quibus figuratur dimensio magnitudinis, nihil relinquitur nisi materia. Unde relinquitur quod ipsae dimensiones ex se indeterminatae, quae per aliud determinantur, sint ipsa materia. 426. From this Plato wished to demonstrate that place is matter. This is what he [Aristotle] says: Because some consider that place is the distance of the magnitude of space distinct from every sensible body, place would seem to be matter. For the distance or dimension of a magnitude is distinct from the magnitude. For magnitude signifies something terminated by some species [or form], as a line is terminated by points, and a surface by line, and a body by surface, and these are species of magnitude. But the dimension of space is contained under a determined form as a body is determined by a plane, i.e., by a surface, as, by a definite boundary. Now whatever is contained under boundaries seems to be in itself not determined. What is not determined in itself but by a form and boundary is matter which has the nature of the infinite. For were we to remove from some spherical body its sensible qualities and the boundaries by which the dimension of its magnitude acquires its definite figure, nothing would remain but the matter. Consequently the dimensions themselves, which are not determined by themselves but by something else, are matter.
Et hoc praecipue sequebatur secundum radices Platonis, qui ponebat numeros et quantitates esse substantias rerum. This followed mainly from the underlying principles of Plato, who posited numbers and quantities as the substance of things.
Quia igitur locus est dimensiones, et dimensiones sunt materia, dicebat Plato in Timaeo, quod idem est locus et materia. Omne enim receptivum alicuius dicebat esse locum, non distinguens inter receptibilitatem loci et materiae: unde cum materia sit receptivum formarum, sequitur quod materia sit locus. 427. Therefore, because place is dimensions and dimensions are matter, Plato said in the Timaeus that place and matter are the same. For he said that whatever is a receptacle of anything is a place (failing to distinguish between the receptiveness of place and of matter). Hence, since matter receives form, it follows that matter is place.
Tamen sciendum est quod de receptivo diversimode Plato loquebatur: quia in Timaeo dixit receptivum esse materiam; in dogmatibus autem dictis et non scriptis, idest cum verbotenus docebat in scholis, dicebat receptivum esse magnum et parvum, quae etiam ex parte materiae ponebat, ut supra dictum est. Tamen, cuicumque attribueret esse receptivum, semper dicebat quod receptivum et locus sint idem. Sic igitur, cum multi dicerent locum esse aliquid, solus Plato conatus est assignare quid sit locus. Yet it should be noted that Plato spoke in various ways about receptacles: for in the Timaeus he said that the receptacle is matter but in his “unwritten teaching,” i.e., his oral teaching in the schools, he said that the receptacle was “the large and the small,” which however he allied with matter, as we have said above. Yet no matter to what he attributed receptivity, he always said that the receptacle and place are the same. Therefore, while many did say that place is something, Plato alone endeavored to say what place is.
Deinde cum dicit: merito autem ex his intendentibus etc., concludit ex praedictis, quod si locus est vel materia vel forma, rationabile videtur quod difficile sit cognoscere quid sit locus: quia tam materia quam forma habent altissimam speculationem et difficilem; et non est facile etiam cognoscere unum eorum sine altero. 428. Then [293] he concludes from the foregoing that if place is either matter or form, it seems reasonable to say that it is difficult to know what place is: because both matter and form involve very lofty and difficult speculation; moreover, it is not easy to know either of them without the other.
Deinde cum dicit: at vero quod impossibile sit etc., ponit quinque rationes in contrarium. Circa quarum primam dicit, quod non est difficile videre locum non esse materiam vel formam: quia forma et materia non separantur a re cuius sunt; sed locum contingit separari, quia in loco in quo erat aer, postea est aqua; et etiam alia corpora ad invicem transmutant locum. Unde manifestum est quod locus non est pars rei ut materia vel forma. Neque est etiam habitus, seu quodcumque accidens: quia partes et accidentia non sunt separabilia a re; sed locus est separabilis. Et hoc manifestat per exemplum: quia locus videtur comparari ad locatum sicut quoddam vas; sed in hoc tantum differt, quod locus est immobilis, vas autem mobile, ut infra exponetur. Sic igitur per hoc quod locus est separabilis, ostenditur quod locus non sit forma. Sed quod locus non sit materia, ostenditur non solum per hoc quod est separabilis, sed etiam per hoc quod continet: materia autem non continet, sed continetur. 429. Then [294] he gives five reasons to the contrary. In the first of these he says that it is not difficult to see that place is neither matter nor form. For form and matter are not separate from the thing of which they are components, whereas place can be separated—in the place where air was, water now is. In like manner, other bodies also mutually change place. Hence it is clear that place is not part of a thing, as matter or form. Nor is place an accident of a thing, because parts and accidents are nor separable from a thing, whereas place is separable. He shows this by an example: place seems to be related to the thing in place as a vessel, the only difference being that place is immobile and the vessel mobile, as will be explained below (L.6). Consequently, since place is separable, it is not form. But that place is not matter is shown not only by the fact that it is separable, but also by the fact that it contains, whereas matter does not contain but is contained.
Secundam rationem ponit ibi: videtur autem semper et cetera. Quia enim ostenderat quod locus non est materia nec forma, per hoc quod locus separatur a locato, vult ostendere quod etiam si locus nunquam separaretur a locato, ex hoc ipso quod dicimus aliquid esse in loco, apparet quod locus non est forma neque materia: quia omne quod dicitur esse alicubi, videtur et ipsum esse aliquid, et alterum aliquid esse ab eo in quo est. Unde cum aliquid dicitur esse in loco, sequitur quod locus sit extra locatum. Materia autem et forma non sunt extra rem: ergo neque materia neque forma est locus. 430. He now gives a second reason [295]. Since he had shown that place is neither matter nor form on the ground that place is separated from the thing in place, he now wishes to show that even if place were never separated from the thing in place, yet the very fact that we say something is in place shows that place is neither form nor matter. For whatever is said to be anywhere seems both to be something and to be distinct from that in which it is. Hence, when something is said to be in place, it follows that place is outside the thing, whereas matter and form are not outside the thing. Therefore, neither matter nor form is place.
Tertiam rationem ponit ibi: Platoni igitur dicendum est et cetera. Hic arguit specialiter contra positionem Platonis digrediendo. Dictum est enim supra in tertio, quod Plato posuit ideas et numeros non esse in loco. Sequebatur autem, secundum eius sententiam de loco, quod essent in loco: quia omne participatum est in participante; species autem et numeros ponebat participari, sive a materia, sive a magno et parvo. Sequitur ergo quod species et numeri sint in materia, sive in magno et parvo. Si igitur materia, vel magnum et parvum est locus, sequitur quod numeri et species sint in loco. 431. In the third reason [296] he makes a digression to argue specifically against the position of Plato. For it was said in Book III that Plato posited ideas and numbers as not in place. But logically, according to his opinion about place, they should be in place, because whatever is participated is in the participant—and he said that species and numbers are participated either by matter or by “the large and the small.” Accordingly, species and number exist in matter or in “the large and small,” Therefore, if matter or “the large and the small” are place, it follows that numbers and species are in place.
Quartam rationem ponit ibi: amplius quomodo ferretur et cetera. Circa quam dicit quod non poterit convenienter assignari quomodo aliquid moveatur secundum locum, si materia et forma sint locus. Impossibile est enim assignare locum in iis quae non moventur sursum vel deorsum, vel quomodocumque aliter secundum locum; unde in illis quaerendus est locus, quae secundum locum moventur. Sed si in ipso quod movetur est locus quasi aliquid ei intrinsecum (quod oportet dicere si materia vel forma sit locus), sequitur quod locus erit in loco: quia omne quod transmutatur secundum locum, est in loco; sed ea quae sunt in re ut species et infinitum, idest materia, moventur simul cum re, quia non semper sunt in eodem loco, sed sunt ubi est res. Ergo oportet quod materia et forma sint in loco. Si igitur alterum eorum sit locus, sequitur quod locus sit in loco, quod est inconveniens. 432. He gives the fourth reason [297]. In this regard he says that no good explanation could be given of how something could be moved according to place, if matter and form are place. For it is impossible to assign a place in things that are not moved up or down or in any direction of place; hence place must be sought in things that are moved according to place. But if place is something intrinsic to what is moved (which would be the case if matter or form were place), it follows that place will be in a place, for whatever is changed in respect to place is itself in place. Now whatever is in a thing, such as its species and the infinite, i.e., its matter, is moved with the thing, since they are not always in the same place, but are wherever the thing is. Therefore, matter and form must be in a place. Therefore, if either of them is place, it follows that place is in a place, which is unacceptable.
Quintam rationem ponit ibi: amplius cum ex aere fit aqua etc.: quae talis est. Quandocumque aliquid corrumpitur, corrumpuntur aliquo modo partes speciei ipsius; materia autem et forma sunt partes speciei; ergo corrupta re, ad minus per accidens forma et materia corrumpuntur. Si igitur materia et forma sit locus, sequitur quod locus corrumpatur, si locus pertinet ad speciem: quia corpus quod generatur non esset in eodem loco, si locus aeris pertineret ad speciem eius, sicut cum aqua generatur ex aere. Sed non est assignare qualiter locus corrumpatur: ergo non potest dici quod materia vel forma sit locus. 433. The fifth reason is then given [298]. Whenever anything is corrupted, the parts of its species are somehow corrupted. Now matter and form are the parts of the species. Therefore, when the thing corrupts, then, at least per accidens, the matter and form are corrupted. Consequently, if matter and form are place, it follows that place is corrupted, if place pertains to the species. Now the body which is generated would not be in the same place, if the place of air pertained to the species of the air, as when water is generated from air. But no explanation can be given of how place is corrupted; hence it cannot be said that matter or form are place.
Ultimo autem epilogat, quod dictum est per quae videtur necessarium esse quod sit locus, et per quae aliquis potest dubitare de substantia eius. Finally, he summarizes by asserting that we have stated why it seems place must exist and what causes doubt about its existence.

Lecture 4
Prerequisites to determining the truth about place.
Lectio 4
Chapter 3
Μετὰ δὲ ταῦτα ληπτέον ποσαχῶς ἄλλο ἐν ἄλλῳ λέγεται. The next step we must take is to see in how many senses one thing is said to be 'in' another.
ἕνα μὲν δὴ τρόπον ὡς ὁ δάκτυλος ἐν τῇ χειρὶ καὶ ὅλως τὸ μέρος ἐν τῷ ὅλῳ. (1) As the finger is 'in' the hand and generally the part 'in' the whole.
ἄλλον δὲ ὡς τὸ ὅλον ἐν τοῖς μέρεσιν· οὐ γάρ ἐστι παρὰ τὰ μέρη τὸ ὅλον. (2) As the whole is 'in' the parts: for there is no whole over and above the parts.
ἄλλον δὲ τρόπον ὡς ὁ ἄνθρωπος ἐν ζῴῳ καὶ ὅλως εἶδος ἐν γένει. (3) As man is 'in' animal and generally species 'in' genus.
ἄλλον δὲ ὡς τὸ γένος ἐν τῷ εἴδει καὶ ὅλως τὸ μέρος τοῦ εἴδους ἐν τῷ λόγῳ. (4) As the genus is 'in' the species and generally the part of the specific form 'in' the definition of the specific form.
ἔτι ὡς ἡ ὑγίεια ἐν θερμοῖς καὶ ψυχροῖς καὶ ὅλως τὸ εἶδος ἐν τῇ ὕλῃ. (5) As health is 'in' the hot and the cold and generally the form 'in' the matter.
ἔτι ὡς ἐν βασιλεῖ τὰ τῶν Ἑλλήνων καὶ ὅλως ἐν τῷ πρώτῳ κινητικῷ. (6) As the affairs of Greece centre 'in' the king, and generally events centre 'in' their primary motive agent.
ἔτι ὡς ἐν τῷ ἀγαθῷ καὶ ὅλως ἐν τῷ τέλει· τοῦτο δ' ἐστὶ τὸ οὗ ἕνεκα. (7) As the existence of a thing centres 'in its good and generally 'in' its end, i.e. in 'that for the sake of which' it exists.
πάντων δὲ κυριώτατον τὸ ὡς ἐν ἀγγείῳ καὶ ὅλως ἐν τόπῳ. (8) In the strictest sense of all, as a thing is 'in' a vessel, and generally 'in' place.
ἀπορήσειε δ' ἄν τις, ἆρα καὶ αὐτό τι ἐν ἑαυτῷ ἐνδέχεται εἶναι, ἢ οὐδέν, ἀλλὰ πᾶν ἢ οὐδαμοῦ ἢ ἐν ἄλλῳ. One might raise the question whether a thing can be in itself, or whether nothing can be in itself—everything being either nowhere or in something else.
διχῶς δὲ τοῦτ' ἔστιν, ἤτοι καθ' αὑτὸ ἢ καθ' ἕτερον. ὅταν μὲν γὰρ ᾖ μόρια τοῦ ὅλου τὸ ἐν ᾧ καὶ τὸ ἐν τούτῳ, λεχθήσεται τὸ ὅλον ἐν αὑτῷ· λέγεται γὰρ καὶ κατὰ τὰ μέρη, οἷον λευκὸς ὅτι ἡ ἐπιφάνεια λευκή, καὶ ἐπιστήμων ὅτι τὸ λογιστικόν. ὁ μὲν οὖν ἀμφορεὺς οὐκ ἔσται ἐν αὑτῷ, οὐδ' ὁ οἶνος· ὁ δὲ τοῦ οἴνου ἀμφορεὺς ἔσται· ὅ τε γὰρ καὶ ἐν ᾧ, ἀμφότερα τοῦ αὐτοῦ μόρια. The question is ambiguous; we may mean the thing qua itself or qua something else. When there are parts of a whole—the one that in which a thing is, the other the thing which is in it—the whole will be described as being in itself. For a thing is described in terms of its parts, as well as in terms of the thing as a whole, e.g. a man is said to be white because the visible surface of him is white, or to be scientific because his thinking faculty has been trained. The jar then will not be in itself and the wine will not be in itself. But the jar of wine will: for the contents and the container are both parts of the same whole.
οὕτω μὲν οὖν ἐνδέχεται αὐτό τι ἐν αὑτῷ εἶναι, πρώτως δ' οὐκ ἐνδέχεται. οἷον τὸ λευκὸν ἐν σώματι (ἡ (210b.) ἐπιφάνεια γὰρ ἐν σώματι), ἡ δ' ἐπιστήμη ἐν ψυχῇ· κατὰ ταῦτα δὲ αἱ προσηγορίαι μέρη ὄντα, ὥς γε ἐν ἀνθρώπῳ (ὁ δὲ ἀμφορεὺς καὶ ὁ οἶνος χωρὶς μὲν ὄντα οὐ μέρη, ἅμα δέ· διὸ ὅταν ᾖ μέρη, ἔσται αὐτὸ ἐν αὑτῷ)· οἷον τὸ λευκὸν ἐν ἀνθρώπῳ ὅτι ἐν σώματι, καὶ ἐν τούτῳ ὅτι ἐν ἐπιφανείᾳ· ἐν δὲ ταύτῃ οὐκέτι κατ' ἄλλο. καὶ ἕτερά γε τῷ εἴδει ταῦτα, καὶ ἄλλην φύσιν ἔχει ἑκάτερον καὶ δύναμιν, ἥ τ' ἐπιφάνεια καὶ τὸ λευκόν. In this sense then, but not primarily, a thing can be in itself, namely, as 'white' is in body (for the visible surface is in body), and science is in the mind. It is from these, which are 'parts' (in the sense at least of being 'in' the man), that the man is called white, etc. But the jar and the wine in separation are not parts of a whole, though together they are. So when there are parts, a thing will be in itself, as 'white' is in man because it is in body, and in body because it resides in the visible surface. We cannot go further and say that it is in surface in virtue of something other than itself. (Yet it is not in itself: though these are in a way the same thing,) they differ in essence, each having a special nature and capacity, 'surface' and 'white'.
οὔτε δὴ ἐπακτικῶς σκοποῦσιν οὐδὲν ὁρῶμεν ἐν ἑαυτῷ κατ' οὐδένα τῶν διορισμῶν, τῷ τε λόγῳ δῆλον ὅτι ἀδύνατον· δεήσει γὰρ ἀμφότερα ἑκάτερον ὑπάρ χειν, οἷον τὸν ἀμφορέα ἀγγεῖόν τε καὶ οἶνον εἶναι καὶ τὸν οἶνον οἶνόν τε καὶ ἀμφορέα, εἴπερ ἐνδέχεται αὐτό τι ἐν αὑτῷ εἶναι. ὥστ' εἰ ὅτι μάλιστα ἐν ἀλλήλοις εἶεν, ὁ μὲν ἀμφορεὺς δέξεται τὸν οἶνον οὐχ ᾗ αὐτὸς οἶνος ἀλλ' ᾗ ἐκεῖνος, ὁ δ' οἶνος ἐνέσται ἐν τῷ ἀμφορεῖ οὐχ ᾗ αὐτὸς ἀμφορεὺς ἀλλ' ᾗ ἐκεῖνος. κατὰ μὲν οὖν τὸ εἶναι ὅτι ἕτερον, δῆλον· ἄλλος γὰρ ὁ λόγος τοῦ ἐν ᾧ καὶ τοῦ ἐν τούτῳ. Thus if we look at the matter inductively we do not find anything to be 'in' itself in any of the senses that have been distinguished; and it can be seen by argument that it is impossible. For each of two things will have to be both, e.g. the jar will have to be both vessel and wine, and the wine both wine and jar, if it is possible for a thing to be in itself; so that, however true it might be that they were in each other, the jar will receive the wine in virtue not of its being wine but of the wine's being wine, and the wine will be in the jar in virtue not of its being a jar but of the jar's being a jar. Now that they are different in respect of their essence is evident; for 'that in which something is' and 'that which is in it' would be differently defined.
ἀλλὰ μὴν οὐδὲ κατὰ συμβεβηκὸς ἐνδέχεται· ἅμα γὰρ δύο ἐν ταὐτῷ ἔσται· αὐτός τε γὰρ ἐν αὑτῷ ὁ ἀμφορεὺς ἔσται, εἰ οὗ ἡ φύσις δεκτική, τοῦτ' ἐνδέχεται ἐν αὑτῷ εἶναι, καὶ ἔτι ἐκεῖνο οὗ δεκτικόν, οἷον, εἰ οἴνου, ὁ οἶνος. ὅτι μὲν οὖν ἀδύνατον ἐν αὑτῷ τι εἶναι πρώτως, δῆλον· Nor is it possible for a thing to be in itself even incidentally: for two things would at the same time in the same thing. The jar would be in itself—if a thing whose nature it is to receive can be in itself; and that which it receives, namely (if wine) wine, will be in it. Obviously then a thing cannot be in itself primarily.
ὃ δὲ Ζήνων ἠπόρει, ὅτι εἰ ὁ τόπος ἐστί τι, ἔν τινι ἔσται, λύειν οὐ χαλεπόν· οὐδὲ γὰρ κωλύει ἐν ἄλλῳ εἶναι τὸν πρῶτον τόπον, μὴ μέντοι ὡς ἐν τόπῳ ἐκείνῳ, ἀλλ' ὥσπερ ἡ μὲν ὑγίεια ἐν τοῖς θερμοῖς ὡς ἕξις, τὸ δὲ θερμὸν ἐν σώματι ὡς πάθος. ὥστε οὐκ ἀνάγκη εἰς ἄπειρον ἰέναι. Zeno's problem—that if Place is something it must be in something—is not difficult to solve. There is nothing to prevent the first place from being 'in' something else—not indeed in that as 'in' place, but as health is 'in' the hot as a positive determination of it or as the hot is 'in' body as an affection. So we escape the infinite regress.
ἐκεῖνο δὲ φανερόν, ὅτι ἐπεὶ οὐδὲν τὸ ἀγγεῖον τοῦ ἐν αὐτῷ (ἕτερον γὰρ τὸ πρώτως ὅ τε καὶ ἐν ᾧ), οὐκ ἂν εἴη οὔτε ἡ ὕλη οὔτε τὸ εἶδος ὁ τόπος, ἀλλ' ἕτερον. ἐκείνου γάρ τι ταῦτα τοῦ ἐνόντος, καὶ ἡ ὕλη καὶ ἡ μορφή. ταῦτα μὲν οὖν ἔστω διηπορημένα. Another thing is plain: since the vessel is no part of what is in it (what contains in the strict sense is different from what is contained), place could not be either the matter or the form of the thing contained, but must different—for the latter, both the matter and the shape, are parts of what is contained. This then may serve as a critical statement of the difficulties involved.
Postquam philosophus inquisivit disputative an locus sit et quid sit, hic accedit ad determinandum veritatem. Et primo praemittit quaedam quae sunt necessaria ad considerationem veritatis; secundo determinat veritatem, ibi: quid autem forte et cetera. 434. After inquiring dialectically into the existence and nature of place, the Philosopher now proceeds to the task of determining the truth. First he lays down certain things necessary to the consideration of the truth: Secondly, he determines the truth, at no. 445.
Circa primum tria facit: primo ostendit quot modis dicitur aliquid esse in aliquo; secundo inquirit utrum aliquid possit esse in seipso, ibi: dubitabit autem aliquis etc., tertio solvit quaedam prius dubitata, ibi: quod autem Zeno opposuit et cetera. As to the first he does three things: First he points out the ways in which one thing is said to be in another; Secondly, he asks whether anything can be in itself, at no. 437; Thirdly, he settles some difficulties previously raised, at no. 443.
Ponit ergo octo modos quibus aliquid in aliquo dicitur esse. 435. He lists [299] eight ways in which something is said to be in something.
Quorum primus est, sicut digitus dicitur esse in manu, et universaliter quaecumque alia pars in suo toto. The first of these is the way in which a finger is said to be in the hand and in general how any part is in its whole.
Secundus modus est, prout totum dicitur esse in partibus. Et quia iste modus non est adeo consuetus sicut primus, ad eius manifestationem subiungit quod totum non est praeter partes, et sic oportet ut intelligatur esse in partibus. The second way is as the whole is said to be in the parts. And because this way is not so customary as the first, he explains it by adding that the whole is not something outside the parts, and thus must be understood as existing in the parts.
Tertius modus est, sicut homo dicitur esse in animali, vel quaecumque alia species in suo genere. The third way is as “man” is said to be in “animal,” and any species in its genus.
Quartus modus est, sicut genus dicitur esse in speciebus. Et ne iste modus extraneus videatur, rationem innuit quare hoc dicit: nam genus est pars definitionis speciei, et etiam differentia; unde quodammodo et genus et differentia dicuntur esse in specie sicut partes in toto. The fourth way is as the genus is said to be in the species. And lest this way seem out of place, he gives a reason for mentioning it: the genus is part of the definition of the species as is the difference; hence in some way both the genus and the difference are said to be in the species as parts in the whole.
Quintus modus est, sicut sanitas dicitur esse in calidis et frigidis, quorum contemperantia constituit sanitatem; et universaliter quaecumque alia forma in materia vel subiecto, sive sit accidentalis sive substantialis. The fifth way is as health is said to be in hot and cold things, the balance between which constitutes health; and in general as any other form is in matter or a subject, whether it be an accidental or a substantial form.
Sextus modus, sicut res Graecorum dicuntur esse in rege Graeciae, et universaliter omne quod movetur est in primo motivo. Per hunc etiam modum dicere possum aliquid esse in me, quia est in potestate mea ut faciam illud. The sixth way is as the affairs of the Greeks are said to exist in the king of Greece, and generally as everything that is moved is in the first mover. According to this way, I can say that something is in me, because it is in my power to do it.
Septimo modo dicitur aliquid esse in aliquo, sicut in quodam optimo diligibili et desiderabili, et universaliter sicut in fine. Et per hunc modum dicitur esse cor alicuius in aliqua re quam desiderat et amat. In the seventh way something is said to be in something as in something supremely loveable and desirable, and generally as in an end. in this way someone’s heart is said to be in what he desires and loves.
Octavo modo dicitur esse aliquid in aliquo sicut in vase, et universaliter sicut locatum in loco. Finally in an eighth way something is said to be in something as in a vessel, and in general as a thing in place is in its place.
Videtur autem praetermittere modum quo aliquid est in aliquo sicut in tempore: sed hic reducitur ad hunc octavum modum; nam sicut locus est mensura mobilis, ita tempus est mensura motus. He seems to have skipped the way in which something is in something as in time. But this is reduced to the eighth way. For just as place is the measure of the mobile thing, so time is the measure of motion.
Dicit autem quod secundum hunc octavum modum maxime proprie dicitur esse aliquid in aliquo. Unde oportet secundum regulam quam tradit in IV et V Metaphys. quod omnes alii modi reducantur aliquo modo ad hunc modum quo aliquid est in aliquo sicut in loco. Quod sic patet. 436. Then he says that it is according to the eighth way that something is in a very proper sense said to be in something. Hence, according to the rule given in Metaphysics IV and V, all the other modes must somehow be reduced to this eighth way, according to which, something is in something as in a place. This is done in the following way.
Locatum enim continetur, sive includitur a loco, et in eo habet quietem et fixionem. Propinquissime igitur ad hunc modum pars dicitur esse in toto integrali, in quo actu includitur: unde etiam infra dicetur quod locatum est sicut pars separata, et pars est sicut quoddam locatum coniunctum. The thing in place is contained or included by its place and has rest and it has rest and immobility therein. Therefore the way closest to this one is that in which a part is said to be in the integral whole in which it is actually included. Accordingly, it will be said below that a thing in place is as a “separated” part, and a part as a “conjoined” thing in place.
Totum autem quod est secundum rationem, ad similitudinem huius totius sumitur: unde consequenter dicitur id quod est in ratione alicuius, esse in eo; ut animal in homine. The whole which is according to reason is like this whole; hence it is said that what is in the notion of something is in it, as “animal” in “man.”
Contingit autem sicut partem totius integralis includi in toto secundum actum, ita partem totius universalis includi in toto secundum potentiam: nam genus ad plura se extendit in potentia quam species, licet species habeat plura in actu: unde consequenter dicitur esse etiam species in genere. Now just as it happens that the part of an integral whole is enclosed in a whole according to act, so the part of a universal whole is enclosed in a whole according to potency for the genus extends to more things potentially than the species does, although the species may have more elements in act. Consequently, species is also said to be in the genus.
Et quia sicut species continetur in potentia generis, ita forma in potentia materiae, ulterius dicitur forma esse in materia. And because, just as the species is contained in the potency of the genus, so form is contained in the potency of matter, it is further said that form is in the matter.
Et quia totum habet rationem formae respectu partium, ut dictum est in secundo; consequenter etiam totum dicitur esse in partibus. Sicut autem forma includitur sub potentia passiva materiae, ita effectus includitur sub potentia activa agentis: unde et dicitur aliquid esse in primo motivo. And because the whole has the notion of form in relation to the parts, as was said in Book II, consequently the whole is also said to be in the parts. But just as form is enclosed under the passive potency of matter, so the effect is enclosed under the active potency of the agent. Whence it is that something is said to be in a first mover.
Deinde autem manifestum est quod appetitus quiescit in bono desiderato et amato, et in eo figitur, sicut et locatum in loco: unde etiam dicitur affectus amantis esse in amato. Finally, it is clear that the appetite rests in the good it desires and loves and is, indeed, fixed in it, just as the thing in place is fixed in place. Hence the affection of the lover is said to be in the thing loved.
Et sic patet quod omnes alii modi derivantur ab ultimo, qui est maxime proprius. And thus it is evident that all the other ways are derived from the last, which is the most proper.
Deinde cum dicit: dubitabit autem aliquis etc., inquirit utrum aliquid possit esse in seipso: nam Anaxagoras supra dixit infinitum esse in seipso. 437. Then [302] he asks whether anything can be in itself, for Anaxagoras said above that the infinite exists in itself.
Primo ergo movet dubitationem: utrum scilicet aliquid unum et idem possit esse in seipso, vel nihil; sed omnia vel nusquam sint, vel sint in aliquo alio. Therefore, he first raises the question: whether one and the same thing can be in itself; or whether nothing can, but all things either never are or are in something else.
Secundo, ibi: dupliciter autem hoc est etc., solvit. 438. Secondly [302] he answers this; First he shows how something can be in itself; Secondly, how it cannot, at no. 439.
Et primo ostendit quomodo possit esse aliquid in seipso; secundo quomodo non possit, ibi: primum autem non contingit et cetera. Dicit ergo primo quod dupliciter potest intelligi aliquid esse in seipso: uno modo primo et per se; alio modo secundum alterum, idest secundum partem. Et isto secundo modo potest dici aliquid esse in seipso. Cum enim alicuius totius duae partes ita se habeant quod una sit in quo est aliquid, et alia sit quod est in illa, sequitur quod totum dicatur et in quo est ratione unius partis, et quod est in hoc ratione alterius: et sic totum dicetur esse in seipso. He says first, therefore [301] that something may be understood to be in itself in two ways: in one way, primarily and per se; in another way, in relation to something else, i.e., in relation to a part. And it is in this second way that something may be said to be in itself. For when two parts of some whole are so related that one part is that in which the other exists and the other is that which is in the first, it follows that the whole is both that “in which” something exists (by reason of one part) and that which is “in this” (by reason of the other), and thus is the whole said to be in itself.
Invenimus enim quod aliquid dicitur de aliquo secundum partem, sicut aliquis dicitur albus quia superficies eius est alba, et homo dicitur sciens quia scientia est in parte ratiocinativa. Si igitur accipiatur amphora plena vino sicut quoddam totum cuius partes sunt amphora et vinum, neutra partium eius erit in seipsa, idest neque amphora neque vinum, sed hoc totum, scilicet amphora vini, erit in seipsa, inquantum utrumque est pars eius, scilicet et vinum quod est in amphora, et amphora in qua est vinum. Per hunc igitur modum contingit aliquid idem esse in seipso. For we observe that something is said of something according to a part, for example, someone is called “white” because his surface is white, and a man is called “knowing” because science is in his rational part. If therefore we take a jug full of wine as a certain “whole” whose parts are jug and wine, neither of the parts will exist in itself, i.e., neither the jug nor the wine, but this whole, which is a jug of wine, will be in itself inasmuch as each is a part of it, i.e., both the wine which is in the jug and the jug in which the wine is. It is in this way, therefore, that one and the same thing can be in itself.
Deinde cum dicit: primum autem non contingit etc., ostendit quod non contingit aliquid esse primo in seipso. Et primo proponit quod intendit, distinguens utrumque modum quo aliquid est in seipso, et quo non est; secundo probat propositum, ibi: neque igitur inductive considerantibus et cetera. 439. Then [302] he shows that nothing can be primarily in itself. First he proposes what he intends, distinguishing both the way in which something is in itself and the way in which it is not; Secondly, he proves his proposition, at no. 440.
Dicit ergo quod non contingit aliquid esse primo in seipso. Et manifestat quid sit aliquid esse primo in seipso, per oppositum. Album enim dicitur esse in corpore, quia superficies est in corpore: unde non est primo in corpore, sed in superficie. Et similiter scientia primo dicitur esse in anima, non autem in homine, in quo est per animam. Et secundum hoc, scilicet secundum animam et superficiem, sunt appellationes quibus nominatur homo albus vel sciens, cum anima et superficies sint sicut partes in homine: non quod superficies sit pars, sed quia se habet ad modum partis, inquantum est aliquid hominis, ut terminus corporis. He says, therefore, that there is no case of anything being primarily in itself. And he makes clear what it is for something to be primarily in itself by citing an example of the opposite. For something white is said to be in a body, because the surface is in the body: hence the white is nor primarily in the body but in the surface. In like manner, science is said to be primarily in the soul, and not in the man, in whom science exists by reason of the soul. And it is according to this, i.e., according to the soul and the surface, that the appellations whereby a man is called “white” or “knowing” are verified, since the soul and the surface are as parts of man—not that the surface is a part, but it is like a part, inasmuch as it is something of the man, as The boundary of his body.
Si autem accipiatur vinum et amphora seorsum ab invicem, non sunt partes: unde neutri competit esse in seipso. Sed cum sunt simul, utpote cum amphora est plena vino, propter hoc quod et amphora et vinum sunt partes, idem erit in seipso, ut expositum est, non primo, sed per partes: sicut album non primo est in homine, sed per corpus, et in corpore per superficiem. In superficie autem non est per aliquid aliud: unde primo dicitur esse in superficie. Nec est idem id in quo est aliquid primo, et quod est in eo, sicut album et superficies: quia altera sunt secundum speciem superficies et album, et alia est natura et potentia utriusque. Now, if wine and jug are taken as separated one from the other, they are not parts; hence it belongs to neither of them to exist in itself. But when they are together, as when a jug is full of wine, then because both jug and wine are parts, the same thing will be existing in itself (as was explained above), not primarily but through its parts, just as white is not primarily in the man but is there through the body, and in the body through the surface. But it is not in the surface through anything else; hence it is said to be in the surface primarily. Nor is that in which something exists primarily, and that which is in it, the same, as in the case of white and surface. For surface and white are specifically different, and the nature and potency of each is different.
Deinde cum dicit: neque igitur inductive etc., ostensa differentia inter hoc quod est esse primo in aliquo et non primo, ostendit iam quod nihil est primo in seipso. Et primo ostendit quod non sit aliquid primo in seipso per se; secundo quod non sit aliquid primo in seipso per accidens, ibi: at vero neque secundum accidens et cetera. 440. Then [303] having pointed out the difference between being primarily in something and not being primarily in something, he now shows that nothing is primarily in itself. First he shows that nothing is primarily in itself per se; Secondly, per accidens, at no. 442.
Primum ostendit dupliciter, scilicet inductive et ratione. Dicit ergo primo quod considerando per inductionem in singulis modis supra determinatis quibus dicitur aliquid esse in aliquo, apparet quod nihil est in seipso primo et per se: neque enim aliquid est totum sui ipsius, neque pars neque genus, et sic de aliis. Ponit autem hoc concludendo ex praemissis, quia sicut manifestum est in albo et in superficie, quae se habent ut forma et materia, quod sunt aliud secundum speciem et virtutem, ita etiam potest in omnibus aliis modis considerari. And he explains the first point in two ways: namely, inductively and with an argument. He says therefore first, that by considering inductively all the ways determined above in which something is said to be in itself, it is found that nothing exists in itself primarily and per se: for nothing is the totality of itself, [i.e., in itself as whole in part?], nor as part [in whole?] as genus [in species?], and so on. He lays this down by concluding from what has gone before, because just as it is clear in the case of the white and of the surface (which are related as form and matter) that they differ both in species and in power, the same thing can be considered in all the other modes.
Deinde cum dicit: et ratione manifestum est etc., probat idem ratione. Et dicit manifestum esse per rationem quod impossibile est aliquid esse primo et per se in seipso. Si enim aliquid primo et per se sit in seipso, oportet quod eidem et secundum idem conveniat ratio eius in quo est aliquid, et ratio eius quod est in eo. Unde oportet quod utrumque, scilicet tam continens quam contentum, sit utrumque; ut puta quod amphora sit vas et vinum, et vinum sit vinum et amphora, si primo et per se contingit aliquid esse in seipso. Unde hoc posito, scilicet quod vinum sit amphora et vinum, et amphora sit vinum et amphora, si quis dicat quod alterum eorum sit in altero, ut puta vinum in amphora, sequitur quod vinum recipiatur in amphora non inquantum vinum est, sed inquantum vinum est illa, scilicet amphora. Quare, si esse in amphora primo et per se convenit amphorae ex eo quod ponitur aliquid primo et per se in seipso esse, sequitur quod nihil possit dici esse in amphora, nisi inquantum ipsum est amphora. Et sic, si vinum dicatur esse in amphora, sequitur quod esse in amphora competit vino, non secundum quod vinum est vinum, sed secundum quod vinum est amphora. 441. Then [304] he proves the same thing with an argument and says that it is clear by reasoning that it is impossible for anything to be primarily and per se in itself. For if there be anything such, necessarily the same thing, in the same way, will have the notion both of that in which something is, and that which is in it. Hence, each would have to be both the container and the content; for example, the jug would be the vessel and the wine, and the wine both the wine and jug, if something could be primarily and per se in itself. Now on this assumption (namely, that the wine is both the jug and wine, and the jug both wine and jug), if anyone were to say that either is in the other, for example, that the wine is in the jug, it would follow that the wine is received into the jug not inasmuch it is wine, but inasmuch as wine is the jug. Wherefore, if to be in the jug primarily and per se is a property of the jug (on the assumption that something is primarily and per se in itself), it follows that nothing can be said to be in the jug except inasmuch as that something is the jug. And so, if the wine is said to be in the jug, it follows that to be in the jug belongs to the wine, not inasmuch as it is wine, but inasmuch as the wine is the jug.
Et eadem ratione, si amphora recipiat vinum, recipiet ipsum non inquantum amphora est amphora, sed inquantum amphora est vinum. Hoc autem est inconveniens. Unde manifestum est, quod secundum alteram rationem est id in quo, et quod in hoc. Alia est enim ratio eius quod est in aliquo, et eius in quo est aliquid. Non potest ergo per se et primo aliquid esse in seipso. For the same reason, if the jug receives the wine, it will receive it not inasmuch as the jug is jug but inasmuch as the jug is wine. Now this is unacceptable. Hence, it is clear that it is under different aspects that something is “that in which” and “that which is in.” For it is one thing to be that which is in something, and another to be that in which something is. Consequently, nothing can be primarily and per se in itself.
Deinde cum dicit: at vero neque secundum accidens etc., ostendit quod non sit aliquid primo in seipso etiam secundum accidens. Dicitur enim aliquid esse in aliquo secundum accidens, quando est in eo propter aliquid aliud in eo existens; ut si dicamus hominem esse in mari, quia est in navi, quae est in mari: in hac tamen primo dicitur esse, idest non propter partem. Si igitur contingat aliquid esse in seipso primo, non per se quidem, sed per accidens, sequitur quod sit in seipso propter hoc quod aliquid aliud sit in ipso. Et sic sequitur quod duo corpora sint in eodem, scilicet illud corpus quod est in eo, et ipsummet quod est in seipso. Sic enim amphora erit in seipsa per accidens, si ipsa amphora, cuius natura est ut recipiat aliquid, sit in seipsa, et iterum illud cuius est receptivum, scilicet vinum: ergo in amphora erit et amphora et vinum, si propter hoc quod vinum est in amphora, sequitur amphoram esse in seipsa: et sic duo corpora essent in eodem. Sic igitur patet quod impossibile est aliquid esse primo in seipso. 442. Then [305] he shows that nothing exists primarily in itself even according to accident. For something is said to be in something according to accident, when it is in it on account of something else existing in it; as, for example, when we say that a man is in the sea because he is in a boat which is in the sea: he is nevertheless said to be in the boat primarily, i.e., not according to a part. If therefore something could be in itself primarily, though not per se but per accidens, it would be in itself on account of something else being in it. And so it follows that two bodies are in the same thing; namely, the body which is in something and that same thing as existing in itself. In this way a jug will be in itself per accidens, if the jug itself, whose nature it is to receive something, is in itself, and again that which it receives, i.e., the wine. Therefore, in the jug will exist both jug and wine, if, because the wine is in the jug it follows that the jug is in itself; and so two bodies would be in the same. Consequently, it is clearly impossible for anything to be primarily in itself.
Sciendum tamen quod aliquando dicitur aliquid esse in seipso, non secundum intellectum affirmativum, sicut hic reprobat philosophus, sed secundum intellectum negativum, prout esse in seipso non significat nisi non esse in alio. Notice, however, that sometimes something is said to be “in itself” not according to an affirmation but according to a negation, inasmuch as to be in itself signifies nothing more than not to be in something else.
Deinde cum dicit: quod autem Zeno etc., solvit quaedam dubitata. Et primo removet rationem Zenonis, quae inducebatur ad probandum quod locus non sit, per hoc quia si est, oportet quod locus non sit, per hoc quia si est, oportet quod sit in alio, et sic itur in infinitum. Sed hoc, ut dicit, non est difficile solvere postquam iam sunt distincti modi quibus aliquid dicitur esse in aliquo. 443. Then [306] he settles certain doubts. First he destroys Zeno’s reason which was appealed to as proof that place does not exist on the assumption that, if it did, it must exist in something else and so on ad infinitum. But this, as he says, is not difficult to answer after one knows the various ways in which something is said to be “in” something else.
Nihil enim prohibet dicere quod locus est in aliquo: non tamen est in illo sicut in loco, sed per quendam alium modum, sicut forma est in materia vel accidens in subiecto; inquantum scilicet locus est terminus continentis. Et hoc est quod subdit: sicut sanitas est in calidis ut habitus, et calor in corpore ut passio vel accidens. Unde non necesse est quod procedatur in infinitum. For there is nothing to prevent our saying that place is in something: for while it is not in something as in a place, it is in something in some other way, as form is in matter or an accident in a subject, inasmuch as place is a boundary of the container. And this is what he adds: as health is in the hot as a habit, and heat is in a body as a passion or accident. Hence it is not necessary to proceed to infinity.
Deinde cum dicit: illud autem manifestum etc., solvit etiam dubitationes supra positas de quidditate loci, an scilicet sit forma vel materia, ex hoc quod ostensum est, quod nihil primo et per se est in seipso. Ex hoc enim manifestum est quod nihil potest esse sicut vas vel locus eius quod continetur in ipso sicut pars quae sit materia vel forma: oportet enim primo et per se alterum esse, quod est in aliquo, et in quo est aliquid, ut ostensum est. Unde sequitur quod neque forma neque materia sit locus, sed aliquid alterum a locato sit locus: materia enim et forma sunt aliquid locati sicut partes intrinsecae eius. 444. Then [307] he also settles the doubts mentioned above about the nature of place (namely, whether it be form or matter) by appealing to his proof that nothing exists in itself primarily and per se. For it is clear from this proof that nothing can be the vessel or place of that which is contained in it after the manner of a part such as matter or form is: for that which is in something and that in which something is must be primarily and per se distinct, as we have shown. Hence, it follows that neither form nor matter is place; rather place is something entirely different from the thing in place, whereas matter and form belong to the thing in place as intrinsic parts thereof.
Ultimo autem concludit quod supra dicta per modum oppositionis dicta sunt de loco: quarum quidem oppositionum aliquae iam solutae sunt, aliquae vero solventur post manifestatam naturam loci. Finally he concludes that the things said above about place were said as contesting it. Some of these oppositions have now been solved; others will be solved after the nature of place is manifested.

Lecture 5
Necessary previous notions for the definition of place.
Lectio 5
Chapter 4
Τί δέ ποτ' ἐστὶν ὁ τόπος, ὧδ' ἂν γένοιτο φανερόν. λάβωμεν δὲ περὶ αὐτοῦ ὅσα δοκεῖ ἀληθῶς καθ' αὑτὸ ὑπάρχειν αὐτῷ. ἀξιοῦμεν δὴ τὸν τόπον εἶναι
  1. πρῶτον μὲν (211a.) περιέχον ἐκεῖνο οὗ τόπος ἐστί,
  2. καὶ μηδὲν τοῦ πράγματος, ἔτι τὸν πρῶτον μήτ' ἐλάττω μήτε μείζω,
  3. ἔτι ἀπολείπεσθαι ἑκάστου καὶ χωριστὸν εἶναι,
  4. πρὸς δὲ τούτοις πάντα τόπον ἔχειν τὸ ἄνω καὶ κάτω, καὶ φέρεσθαι φύσει καὶ μένειν ἐν τοῖς οἰκείοις τόποις ἕκαστον τῶν σωμάτων, τοῦτο δὲ ποιεῖν ἢ ἄνω ἢ κάτω.
ὑποκειμένων δὲ τούτων τὰ λοιπὰ θεωρητέον.
What then after all is place? The answer to this question may be elucidated as follows. Let us take for granted about it the various characteristics which are supposed correctly to belong to it essentially. We assume then:
  1. Place is what contains that of which it is the place.
  2. Place is no part of the thing.
  3. The immediate place of a thing is neither less nor greater than the thing.
  4. Place can be left behind by the thing and is separable. In addition:
  5. All place admits of the distinction of up and down, and each of the bodies is naturally carried to its appropriate place and rests there, and this makes the place either up or down.
Having laid these foundations, we must complete the theory.
δεῖ δὲ πειρᾶσθαι τὴν σκέψιν οὕτω ποιεῖσθαι ὅπως τὸ τί ἐστιν ἀποδοθήσεται, ὥστε τά τε ἀπορούμενα λύεσθαι, καὶ τὰ δοκοῦντα ὑπάρχειν τῷ τόπῳ ὑπάρχοντα ἔσται, καὶ ἔτι τὸ τῆς δυσκολίας αἴτιον καὶ τῶν περὶ αὐτὸν ἀπορημά των ἔσται φανερόν· οὕτω γὰρ ἂν κάλλιστα δεικνύοιτο ἕκαστον. We ought to try to make our investigation such as will render an account of place, and will not only solve the difficulties connected with it, but will also show that the attributes supposed to belong to it do really belong to it, and further will make clear the cause of the trouble and of the difficulties about it. Such is the most satisfactory kind of exposition.
πρῶτον μὲν οὖν δεῖ κατανοῆσαι ὅτι οὐκ ἂν ἐζητεῖτο ὁ τόπος, εἰ μὴ κίνησις ἦν ἡ κατὰ τόπον· διὰ γὰρ τοῦτο καὶ τὸν οὐρανὸν μάλιστ' οἰόμεθα ἐν τόπῳ, ὅτι ἀεὶ ἐν κινήσει. ταύτης δὲ τὸ μὲν φορά, τὸ δὲ αὔξησις καὶ φθίσις· καὶ γὰρ ἐν τῇ αὐξήσει καὶ φθίσει μεταβάλλει, καὶ ὃ πρότερον ἦν ἐνταῦθα, πάλιν μεθέστηκεν εἰς ἔλαττον ἢ μεῖζον. First then we must understand that place would not have been thought of, if there had not been a special kind of motion, namely that with respect to place. It is chiefly for this reason that we suppose the heaven also to be in place, because it is in constant movement. Of this kind of change there are two species—locomotion on the one hand and, on the other, increase and diminution. For these too involve variation of place: what was then in this place has now in turn changed to what is larger or smaller.
ἔστι δὲ κινούμενον τὸ μὲν καθ' αὑτὸ ἐνεργείᾳ, τὸ δὲ κατὰ συμβεβηκός· κατὰ συμβεβηκὸς δὲ τὸ μὲν ἐνδεχόμενον κινεῖσθαι καθ' αὑτό, οἷον τὰ μόρια τοῦ σώματος καὶ ὁ ἐν τῷ πλοίῳ ἧλος, τὰ δ' οὐκ ἐνδεχόμενα ἀλλ' αἰεὶ κατὰ συμβεβηκός, οἷον ἡ λευκότης καὶ ἡ ἐπιστήμη· ταῦτα γὰρ οὕτω μεταβέβληκε τὸν τόπον, ὅτι ἐν ᾧ ὑπάρχουσι μεταβάλλει. Again, when we say a thing is 'moved', the predicate either (1) belongs to it actually, in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter case it may be either (a) something which by its own nature is capable of being moved, e.g. the parts of the body or the nail in the ship, or (b) something which is not in itself capable of being moved, but is always moved through its conjunction with something else, as 'whiteness' or 'science'. These have changed their place only because the subjects to which they belong do so.
ἐπεὶ δὲ λέγομεν εἶναι ὡς ἐν τόπῳ ἐν τῷ οὐρανῷ, διότι ἐν τῷ ἀέρι οὗτος δὲ ἐν τῷ οὐρανῷ· καὶ ἐν τῷ ἀέρι δὲ οὐκ ἐν παντί, ἀλλὰ διὰ τὸ ἔσχατον αὐτοῦ καὶ περιέχον ἐν τῷ ἀέρι φαμὲν εἶναι (εἰ γὰρ πᾶς ὁ ἀὴρ τόπος, οὐκ ἂν ἴσος εἴη ἑκάστου ὁ τόπος καὶ ἕκαστον, δοκεῖ δέ γε ἴσος εἶναι, τοιοῦτος δ' ὁ πρῶτος ἐν ᾧ ἐστιν)· We say that a thing is in the world, in the sense of in place, because it is in the air, and the air is in the world; and when we say it is in the air, we do not mean it is in every part of the air, but that it is in the air because of the outer surface of the air which surrounds it; for if all the air were its place, the place of a thing would not be equal to the thing—which it is supposed to be, and which the primary place in which a thing is actually is.
ὅταν μὲν οὖν μὴ διῃρημένον ᾖ τὸ περιέχον ἀλλὰ συνεχές, οὐχ ὡς ἐν τόπῳ λέγεται εἶναι ἐν ἐκείνῳ, ἀλλ' ὡς μέρος ἐν ὅλῳ· ὅταν δὲ διῃρημένον ᾖ καὶ ἁπτόμενον, ἐν πρώτῳ ἐστὶ τῷ ἐσχάτῳ τοῦ περιέχοντος, ὃ οὔτε ἐστὶ μέρος τοῦ ἐν αὐτῷ οὔτε μεῖζον τοῦ διαστήματος ἀλλ' ἴσον· ἐν γὰρ τῷ αὐτῷ τὰ ἔσχατα τῶν ἁπτομένων. When what surrounds, then, is not separate from the thing, but is in continuity with it, the thing is said to be in what surrounds it, not in the sense of in place, but as a part in a whole. But when the thing is separate and in contact, it is immediately 'in' the inner surface of the surrounding body, and this surface is neither a part of what is in it nor yet greater than its extension, but equal to it; for the extremities of things which touch are coincident.
καὶ συνεχὲς μὲν ὂν οὐκ ἐν ἐκείνῳ κινεῖται ἀλλὰ μετ' ἐκείνου, διῃρημένον δὲ ἐν ἐκείνῳ· καὶ ἐάν τε κινῆται τὸ περιέχον ἐάν τε μή, (211b.) οὐδὲν ἧττον. Further, if one body is in continuity with another, it is not moved in that but with that. On the other hand it is moved in that if it is separate. It makes no difference whether what contains is moved or not.
[ἔτι ὅταν μὴ διῃρημένον ᾖ, ὡς μέρος ἐν ὅλῳ λέγεται, οἷον ἐν τῷ ὀφθαλμῷ ἡ ὄψις ἢ ἐν τῷ σώματι ἡ χείρ, ὅταν δὲ διῃρημένον, οἷον ἐν τῷ κάδῳ τὸ ὕδωρ ἢ ἐν τῷ κεραμίῳ ὁ οἶνος· ἡ μὲν γὰρ χεὶρ μετὰ τοῦ σώματος κινεῖται, τὸ δὲ ὕδωρ ἐν τῷ κάδῳ.] Again, when it is not separate it is described as a part in a whole, as the pupil in the eye or the hand in the body: when it is separate, as the water in the cask or the wine in the jar. For the hand is moved with the body and the water in the cask.
Praemissa disputatione de loco an sit et quid sit, et solutis quibusdam dubitationibus, hic accedit ad determinandum veritatem de loco. Et primo praemittit quasdam suppositiones de loco, quibus utetur determinando de loco; secundo ostendit qualis debeat esse definitio danda de loco, ibi: oportet autem tentare etc.; tertio incipit determinare de loco, ibi: primum quidem igitur et cetera. 445. After setting forth a preliminary discussion about whether place exists and what it is, and after solving some doubtful points on these matters, the Philosopher now begins the task of determining the truth about place. First he gives some presuppositions to be used in determining about place; Secondly, he shows what qualities a definition of place should have, at no. 447; Thirdly, he begins to determine about place, at no. 448.
Dicit ergo primo quod manifestum fiet ex sequentibus quid sit locus: sed oportet prius accipere quasi quasdam suppositiones et principia per se nota, illa scilicet quae videntur per se inesse loco. Quae quidem sunt quatuor. 446. He says first therefore [308] that it will be clear from the following just what place is. But we must first adopt as it were certain suppositions and self-evident principles, those namely, which appear intrinsic to place. Indeed, there are four such:
Omnes enim reputant hoc esse dignum: primo quidem quod locus contineat id cuius est locus; ita tamen quod locus non sit aliquid locati. Quod quidem dicit ad excludendum continentiam formae, quae est aliquid rei, et alio modo continet quam locus. For all agree on this maxim, that place contains that of which it is the place, yet in such a way that place is not any part of the thing in place. He says this to exclude the containing force of form, which is part of a thing, but contains in a manner different from place.
Secunda suppositio est, quod primus locus, idest in quo aliquid primo est, est aequalis locato, non maior neque minor. The second supposition is that the primary place, i.e., that in which something exists primarily, is equal to, and neither greater nor less than, the thing in place.
Tertia suppositio est, quod locus non deficit unicuique locato, quin omne locatum habeat locum; non tamen ita quod unus et idem locus nunquam deficiat eidem locato; quia locus est separabilis a locato: sed quando locus unus deficit alicui locato, tunc locatum fit in alio loco. The third supposition is that a place exists for everything in place, i.e., that everything in place has a place, but not in the sense that one and the same place is never lost by one and the same thing capable of being in a place; for a place can be separated from a thing in place. However, when one place is lost by a thing in place, it acquires another place.
Quarta suppositio est, quod in omni loco invenitur, quasi differentia loci, sursum et deorsum: et quod naturaliter unumquodque corpus, cum est extra proprium locum, fertur ad ipsum, et cum est in eo, manet in ipso. Propria autem loca naturalium corporum sunt sursum et deorsum, ad quae naturaliter moventur, et in quibus manent. Sed hoc dicit secundum eorum opinionem qui non ponebant aliquod corpus praeter naturam quatuor elementorum: nondum enim probaverat corpus caeleste esse neque grave neque leve, sed postea hoc probabit in primo libro de caelo. Ex his autem nunc suppositis, procedetur ad considerationem aliorum. The fourth supposition is that in all places there is found, as a [specific] difference of place, an “up” and a “down,” and that each body, when it is outside its proper place, naturally seeks it and, when it is in it, naturally remains there. Now the proper places of natural bodies are “up” and down,” to which they are naturally borne and in which they remain. But he says this in keeping with the opinion of those who posited no body other than the four elements: for he has not yet proved the heavenly body to be neither light nor heavy—which he will prove later in De Coelo, I. From these presuppositions he proceeds to the consideration of what remains.
Deinde cum dicit: oportet autem tentare etc., ostendit qualis debeat esse definitio danda de loco. Et dicit quod in definiendo locum, intentio nostra debet ad quatuor attendere, quae quidem necessaria sunt ad definitionem perfectam. 447. He then [309] shows what qualities should be found in a definition of place. And he says that in defining place our attention should be focused on four things which indeed are necessary for a perfect definition:
Primo quidem, ut ostendatur quid sit locus: nam definitio est oratio indicans quid est res. First, that one show what place is, for a definition is an expression indicating what a thing is.
Secundo, ut solvantur quaecumque opposita sunt circa locum: nam cognitio veritatis est solutio dubitatorum. Secondly, that one resolve conflicting arguments about place: for the knowledge of truth involves the solution of doubts.
Tertium est, quod ex definitione data manifestentur proprietates loci, quae insunt ei: quia definitio est medium in demonstratione, qua propria accidentia demonstrantur de subiectis. Thirdly, that the given definition reveal the properties of place, which inhere in it, because a definition is the middle term in a demonstration, by which the proper accidents are demonstrated of the subject.
Quartum est, quod ex definitione loci erit manifesta causa, quare aliqui discordaverunt circa locum; et omnium quae sunt opposita circa ipsum. Et sic pulcherrime definitur unumquodque. Fourthly, that from the definition of place the cause will be clear why there is disagreement about place and of all the conflicting things said about it. Such a procedure is the most beautiful way of defining anything.
Deinde cum dicit: primum quidem igitur oportet etc., determinat de loco. Et primo ostendit quid sit locus; secundo solvit dubitationes prius positas, ibi: manifestum autem ex his etc.: tertio assignat causam naturalium proprietatum loci, ibi: et fertur igitur in sui ipsius et cetera. 448. Then [310] he determines about place; First he shows what place is; Secondly, at no. 487, he settles the doubts previously mentioned; Thirdly, he assigns the cause of the natural properties of place, at no. 492.
Circa primum duo facit: primo ostendit quid sit locus; secundo quomodo aliquid sit in loco, ibi: cui quidem igitur et cetera. About the first he does two things: First he shows what place is; Secondly, how something exists in place, at no. 472(L.7).
Circa primum duo facit: primo praemittit quaedam quae sunt necessaria ad investigandum definitionem loci; secundo incipit investigare loci definitionem, ibi: iam igitur manifestum ex et cetera. As to the first he does two things: First he mentions some facts preliminary to his hunt for the definition; Secondly, he begins to investigate the definition of place, at no. 455 (L.6).
Circa primum quatuor praemittit. Quorum primum est, quod nunquam fuisset inquisitum de loco, nisi esset aliquis motus secundum locum. Ex hoc enim necesse fuit ponere locum aliud a locato, quia inveniuntur in eodem loco successive duo corpora, et similiter unum corpus in duobus locis; sicut etiam transmutatio formarum circa unam materiam, induxit in cognitionem materiae. Et propter hoc maxime opinantur aliqui quod caelum sit in loco, quia semper movetur. Sed motuum aliquis est secundum locum per se, scilicet loci mutatio: alius autem ex consequenti, scilicet augmentum et decrementum; quia augmentata quantitate vel diminuta, corpus accipit maiorem vel minorem locum. 449. In regard to the first, be makes four preliminary statements, the first of which is that the question of place would never have arisen were there no motion in regard to place. For it was necessary to posit place as something distinct from the object in place, because two bodies are found successively in the same place, and, in like manner, one body successively in two places. (Similarly, it was the successive change of forms in one and the same matter that led to the knowledge of matter). For this reason some are convinced that the heavens are in place, since they are always in motion. Now, of motions, one is according to place per se, namely, the change of place; another is consequently related to place, namely, increase and decline, because as a body grows or decreases, it acquires a larger or a smaller place.
Secundum ponit ibi: est autem quod movetur aliud et cetera. Et dicit quod aliquid movetur per se in actu, sicut quodcumque corpus; aliud vero secundum accidens. Quod quidem contingit dupliciter. Quaedam enim moventur secundum accidens, quae tamen sunt possibilia moveri per se; sicut partes alicuius corporis, dum sunt in toto, moventur per accidens; sed quando separantur, moventur per se; ut clavus, quando est infixus navi, movetur per accidens, sed quando extrahitur, movetur per se. Quaedam vero non possunt moveri per se, sed semper moventur per accidens; sicut albedo et scientia, quae mutant locum inquantum mutatur illud in quo sunt. Hoc autem induxit, quia hoc modo aliquid per se vel per accidens, actu vel potentia natum est esse in loco, sicut et moveri. 450. He gives the second [311], saying that some things are moved, per se in act as in the case with every body, while others according to accident. This latter can occur in two ways. For some things that could be moved essentially are de facto moved accidentally, as the parts of a body while they are in the whole body are moved per accidens but when they are separated they are moved per se. Thus, a nail, when it is embedded in a ship, is moved per accidens, but when it is extracted it is moved per se. Other things are not be moved per se, but only per accidens, as is the case with whiteness and knowledge, which change place as that in which they are changes place. This point was brought up because things are apt to be in place per se or per accidens, actually or potentially in the same way as they are apt to be moved in those ways.
Tertium ponit ibi: quoniam autem dicimus esse et cetera. Et dicit quod aliquis dicitur esse in caelo sicut in loco, propter hoc quod est in aere, qui quidem est in caelo. Nec tamen dicimus quod in toto aere sit aliquis primo et per se; sed propter ultimam extremitatem aeris, quae continet aliquem, dicitur aliquis esse in aere; quia si totus aer esset locus alicuius, puta hominis, non esset aequalis locus et locatum; quod est contra suppositionem prius positam. Sed id in quo est aliquid primo, videtur esse extremum corporis continentis, et sic est huiusmodi, scilicet aequale. 451. He gives the third [312] when he says that someone is said to be in the heavens as in a place because he is in the air which indeed is in the heavens. Yet we do not say that anyone is in the entire air primarily and per se, but by reason of the ultimate boundary of the air containing him he is said to be in the air. For if the whole air were anything’s place, e.g., a man’s, the place and the thing in place would not be equal—which is against what was supposed above. But that in which something exists primarily is seen to be the boundary of the containing body; and this is what primary place means, i.e., equal.
Quartum ponit ibi: cum quidem igitur non divisum et cetera. Et primo ponit; secundo probat, ibi: et cum continuum et cetera. 452. He gives the fourth reason [313]. First, he mentions it; secondly, he proves it, at no. 453.
Dicit ergo primo quod cum continens non est divisum a contento, sed est ei continuum, non dicitur esse in illo sicut in loco, sed sicut pars in toto; utpote, si dicamus unam partem aeris contineri a toto aere. Et hoc concludit ex praemissis, quia ubi est continuum, ibi non est accipere ultimum in actu, quod supra dixit requiri ad locum. Sed cum continens est divisum, et contiguum contento, tunc, contentum scilicet, est in loco, existens in ultimo continentis primo et per se: illud inquam continens, quod non est pars eius, neque est maius neque minus secundum dimensionem, sed aequale. Et quomodo possint esse continens et contentum aequalia, ostendit per hoc quod ultima contingentium se sunt simul; unde oportet eorum ultima esse aequalia. He says therefore first that whenever the container is not separate from the thing contained but is continuous with it, the latter is not said to be in it as in a place, but as a part in a whole; as, for example, when we say that one part of the air is contained by the totality of air. And he concludes this from what went before, because where there is a continuum there is no ultimate boundary in act, something that is required for place, as was stated above. But when the container is separated, and contiguous to the thing contained, this latter is in place and exists in the ultimate boundary of the container primarily and per se, of a container, that is, which is not a part of the contained and neither greater nor less but equal in dimension. But how the container and the thing contained can be equal he shows by pointing out that the ultimate boundaries of things touching are together: whence, their ultimate boundaries must be equal.
Deinde cum dicit: et cum continuum quidem sit etc., probat istud quartum duabus rationibus. Quarum prima est, quod contentum continuum continenti, non movetur in continente, sed simul cum illo, sicut pars simul cum toto: sed quando est divisum contentum a continente, tunc potest moveri in illo, sive continens moveatur sive non; homo enim movetur in navi, vel quiescente vel mota. Cum ergo aliquid moveatur in loco, sequitur quod locus sit continens divisum. 453. Then he proves the fourth point by two arguments [314]. The first of these is that something contained that forms a continuum with the container is not moved in the container but with the container, as the part is moved simultaneously with the whole; but when it is separate from the container, then it can be moved in it, whether the container be moved or not—for a man is moved on a ship whether it be moving or at rest. Therefore, since something can be moved in a place, it follows that place is a separated container.
Secundam rationem ponit ibi: amplius, cum non divisum sit et cetera. Et dicit quod cum contentum non sit divisum a continente sed continuum ei, tunc dicitur esse in eo sicut pars in toto; ut visus est sicut pars formalis in oculo, et manus sicut pars organica in corpore: sed cum divisum est contentum a continente, tunc dicitur esse in eo ut in vase, sicut aqua in cado et vinum in scypho: quorum haec est differentia, quod manus movetur cum corpore sed non in corpore, sed aqua movetur in cado. 454. He gives a second argument for the fourth point [315], saying that when the thing contained is not separate from the container but continuous with it, then it is said to be in it as a part in a whole, as sight is in the eye as a formal part and the hand in the body as an organic part. But when the container and the thing contained are separate, then the latter is in it as in a vessel; as water in a barrel or wine in a cup. The difference between the example in the first case and in the second is that the hand is moved with the body, but not in the body, but the water is moved in the barrel.
Cum ergo supra dictum sit quod esse in loco sit sicut esse in vase, non autem sicut pars in toto, sequitur quod locus sit sicut continens divisum. Therefore, since we have said above that to be in place is to be there as in a vessel but not as a part in a whole, it follows that place is like a separated container.

Lecture 6
The definition of place
Lectio 6
Chapter 4 cont.
ἤδη τοίνυν φανερὸν ἐκ τούτων τί ἐστιν ὁ τόπος. σχεδὸν γὰρ τέτταρά ἐστιν ὧν ἀνάγκη τὸν τόπον ἕν τι εἶναι· ἢ γὰρ μορφὴ ἢ ὕλη ἢ διάστημά τι τὸ μεταξὺ τῶν ἐσχάτων, ἢ τὰ ἔσχατα εἰ μὴ ἔστι μηδὲν διάστημα παρὰ τὸ τοῦ ἐγγιγνομένου σώματος μέγεθος. It will now be plain from these considerations what place is. There are just four things of which place must be one—the shape, or the matter, or some sort of extension between the bounding surfaces of the containing body, or this boundary itself if it contains no extension over and above the bulk of the body which comes to be in it.
τούτων δ' ὅτι οὐκ ἐνδέχεται τὰ τρία εἶναι, φανερόν· Three of these it obviously cannot be:
ἀλλὰ διὰ μὲν τὸ περιέχειν δοκεῖ ἡ μορφὴ εἶναι· ἐν ταὐτῷ γὰρ τὰ ἔσχατα τοῦ περιέχοντος καὶ τοῦ περιεχομένου. (1) The shape is supposed to be place because it surrounds, for the extremities of what contains and of what is contained are coincident.
ἔστι μὲν οὖν ἄμφω πέρατα, ἀλλ' οὐ τοῦ αὐτοῦ, ἀλλὰ τὸ μὲν εἶδος τοῦ πράγματος, ὁ δὲ τόπος τοῦ περιέχοντος σώματος. Both the shape and the place, it is true, are boundaries. But not of the same thing: the form is the boundary of the thing, the place is the boundary of the body which contains it.
διὰ δὲ τὸ μεταβάλλειν πολλάκις μένοντος τοῦ περιέχοντος τὸ περιεχόμενον καὶ διῃρημένον, οἷον ἐξ ἀγγείου ὕδωρ, τὸ μεταξὺ εἶναί τι δοκεῖ διάστημα, ὡς ὄν τι παρὰ τὸ σῶμα τὸ μεθιστάμενον. (2) The extension between the extremities is thought to be something, because what is contained and separate may often be changed while the container remains the same (as water may be poured from a vessel)—the assumption being that the extension is something over and above the body displaced.
τὸ δ' οὐκ ἔστιν, ἀλλὰ τὸ τυχὸν ἐμπίπτει σῶμα τῶν μεθισταμένων καὶ ἅπτεσθαι πεφυκότων. εἰ δ' ἦν τι [τὸ] διάστημα <�καθ' αὑ>τὸ πεφυκὸς <�εἶναι> καὶ μένον, ἐν τῷ αὐτῷ ἄπειροι ἂν ἦσαν τόποι (μεθισταμένου γὰρ τοῦ ὕδατος καὶ τοῦ ἀέρος ταὐτὸ ποιήσει τὰ μόρια πάντα ἐν τῷ ὅλῳ ὅπερ ἅπαν τὸ ὕδωρ ἐν τῷ ἀγγείῳ)· But there is no such extension. One of the bodies which change places and are naturally capable of being in contact with the container falls in whichever it may chance to be. If there were an extension which were such as to exist independently and be permanent, there would be an infinity of places in the same thing. For when the water and the air change places, all the portions of the two together will play the same part in the whole which was previously played by all the water in the vessel;
ἅμα δὲ καὶ ὁ τόπος ἔσται μεταβάλλων· ὥστ' ἔσται τοῦ τόπου τ' ἄλλος τόπος, καὶ πολλοὶ τόποι ἅμα ἔσονται. οὐκ ἔστι δὲ ἄλλος ὁ τόπος τοῦ μορίου, ἐν ᾧ κινεῖται, ὅταν ὅλον τὸ ἀγγεῖον μεθίστηται, ἀλλ' ὁ αὐτός· ἐν ᾧ γὰρ ἔστιν, ἀντιμεθίσταται ὁ ἀὴρ καὶ τὸ ὕδωρ ἢ τὰ μόρια τοῦ ὕδατος, ἀλλ' οὐκ ἐν ᾧ γίγνονται τόπῳ, ὃς μέρος ἐστὶ τοῦ τόπου ὅς ἐστι τόπος ὅλου τοῦ οὐρανοῦ. at the same time the place too will be undergoing change; so that there will be another place which is the place of the place, and many places will be coincident. There is not a different place of the part, in which it is moved, when the whole vessel changes its place: it is always the same: for it is in the (proximate) place where they are that the air and the water (or the parts of the water) succeed each other, not in that place in which they come to be, which is part of the place which is the place of the whole world.
καὶ ἡ ὕλη δὲ δόξειεν ἂν εἶναι τόπος, εἴ γε ἐν ἠρεμοῦντί τις σκοποίη καὶ μὴ κεχωρισμένῳ ἀλλὰ συνεχεῖ. ὥσπερ γὰρ εἰ ἀλλοιοῦται, ἔστι τι ὃ νῦν μὲν λευκὸν πάλαι δὲ μέλαν, καὶ νῦν μὲν σκληρὸν πάλαι δὲ μαλακόν (διό φαμεν εἶναί τι τὴν ὕλην), οὕτω καὶ ὁ τόπος διὰ τοιαύτης τινὸς εἶναι δοκεῖ φαντασίας, πλὴν ἐκεῖνο μὲν διότι ὃ ἦν ἀήρ, τοῦτο νῦν ὕδωρ, ὁ δὲ τόπος ὅτι οὗ ἦν ἀήρ, ἐνταῦθ' ἔστι νῦν ὕδωρ. (3) The matter, too, might seem to be place, at least if we consider it in what is at rest and is thus separate but in continuity. For just as in change of quality there is something which was formerly black and is now white, or formerly soft and now hard—this is just why we say that the matter exists—so place, because it presents a similar phenomenon, is thought to exist—only in the one case we say so because what was air is now water, in the other because where air formerly was there a is now water.
ἀλλ' ἡ μὲν ὕλη, (212a.) ὥσπερ ἐλέχθη ἐν τοῖς πρότερον, οὔτε χωριστὴ τοῦ πράγματος οὔτε περιέχει, ὁ δὲ τόπος ἄμφω. But the matter, as we said before, is neither separable from the thing nor contains it, whereas place has both characteristics.
εἰ τοίνυν μηδὲν τῶν τριῶν ὁ τόπος ἐστίν, μήτε τὸ εἶδος μήτε ἡ ὕλη μήτε διάστημά τι ἀεὶ ὑπάρχον ἕτερον παρὰ τὸ τοῦ πράγματος τοῦ μεθισταμένου, ἀνάγκη τὸν τόπον εἶναι τὸ λοιπὸν τῶν τεττά ρων, τὸ πέρας τοῦ περιέχοντος σώματος <�καθ' ὃ συνάπτει τῷ περιεχομένῳ>. λέγω δὲ τὸ περιεχόμενον σῶμα τὸ κινητὸν κατὰ φοράν. Well, then, if place is none of the three—neither the form nor the matter nor an extension which is always there, different from, and over and above, the extension of the thing which is displaced—place necessarily is the one of the four which is left, namely, the boundary of the containing body at which it is in contact with the contained body. (By the contained body is meant what can be moved by way of locomotion.)
δοκεῖ δὲ μέγα τι εἶναι καὶ χαλεπὸν ληφθῆναι ὁ τόπος διά τε τὸ παρεμφαίνεσθαι τὴν ὕλην καὶ τὴν μορφήν, καὶ διὰ τὸ ἐν ἠρεμοῦντι τῷ περιέχοντι γίγνεσθαι τὴν μετάστασιν τοῦ φερομένου· ἐνδέχεσθαι γὰρ φαί νεται εἶναι διάστημα μεταξὺ ἄλλο τι τῶν κινουμένων μεγεθῶν. συμβάλλεται δέ τι καὶ ὁ ἀὴρ δοκῶν ἀσώματος εἶναι· φαίνεται γὰρ οὐ μόνον τὰ πέρατα τοῦ ἀγγείου εἶναι ὁ τόπος, ἀλλὰ καὶ τὸ μεταξὺ ὡς κενὸν <�ὄν>. Place is thought to be something important and hard to grasp, both because the matter and the shape present themselves along with it, and because the displacement of the body that is moved takes place in a stationary container, for it seems possible that there should be an interval which is other than the bodies which are moved. The air, too, which is thought to be incorporeal, contributes something to the belief: it is not only the boundaries of the vessel which seem to be place, but also what is between them, regarded as empty.
ἔστι δ' ὥσπερ τὸ ἀγγεῖον τόπος μεταφορητός, οὕτως καὶ ὁ τόπος ἀγγεῖον ἀμετακί νητον. διὸ ὅταν μὲν ἐν κινουμένῳ κινῆται καὶ μεταβάλλῃ τὸ ἐντός, οἷον ἐν ποταμῷ πλοῖον, ὡς ἀγγείῳ χρῆται μᾶλλον ἢ τόπῳ τῷ περιέχοντι. βούλεται δ' ἀκίνητος εἶναι ὁ τόπος· διὸ ὁ πᾶς μᾶλλον ποταμὸς τόπος, ὅτι ἀκίνητος ὁ πᾶς. Just, in fact, as the vessel is transportable place, so place is a non-portable vessel. So when what is within a thing which is moved, is moved and changes its place, as a boat on a river, what contains plays the part of a vessel rather than that of place. Place on the other hand is rather what is motionless: so it is rather the whole river that is place, because as a whole it is motionless.
ὥστε τὸ τοῦ περιέχοντος πέρας ἀκίνητον πρῶτον, τοῦτ' ἔστιν ὁ τόπος. Hence we conclude that the innermost motionless boundary of what contains is place.
καὶ διὰ τοῦτο τὸ μέσον τοῦ οὐρανοῦ καὶ τὸ ἔσχατον τὸ πρὸς ἡμᾶς τῆς κύκλῳ φορᾶς δοκεῖ εἶναι τὸ μὲν ἄνω τὸ δὲ κάτω μάλιστα πᾶσι κυρίως, ὅτι τὸ μὲν αἰεὶ μένει, τοῦ δὲ κύκλῳ τὸ ἔσχατον ὡσαύτως ἔχον μένει. ὥστ' ἐπεὶ τὸ μὲν κοῦφον τὸ ἄνω φερόμενόν ἐστι φύσει, τὸ δὲ βαρὺ τὸ κάτω, τὸ μὲν πρὸς τὸ μέσον περιέχον πέρας κάτω ἐστίν, καὶ αὐτὸ τὸ μέσον, τὸ δὲ πρὸς τὸ ἔσχατον ἄνω, καὶ αὐτὸ τὸ ἔσχατον· This explains why the middle of the heaven and the surface which faces us of the rotating system are held to be 'up' and 'down' in the strict and fullest sense for all men: for the one is always at rest, while the inner side of the rotating body remains always coincident with itself. Hence since the light is what is naturally carried up, and the heavy what is carried down, the boundary which contains in the direction of the middle of the universe, and the middle itself, are down, and that which contains in the direction of the outermost part of the universe, and the outermost part itself, are up.
καὶ διὰ τοῦτο δοκεῖ ἐπίπεδόν τι εἶναι καὶ οἷον ἀγγεῖον ὁ τόπος καὶ περιέχον. For this reason, too, place is thought to be a kind of surface, and as it were a vessel, i.e. a container of the thing.
ἔτι ἅμα τῷ πράγματι ὁ τόπος· ἅμα γὰρ τῷ πεπερασμένῳ τὰ πέρατα. Further, place is coincident with the thing, for boundaries are coincident with the bounded.
Praemissis his quae sunt necessaria ad investigandum definitionem loci, hic investigat loci definitionem. Et circa hoc tria facit: primo investigat particulas definitionis; secundo concludit definitionem, ibi: quare terminus etc., tertio ostendit eam bene assignatam, ibi: et propter hoc medium et cetera. 455. After positing the preliminary notions required for the search of the definition of place, the Philosopher now begins his search for the definition. About this he does three things: First, he looks into each part of the definition; Secondly, he shows that it is a good definition, at no. 471
Circa primum duo facit: primo investigat genus loci; secundo differentiam completivam definitionis eius, ibi: videtur autem magnum aliquid et cetera. As to the first he does two things: First, he searches for the genus of place; Secondly, for the differentia that will complete the definition, at no.467.
Ad investigandum autem genus loci utitur divisione quadam. Unde circa hoc tria facit: primo proponit divisionem; secundo excludit tria membra divisionis, ibi: horum autem, quod non contingat etc.; tertio concludit quartum, ibi: si igitur nihil horum et cetera. In searching for the genus of place he divides. In connection with this he does three things: First he gives the division; Secondly, he excludes three members of the division, at no. 457; Thirdly, he concludes to the fourth member, at no. 466.
Dicit ergo primo quod iam ex praemissis potest esse manifestum quid sit locus. Videtur enim secundum ea quae consueverunt de loco dici, quod locus sit unum de quatuor; scilicet vel materia, vel forma, vel aliquod spatium inter extrema continentis; vel si nullum spatium est inter extrema continentis, quod habeat aliquas dimensiones, praeter magnitudinem corporis quod ponitur infra corpus continens, oportebit dicere quartum, scilicet quod extrema corporis continentis sit locus. 456. He says therefore first [316] that from the previous discussion the nature of place may already be clear. For it seems that according to what is ordinarily said of place that it is one of four things: namely, matter or form or the space between and within the boundaries of the container, or, if there is no space within the boundaries of the container which has its own dimensions over and above the dimensions of the body existing within the confines of the container, then it will be necessary to posit a fourth possibility, namely, that place is the boundary of the containing body.
Deinde cum dicit: horum autem, quod non contingat etc., excludit tria membra praedictae divisionis. Et primo proponit quod intendit, dicens manifestum esse per sequentia, quod non contingit locum esse aliquod horum trium. Secundo prosequitur, ibi: sed propter id quod continet, videtur forma etc.: et primo de forma; secundo de spatio, ibi: sed ex eo quod mutatur etc.; tertio de materia, ibi: et materia etiam videtur et cetera. 457. Then [317] he excludes three members of this division. First, he proposes what he intends, saying that it is clear from what follows that place is not any of these three; Secondly, he pursues his intention, at no. 458. First, that it is not form; Secondly, that it is not space, at no. 460; Thirdly, that it is not matter, at no. 464.
Circa primum duo facit: primo ponit quare forma videatur esse locus: quia scilicet forma continet; quod videtur esse proprium loci. Extrema vero corporis continentis et contenti sunt simul, cum continens et contentum sint contigua ad invicem: et sic terminus continens, qui est locus, non videtur separatus esse a termino corporis contenti; et sic videtur locus non differre a forma. 458, In regard to the first he does two things. First [318] he sets down why form seems to be place: it is because form is a container, and this seems to be a property of place. Now the boundaries of the containing body and those of the contained are together, since the container and the contained are contiguous. Thus it does not seem that the containing boundary, which is place, is separate from that of the body contained. Consequently, there does not seem to be any difference between place and form.
Secundo, ibi: sunt quidem igitur utraque etc., ostendit quod forma non sit locus. Quia quamvis locus et forma in hoc conveniant, quod utrumque eorum est quidam terminus, non tamen unius et eiusdem; sed forma est terminus corporis cuius est forma, locus autem non est terminus corporis cuius est locus, sed corporis continentis ipsum; et licet sint simul termini continentis et contenti, non tamen sunt idem. 459. Secondly, [319], he shows that form is not place. For although place and form are alike in this, that each is a kind of boundary, nevertheless they are not the boundary of one and the same thing: for form is the boundary of the body of which it is the form, while place is not a boundary of the body of which it is the place, but of the body containing it. So, although the boundaries of the container and of the contained are together, they are not identical.
Deinde cum dicit: sed ex eo quod mutatur etc., prosequitur de spatio, et primo ponit quare spatium videtur esse locus; secundo ostendit quod non sit locus, ibi: hoc autem non est et cetera. 460. Then [320] he takes up the question of space. First he sets down why space seems to be place; Secondly, he shows that it is not place, at no. 461.
Dicit ergo primo, quod quia multoties mutatur corpus contentum a loco et divisum ab eo, de loco in locum, et succedunt sibi corpora invicem in eodem loco, ita quod continens remanet immobile, eo modo quo aqua exit a vase; propter hoc videtur quod locus sit aliquod spatium medium inter extremitates corporis continentis; ac si aliquid esset ibi praeter corpus quod movetur de uno loco ad alium. Quia si non esset ibi aliud praeter illud corpus, sequeretur quod vel locus non esset aliud a locato, vel quod id quod est medium inter extremitates continentis, non posset esse locus. Sicut autem oportet locum esse aliquid praeter corpus contentum, ita videtur quod oporteat locum esse aliquid praeter corpus continens; ex eo quod locus manet immobilis, corpus autem continens, et omne quod est in eo, contingit transmutari. Nihil autem aliud potest intelligi esse praeter corpus continens et contentum, nisi dimensiones spatii in nullo corpore existentes. Sic igitur ex hoc quod locus est immobilis, videtur quod spatium sit locus. He says therefore first that frequently a body contained by place, and distinct from it, is changed from one place to another, and any number of bodies can succeed into its original place (but always in such a way that the container remains immobile) in the way that water goes out of a vessel. For this reason it seems that place is some middle space between the boundaries of the containing body, as though there were something there besides the body moved from one place to another. For if nothing were there besides the contained body, it would follow either that place is not distinct from the thing in place, or that what exists within the confines of the container’s boundaries cannot be place. Now just as place must be something over and above the contained body, so it must be something other than the containing body, due to the fact that place remains immobile, whereas the containing body and everything in it can be changed about. But in addition to the containing body and the contained body there is nothing present except the dimensions of space, which exist in no body. Consequently, because place is immobile, it seems that space is place.
Deinde cum dicit: hoc autem non est etc., ostendit quod spatium non sit locus, duabus rationibus. Circa quarum primam dicit, quod hoc non est verum, quod aliquid sit ibi infra extremitates corporis continentis, praeter corpus contentum, quod transfertur de loco in locum: sed infra illas extremitates corporis continentis incidit aliquod corpus, quodcumque illud esse contingat, ita tamen quod sit de numero corporum mobilium, et iterum de numero eorum quae sunt apta nata tangere corpus continens. Sed si posset esse aliquod spatium continens medium, praeter dimensiones corporis contenti, quod semper maneret in eodem loco, sequeretur hoc inconveniens, quod infinita loca simul essent. Et hoc ideo, quia cum aqua et aer habeant proprias distantias, et quodlibet corpus, et quaelibet pars corporis; omnes partes idem facient in toto quod tota aqua facit in vase. Secundum vero eorum positionem qui tenent sententiam de spatio, dum tota aqua est in vase, sunt ibi aliae dimensiones spatii praeter dimensiones aquae. Omnis autem pars continetur a toto sicut locatum a vase: nec differt nisi solum quantum ad hoc, quod pars non est divisa, locatum autem est divisum. Si ergo pars dividatur in actu, sequetur quod sint ibi aliae dimensiones totius continentis praeter dimensiones partis. 461. Then [321] he shows that space is not place by two arguments. As to the first of these, he states it is not true that there is anything within the confines of the containing body other than the contained body which is transferred from place to place. Rather, within the confines of the containing body there happens a body of some kind, having, nevertheless, the following two characteristics: that it be a mobile body, and be naturally apt to touch the containing body. But if, in addition to the dimensions of the contained body, there were present a space which always remained in the same place, the embarrassing conclusion would follow that there would be infinite places together. The reason is because water and air have their own dimensions, and so does each body, and each part of a body. Now all these parts will do the same thing in the whole body that the whole water does in a vessel. According to those who hold the opinion that space is place, when the entire water is in the vessel there are present, in addition to the dimensions of the water, also other dimensions of space. Now every part of a whole is contained by the whole as a thing in place is contained by a vessel: the only difference being that the part is not separated from the whole, whereas the thing in place is separated from place. If therefore a part be actually separated within the whole, it will follow that, in addition to the dimensions of the part, also other dimensions of the containing whole will be present.
Non potest autem dici quod divisio faceret ibi esse de novo aliquas dimensiones: non enim divisio causat dimensionem, sed praeexistentem dividit. Ergo antequam pars esset divisa a toto, erant aliae propriae dimensiones partis, praeter dimensiones totius penetrantes etiam partem. Quot ergo partes est accipere per divisionem in aliquo toto, ita quod una contineat aliam, tot dimensiones ab invicem distinctae erunt ibi, quarum quaedam alias penetrabunt. Est autem accipere in infinitum in aliquo toto continuo partes, quae alias continent, propter hoc quod continuum in infinitum dividitur. Relinquitur igitur quod sint infinitae dimensiones se invicem penetrantes. Si igitur dimensiones corporis continentis penetrantes locatum sunt locus, sequitur quod sint infinita loca simul, quod est impossibile. But it cannot be said that such division would make new dimensions to exist: for division does not cause dimension; rather it divides dimension already existing. Therefore, before that part was divided in the whole, there were present other proper dimensions of the part, in addition to the whole’s dimensions, which also penetrate that part. Now there will be as many sets of dimensions all distinct, some of which interpenetrate others, as there are parts obtainable by division of the whole, parts, namely, so divided that one contains another. But it is possible in a continuous whole to obtain ad infinitum parts which contain other parts, because a continuum can be divided ad infinitum, Consequently, we should have infinite dimensions mutually penetrating themselves. If, therefore, the containing body’s dimensions, penetrating the thing in place, are place, it follows that there are infinite places together—which is impossible.
Deinde cum dicit: simul autem erit et locus etc., ponit secundam rationem, quae talis est. Si dimensiones spatii quod est inter extremitates corporis continentis, sint locus, sequitur quod locus transmutetur: manifestum est enim quod transmutato aliquo corpore, ut puta amphora, transmutatur illud spatium quod est infra extremitates amphorae, cum nusquam sit nisi ubi est amphora. Omne autem quod transmutatur in aliquem locum, penetratur secundum eorum positionem, a dimensionibus spatii in quod transmutatur. Sequitur ergo quod aliquae aliae dimensiones subintrant dimensiones illius spatii amphorae; et sic loci erit alius locus, et multa loca erunt simul. 462. Then [322] he gives a second reason, which is the following. If the dimensions of the space which is between the boundaries of the containing body are place, it follows that place can be transported. For it is clear that when a body is transported, as, for example, a jug, the space within the jug is transported, since that space can never be except where the jug is. Now whatever is transported to another place is penetrated (according to those who hold the doctrine of space as place) by the dimensions of the space into which it is transported. Therefore it follows that other dimensions enter the dimensions of the jug’s space; consequently there would be another place of place, and many places would be existing together.
Hoc ergo inconveniens accidit quia ponitur alius esse locus corporis contenti, ut aquae, et vasis, ut amphorae. Nam secundum illorum opinionem, locus aquae est spatium quod est infra extremitates amphorae: locus autem totius amphorae est spatium, quod est infra extremitates corporis continentis amphoram. Sed nos non dicimus quod alius sit locus partis, in quo movetur pars, cum totum vas transmutatur secundum idem (dicit autem hic partem, corpus contentum in vase, ut aquam contentam in amphora): quia secundum Aristotelem aqua movetur per accidens vase transmutato, et non mutat locum nisi inquantum amphora locum mutat. Unde non oportet quod locus in quem vadit, sit locus partis per se; sed solum inquantum est locus amphorae. Sed secundum tenentes opinionem de spatio, sequitur quod ille locus per se respondeat aquae, sicut et amphorae; et quod per se etiam respondeat spatio: et per se loquendo spatium illud movebitur et habebit locum, et non solum per accidens. 463. This unacceptable consequence arises from positing one place for the contained body, for example, the water; and another place for the vessel, for example, the jug. For according to the opinion we are discussing, the place of the water is the space within the boundaries of the jug, while the place of the whole jug is the space within the boundaries of the body containing the jug. We, however, do not assign a special place for the part, in which the part moves, as distinct from the whole, when the entire vessel is transported (by “part” he means the body contained in the vessel, as the water contained in the jug): because, according to Aristotle, the water is moved per accidens when the vessel is transported, and it changes place only inasmuch as the jug changes its place. Hence it is not necessary that the place into which the transfer is made, be the place of the part per se, but only inasmuch as it becomes the place of the jug. But according to those who hold the opinion about space as place, it follows that the new place would belong per se both to water and to the jug. Likewise, that space would be transported and would have a place per se, and not only per accidens.
Et licet corpus continens quandoque moveatur, non tamen sequitur secundum opinionem Aristotelis, quod locus moveatur, aut quod loci sit locus. Contingit quidem enim aliquod corpus continens, in quo est aliquid contentum, moveri, sicut aer vel aqua aut aliquae partes aquae: ut puta si navis est in fluvio, partes aquae quae inferius continent navem moventur; sed tamen locus non movetur. Now although the containing body is sometimes moved, it does not follow according to the opinion of Aristotle, that the place is moved, or that there is a place of a place. For it does indeed happen that a containing body, in which something is contained, is sometimes moved, as are air or water or certain parts of the water, For example, if a boat is in a river, the parts of the water which surround the boat from below are in motion, but the boat’s place is not moved. Hence, he adds, “but not that place where they occur,”, i.e., that in which things occur as in a place is not moved.
Et hoc est quod subdit, sed non in quo fiunt loco, idest sed non illud in quo aliqua fiunt sicut in loco, movetur. Et quomodo hoc sit verum, ostendit per hoc quod subdit, qui est pars loci qui est locus totius caeli. Licet enim hoc continens moveatur prout est hoc corpus, tamen prout consideratur secundum ordinem quem habet ad totum corpus caeli non movetur: nam aliud corpus quod succedit, eundem ordinem vel situm habet per comparationem ad totum caelum, quem habuit corpus quod prius effluxerat. Hoc est ergo quod dicit, quod licet aqua vel aer moveatur, non tamen movetur locus prout consideratur ut pars quaedam loci totius caeli, habens determinatum situm in universo. How this is true he makes clear by adding, “which is a part of the place which is the place of the whole heavens.” For although this container [e.g., the water surrounding the boat] be moved inasmuch as it is this body, yet in regard to its relation to the whole body of the heavens it is not moved: the body which succeeds it has the same order or position in relation to the whole heavens as had the body which previously flowed on. This therefore is what he says, namely, that although the water or the air be moved, not so the place, considered precisely as a certain part of the place of the whole heavens and as having a definite position in the universe.
Deinde cum dicit: et materia etiam videtur etc., prosequitur de materia. Et primo ostendit quare materia videtur esse locus; secundo ostendit quod non sit locus, ibi: sed materia quidem et cetera. 464. Then [323] he continues by considering matter. First he shows why matter seems to be place; Secondly, that it is not place, at no. 465.
Dicit ergo primo quod materia videtur esse locus, si aliquis consideret transmutationem corporum succedentium sibi in eodem loco, in aliquo uno subiecto quiescente secundum locum; et non habeatur respectus ad hoc quod locus est separatus, sed attendatur solummodo transmutatio in aliquo uno continuo. Aliquod enim corpus continuum et quietum secundum locum, cum alteratur, unum et idem numero nunc quidem est album, nunc autem nigrum, et nunc est durum et prius molle. Et propter istam transmutationem formarum circa subiectum, dicimus quod materia est aliquid, quae manet una, facta transmutatione secundum formam. Et per talem etiam apparentiam videtur locus esse aliquid: quia in eo permanente succedunt sibi diversa corpora. Sed tamen alio modo loquendi utimur in utroque. Nam ad designandum materiam vel subiectum, dicimus quod id quod nunc est aqua, prius erat aer: ad designandum autem unitatem loci, dicimus quod ubi nunc est aqua, ibi prius erat aer. He says therefore first that matter appears to be place, should one consider the transmutation of the bodies which succeed each other in the same place, as this occurs in some, one subject that is at rest in a place, with attention being paid, not to the fact that place is separate, but only to the fact that the transmutation is occurring in one and the same continuum. For some continuous body, at rest according to place, when it is being altered in quality, now white, now black; now hard, while previously soft. Yet it remains one and the same in number. And on account of this transmutation of forms in the subject we say that matter is something that remains one whole change taken place with respect to forms. Because of this, place seems to be something, because in it as remaining different bodies succeed each other. Nevertheless we use different terminology when referring to these two cases: to designate matter or the subject, we say, “What is now water, was previously air”; to designate unity in place, we say, “Where water is now there was air previously.”
Deinde cum dicit: sed materia quidem, sicut dictum est etc., ostendit quod materia non sit locus: quia sicut supra dictum est, materia non est divisa a re cuius est materia, neque continet eam: quorum utrumque competit loco. Locus igitur non est materia. 465. Then [324] he shows that matter is not place, because, as we said above, matter is not separated from the thing of which it is the matter, nor does it contain the latter: both of which characteristics belong to place. Place, therefore, is not matter.
Deinde cum dicit: si igitur nihil horum trium etc., remotis tribus membris, concludit quartum. Et dicit quod quia locus non est aliquod trium, idest neque forma, neque materia, neque aliquod spatium quod sit alterum praeter distantias rei locatae, necesse est quod locus sit reliquum de quatuor supra nominatis, scilicet quod sit terminus corporis continentis. Et ne aliquis intelligat contentum vel locatum esse aliquod spatium medium, subiungit, quod corpus contentum dicitur illud, quod est natum moveri secundum loci mutationem. 466. Then [325], having eliminated the first three members, he concludes to the fourth. And he says that since place is not any of these three, i.e., neither form, nor matter, nor some space which is other than the internal distances of the things in place, it must be the fourth of the above named, i.e., the boundary of the containing body. And lest anyone understand that the thing contained or in place is some middle space, he adds that the contained body is what is apt to be moved in respect to change of place.
Deinde cum dicit: videtur autem magnum aliquid etc., investigat differentiam loci, scilicet quod sit immobilis. Et circa hoc duo facit: primo ostendit quod ex hac differentia non debite considerata insurrexit quidam error circa locum; secundo ostendit quomodo sit intelligenda immobilitas loci, ibi: est autem sicut vas et cetera. 467. Then [326] he tracks down the specific difference of place; namely, that it is immobile. In regard to this he does two things: First, he shows that an error arose from improperly considering this difference; Secondly, how we must understand the immobility of place, at no. 468.
Dicit ergo primo, quod videtur magnum aliquid et difficile accipere quid sit locus; tum propter hoc quod quibusdam videtur, quod locus sit materia vel forma, quae habent altissimam considerationem, ut supra dictum est; tum propter hoc quod mutatio eius quod fertur secundum locum, fit in quodam quiescente et continente. Cum igitur nihil videatur esse continens et immobile nisi spatium, videtur contingere quod locus sit quoddam spatium medium, quod sit aliud a magnitudinibus quae moventur secundum locum. Et ad credulitatem huius opinionis multum proficit, quod aer videtur esse incorporeus: quia ubi est aer, videtur quod non sit corpus, sed quoddam spatium vacuum. Et sic videtur locus non solum esse terminus vasis, sed quoddam medium, tanquam vacuum. He says therefore that it is a large undertaking and a difficult one to understand what place is, both because some have thought it is matter or form, both of which involve lofty speculation, as was said above (L.3), and because the change that occurs when things change place, occurs in something both at rest and containing, Now, since nothing seems to be containing and immobile except space, it seems that place is a sort of middle space distinct from the magnitudes which are moved in respect to place. And the fact that air seems to be incorporeal helps to make this opinion credible: for where air is there appears to be no body but a certain empty space. Thus place seems to be not only the boundaries of a vessel but something between the boundaries as a vacuum or void.
Deinde cum dicit: est autem sicut vas etc., ostendit quomodo intelligenda sit immobilitas loci, ut excludatur opinio praedicta. Et dicit quod vas et locus in hoc differre videntur, quod vas transmutatur, locus autem non. Unde sicut vas potest dici locus transmutabilis, ita locus potest dici vas immobile. Et ideo, cum aliquid movetur in aliquo corpore quod movetur, sicut navis in flumine, utitur isto in quo movetur magis sicut vase, quam sicut loco continente: quia locus vult esse immobilis, idest de aptitudine et natura loci est quod sit immobilis; et propter hoc magis potest dici quod totus fluvius sit locus navis, quia totus fluvius est immobilis. Sic igitur fluvius totus inquantum est immobilis, est locus communis. 468. Then [327], in order to exclude the aforesaid opinion, he shows how we must understand the immobility of place. And he says that a vessel and place are seen to differ in this, that a vessel can be transported but place cannot, Hence, just as a vessel can be called “a transportable place,” so place can be called “an immobile (non-transportable) vessel.” Therefore, when something is being moved in a body that is in motion, as a ship in a river, we speak of that in which it is being moved as a vessel rather than of a containing place, because place “wants to-be immobile,” i.e., it is of the very nature and aptitude of the place to be immobile.. On this account it is better to speak of the whole river as being the place of the ship, because the river as a whole is immobile. Thus the whole river inasmuch as it is immobile is the common place.
Cum autem locus proprius sit pars loci communis, oportet accipere proprium locum navis in aqua fluminis, inquantum habet ordinem ad totum fluvium ut est immobilis. Est igitur accipere locum navis in aqua fluente, non secundum hanc aquam quae fluit, sed secundum ordinem vel situm quem habet haec aqua fluens ad totum fluvium: qui quidem ordo vel situs idem remanet in aqua succedente. Et ideo licet aqua materialiter praeterfluat, tamen secundum quod habet rationem loci, prout scilicet consideratur in tali ordine et situ ad totum fluvium, non mutatur. However, since proper place is a part of common place, we must consider the proper place of the ship in flowing water, not the water inasmuch as it is flowing, but in its relation to the order or position which this flowing water has to the river as a whole: it is this order or position that remains constant, while the water flows on. Therefore, although the water materially passes on, yet, insofar as it has the motion of place, i.e. insofar as it is considered as having a certain order and position with respect to the whole river it does not change.
Et per hoc similiter accipere debemus quomodo extremitates corporum mobilium naturalium sint locus, per respectum ad totum corpus sphaericum caeli, quod habet fixionem et immobilitatem propter immobilitatem centri et polorum. Sic igitur, licet haec pars aeris quae continebat, vel haec pars aquae effluat et moveatur inquantum est haec aqua; tamen secundum quod habet haec aqua rationem loci, scilicet situs et ordinis ad totum sphaericum caeli, semper manet. Sicut etiam dicitur idem ignis manere quantum ad formam, licet secundum materiam varietur consumptis et additis quibusdam lignis. This also shows how we ought to consider how the boundaries of natural mobile bodies are place with respect to the entire spherical body of the heavens, which is fixed and immobile on account of the immobility of the center and of the poles. Therefore, although this part of air which contains, or this part of water, flow by and move as this water, yet, insofar as this water has the motion of place, viz., a position and order to the whole spherical body of the heavens, it always remains. This is like the same fire remaining as to its form, although as to its matter it is varied as wood is consumed and other wood added.
Et per hoc cessat obiectio quae potest fieri contra hoc quod ponimus locum esse terminum continentis: quia cum continens sit mobile, et terminus continentis erit mobilis; et sic aliquod quietum existens, habebit diversa loca. Sed hoc non sequitur: quia terminus continentis non erat locus inquantum est haec superficies istius corporis mobilis, sed secundum ordinem vel situm quem habet in toto immobili. Ex quo patet quod tota ratio loci in omnibus continentibus est ex primo continente et locante, scilicet caelo. 469. This removes an objection that could be lodged against positing place as the boundary of the container, for since the container is mobile, its boundary will also be mobile; consequently, a thing at rest will have diverse places. But this does not follow: because the boundary of the container is not place insofar as it is this surface of this particular mobile body, but by reason of the order or position it has in the immobile whole. From which it is evident that the whole notion of place in all containers is taken from the first container and locator, namely, the heavens.
Deinde cum dicit: quare terminus continentis etc., concludit ex praemissis definitionem loci, scilicet quod locus est terminus immobilis continentis primum. Dicit autem primum, ut designet locum proprium, et excludat locum communem. 470. Then [328] he concludes form the foregoing the definition of place, namely, that place is the immobile boundary of that which contains first. He says “first” to designate proper place and exclude common place.
Deinde cum dicit: et propter hoc medium caeli etc., ostendit definitionem esse bene assignatam, per hoc quod ea quae dicuntur de loco, congruunt secundum hanc definitionem. Et ponit tria. Quorum primum est, quod propter hoc quod locus est continens immobile, medium caeli, idest centrum, et ultimum circularis loci mutationis, idest corporum circulariter motorum, ultimum dico versus nos, scilicet superficies orbis lunae, videtur hoc quidem esse sursum, scilicet ultimum praedictum, illud vero esse deorsum, scilicet medium. Et hoc maxime proprie videtur dici inter omnia: quia centrum sphaerae semper manet. 471. Then [329] he shows that the definition is well assigned, because the things said about place concur with this definition. And he gives three such things: The first is that, since place is an immobile container, the middle of the heavens, i.e., the center, and the boundary of circular change of place, i.e., of the bodies moved in a circle, namely, the boundary as to us, i.e., the surface of the sphere of the moon, is (namely, the latter) seen as “up”, and the other (namely, the middle) as “down”. Things absolutely in place, and things in place in a certain respect and this last named (the middle or center) is seen to be said most properly of all. For the center of a sphere is always at rest.
Illud autem quod est ultimum in corporibus circulariter motis versus nos, licet moveatur circulariter, tamen manet inquantum similiter se habet, idest in eadem elongatione ad nos. Et quia ad propria loca moventur corpora naturalia, inde est quod levia naturaliter moventur sursum et gravia deorsum: quia ipsum medium et terminus continens versus medium, vocatur deorsum; et similiter ipsum ultimum, et quod est versus ultimum, dicitur esse sursum. Utitur autem tali modo loquendi, quia terrae, quae est simpliciter gravis, locus est medium; aquae autem locus est versus medium. Et similiter locus ignis, qui est simpliciter levis, est ultimum; locus autem aeris est versus ultimum. Now that which is the boundary in relation to us of the bodies moved in a circle [namely, the surface of the sphere of the moon], although it moves in a circle, nevertheless remains, insofar as it remains in the same way, i.e., at the same distance from us. Hence, since natural bodies are moved to their proper places, it follows that light bodies naturally move “up”, and heavy bodies “down”—for both the middle (center) and the containing boundary in the direction of the middle are called “down”; and likewise the boundary in the other sense [ the surface of the sphere of the moon], and what is in the direction of that boundary, are called “up”. He uses this manner of speaking, because it is the center that is the place of the earth, which is simply heavy, while toward the center the place of water is found. In like manner, the place of fire, which is simply light, is the outermost, while the place of air is toward the outermost.
Secundum ponit ibi: et propter hoc planum videtur et cetera. Et dicit quod quia locus est terminus, propter hoc locus videtur esse sicut quaedam superficies, et sicut quoddam vas continens: non autem sicut spatium vasis continentis. He gives the second [330], saying that because place is a boundary, place seems to be like a certain surface and like a containing vessel, but not like the space [or volume] of the containing vessel.
Tertium ponit ibi: amplius, simul cum re et cetera. Et dicit quod quia locus est terminus, propter hoc simul est locus et locatum: quia simul est finis locati et terminus continentis, qui est locus; quia tangentium ultima simul sunt. Et secundum hoc etiam intelligitur quod locus aequatur locato: quia scilicet aequantur secundum extrema. He gives the third [331] when he says that, because place is a boundary, the place and the thing in place are together; for the limits of the thing in place and the boundary of the container, which is place, are together (for the boundaries of things that touch are together). This also explains why place is equal to the thing in place: namely, because they are equated as to their boundaries.

Lecture 7
How something exists in place
Lectio 7
Chapter 5
Ὧι μὲν οὖν σώματι ἔστι τι ἐκτὸς σῶμα περιέχον αὐτό, τοῦτο ἔστιν ἐν τόπῳ, ᾧ δὲ μή, οὔ. If then a body has another body outside it and containing it, it is in place, and if not, not.
διὸ κἂν ὕδωρ γένηται τοιοῦτο, τὰ μὲν μόρια κινήσεται αὐτοῦ (περιέχεται γὰρ ὑπ' ἀλλήλων), τὸ δὲ πᾶν ἔστι μὲν ὡς κινήσεται ἔστι δ' ὡς οὔ. ὡς μὲν γὰρ ὅλον, ἅμα τὸν τόπον οὐ μεταβάλλει, κύκλῳ (212b.) δὲ κινεῖται—τῶν μορίων γὰρ οὗτος ὁ τόπος—καὶ ἄνω μὲν καὶ κάτω οὔ, κύκλῳ δ' ἔνια· τὰ δὲ καὶ ἄνω καὶ κάτω, ὅσα ἔχει πύκνωσιν καὶ μάνωσιν. That is why, even if there were to be water which had not a container, the parts of it, on the one hand, will be moved (for one part is contained in another), while, on the other hand, the whole will be moved in one sense, but not in another. For as a whole it does not simultaneously change its place, though it will be moved in a circle: for this place is the place of its parts. (Some things are moved, not up and down, but in a circle; others up and down, such things namely as admit of condensation and rarefaction.)
ὥσπερ δ' ἐλέχθη, τὰ μέν ἐστιν ἐν τόπῳ κατὰ δύναμιν, τὰ δὲ κατ' ἐνέργειαν. διὸ ὅταν μὲν συνεχὲς ᾖ τὸ ὁμοιομερές, κατὰ δύναμιν ἐν τόπῳ τὰ μέρη, ὅταν δὲ χωρισθῇ μὲν ἅπτηται δ' ὥσπερ σωρός, κατ' ἐνέργειαν. As was explained, some things are potentially in place, others actually. So, when you have a homogeneous substance which is continuous, the parts are potentially in place: when the parts are separated, but in contact, like a heap, they are actually in place.
καὶ τὰ μὲν καθ' αὑτά (οἷον πᾶν σῶμα ἢ κατὰ φορὰν ἢ κατ' αὔξησιν κινητὸν καθ' αὑτό που, ὁ δ' οὐρανός, ὥσπερ εἴρηται, οὔ που ὅλος οὐδ' ἔν τινι τόπῳ ἐστίν, εἴ γε μηδὲν αὐτὸν περιέχει σῶμα· ἐφ' ᾧ δὲ κινεῖται, ταύτῃ καὶ τόπος ἔστι τοῖς μορίοις· ἕτερον γὰρ ἑτέρου ἐχόμενον τῶν μορίων ἐστίν)· τὰ δὲ κατὰ συμβεβηκός, οἷον ἡ ψυχὴ καὶ ὁ οὐρανός· τὰ γὰρ μόρια ἐν τόπῳ πως πάντα· ἐπὶ τῷ κύκλῳ γὰρ περιέχει ἄλλο ἄλλο. Again, (1) some things are per se in place, namely every body which is movable either by way of locomotion or by way of increase is per se somewhere, but the heaven, as has been said, is not anywhere as a whole, nor in any place, if at least, as we must suppose, no body contains it. On the line on which it is moved, its parts have place: for each is contiguous the next. But (2) other things are in place indirectly, through something conjoined with them, as the soul and the heaven. The latter is, in a way, in place, for all its parts are: for on the orb one part contains another.
διὸ κινεῖται μὲν κύκλῳ τὸ ἄνω, τὸ δὲ πᾶν οὔ που. τὸ γάρ που αὐτό τέ ἐστί τι, καὶ ἔτι ἄλλο τι δεῖ εἶναι παρὰ τοῦτο ἐν ᾧ, ὃ περιέχει· παρὰ δὲ τὸ πᾶν καὶ ὅλον οὐδέν ἐστιν ἔξω τοῦ παντός, καὶ διὰ τοῦτο ἐν τῷ οὐρανῷ πάντα· ὁ γὰρ οὐρανὸς τὸ πᾶν ἴσως. ἔστι δ' ὁ τόπος οὐχ ὁ οὐρανός, ἀλλὰ τοῦ οὐρανοῦ τι τὸ ἔσχατον καὶ ἁπτόμενον τοῦ κινητοῦ σώματος [πέρας ἠρεμοῦν]. καὶ διὰ τοῦτο ἡ μὲν γῆ ἐν τῷ ὕδατι, τοῦτο δ' ἐν τῷ ἀέρι, οὗτος δ' ἐν τῷ αἰθέρι, ὁ δ' αἰθὴρ ἐν τῷ οὐρανῷ, ὁ δ' οὐρανὸς οὐκέτι ἐν ἄλλῳ. That is why the upper part is moved in a circle, while the All is not anywhere. For what is somewhere is itself something, and there must be alongside it some other thing wherein it is and which contains it. But alongside the All or the Whole there is nothing outside the All, and for this reason all things are in the heaven; for the heaven, we may say, is the All. Yet their place is not the same as the heaven. It is part of it, the innermost part of it, which is in contact with the movable body; and for this reason the earth is in water, and this in the air, and the air in the aether, and the aether in heaven, but we cannot go on and say that the heaven is in anything else.
Postquam philosophus definivit locum, hic ostendit qualiter aliquid sit in loco. Et circa hoc duo facit: primo ostendit qualiter aliquid simpliciter sit in loco, et qualiter non; secundo ostendit quomodo illud quod non est simpliciter in loco, secundum quid in loco sit, ibi: unde et si aqua fiat et cetera. 472. After defining place, the Philosopher now shows how something exists in place. About this he does two things: First he shows how something is absolutely in place and how not; Secondly, how a thing not absolutely in place. is in place in a certain respect, at 482.
Concludit ergo primo ex praemissis, quod cum locus sit terminus continentis, cuicumque corpori adiacet aliquod corpus continens ipsum exterius, hoc est in loco simpliciter et per se: cui vero corpori non adiacet aliquod corpus exterius continens ipsum, minime est in loco. Tale autem corpus in mundo non est nisi unum, scilicet ultima sphaera, quaecumque sit illa. Unde secundum hanc determinationem sequitur quod ultima sphaera non sit in loco. 473. He concludes therefore first [332] from the foregoing that, since place is the boundary of the container, whenever a body has another body outside it and containing it, it is in place absolutely and per se; if such a body does not have an external body containing it, it is not in place at all. The only body in the universe that exemplifies this second case is the outermost sphere, whatever it may be. Hence, according to this definition, it follows that the outermost orb is not in place.
Sed hoc videtur impossibile: quia ultima sphaera movetur in loco; nihil autem movetur in loco, quod non sit in loco. Huius igitur dubitationis difficultas non accidit iis qui tenent sententiam de spatio. Non est enim eis necesse dicere quod ad hoc quod sphaera ultima sit in loco, quod habeat corpus continens; sed spatium quod intelligitur penetrare totum mundum et omnes partes eius, est locus totius mundi et cuiuslibet partium eius, secundum eos. 474. But this seems to be impossible, because the outermost sphere is in motion in place and nothing is moved in place unless it is in place. Now this difficulty does not arise for those who hold the opinion that space is place. For they are not forced to say that, in order to be in place, the outermost sphere must have a body containing it; rather, the space penetrating the entire universe and all its parts is the place of the entire universe and of each of its parts, according to these Philosophers.
Sed haec positio est impossibilis: quia vel oportet dicere quod locus non sit aliquid praeter locatum, vel quod sint aliquae dimensiones spatii per se existentes, et tamen subintrantes dimensiones corporum sensibilium: quae sunt impossibilia. But this position is impossible, for one must admit either that place is not distinct from the thing in place, or that space has dimensions existing per se but yet penetrating the dimensions of sensible bodies—both of which positions are impossible.
Unde Alexander dixit quod ultima sphaera nullo modo est in loco: non enim omne corpus de necessitate est in loco, cum locus non cadat in definitione corporis. Et propter hoc dixit quod ultima sphaera non movetur in loco, neque secundum totum, neque secundum partes. 475. Wherefore Alexander said that the outermost orb is not in place at all: for it is not necessary for every body to be in place, since place is not in the definition of body. For this reason he held that the outermost sphere is not in motion in place, neither as a whole, nor as to its parts.
Sed quia oportet omnem motum in aliquo genere motus poni, Avicenna eum secutus, dixit quod motus ultimae sphaerae non est motus in loco, sed motus in situ, contra Aristotelem, qui dicit in quinto huius, quod motus est tantum in tribus generibus, scilicet in quantitate, qualitate et ubi. But since every motion must fit into one of the genera of motion, Avicenna, following him, said that the motion of the outermost sphere is not motion in place but motion in situs [position in place]. This is against Aristotle, who says in Book V (L. 4) that motion is present only in three genera, namely, quality, quantity, and “where.”
Sed hoc non potest stare: impossibile est enim quod motus sit per se loquendo in aliquo genere cuius specierum ratio in indivisibili consistit. Propter hoc enim in substantia non est motus, quia ratio cuiuslibet speciei substantiae consistit in indivisibili, eo quod species substantiae non dicuntur secundum magis et minus: et propter hoc, cum motus habeat successionem, non producitur in esse forma substantialis per motum, sed per generationem, quae est terminus motus. Secus autem est de albedine et similibus, quae participantur secundum magis et minus. Quaelibet autem species situs habet rationem in indivisibili consistentem; ita quod si aliquid additur vel minuitur, non est eadem species situs. Unde impossibile est quod in genere situs sit motus. Avicenna’s position is untenable because it is impossible that motion strictly speaking be in a genus the notion of whose species consists in an indivisible. For the reason why there is not motion in the genus “substance” is that the nature of every species of substance consists in an indivisible, due to the fact that the species of substances do not admit of more or less; on this account, since motion is successive, a substantial form is not made existent by motion but by generation, which is the terminus of motion. The case is different with whiteness and like things, which can be participated according to more or less. But every species of situs has a nature that consists in an indivisible, so that if anything be added or taken away the original species does not remain. Hence it is impossible for motion to exist in the genus of situs.
Et praeterea, remanet eadem difficultas. Nam situs, secundum quod ponitur praedicamentum, importat ordinem partium in loco: licet secundum quod ponitur differentia quantitatis, non importet nisi ordinem partium in toto. Omne igitur quod movetur secundum situm, oportet quod moveatur secundum locum. Besides, the same difficulty remains. For situs taken as a predicament implies the order of parts in place; although if it be taken as a difference in the genus of quantity it implies merely an order of parts in a whole. Therefore, whatever is moved according to situs, must be moved according to place.
Quidam autem alii dixerunt, scilicet Avempace, quod aliter assignandus est locus corpori quod movetur circulariter, et aliter corpori quod movetur motu recto. Quia enim linea recta est imperfecta, additionem recipiens, corpus quod movetur motu recto requirit locum exterius continentem: quia vero linea circularis in seipsa perficitur, corpus quod circulariter movetur non requirit locum exterius continentem, sed locum circa quem revolvatur: unde et motus circularis dicitur esse motus circa medium. Sic igitur dicunt quod superficies convexa sphaerae contentae, est locus primae sphaerae. Sed hoc est contra suppositiones communes prius de loco positas: scilicet quod locus sit continens, et quod locus sit aequalis locato. 476. Others such as Avempace said that place should be assigned in one way to a body moving in a circle and in another way to a body moving in a straight line. For since a straight line is imperfect, since it can be added to, a body moving in a straight line requires a place externally containing it, but because a circular line is perfect within itself, a body moving in a circle does not require an external place to contain it, but merely a place about which it may revolve; hence it is that circular motion is said to be motion about a center. So therefore they say that the convex surface of the sphere contained is the place of the first sphere. But this is against the common suppositions about place already laid down; namely, that place is a container, and that it is equal to the thing in place.
Et ideo Averroes dixit quod ultima sphaera est in loco per accidens. Ad cuius evidentiam considerandum est, quod omne illud quod habet fixionem per alterum, dicitur esse per accidens in loco, ex hoc quod id per quod figitur, in loco est; ut patet de clavo infixo navi et de homine quiescente in navi. Manifestum est autem quod corpora circulariter mota habent fixionem per immobilitatem centri: unde ultima sphaera dicitur esse in loco per accidens, inquantum centrum circa quod revolvitur, habet esse in loco. Quod autem aliae sphaerae inferiores habent per se locum in quo continentur, hoc accidit, et non est de necessitate corporis circulariter moti. 477. And therefore Averroes said that the outermost sphere is in place per accidens. To understand this, one should consider that everything which has fixity by means of something else, is said to be in place per accidens, due to the fact that that by means of which it is fixed is in place, as it evident in the case of a nail fixed in a ship and of a man at rest in a ship. Now it is clear that bodies moving rotationally are fixed because their center is immobile; hence the outermost sphere is said to be in place per accidens, insofar as the center about which it is revolving has existence in place, The fact that the lower spheres have a per se place in which they are contained is incidental and not essential to a body moving rotationally.
Sed contra hoc obiicitur quia, si ultima sphaera sit in loco per accidens, sequitur quod moveatur in loco per accidens, et sic motus per accidens est prior motu per se. Sed ad hoc respondetur quod ad motum circularem non requiritur quod id quod movetur per se circulariter, sit per se in loco: requiritur autem ad motum rectum. But against this it is objected that, if the outermost sphere is in place per accidens, then it is in motion in place per accidens, and so per accidens motion is prior to per se motion. To this the answer is given that for rotational motion it is not necessary for a body moving per se rotationally to be in place per se, although it is necessary for straight line motion.
Sed hoc videtur esse contra definitionem Aristotelis, quam supra posuit, de eo quod est in loco per accidens. Dixit enim aliqua esse vel moveri in loco per accidens, ex hoc quod movetur id in quo sunt: non autem dicitur aliquid esse in loco per accidens, ex hoc quod aliquid quod est omnino extrinsecum ab ipso, est in loco. Cum igitur centrum sit omnino extrinsecum a sphaera ultima, ridiculum videtur dicere quod sphaera ultima sit in loco per accidens ex hoc quod centrum est in loco. But this seems to be against Aristotle’s definition, given above, of what is in place per accidens. For he said that some things exist or are in motion place per accidens, because that in which they exist is in motion. But nothing is said to be in place per accidens because something entirely outside it is in place. Now since the center is completely extrinsic to the outermost sphere, it seems ridiculous to say that the outermost sphere is in place per accidens because the center is in place.
Et ideo magis approbo sententiam Themistii, qui dixit quod ultima sphaera est in loco per suas partes. 478. And therefore I favor more the opinion of Themistius, who said that the outermost sphere is in place by means of its parts.
Ad cuius evidentiam considerandum est, quod sicut Aristoteles supra dixit, non quaereretur locus nisi propter motum, qui demonstrat locum ex hoc quod corpora succedunt sibi in uno loco. Unde, licet locus non sit de necessitate corporis, est tamen de necessitate corporis quod movetur secundum locum. Sic igitur alicui corpori moto localiter, necesse est assignare locum, secundum quod in illo motu consideratur successio diversorum corporum in eodem loco. In his igitur quae moventur motu recto, manifestum est quod duo corpora succedunt sibi in loco secundum totum; quia totum unum corpus dimittit totum locum, et in ipsum totum subintrat aliud corpus. Unde necesse est quod corpus quod movetur motu recto, sit in loco secundum se totum. To understand this it must be recalled that Aristotle said above that there would be no discussion about place except for the act of motion, which reveals the existence of place from the fact that bodies succeed one another in the same place. Hence, although place is not of the essence of body, yet it is necessary for a body moved according to place. In the case of a body moving locally, the reason it is necessary to assign a place is because in that motion a succession of diverse bodies in the same place is considered. Therefore, in the case of bodies moving in a straight line it is clear that one body succeeds another in the same place according to their totality, for one whole body leaves one whole place which is then occupied by another whole body. Hence a body which is in motion in a straight line must be in place in its entirety.
In motu autem circulari, licet totum fiat in diversis locis ratione, non tamen totum mutat locum subiecto: semper enim remanet idem locus subiecto, sed diversificatur ratione tantum, ut in sexto huius dicetur. Sed partes mutant locum non solum ratione, sed subiecto. Attenditur ergo in motu circulari successio in eodem loco, non totorum corporum, sed partium eiusdem corporis. Non igitur corpori quod movetur circulariter, debetur ex necessitate locus secundum totum, sed secundum partes. But in the case of rotational motion, although the whole body comes to be in different places as distinguished by reason, nevertheless the whole body does not change its place as to subject: for the place remains ever the same as to subject; but varies only according to reason, as will be said in Book VI (L.2). Nevertheless the parts change place not only as to reason but as to subject also. Therefore in the case of rotational motion there is not a succession of whole bodies in the same place but of parts of the same body. Therefore a rotating body does not essentially require a place according to its totality but according to its parts.
Sed contra hoc esse videtur quod partes corporis continui non sunt in loco, neque moventur secundum locum: sed totum movetur, et totum est in loco. Manifestum est autem quod ultima sphaera est corpus continuum: partes igitur eius nec sunt in loco, nec moventur secundum locum. Et sic non videtur verum quod ultimae sphaerae debeatur locus ratione partium. 479. But against this there seems to be the objection that the parts of a continuous body are neither in place nor moved in respect to place; rather, it is the whole that is both moved and in place. But it is clear that the outermost sphere is a continuous body; therefore, its parts are neither in place nor in motion in place. Consequently, it does not seem to be true that place should be attributed to the outermost sphere by reason of its parts.
Sed ad hoc dicendum est quod partes totius continui, licet non sint in loco in actu, sunt tamen in loco in potentia, secundum quod continuum est divisibile. Pars enim, si sit divisa, erit in toto sicut in loco: unde per hunc modum partes continui moventur in loco. Et hoc maxime apparet in continuis humidis, quae sunt facilis divisionis, sicut in aqua, cuius partes inveniuntur moveri infra totam aquam. Sic igitur, quia aliquid dicitur de toto ratione partium, inquantum partes ultimae sphaerae sunt in loco in potentia, tota ultima sphaera est in loco per accidens ratione partium: et sic esse in loco sufficit ad motum circularem. The answer to this objection is that, although the parts of a continuous body are not actually in place, they are so potentially, insofar as the continuum is divisible. For a part, if it is separated, will be in the whole as in a place; hence, in this manner the parts of a continuum are moved in place. This is clearly evident in liquid continua which are easy to divide—for example, in the case of water, whose parts are found to be in motion within the whole water. Consequently, because something is said of a whole by reason of its parts, insofar as the parts of the outermost sphere are potentially in place the entire outermost sphere is in place per accidens by reason of its parts: and to be in place in that way is enough for rotational motion.
Si quis autem obiiciat quod id quod est in actu, est prius eo quod est in potentia; et sic videtur inconveniens quod primus motus localis sit corporis existentis in loco per partes, quae sunt in potentia in loco: dicendum est ergo quod hoc optime congruit primo motui. Necesse est enim quod gradatim ab uno immobili descendatur ad diversitatem quae est in mobilibus. Minor est autem variatio quae est secundum partes existentes in loco in potentia, quam quae est secundum tota existentia in loco in actu. Unde primus motus, qui est circularis, minus habet de difformitate, et plus retinet de uniformitate, propinquior existens substantiis immobilibus. Multo autem convenientius est dicere quod ultima sphaera sit in loco propter partes suas intrinsecas, quam propter centrum, quod est omnino extra substantiam eius; et magis consonat opinioni Aristotelis, ut patet inspicienti sequentia, in quibus philosophus manifestat quomodo caelum sit in loco, ibi: unde et si aqua fiat et cetera. 480. If a further objection is raised that what is in act is prior to what is in potency and that consequently it seems Improper that the first local motion be that of a body existing in place by means of its parts which are potentially in place, the reply is that this is most fitting to the first motion. For it is necessary that the descent from the one immobile being to the diversity which is found in mobile things be made step by step. Now the variation based on parts existing in place potentially, is less than that of wholes existing in place actually. Hence the first motion, which is rotational has less deformity and retains greater uniformity, being closer to the immobile substances. Now it is much better to say that the outermost sphere is in place on account of its intrinsic parts, than an account of the center which is entirely extrinsic to its substance; and this is more in agreement with Aristotle’s opinion, as is clear if one considers the passage following, in which Aristotle shows how the heavens are in place.
Circa hoc enim duo facit: primo enim manifestat quomodo sphaera ultima est in loco; secundo infert conclusionem ex dictis, ibi: unde movetur circulariter et cetera. 481. For in regard to this he does two things: First he shows how the outermost sphere is in place; Secondly, he draws-a conclusion from what has been said, at 485.
Circa primum tria facit: primo manifestat quod ultima sphaera est in loco per partes; secundo quomodo partes eius sunt in loco, ibi: sicut autem dictum est, alia quidem etc.; tertio quomodo ex partibus competat toti esse in loco, ibi: et alia quidem per se et cetera. About the first he does three things: First, he shows that the outermost sphere is in place through its parts; Secondly, how its parts are in place, at no. 481, Thirdly, how the parts make the whole to be in place, at no. 434.
Quia ergo dixerat quod cui non est aliquod extra continens, non est in loco per se, concludit quod si aliquod huiusmodi corpus quod non continetur ab alio, sicut est ultima sphaera, sit aqua (in qua magis apparet quod dicitur propter facilem divisionem partium), partes eius movebuntur, inquantum continentur sub invicem, sic quodammodo in loco existentes. Sed tota aqua quodammodo movebitur, et quodammodo non. Non enim sic movebitur quod tota simul mutet locum, quasi translata in alium locum subiecto diversum: sed movebitur circulariter; qui quidem motus requirit locum partium, et non totius. Et non movebitur sursum et deorsum, sed circulariter: quaedam autem movebuntur sursum et deorsum, mutantia locum secundum totum, scilicet corpora rara et densa, vel gravia et levia. 482. Therefore, because he had said that if a body does not have something outside of it containing it, it is not in place per se, he concludes [333] that if a body of this kind, such as the outermost sphere is, be water (which will more easily illustrate what we are about to say on account of its easy divisibility), its parts will be in motion inasmuch as one part contains another, thus making it exist in place after a fashion. But the entire water will be in motion in one sense and in another sense not. For it will not be in motion in such a way that the entire water will change its place as though being transferred to another place distinct as to subject, but it will be moved rotationally—a motion that requires place for the parts and not for the whole. And it will be moved, not up and down, but circularly: for some things are moved up and down and change place in their entirety, namely, rare and dense bodies, or light and heavy things.
Deinde cum dicit: sicut autem dictum est etc., ostendit quomodo partes ultimae sphaerae sunt in loco. Et dicit quod sicut supra dictum est, quaedam sunt in loco in actu, quaedam secundum potentiam. Unde cum aliquod sit continuum similium partium, partes eius sunt in loco secundum potentiam, sicuti est in ultima sphaera: sed quando partes sunt separatae, et solum contiguae, sicut accidit in collectione lapidum, tunc partes sunt in loco secundum actum. 483. Then [334] he indicates how the parts of the outermost sphere exist in place, saying that, as was mentioned above, some things are actually in place, others potentially. Hence in the case of a continuum of similar parts the parts are in place potentially, as in the case of the outermost sphere; but when the parts are separated and merely contiguous, as occurs in a pile of stones, the parts are in place actually.
Deinde cum dicit: et alia quidem per se sunt etc., ostendit quomodo ex hoc sequitur totam sphaeram esse in loco. Et dicit quod quaedam sunt per se in loco, sicut omne corpus quod per se movetur in loco, vel secundum loci mutationem vel secundum augmentum, ut supra dictum est. Sed caelum, idest ultima sphaera, non est hoc modo in loco, sicut dictum est, cum nullum corpus contineat ipsum: sed secundum quod movetur circulariter, partibus sibi invicem succedentibus, sic et locus debetur partibus eius in potentia, ut dictum est, inquantum scilicet una pars eius est habita, idest consequenter se habens, ad aliam. 484. Then [335] he shows how from this it follows that the entire sphere is in place. And he says that some things are per se in place—as any body that is per se in motion in place, whether it be in respect to local motion or increase, as was said above (L.5). But the heavens, i.e., the outermost sphere, are not in place in this manner, as was said, since no body contains them; but inasmuch as they are moved rotationally, with part succeeding part, place is attributed to the parts potentially, as was said, inasmuch as one part-is “had,” i.e., is consecutive, with respect to another.
Quaedam vero secundum accidens sunt in loco, sicut anima et omnes formae: et hoc etiam modo caelum, idest ultima sphaera, est in loco, inquantum omnes eius partes sunt in loco, ex eo quod unaquaeque pars eius continetur sub alia secundum circulationem. In corpore enim non circulari pars extrema remanet non contenta, sed continens tantum: sed in corpore circulari quaelibet pars est continens et contenta, in potentia tamen. Unde ratione omnium partium suarum corpus circulare est in loco. Et hoc accipit esse per accidens, scilicet per partes, sicut supra, cum dixit quod partes corporis moventur per accidens in loco. Certain things, indeed, are in place per accidens, e.g., the soul, and all forms; and in this manner the heavens, i.e., the outermost sphere, is in place insofar as all its parts are in place, since each of its parts is contained under another in the rotation of the sphere. For in a non-round body the outermost part remains uncontained and merely containing; but in a round body each part is both container and contained, potentially however. Hence it is by reason of all its parts that a found body is in place. And this Aristotle takes to per accidens, namely, what is true of the parts, as above when he said that the parts of a body are in motion per accidens in place.
Deinde cum dicit: unde movetur circulariter etc., inducit quandam conclusionem ex praedictis. Quia enim dixerat quod corpus quod circulariter movetur, non oportet esse in loco secundum totum, sed solum per accidens, ratione partium, concludit quod corpus supremum movetur solum circulariter, propter hoc quod ipsum totum non est alicubi; quia quod est alicubi, ipsum est aliquid, et habet aliquid extra se a quo continetur; sed extra totum nihil est. Et propter hoc omnia dicuntur esse in caelo sicut in ultimo continente, quia caelum fortassis est quod est totum continens. Dicit autem fortassis, quia nondum probatum est quod extra caelum nihil sit. Non est autem sic intelligendum, quod ipsum corpus caeli sit locus: sed quaedam superficies ultima eius versus nos; et est sicut terminus tangens corpora mobilia quae in ipso sunt. Et propter hoc dicimus quod terra est in aqua, quae est in aere, qui est in aethere, idest igne, qui est in caelo, quod non est ulterius in alio. 485. Then [336] he draws a conclusion from the foregoing. For since he had said that a body in rotational motion need not be in place in its entirety but only per accidens by reason of its parts, he concludes that the outermost body is moved only rotationally, because the whole in question is not anywhere; what is somewhere is itself something, and has something outside of it by which it is contained; but there is nothing outside the whole. For this reason all things are said to be in the heavens as in the outermost container, because the heavens are probably the containing whole. He says “probably,” because it has not yet been proved that there is nothing outside the heavens. It is not to be thought that the very body of the heavens is a place; rather, it is a certain final surface of it turned toward us which is as a boundary in contact with the mobile bodies existing in it. For this reason we say that earth is in water which is in air, which is in either, i.e., fire, which is in the heavens, which are not in anything else.
Secundum vero intentionem Averrois, littera ista aliter exponenda est. Nam exemplum de aqua quod primo inducit, non est referendum secundum ipsum ad ultimam sphaeram, sed ad totum universum: quod quidem movetur inquantum partes eius moventur, quaedam quidem circulariter, ut corpora caelestia, quaedam vero motu sursum vel deorsum, ut inferiora corpora. Quod vero postmodum inducitur, quod quaedam sunt in loco actu, quaedam potentia, non est referendum ad prius dicta, sed oportet ut propter se dictum accipere. Quia enim dixerat quod quaedam sunt in loco secundum partes, quaedam secundum totum, consequenter adiungit quod quaedam sunt in loco secundum actum, quaedam secundum potentiam: et ulterius, quod quaedam sunt in loco per se, quaedam per accidens. 486. However, according to the intention of Aristotle, this passage must be explained differently. For the example of water which he first adduced is not to be referred, according to him, to the outermost sphere only, but to the entire universe, which indeed is moved insofar as its parts are moved—some rotationally, as are the heavenly bodies; some up and down, as are the lower bodies. As to what he said later on, that some things are actually in place and other potentially, this is not to be referred to what he said previously but is to be taken independently. For since he had said that some things are in place according to their parts and others according to their totality, he adds after that, that some things are in place according to act and others according to potency; finally, he says that some things are in place per se and others per accidens.
Ubi notandum est quod caelum secundum ipsum dupliciter accipitur hic: nam primo caelum accipitur pro universitate corporum, et maxime caelestium; secundo pro ultima sphaera. Dicit ergo quod per se sunt in loco, quae moventur secundum locum, sive secundum totum sive secundum partes, ut caelum, idest universum: per accidens autem sunt in loco, ut anima et caelum, idest ultima sphaera. Quia oportet dicere quod omnes partes universi sint aliquo modo in loco, ultima quidem sphaera per accidens, alia vero corpora per se, inquantum ab exteriori corpore continentur. Et hoc manifestat usque in finem. In this connection note that according to Aristotle “the heavens” are to be taken in two senses here: first, they are taken for the entire universe of bodies and especially of the heavenly; secondly, for the outermost sphere. He says therefore that those things are in place per se which are in motion according to place, whether they are in motion according to their totality or according to their parts, as are the heavens, i.e., the universe; in place per accidens are the soul and the heavens, i.e., the outermost sphere. For it is necessary to say that all the parts of the universe are somehow in place: the outermost sphere per accidens and other bodies per se, inasmuch as they are contained by a body outside of them. And he manifesto this up to the end.

Lecture 8

The definition of place is used to solve the original problems;
the properties of place are justified.

Lectio 8
Chapter 5 cont.
φανερὸν δ' ἐκ τούτων ὅτι καὶ αἱ ἀπορίαι πᾶσαι λύοιντ' ἂν οὕτω λεγομένου τοῦ τόπου.
  1. οὔτε γὰρ συναύξεσθαι ἀνάγκη τὸν τόπον,
  2. οὔτε στιγμῆς εἶναι τόπον,
  3. οὔτε δύο σώματα ἐν τῷ αὐτῷ τόπῳ,
  4. οὔτε διάστημά τι εἶναι σωματικόν (σῶμα γὰρ τὸ μεταξὺ τοῦ τόπου τὸ τυχόν, ἀλλ' οὐ διάστημα σώματος).
  5. καὶ ἔστιν ὁ τόπος καὶ πού, οὐχ ὡς ἐν τόπῳ δέ, ἀλλ' ὡς τὸ πέρας ἐν τῷ πεπερασμένῳ. οὐ γὰρ πᾶν τὸ ὂν ἐν τόπῳ, ἀλλὰ τὸ κινητὸν σῶμα.
It is clear, too, from these considerations that all the problems which were raised about place will be solved when it is explained in this way:
  1. There is no necessity that the place should grow with the body in it,
  2. Nor that a point should have a place,
  3. Nor that two bodies should be in the same place,
  4. Nor that place should be a corporeal interval: for what is between the boundaries of the place is any body which may chance to be there, not an interval in body.
  5. Further, place is also somewhere, not in the sense of being in a place, but as the limit is in the limited; for not everything that is is in place, but only movable body.
καὶ φέρεται δὴ εἰς τὸν αὑτοῦ τόπον ἕκαστον εὐλόγως (ὃ γὰρ ἐφεξῆς καὶ ἁπτόμενον μὴ βίᾳ, συγγενές· καὶ συμπεφυκότα μὲν ἀπαθῆ, ἁπτόμενα δὲ παθητικὰ καὶ ποιητικὰ ἀλλήλων)· Also it is reasonable that each kind of body should be carried to its own place. For a body which is next in the series and in contact (not by compulsion) is akin, and bodies which are united do not affect each other, while those which are in contact interact on each other.
καὶ μένει δὴ φύσει πᾶν ἐν τῷ οἰκείῳ τόπῳ οὐκ ἀλόγως· καὶ γὰρ τὸ μέρος, τὸ δὲ ἐν [τῷ] τόπῳ ὡς διαιρετὸν μέρος πρὸς ὅλον ἐστίν, οἷον ὅταν ὕδατος κινήσῃ τις (213a.) μόριον ἢ ἀέρος. οὕτω δὲ καὶ ἀὴρ ἔχει πρὸς ὕδωρ· οἷον ὕλη γάρ, τὸ δὲ εἶδος, τὸ μὲν ὕδωρ ὕλη ἀέρος, ὁ δ' ἀὴρ οἷον ἐνέργειά τις ἐκείνου· τὸ γὰρ ὕδωρ δυνάμει ἀήρ ἐστιν, ὁ δ' ἀὴρ δυνάμει ὕδωρ ἄλλον τρόπον. διοριστέον δὲ περὶ τούτων ὕστερον· ἀλλὰ διὰ τὸν καιρὸν ἀνάγκη μὲν εἰπεῖν, ἀσαφῶς δὲ νῦν ῥηθὲν τότ' ἔσται σαφέστερον. εἰ οὖν τὸ αὐτὸ [ἡ] ὕλη καὶ ἐντελέχεια (ὕδωρ γὰρ ἄμφω, ἀλλὰ τὸ μὲν δυνάμει τὸ δ' ἐντελεχείᾳ), ἔχοι ἂν ὡς μόριόν πως πρὸς ὅλον. διὸ καὶ τούτοις ἁφὴ ἔστιν· σύμφυσις δέ, ὅταν ἄμφω ἐνεργείᾳ ἓν γένωνται. καὶ περὶ μὲν τόπου, καὶ ὅτι ἔστι καὶ τί ἐστιν, εἴρηται. Nor is it without reason that each should remain naturally in its proper place. For this part has the same relation to its place, as a separable part to its whole, as when one moves a part of water or air: so, too, air is related to water, for the one is like matter, the other form—water is the matter of air, air as it were the actuality of water, for water is potentially air, while air is potentially water, though in another way. These distinctions will be drawn more carefully later. On the present occasion it was necessary to refer to them: what has now been stated obscurely will then be made more clear. If the matter and the fulfilment are the same thing (for water is both, the one potentially, the other completely), water will be related to air in a way as part to whole. That is why these have contact: it is organic union when both become actually one. This concludes my account of place—both of its existence and of its nature.
Postquam philosophus ostendit quid sit locus, hic ex definitione data solvit dubitationes supra positas de loco. Fuerunt autem supra positae sex rationes ad ostendendum locum non esse; quarum duas praetermittit, illam scilicet in qua inquirebatur utrum locus esset elementum vel ex elementis, et iterum illam in qua ostendebatur quod ad nullum genus causae locus reducatur: non enim a ponentibus locum, sic ponitur quasi elementum vel causa rerum. Unde facit mentionem solum de quatuor residuis. 487. After explaining what place is, the Philosopher now uses his definition to resolve the doubts that were raised about place (L.2). Now there were mentioned above six reasons to show that place does not exist. Of these he bypasses two: the one in which it was asked whether place be an element or a composite of elements; the other in which it was shown that place cannot be reduced to any genus of cause. He bypasses them because no one who posited place took it either as an element or as a cause of things. Hence he makes mention only of the four remaining.
Quarum una erat, quod cum locus non deesset corpori nec corpus loco, videbatur sequi quod augmentato corpore, augmentetur locus. 488. One of these was that, since place never lacks a body, and a body never lacks a place, it seemed to follow that if the body grew, the place would grow.
Sed hoc sequitur si supponatur quod locus sit spatium quoddam coextensum dimensionibus corporis, ut intelligatur illud spatium crescere, crescente corpore. Sed hoc non est necesse secundum definitionem praedictam de loco, quod sit terminus continentis. Now this would follow if it were supposed that place were a space co-extensive with the dimensions of the body, so that, as the body increased, so would the space. But this does not follow from the aforesaid definition of place, namely, that it is the boundary of the container.
Alia ratio fuit, quod si locus corporis est aliud a corpore, quod etiam locus puncti sit aliud a puncto: quare non videbatur possibile quod locus sit aliud a corpore, cum locus puncti non sit aliud a puncto. Sed haec etiam ratio procedit secundum imaginationem eorum qui opinabantur locum esse spatium coaequatum dimensionibus corporis: unde oportebat quod cuilibet dimensioni corporis responderet dimensio spatii, et similiter cuilibet puncto corporis. Sed hoc non oportet dicere, si ponamus locum esse terminum continentis. 469. Another argument was that, if the place of a body be distinct from the body, then the place of a point would be distinct from the point; wherefore, it did not seem possible for place to be distinct from the body, since the place of a point is not distinct from the point. But this argument was based on the imagining of those who opined, that place, is the space coextensive with the volume of the body, so that a dimension of space would correspond to a dimension of the body and in like manner to each point of the body, This, however, need not be said if we suppose that place is the boundary of the container.
Alia ratio fuit, quod si locus est aliquid, oportet quod sit corpus, cum habeat tres dimensiones; et sic sequetur duo corpora esse in eodem loco. Sed secundum eos qui ponunt locum esse terminum corporis continentis, non oportet dicere, neque quod duo corpora sint in eodem loco, neque quod sit aliquod spatium corporeum medium inter extremitates corporis continentis: sed quod sit ibi quoddam corpus. 490. Another argument was that, if place is anything, it must be a body, since it has three dimensions. Consequently, there would be two bodies in the same place. But according to those who agree that place is the boundary of the containing body it is not necessary to say that two bodies would be in the same place, or that there is some bodily space intervening between the boundaries of the containing body, but that there is some body there.
Item alia ratio fuit, quod si omne quod est, est in loco, sequetur quod etiam locus sit in loco. Quae quidem ratio de facili solvitur, supposito quod locus sit terminus continentis. Manifestum est enim secundum hoc, quod locus est in aliquo, scilicet in corpore continente; non tamen sicut in loco, sed sicut terminus in aliqua re finita, ut punctum in linea et superficies in corpore. Non enim necessarium est quod omne quod est, sit in aliquo sicut in loco; sed hoc necesse est solum de corpore mobili: motus enim induxit ad distinguendum inter locatum et locum 491. Likewise another argument was that, if everything that exists is in place, it will follow that even a place is in place. This argument is easy to answer, if we suppose that place is the boundary of the container, For according to this it is clear that place is in something; namely, in the containing body, but it is there, not as in a place, but as a boundary in a finite thing, just as a point is in a line and a surface in a body. For it is not required that everything that is, be in something as in a place; this is required only of a mobile body, for it is motion that led to distinguishing between the thing in place and the place itself.
Deinde cum dicit: et fertur igitur in sui etc., assignat ex praedicta definitione rationem proprietatum loci. Et primo quantum ad hoc, quod corpus naturaliter fertur ad proprium locum; secundo quantum ad hoc, quod corpus naturaliter quiescit in suo loco, ibi: et manet igitur natura et cetera. 492. Then [338] he uses his definition to give a reason for the properties of place. First, as to the fact that a body is naturally borne to its proper place; Secondly, as to the fact that a body naturally rests in its own place, at no. 493.
Dicit ergo primo, quod si ponatur locus esse terminus continentis, rationabiliter assignari potest causa, quare unumquodque corpus feratur ad proprium locum: quia illud corpus continens, ad quod consequenter se habet corpus contentum et locatum, et quod ab eo tangitur terminis simul existentibus, et hoc non per violentiam, est proximum ei secundum naturam. Ordo enim situs in partibus universi attenditur secundum ordinem naturae. Nam corpus caeleste, quod est supremum, est nobilissimum: post quod inter alia corpora secundum nobilitatem naturae est ignis; et sic deinceps usque ad terram. Unde manifestum est quod corpus inferius, quod se habet consequenter secundum situm ad corpus superius, est proximum sibi in ordine naturae. Et ideo addit non vi, ut ostendat naturalem ordinem situs, cui respondet ordo naturarum, et excludat ordinem situs violentum, sicut aliquando per violentiam corpus terrestre est super aerem vel aquam. Et huiusmodi duo corpora se consequentia in naturali ordine situs, et in ordine naturarum simul apta nata esse, sunt impassibilia: idest, cum continuantur ad invicem et fiunt unum, ad quod aptitudinem habent propter propinquitatem naturae, tunc sunt impassibilia. Sed dum tanguntur distincta existentia, propter contrarietatem qualitatum activarum et passivarum, sunt activa et passiva ad invicem. Sic igitur proximitas naturae, quae est inter corpus continens et contentum, est causa quare corpus naturaliter movetur ad suum locum: quia oportet quod gradus naturalium locorum respondeat gradui naturarum, ut dictum est. Sed haec ratio non potest assignari si ponatur locus esse spatium: quia in dimensionibus spatii separatis nullus ordo naturae considerari potest. He says first therefore, that if place be taken to the boundary of the container, the reason why each body is naturally borne to its own place can be given: it is because the containing body (which is next to the contained and located body, and which is touched by it so that the boundaries of both are together not by compulsion) is akin to it in nature. For the order of situs in the parts of the universe follows upon the order of nature. For the heavenly body, which is supreme, is the most noble; after it, among the other bodies the noblest in nature is fire, and so on down to earth. Hence it is clear that the lower body which is situated according to position, next to the higher body, is akin to it in the order of nature. And therefore he adds, “not by compulsion,” in order to point out the natural order of situs to which the order of nature corresponds and to exclude a compulsive order of situs, as when by compulsion a body of earth is above air or water. Two such bodies next to one another in the natural order of situs and which, in the natural order of natures, are disposed to be together, do not affect each other; i.e., when they are made continuous to each other and become one—and for this they have an aptitude on account of the similarity of their natures—then they do not interact. But when distinct things are in contact, their mutually interact on account of the contrariety of their active and passive qualities. Therefore it is the kinship of nature existing between the container and the thing contained that explains why a body is naturally moved to its own place: because the rank in natural places must correspond to the rank in natures, as was said. But such a reason cannot be assigned if place is taken to be space: because in the separated dimensions of space no order of nature can be considered.
Deinde cum dicit: et manet igitur natura etc., assignat causam quare corpora naturaliter quiescant in suis locis. Et dicit quod hoc accidit rationabiliter, si ponamus locum esse terminum corporis continentis: quia secundum hoc corpus locatum se habet ad corpus continens sicut quaedam pars ad totum, divisa tamen. Et hoc manifestius apparet in corporibus quae sunt facilis divisionis, sicut est aer vel aqua: horum enim partes possunt moveri ab aliquo in toto, sicut locatum movetur in loco. Et hoc etiam non solum verum est secundum figuram continendi unum sub alio, sed etiam secundum proprietatem naturae. Aer enim se habet ad aquam ut totum, quia aqua est ut materia, aer autem ut forma; nam aqua est quasi materia aeris, et aer est sicut forma eius. Quod ex hoc apparet, quia aqua est in potentia ad aerem simpliciter. 493. Then [330] he gives the reason why bodies naturally rest in their own place. And he says that this happens reasonably, if we grant that place is the boundary of the containing body: because according to this the contained body is related to the containing body after the manner of a part to a whole—a separated part, however. This is abundantly clear in bodies that are easy to divide, such as air or water: for their parts can be moved by something in the whole just as a thing in place is moved in a place. And this also is not only true according to the figure of containing one under the other, but even according to the properties of their nature. For air is related to water as the whole, because water is like matter and air like the form: water is as the matter of air, and air is as the form of water. This is so because water is in potency to air absolutely.
Sed verum est quod etiam aer est quodam alio modo in potentia ad aquam, ut determinabitur posterius in libro de generatione: sed ad praesens tempus necesse est hoc accipere ad ostensionem propositi. Sed hic non declaratur per certitudinem, sed in libro de generatione declarabitur certius. Ibi enim dicetur quod cum ex aqua generatur aer, est corruptio secundum quid, et generatio simpliciter, propter hoc quod perfectior forma introducitur, et imperfectior abiicitur. Cum autem ex aere generatur aqua, est corruptio simpliciter et generatio secundum quid, quia perfectior forma abiicitur, et imperfectior introducitur. Sic igitur aqua simpliciter est in potentia ad aerem, sicut imperfectum ad perfectum: aer autem est in potentia ad aquam, sicut perfectum ad imperfectum. Unde aer se habet ut forma et ut totum, quod habet rationem formae: aqua vero se habet ut materia et ut pars, quae pertinet ad rationem materiae. Quamvis igitur idem sit et materia et actus, quia aqua in se continet utrumque; sed tamen hoc quidem est in potentia proprie loquendo, scilicet aqua, sicut imperfectum: illud vero, scilicet aer, in actu ut perfectum. Unde habebit se aqua ad aerem quodammodo sicut pars ad totum. Et ideo his, scilicet aeri et aquae, cum sint duo distincta, inest tactus: sed cum ex utrisque fit unum, uno transeunte in naturam alterius, tunc fit copulatio, idest continuatio. Sicut igitur pars naturaliter quiescit in toto, ita et naturaliter corpus quiescit in suo loco naturali. Now while it is true that in some other ways air is in potency to water, as will be explained later in De Generatione, it is necessary for the present to accept this in order that we may explain our proposition. Here it is not declared as a certainty, but in the De Generatione it will be proved with greater certainty. For it will be said there that, when air is generated from water, it is corruption secundum quid and generation simply, because a more perfect form is being introduced and a less perfect one is being put off. But when water is generated from air, it is corruption simply and generation secundum quid, because. a more perfect form is being put off and an imperfect one being introduced. Consequently, water is in potency to air absolutely as the imperfect to the perfect; but air is in potency in water as the perfect to the imperfect. Hence air is as the form, and as the whole which is like the form; water, however, is as the matter and as a part, which pertains to the notion of matter. Therefore, although the same thing is both matter and act, because the water contains both in itself; yet properly speaking, the latter, i.e., the water, is in potency as an imperfect thing, but the former, i.e., the air, in act as a perfect. Hence water will be related to air somewhat as part to whole. And therefore these things, the air and the water, when they are distinct things, they are in contact; but when they form a unity, by one passing into the nature of the other, then coupling, i.e., continuity occurs. Therefore, just as the part naturally is at rest in the whole, so also a body naturally rests in its natural place.
Considerandum tamen est quod philosophus hic loquitur de corporibus secundum formas substantiales, quas habent ex influentia corporis caelestis, quod est primus locus, et dans virtutem locativam omnibus aliis corporibus: secundum autem qualitates activas et passivas est contrarietas inter elementa, et unum est corruptivum alterius. Note, however, that the Philosopher is speaking here of bodies according to the substantial forms which they have under the influence of the heavenly body which is the first place, and which gives to all other bodies the power to act as places. But if we consider active and passive qualities, there is contrariety among the elements and one tends to destroy another.
Ultimo autem epilogando concludit, quod dictum est de loco et quod est et quid est. Finally he concludes in summary that it has been stated that place exists and what place is.

Lecture 9
The void—reasons for and against
Lectio 9
Chapter 6
Τὸν αὐτὸν δὲ τρόπον ὑποληπτέον εἶναι τοῦ φυσικοῦ θεωρῆσαι καὶ περὶ κενοῦ, εἰ ἔστιν ἢ μή, καὶ πῶς ἔστι, καὶ τί ἐστιν, ὥσπερ καὶ περὶ τόπου· καὶ γὰρ παραπλησίαν ἔχει τήν τε ἀπιστίαν καὶ τὴν πίστιν διὰ τῶν ὑπολαμβανομένων· οἷον γὰρ τόπον τινὰ καὶ ἀγγεῖον τὸ κενὸν τιθέασιν οἱ λέγοντες, δοκεῖ δὲ πλῆρες μὲν εἶναι, ὅταν ἔχῃ τὸν ὄγκον οὗ δεκτικόν ἐστιν, ὅταν δὲ στερηθῇ, κενόν, ὡς τὸ αὐτὸ μὲν ὂν κενὸν καὶ πλῆρες καὶ τόπον, τὸ δ' εἶναι αὐτοῖς οὐ ταὐτὸ ὄν. The investigation of similar questions about the void, also, must be held to belong to the physicist—namely whether it exists or not, and how it exists or what it is—just as about place. The views taken of it involve arguments both for and against, in much the same sort of way. For those who hold that the void exists regard it as a sort of place or vessel which is supposed to be 'full' when it holds the bulk which it is capable of containing, 'void' when it is deprived of that—as if 'void' and 'full' and 'place' denoted the same thing, though the essence of the three is different.
ἄρξασθαι δὲ δεῖ τῆς σκέψεως λαβοῦσιν ἅ τε λέγουσιν οἱ φάσκοντες εἶναι καὶ πάλιν ἃ λέγουσιν οἱ μὴ φάσκοντες, καὶ τρίτον τὰς κοινὰς περὶ αὐτῶν δόξας. We must begin the inquiry by putting down the account given by those who say that it exists, then the account of those who say that it does not exist, and third the current view on these questions.
οἱ μὲν οὖν δεικνύναι πειρώμενοι ὅτι οὐκ ἔστιν, οὐχ ὃ βούλονται λέγειν οἱ ἄνθρωποι κενόν, τοῦτ' ἐξελέγχουσιν, ἀλλ' <�ὃ> ἁμαρτάνοντες λέγουσιν. ὥσπερ Ἀναξαγόρας καὶ οἱ τοῦτον τὸν τρόπον ἐλέγχοντες. ἐπιδεικνύουσι γὰρ ὅτι ἐστίν τι ὁ ἀήρ, στρεβλοῦντες τοὺς ἀσκοὺς καὶ δεικνύντες ὡς ἰσχυρὸς ὁ ἀήρ, καὶ ἐναπολαμβάνοντες ἐν ταῖς κλεψύδραις. οἱ δὲ ἄνθρωποι βούλονται κενὸν εἶναι διάστημα ἐν ᾧ μηδέν ἐστι σῶμα αἰσθητόν· οἰόμενοι δὲ τὸ ὂν ἅπαν εἶναι σῶμα φασίν, ἐν ᾧ ὅλως μηδέν ἐστι, τοῦτ' εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι. οὔκουν τοῦτο δεῖ δεικνύναι, ὅτι ἐστί τι ὁ ἀήρ, ἀλλ' ὅτι οὐκ ἔστι διάστημα ἕτερον τῶν σωμάτων, οὔτε χωριστὸν οὔτε ἐνεργείᾳ ὄν, ὃ διαλαμβάνει τὸ πᾶν σῶμα ὥστε εἶναι μὴ συνεχές, καθάπερ λέγουσιν Δημόκριτος καὶ Λεύκιππος καὶ (213b.) ἕτεροι πολλοὶ τῶν φυσιολόγων, ἢ καὶ εἴ τι ἔξω τοῦ παντὸς σώματός ἐστιν ὄντος συνεχοῦς. οὗτοι μὲν οὖν οὐ κατὰ θύρας πρὸς τὸ πρόβλημα ἀπαντῶσιν, Those who try to show that the void does not exist do not disprove what people really mean by it, but only their erroneous way of speaking; this is true of Anaxagoras and of those who refute the existence of the void in this way. They merely give an ingenious demonstration that air is something—by straining wine-skins and showing the resistance of the air, and by cutting it off in clepsydras. But people really mean that there is an empty interval in which there is no sensible body. They hold that everything which is in body is body and say that what has nothing in it at all is void (so what is full of air is void). It is not then the existence of air that needs to be proved, but the non-existence of an interval, different from the bodies, either separable or actual—an interval which divides the whole body so as to break its continuity, as Democritus and Leucippus hold, and many other physicists—or even perhaps as something which is outside the whole body, which remains continuous. These people, then, have not reached even the threshold of the problem,
ἀλλ' οἱ φάσκοντες εἶναι μᾶλλον. λέγουσιν δ' ἓν μὲν ὅτι κίνησις ἡ κατὰ τόπον οὐκ ἂν εἴη (αὕτη δ' ἐστὶ φορὰ καὶ αὔξησις)· οὐ γὰρ ἂν δοκεῖν εἶναι κίνησιν, εἰ μὴ εἴη κενόν· τὸ γὰρ πλῆρες ἀδύνατον εἶναι δέξασθαί τι. εἰ δὲ δέξεται καὶ ἔσται δύο ἐν ταὐτῷ, ἐνδέχοιτ' ἂν καὶ ὁποσαοῦν εἶναι ἅμα σώματα· τὴν γὰρ διαφοράν, δι' ἣν οὐκ ἂν εἴη τὸ λεχθέν, οὐκ ἔστιν εἰπεῖν. εἰ δὲ τοῦτο ἐνδέχεται, καὶ τὸ μικρότατον δέξεται τὸ μέγιστον· πολλὰ γὰρ μικρὰ τὸ μέγα ἐστίν· ὥστε εἰ πολλὰ ἴσα ἐνδέχεται ἐν ταὐτῷ εἶναι, καὶ πολλὰ ἄνισα. but rather those who say that the void exists. (1) They argue, for one thing, that change in place (i.e. locomotion and increase) would not be. For it is maintained that motion would seem not to exist, if there were no void, since what is full cannot contain anything more. If it could, and there were two bodies in the same place, it would also be true that any number of bodies could be together; for it is impossible to draw a line of division beyond which the statement would become untrue. If this were possible, it would follow also that the smallest body would contain the greatest; for 'many a little makes a mickle': thus if many equal bodies can be together, so also can many unequal bodies.
Μέλισσος μὲν οὖν καὶ δείκνυσιν ὅτι τὸ πᾶν ἀκίνητον ἐκ τούτων· εἰ γὰρ κινήσεται, ἀνάγκη εἶναι (φησί) κενόν, τὸ δὲ κενὸν οὐ τῶν ὄντων. ἕνα μὲν οὖν τρόπον ἐκ τούτων δεικνύουσιν ὅτι ἔστιν τι κενόν, Melissus, indeed, infers from these considerations that the All is immovable; for if it were moved there must, he says, be void, but void is not among the things that exist. This argument, then, is one way in which they show that there is a void.
ἄλλον δ' ὅτι φαίνεται ἔνια συνιόντα καὶ πιλούμενα, οἷον καὶ τὸν οἶνόν φασι δέχεσθαι μετὰ τῶν ἀσκῶν τοὺς πίθους, ὡς εἰς τὰ ἐνόντα κενὰ συνιόντος τοῦ πυκνουμένου σώματος. (2) They reason from the fact that some things are observed to contract and be compressed, as people say that a cask will hold the wine which formerly filled it, along with the skins into which the wine has been decanted, which implies that the compressed body contracts into the voids present in it.
ἔτι δὲ καὶ ἡ αὔξησις δοκεῖ πᾶσι γίγνεσθαι διὰ κενοῦ· τὴν μὲν γὰρ τροφὴν σῶμα εἶναι, δύο δὲ σώματα ἀδύνατον ἅμα εἶναι. Again (3) increase, too, is thought to take always by means of void, for nutriment is body, and it is impossible for two bodies to be together.
μαρτύριον δὲ καὶ τὸ περὶ τῆς τέφρας ποιοῦνται, ἣ δέχεται ἴσον ὕδωρ ὅσον τὸ ἀγγεῖον τὸ κενόν. A proof of this they find also in what happens to ashes, which absorb as much water as the empty vessel.
εἶναι δ' ἔφασαν καὶ οἱ Πυθαγόρειοι κενόν, καὶ ἐπεισιέναι αὐτὸ τῷ οὐρανῷ ἐκ τοῦ ἀπείρου πνεύματος ὡς ἀναπνέοντι καὶ τὸ κενόν, ὃ διορίζει τὰς φύσεις, ὡς ὄντος τοῦ κενοῦ χωρισμοῦ τινὸς τῶν ἐφεξῆς καὶ [τῆς] διορίσεως· καὶ τοῦτ' εἶναι πρῶτον ἐν τοῖς ἀριθμοῖς· τὸ γὰρ κενὸν διορίζειν τὴν φύσιν αὐτῶν. ἐξ ὧν μὲν οὖν οἱ μέν φασιν εἶναι οἱ δ' οὔ φασι, σχεδὸν τοιαῦτα καὶ τοσαῦτά ἐστιν. The Pythagoreans, too, (4) held that void exists and that it enters the heaven itself, which as it were inhales it, from the infinite air. Further it is the void which distinguishes the natures of things, as if it were like what separates and distinguishes the terms of a series. This holds primarily in the numbers, for the void distinguishes their nature. These, then, and so many, are the main grounds on which people have argued for and against the existence of the void.
Postquam philosophus determinavit de loco, hic determinat de vacuo. Et circa hoc duo facit: primo manifestat suam intentionem; secundo prosequitur propositum, ibi: alii quidem igitur et cetera. 494. Having discussed place, the Philosopher now begins to treat of the void. Concerning it he does two things: First he manifests his intention: Secondly, he executes it, at no. 497.
Circa primum duo facit: primo ostendit quod ad philosophum naturalem pertinet determinare de vacuo; secundo ostendit quo ordine de vacuo determinandum sit, ibi: incipere autem et cetera. As to the first, he does too things: First he shows that it is proper for the natural philosopher to deal with the void; Secondly, he shows what order should be followed in determining the matter of the void, at no. 495.
Dicit ergo primo, quod sicut ad philosophum naturalem pertinet determinare de loco an sit et quid sit, ita et de vacuo: quia per similes rationes aliqui crediderunt et discrediderunt esse locum et vacuum. Illi enim qui dicunt esse vacuum, ponunt ipsum ut quemdam locum et quoddam vas: quod quidem vas vel locus videtur esse plenum, cum habet intra se aliquam molem alicuius corporis; sed quando non habet, dicitur esse vacuum: ac si idem subiecto sit locus et vacuum et plenum, sed differant solum secundum rationem. He says therefore, first [346] that it is the task of the natural philosopher to determine about the void just as it was his task to determine about place: whether it exists, what it is. For the same reasons have led to belief or disbelief in the existence both of place and of the void. For those who posit a void think of it as a place and vessel, which vessel or place seems to be full when it has within it the mass of some body; but when it does not it is said to be a void. It is as though the same thing as to subject is place and void and full, any differing among them being only in the mind.
Deinde cum dicit: incipere autem oportet etc., ostendit quo ordine determinandum sit de vacuo. Et dicit quod oportet incipere ab hoc, quod ponamus rationes eorum qui dicunt vacuum esse; et iterum eorum qui dicunt vacuum non esse; et iterum communes opiniones de vacuo, quid scilicet ad rationem vacui pertineat. 495. Then [341] he shows what order must be followed in determining about the void. And he says that we must begin by giving the reasons of those who claim that the void exists; then the opinions of those who claim it does not exist; and then the general opinions about the void; namely, what belongs to the notion of the void.
Deinde cum dicit: alii quidem igitur tentantes monstrare etc., prosequitur quod dictum est. Et primo praemittit ea quae sunt necessaria ad inquirendum veritatem de vacuo; secundo incipit inquirere veritatem, ibi: quoniam autem non est et cetera. 496. Then [342] he begins to follow this program: First sets down preliminary notions that are necessary for discovering the truth about the void; Secondly, he begins to search for the truth, at no. 520 (L.11).
Circa primum duo facit: primo ponit rationes ponentium et negantium esse vacuum; secundo ponit communem opinionem de vacuo, ostendens quid sit de ratione vacui, ibi: ad quale autem et cetera. About the first he does two things: First he gives the reasons of those who posit or deny the existence of the void; Secondly, the common opinion about the void, showing what is included in its notion, at no. 506 (L. 10).
Circa primum duo facit: primo ponit rationem negantium esse vacuum; secundo rationes affirmantium, ibi: sed affirmantes et cetera. As to the first he does two things: First he gives the reason of those who deny the existence of the void; Secondly, the reasons of those who affirm it, at no. 499.
Dicit ergo primo, quod aliqui antiquorum philosophorum, volentes monstrare non esse vacuum, in hoc peccaverunt, quod non arguebant contra rationem ponentium esse vacuum. Non enim ostendebant non esse vacuum, sed inducebant rationes suas ad ostendendum quod plenum aere non est vacuum, ut patet de Anaxagora et aliis similiter argumentantibus, qui ad destruendum vacuum volebant demonstrare quod aer sit aliquid: et ita, cum vacuum sit in quo nihil est, sequitur quod plenum aere non sit vacuum. 497. He says first therefore [342] that some of the earlier philosophers desirous of demonstrating that the void does not exist erred by not arguing against the reasons given for the existence of the void. For they did not show that the void does not exist, but gave their reasons to show that something full of air is not a void, as is evident from Anaxagoras and others who reasoned like him. In order to destroy the void they wanted to demonstrate that air is something, and thus, since the void is that in which nothing exists, it followed that something full of air is not a void.
Quod autem aer sit aliquid, demonstrabant, litigantes cum suis adversariis, per utres; qui cum sint inflati, possunt aliquod pondus sustinere: quod non esset, nisi aer esset aliquid. Et sic demonstrant quod aer est fortis. Et etiam per hoc quod accipiunt aerem in clepsydris, idest in vasis furantibus aquam: in quibus cum attractione aeris attrahitur aqua, vel etiam impeditur introitus aquae, nisi exeat aer. In debating with their adversaries, they showed that air is something by means of wine skins which, when inflated, could support a weight, and which would not happen unless air were something. This also showed that air has strength. Also they showed it by taking the air in clepsydras, i.e., in vessels that absorb water; in these vessels water is drawn in by drawing in air, or water is prevented from entering, unless the air be withdrawn.
Patet igitur quod isti non obiiciunt ad positionem: quia omnes ponentes esse vacuum, volunt esse vacuum spatium, in quo nullum corpus sensibile est: propter hoc quod omne quod est, opinantur esse corpus sensibile, et sic ubi non est corpus sensibile, credunt nihil esse. Unde cum aer sit corpus modicum sensibile, opinantur quod ubi non est nisi aer, sit vacuum. It is clear therefore that they are not objecting against those who posit a void, because all such claim it is empty space in which no sensible body exists, for they assume that whatever exists is body perceptible to sense, and thus, where no sensible body exists, they believe nothing exists. Hence, since air is a body scarcely perceptible to sense, they thought that where there was nothing but air the void existed.
Ad destruendum igitur eorum positionem, non sufficit ostendere quod aer sit aliquid: sed oportet ostendere quod non sit aliquod spatium sine corpore sensibili. Quod quidem dupliciter aliqui ponebant esse vacuum: uno modo sicut separatum a corporibus, ut si diceremus spatium quod est infra extremitates alicuius domus, esse vacuum; alio modo sicut actu existens inter corpora, quod distinguit corpora ab invicem ut non sint continua, ut dixerunt Democritus et Leucippus et multi aliorum naturalium philosophorum. Imaginabantur enim quod si totum ens esset continuum, omnia essent unum: non enim esset assignare quare magis distinguerentur corpora plus hic quam ibi. Unde inter omnia corpora distincta, ponebant interesse aliquod spatium vacuum, in quo nullum ens esset. Et quia Democritus ponebat corpora componi ex multis corporibus indivisibilibus, ponebat in intermedio illorum corporum indivisibilium esse quasdam vacuitates, quas dicebat poros; et sic omnia corpora dicebat componi ex pleno et vacuo. Vel si etiam totum corpus mundi sit continuum, et non sit inter partes universi aliqua vacuitas, ponebant tamen vacuum esse extra totum mundum. 498. Therefore, to destroy their position it is not enough to show that air is something, but also one must show that there is no space without a sensible body. Space was supposed to be a void in two ways: first, as something separated from bodies, as though we were to say that the space within the confines of a house is a void; secondly, as something existing In act between bodies, preventing them from being continuous, as Democritus and Leucippus and many of the other natural philosophers held. For they imagined that if the totality of being were continuous, all things would be one: for there would be no more reason for distinguishing bodies at one point rather than another.. Hence between all distinct bodies they posited intervals of empty space in which no being existed. And since Democritus posited that bodies are composed of many indivisible bodies, he posited between those indivisibles certain empty places which he called “pores”.- in this way he explained that all bodies are composed of the full and of the empty. Or if the entire body of the world are continuous and no such empty place existed between the parts of the universe, they yet posited a void existing outside the universe.
Manifestum est igitur quod praedicti philosophi volentes destruere vacuum, non inducebant rationem ad quaestionem secundum positionem aliorum. Debuissent enim ostendere quod nullo illorum modorum sit vacuum. It is evident therefore that the aforementioned philosophers who tried to reject the void did not answer the problem as laid down by others. For they should have shown that the void does not exist in any of those ways.
Deinde cum dicit: sed affirmantes esse etc., ponit rationes ponentium esse vacuum. Et primo eorum qui locuti sunt de vacuo naturaliter; secundo eorum qui locuti sunt non naturaliter, ibi: esse autem affirmaverunt et cetera. 499. Then [343] he sets forth the reasons of those who posited a void. First, those who spoke of the void naturally; Secondly, of those who spoke of it non-naturally, at no. 505.
Circa primum duo facit: primo ponit rationem eorum qui ponebant vacuum esse quoddam spatium a corporibus separatum; secundo eorum qui ponebant vacuum in corporibus, ibi: alio vero modo et cetera. As to the first he does two things: First he mentions the reason given by those who held that the void is a space separated from bodies; Secondly, by those who held for a void in bodies, at no. 502.
Circa primum duo facit: primo ponit rationem ponentium esse vacuum; secundo ponit quomodo Melissus e converso illa ratione utebatur, ibi: Melissus quidem igitur et cetera. Concerning the first he does two things: First he gives the reason of those who posited a void; Secondly, how Melissus used that reason conversely, at no. 501.
Dicit ergo primo, quod illi qui affirmabant vacuum esse, magis inducebant rationes ad propositum. Quarum una erat, quod motus secundum locum, qui est loci mutatio et augmentatio, ut supra dictum est, non esset si vacuum non esset. Quod sic ostendebant. Si enim aliquid movetur secundum locum, non potest moveri in plenum; quia locus plenus uno corpore, non potest recipere aliud. Quia si reciperet, sequeretur duo corpora esse in eodem loco; et eadem ratione sequeretur de quocumque: non enim potest assignari differentia quare duo corpora sint in eodem loco et non plura. Et si hoc contingit, scilicet quod quotcumque corpora sint in eodem loco, sequetur quod parvissimus locus possit recipere maximum corpus; quia multa parva constituunt unum magnum. Unde si multa parva aequalia sint in uno loco, et multa inaequalia. Sic ergo probata hac conditionali, quod si motus est, vacuum est, arguebant a positione antecedentis: motus est; ergo vacuum est. 500. He says therefore first [343] that those who affirmed the existence of the void gave more opposite reasons. One of which was that motion is respect of place, i.e., change of place and increase, as was said above, would not exist if there were no void. They showed this in the following manner: If something is in motion according to place, it cannot be moved into what is full because a place filled with one body cannot receive another. For, if it received it there would then be two bodies in the same place—and the same would follow for any [additional] body: for there is no reason why many bodies could not be in the same place if two could. And if that were to happen, i.e., that any number of bodies were in the same place, it would follow that the smallest place could receive the largest body—because many small things form one large thing. Hence, if any small equal bodies could exist in the same place, then also many could. And so, having proved this conditional position that there is motion, there is a void, they argue (by positing the antecedent): “But there is motion; therefore, there is a void.”
Deinde cum dicit: Melissus quidem igitur etc., ostendit quod Melissus, supposita eadem conditionali, argumentabatur e contra a destructione consequentis: quia si motus est, vacuum est; sed vacuum non est; ergo motus non est: ergo totum ens est immobile. 501. Then [344] he shows how Melissus, supposing the same conditional, argued in a contrary manner from the denial of the consequent, and reasoned thus: if motion exists, there is a void; but there is no void; therefore motion does not exist. Consequently, the totality of being is immobile.
Iste est igitur unus modus quo aliqui probabant vacuum esse quasi separatum. Thus the foregoing is one way in which some proved that the void exists after the fashion of something separate.
Deinde cum dicit: alio vero modo, quia videntur etc., ponit tres rationes ponentium vacuum esse in corporibus. Quarum prima est ex his quae condensantur. Videntur enim eorum quae inspissantur, partes coire vel convenire in invicem, et se invicem calcare et comprimere, ita quod sicut fertur, dolia tantum de vino recipiunt cum utribus, quantum etiam sine utribus, et praecipue si utres sint subtiles; propter hoc quod vinum in utribus condensari videtur. Hanc autem condensationem fieri existimabant ac si densato corpore, partes subintrarent in quasdam vacuitates. 502. Then [345] he lists three reasons given by those who held that the void exists in bodies. The first of these is based on things that condense. For in the case of things that can be compressed it seems that the parts come together and fit in together and press down and compress each other so that, as is held, casks will hold as much wine with the wine skins as without, especially if the wine skins are thin, because in the wine skins the wine seems to become condensed. This condensation they believed to take place as though in the condensed body the parts entered into certain empty spaces.
Secundam rationem ponit ibi: amplius autem et augmentum etc.: quae sumitur ex augmento. Augentur enim corpora per alimentum, quod corpus quoddam est. Duo autem corpora non possunt esse in eodem loco; ergo oportet esse aliquas vacuitates in corpore augmentato, in quibus recipiatur alimentum. Et sic necesse est esse vacuum ad hoc quod recipiatur alimentum. 503. The second reason he gives [346] is based on increase: For a body grows on account of food, which is a body. But two bodies cannot exist in the same place. Therefore there must be, in the body which has grown, certain voids in which the food may be received. Consequently, there must be a void in order that food be taken in,
Tertiam rationem ponit ibi: testimonium autem et cetera. Quae sumitur ex vase pleno cinere, quod tantum recipit de aqua, quantum si esset vacuum: quod non esset nisi essent aliquae vacuitates inter partes cineris. 504. The third reason [347] is based on a vessel full of ashes being able to absorb as much water as the empty vessel. This would not be the case unless there were empty spaces between the parts of the ashes.
Deinde cum dicit: esse autem affirmaverunt etc., ponit opiniones non naturalium de vacuo. Et dicit quod etiam Pythagorici affirmaverunt esse vacuum: quod quidem ingrediebatur infra partes mundi a caelo, propter vacuum infinitum, quod ponebant esse extra caelum quasi quendam aerem vel spiritum infinitum: ut sicut ille qui respirat, dividit suo flatu aliqua faciliter divisibilia, ut aquam aut huiusmodi, ita ex aliquo quasi respirante, ingrederetur distinctio in res; quam non intelligebant fieri nisi per vacuum, sicut de Democrito dictum est: ac si vacuum nihil esset aliud quam distinctio rerum. Et quia prima distinctio et pluralitas invenitur in numeris, ideo vacuum primo ponebant in numeris: ut per naturam vacui una unitas distingueretur ab alia, ne numerus sit continuus, sed habeat naturam discretam. Sed quia isti quasi aequivoce loquebantur de vacuo, appellantes rerum distinctionem vacuum, propter hoc infra de hac opinione non prosequitur. 505. Then [348] he gives the opinions of the non-natural philosophers about the void. And he says that the Pythagoreans also posited a void which entered into the parts of the universe from the heavens, on account of the infinite void which they supposed existed outside the heavens—a void like some infinite air or infinite spirit [i.e. breath]: just as a person who breathes divides by means of his breath certain things that are easy to divide, such as water or similar things, so it was that the things of this world became distinct by some being as though through breathing. They did not understand this to except through a void, as was mentioned in regard to Democritus—as though the void were nothing other than the distinction between things. And because the first distinction and plurality is found in numbers, therefore they first of all posited a void in numbers, so that it is through the nature of the void that one unit would be distinct from another—so that number would not be continuous but would have a discrete nature. But because they spoke of the void in a quasi-equivocal manner, calling the distinction of things “a void” Aristotle does not discuss this opinion below.
Ultimo autem quasi epilogando concludit, dictum esse propter quid quidam dicunt esse vacuum, et quidam non dicunt. Finally, in summary, he concludes that we have given the reasons why some posit a void and why some do not.

Lecture 10
The meaning of “void”—refutation of those positing the void
Lectio 10
Chapter 7
Πρὸς δὲ τὸ ποτέρως ἔχει δεῖ λαβεῖν τί σημαίνει τοὔνομα. As a step towards settling which view is true, we must determine the meaning of the name.
δοκεῖ δὴ τὸ κενὸν τόπος εἶναι ἐν ᾧ μηδέν ἐστι. τούτου δ' αἴτιον ὅτι τὸ ὂν σῶμα οἴονται εἶναι, πᾶν δὲ σῶμα ἐν τόπῳ, κενὸν δὲ ἐν ᾧ τόπῳ μηδέν ἐστι σῶμα, ὥστ' εἴ που μὴ ἔστι σῶμα, οὐδὲν εἶναι ἐνταῦθα. σῶμα δὲ πάλιν ἅπαν (214a.) οἴονται εἶναι ἁπτόν· τοιοῦτο δὲ ὃ ἂν ἔχῃ βάρος ἢ κουφότητα. συμβαίνει οὖν ἐκ συλλογισμοῦ τοῦτο εἶναι κενόν, ἐν ᾧ μηδέν ἐστι βαρὺ ἢ κοῦφον. ταῦτα μὲν οὖν, ὥσπερ εἴπομεν καὶ πρότερον, ἐκ συλλογισμοῦ συμβαίνει. The void is thought to be place with nothing in it. The reason for this is that people take what exists to be body, and hold that while every body is in place, void is place in which there is no body, so that where there is no body, there must be void. Every body, again, they suppose to be tangible; and of this nature is whatever has weight or lightness. Hence, by a syllogism, what has nothing heavy or light in it, is void. This result, then, as I have said, is reached by syllogism.
ἄτοπον δὲ εἰ ἡ στιγμὴ κενόν· δεῖ γὰρ τόπον εἶναι ἐν ᾧ σώματος ἔστι διά στημα ἁπτοῦ. ἀλλ' οὖν φαίνεται λέγεσθαι τὸ κενὸν ἕνα μὲν τρόπον τὸ μὴ πλῆρες αἰσθητοῦ σώματος κατὰ τὴν ἁφήν· αἰσθητὸν δ' ἐστὶ κατὰ τὴν ἁφὴν τὸ βάρος ἔχον ἢ κουφότητα It would be absurd to suppose that the point is void; for the void must be place which has in it an interval in tangible body. But at all events we observe then that in one way the void is described as what is not full of body perceptible to touch; and what has heaviness and lightness is perceptible to touch.
(διὸ κἂν ἀπορήσειέ τις, τί ἂν φαῖεν, εἰ ἔχοι τὸ διάστημα χρῶμα ἢ ψόφον, πότερον κενὸν ἢ οὔ; ἢ δῆλον ὅτι εἰ μὲν δέχοιτο σῶμα ἁπτόν, κενόν, εἰ δὲ μή, οὔ)· So we would raise the question: what would they say of an interval that has colour or sound—is it void or not? Clearly they would reply that if it could receive what is tangible it was void, and if not, not.
ἄλλον δὲ τρόπον, ἐν ᾧ μὴ τόδε τι μηδ' οὐσία τις σωματική. διό φασίν τινες εἶναι τὸ κενὸν τὴν τοῦ σώματος ὕλην (οἵπερ καὶ τὸν τόπον τὸ αὐτὸ τοῦτο), λέγοντες οὐ καλῶς· ἡ μὲν γὰρ ὕλη οὐ χωριστὴ τῶν πραγμάτων, τὸ δὲ κενὸν ζητοῦσιν ὡς χωριστόν. In another way void is that in which there is no 'this' or corporeal substance. So some say that the void is the matter of the body (they identify the place, too, with this), and in this they speak incorrectly; for the matter is not separable from the things, but they are inquiring about the void as about something separable.
ἐπεὶ δὲ περὶ τόπου διώρισται, καὶ τὸ κενὸν ἀνάγκη τόπον εἶναι, εἰ ἔστιν, ἐστερημένον σώματος, τόπος δὲ καὶ πῶς ἔστι καὶ πῶς οὐκ ἔστιν εἴρηται, φανερὸν ὅτι οὕτω μὲν κενὸν οὐκ ἔστιν, οὔτε κεχωρισμένον οὔτε ἀχώριστον. τὸ γὰρ κενὸν οὐ σῶμα ἀλλὰ σώματος διάστημα βούλεται εἶναι· διὸ καὶ τὸ κενὸν δοκεῖ τι εἶναι, ὅτι καὶ ὁ τόπος, καὶ διὰ ταὐτά. Since we have determined the nature of place, and void must, if it exists, be place deprived of body, and we have stated both in what sense place exists and in what sense it does not, it is plain that on this showing void does not exist, either unseparated or separated; the void is meant to be, not body but rather an interval in body. This is why the void is thought to be something, viz. because place is, and for the same reasons.
ἥκει γὰρ δὴ ἡ κίνησις ἡ κατὰ τόπον καὶ τοῖς τὸν τόπον φάσκουσιν εἶναί τι παρὰ τὰ σώματα τὰ ἐμπίπτοντα καὶ τοῖς τὸ κενόν. αἴτιον δὲ κινήσεως οἴονται εἶναι τὸ κενὸν οὕτως ὡς ἐν ᾧ κινεῖται· τοῦτο δ' ἂν εἴη οἷον τὸν τόπον φασί τινες εἶναι. For the fact of motion in respect of place comes to the aid both of those who maintain that place is something over and above the bodies that come to occupy it, and of those who maintain that the void is something. They state that the void is the condition of movement in the sense of that in which movement takes place; and this would be the kind of thing that some say place is.
οὐδεμία δ' ἀνάγκη, εἰ κίνησις ἔστιν, εἶναι κενόν. ὅλως μὲν οὖν πάσης κινήσεως οὐδαμῶς, δι' ὃ καὶ Μέλισσον ἔλαθεν· ἀλλοιοῦσθαι γὰρ τὸ πλῆρες ἐνδέχεται. ἀλλὰ δὴ οὐδὲ τὴν κατὰ τόπον κίνησιν· ἅμα γὰρ ἐνδέχεται ὑπεξιέναι ἀλλήλοις, οὐδενὸς ὄντος διαστήματος χωριστοῦ παρὰ τὰ σώματα τὰ κινούμενα. καὶ τοῦτο δῆλον καὶ ἐν ταῖς τῶν συνεχῶν δίναις, ὥσπερ καὶ ἐν ταῖς τῶν ὑγρῶν. But there is no necessity for there being a void if there is movement. It is not in the least needed as a condition of movement in general, for a reason which, incidentally, escaped Melissus; viz. that the full can suffer qualitative change. But not even movement in respect of place involves a void; for bodies may simultaneously make room for one another, though there is no interval separate and apart from the bodies that are in movement. And this is plain even in the rotation of continuous things, as in that of liquids.
ἐνδέχεται δὲ καὶ πυκνοῦσθαι μὴ εἰς τὸ κενὸν ἀλλὰ διὰ τὸ τὰ ἐνόντα (214b.) ἐκπυρηνίζειν (οἷον ὕδατος συνθλιβομένου τὸν ἐνόντα ἀέρα), And things can also be compressed not into a void but because they squeeze out what is contained in them (as, for instance, when water is compressed the air within it is squeezed out);
καὶ αὐξάνεσθαι οὐ μόνον εἰσιόντος τινὸς ἀλλὰ καὶ ἀλλοιώσει, οἷον εἰ ἐξ ὕδατος γίγνοιτο ἀήρ. and things can increase in size not only by the entrance of something but also by qualitative change; e.g. if water were to be transformed into air.
ὅλως δὲ ὅ τε περὶ τῆς αὐξήσεως λόγος καὶ τοῦ εἰς τὴν τέφραν ἐγχεομένου ὕδατος αὐτὸς αὑτὸν ἐμποδίζει. ἢ γὰρ οὐκ αὐξάνεται ὁτιοῦν, ἢ οὐ σώματι, ἢ ἐνδέχεται δύο σώματα ἐν ταὐτῷ εἶναι (ἀπορίαν οὖν κοινὴν ἀξιοῦσι λύειν, ἀλλ' οὐ κενὸν δεικνύουσιν ὡς ἔστιν), ἢ πᾶν εἶναι ἀναγκαῖον τὸ σῶμα κενόν, εἰ πάντῃ αὐξάνεται καὶ αὐξάνεται διὰ κενοῦ. ὁ δ' αὐτὸς λόγος καὶ ἐπὶ τῆς τέφρας. ὅτι μὲν οὖν ἐξ ὧν δεικνύουσιν εἶναι τὸ κενὸν λύειν ῥᾴδιον, φανερόν. In general, both the argument about increase of size and that about water poured on to the ashes get in their own way. For either not any and every part of the body is increased, or bodies may be increased otherwise than by the addition of body, or there may be two bodies in the same place (in which case they are claiming to solve a quite general difficulty, but are not proving the existence of void), or the whole body must be void, if it is increased in every part and is increased by means of void. The same argument applies to the ashes. It is evident, then, that it is easy to refute the arguments by which they prove the existence of the void.
Dixerat superius philosophus a tribus esse incipiendum: postquam ergo prosecutus est duo eorum, ponens scilicet opiniones negantium et affirmantium vacuum esse, hic prosequitur tertium, communes scilicet opiniones hominum de vacuo demonstrans. 506. The Philosopher had said above that we I must start with three things. So now, having finished two of them, by giving, namely, the opinions of both of those who posited and of those who rejected the void, he now enters upon the third, by showing, namely, the general notions people have about the void.
Circa hoc igitur tria facit: primo ostendit quid significetur nomine vacui; secundo ostendit quomodo vacuum aliqui esse posuerunt, ibi: quoniam autem de loco etc.; tertio excludit rationes ponentium vacuum esse, ibi: neque una autem et cetera. Concerning this he does three things: First he shows what is meant by the word “void”; Secondly, how some thought that the void exists, at no. 513; Thirdly, he rejects the reasons given by those who posit that a void exists, at no. 515.
Circa primum duo facit: primo dicit de quo est intentio; secundo exequitur propositum, ibi: videtur autem et cetera. As to the first he does two things: First he reveals his intention; Secondly, he executes it, at no. 509.
Dicit ergo primo quod, cum dictum sit quod quidam posuerunt vacuum esse, quidam vero negaverunt; ad cognoscendum qualiter se habeat veritas, oportet accipere tanquam principium, quid significet nomen vacui. Sicut enim cum dubitatur an aliqua passio insit alicui subiecto, oportet accipere pro principio quid sit res, ita cum dubitatur de aliquo an sit, oportet accipere pro medio quid significet nomen. Quaestio enim quid est sequitur quaestionem an est. 507. He says first, therefore [349], that since it was pointed out that some people affirmed a void and others denied it, in order to get at the truth we must begin by the meaning of the word “void.” For just as, when there is question about some property existing in a subject, we must begin by agreeing what the thing is, so when there is question about the existence of something, we must begin by taking as the middle form the meaning of the word. For the question of what something is comes after the question of whether it exists.
Deinde cum dicit: videtur autem vacuum etc., ostendit quid significet nomen vacui: et primo ponit significationem communiorem; secundo significationem secundum usum Platonicorum, ibi: alio autem modo et cetera. 508. Then [350] he shows that it meant by the word “void”. First he gives the more common meaning; Secondly, what the Platonists took it to mean at no. 512.
Circa primum tria facit: primo ostendit quid significet nomen vacui; secundo quid oportet addere ad illam significationem, ibi: sed inconveniens est etc., tertio removet quandam dubitationem, ibi: unde et si et cetera. As to the first he does three things: First he shows what the word “void” means; Secondly, what should be added to that meaning at no. 510; Thirdly, he clears up a doubt, at no. 511.
Dicit ergo quod secundum opinionem hominum, videtur vacuum nihil aliud significare quam locum in quo nihil sit. Et huius causa est, quia proprie vacuum dicitur esse, in quo non est aliquod corpus: quia soli corpori convenit quod sit in loco; et vacuum nihil aliud potest significare quam locum absque locato. Sed quia homines opinantur quod omne ens sit corpus, sequitur secundum eorum opinionem quod ubi non est corpus, nihil sit. 509. He says therefore that according to common opinion, the void seems to signify nothing more than a place In which there is nothing. The reason for this is because properly that is said to be a void in which there is not any body, and since only a body can be in place, void seems to mean nothing more than a place without any thing in it. But because people suppose that every being is a body, it follows that according to their opinion where there is not body, there is nothing.
Et ulterius opinantur quod omne corpus sit tangibile, id est habens tangibiles qualitates. Et huiusmodi corpus est quod est grave vel leve: nondum enim erat notum quod corpus caeleste esset praeter naturam quatuor elementorum. Unde cum proprie de ratione vacui sit quod sit locus in quo non est aliquod corpus, sequitur quod vacuum sit in quo non est corpus grave vel leve: non quidem quod hoc sit de ratione vacui secundum primam impositionem nominis, sed secundum quandam syllogisticam deductionem ex communi opinione hominum, opinantium omne corpus esse grave vel leve: sicut etiam secundum opinionem communem hominum existimantium omne ens esse corpus, sequitur vacuum esse in quo nihil est. And further they believe that every body is tangible, i.e., that it has tactile qualities. And a body of this kind is heavy or light: for in their time it was not yet known that a heavenly body is different in nature from any of the four elements. Hence since it is the very nature of the void to be a place in which there is not a body, it follows that the void is that in which there is neither a light nor a heavy body. However, this is not to say that it belongs to the notion of the void according to the primary meaning of the word, but rather by reason of a certain syllogistic deduction that starts with the general opinion of people that every body is either heavy or light; just as the common opinion of people that every being is a body, leads to the conclusion that the void is that in which there is nothing.
Sic igitur tribus modis potest accipi huius nominis significatio: una est propria, scilicet vacuum est locus in quo non est corpus: aliae duae secundum opinionem hominum; quarum una est communior, scilicet vacuum est locus in quo nihil est; alia vero est magis coarctata, scilicet vacuum est locus in quo non est corpus grave vel leve. Consequently, the meaning of this word “void” is three-fold: one is proper, namely, that the void is that in which there is not any body; the others come from the general opinion of people: the first is more common, namely, that the void is a place in which nothing exists; the second is more restricted, namely, that the void is a place in which there is neither a heavy nor a light body.
Deinde cum dicit: sed inconveniens est etc., ostendit quid addendum sit ad hanc significationem. Dicit enim quod inconveniens est si dicatur quod punctum sit vacuum, cum tamen de puncto dici possit quod in puncto non sit corpus tangibile. Oportet ergo addere quod vacuum sit locus in quo non sit corpus tangibile, sed sit ibi spatium susceptivum corporis tangibilis: sicut caecum dicitur quod caret visu, natum autem habere. Et sic concludit quod uno modo dicitur vacuum, spatium quod non est plenum corpore sensibili secundum tactum, quod scilicet est grave vel leve. 510. Then [351] he shows that must be added to this meaning. For he says that it is not correct to say that a point is a void, even though in a point there is no tangible body. So we must add that the void to a place in which there is not a tangible body, but which has in it space to receive a tangible body, just as a blind person is said to be one who lacks sight but to apt to have it. And so he concludes that in one way the void is called a space which is not full of a body that is sensible by touch, i.e., a body that is heavy or light.
Deinde cum dicit: unde et si dubitabit aliquis etc., removet quandam dubitationem, quae est: utrum si in aliquo spatio sit color vel sonus, dicendum sit vacuum vel non: et hoc propter definitionem primo datam, scilicet vacuum est in quo nihil est. Et solvit quod si spatium in quo est tantum sonus vel color, sit susceptivum corporis tangibilis, vacuum est: si vero non, non est vacuum. Et hoc ideo, quia haec non est propria definitio vacui, vacuum est in quo nihil est, nisi secundum opinionem credentium, ubi non est corpus nihil esse. 511. Then [352] he clears up the following difficulty; If there is color or sound in a certain space, should it be called a void or not? This question arises because the definition first given says that the void is that in which there is nothing. And he answers by saying that if the space in which there is just sound or color has room for a tangible body, it is a void; if not, not. The reason is that the proper definition of the void is not “that in which there is nothing,” and such a definition is held only by people who believe that where no body is, nothing is.
Deinde cum dicit: alio autem modo etc., ponit aliam significationem vacui secundum usum Platonicorum. Et dicit quod alio modo dicitur esse vacuum: in quo non est hoc aliquid, neque aliqua substantia corporea. Fit autem hoc aliquid per formam. Unde aliqui dicunt materiam corporis, secundum quod est absque forma, esse vacuum: qui etiam materiam dicunt esse locum, ut supra dictum est. Sed non bene dicunt: quia materia non est separabilis a rebus quarum est materia; sed homines quaerunt locum et vacuum, tanquam aliquid separabile a corporibus locatis. 512. Then [353] he gives the meaning of “void” as used by the Platonists. And he says that there is another meaning of the void: that in which there is no “this something” or any corporeal substance. Now a “this something” comes about on account of the form. Hence some claim that the matter of a body, insofar as it is apart from its form, is the void. These are the same who claim that matter is place, as was stated above (L.3). But this is poor judgment, for matter is not separable from the things of which it is the matter; whereas men inquire about place and the void as being separable from bodies in place.
Deinde cum dicit: quoniam autem de loco etc., ostendit quomodo aliqui ponebant vacuum esse. Et primo quid dicebant esse vacuum; secundo propter quid vacuum ponebant, ibi: et propter eadem acceptum et cetera. 513. Then [354] he tells how some posited existence of a void; First, what they said the void was; Secondly, why they posited it, at no. 514.
Dicit ergo primo, quod quia vacuum est locus privatus corpore, et determinatum est de loco quomodo sit et quomodo non sit (dictum est enim quod locus non est aliquod spatium, sed terminus continentis); manifestum est etiam quod neque vacuum est spatium separatum a corporibus, neque intrinsecum corporibus, sicut ponebat Democritus. Et hoc ideo, quia ponentes vacuum quocumque istorum modorum, volunt quod vacuum non sit corpus, sed spatium corporis. Ideo enim videbatur aliquid esse vacuum, quia locus aliquid est: et sicut locus videbatur esse spatium, ita et vacuum. Si ergo locus non est aliquod spatium praeter corpora, neque vacuum potest esse spatium praeter corpora. Et cum de ratione vacui sit quod sit spatium corporis praeter corpora, ut supra dictum est, sequitur quod vacuum non sit. He says therefore first that since the void is a place without a body in it, and since we have already decided how place exists and how it does not (for we have said that place is not a space but the boundary of a container), it is clear that the void is neither a space separated from bodies nor intrinsic to them as Democritus supposed. This is so because those who suppose that space exists in either of those two ways, intend the void to be not a body, but the space of a body. For they thought that the void was something because place was something, and just as place seems to be space, so also the void. But if place is not a space outside of bodies, neither can the void be a space outside of bodies. And since it is the very nature of the void to be a bodily space existing outside of bodies, as was said above, it follows that the void does not exist.
Deinde cum dicit: et propter eadem acceptum etc., ostendit quare posuerunt vacuum. Et dicit quod propter idem acceperunt vacuum esse, propter quod acceperunt locum esse, scilicet propter motum, ut supra dictum est: quia provenit ut salvetur motus secundum locum, tam secundum illos qui dicunt locum aliquid esse praeter corpora quae sunt in loco, quam secundum illos qui ponunt vacuum esse. Negantibus autem locum et vacuum, non provenit motum secundum locum esse. Et sic vacuum quodammodo opinantur causam esse motus eo modo quo et locum, ut in quo scilicet est motus. 514. Then [355] he shows why they posited a void. And he says that they admitted the existence of the void for the same reason that they admitted place, namely, on account of motion, as we said above: for it comes about that local motion is saved, both for those who assert that place is something over and above the bodies which are in place and for those who claim that the void exists. But for those who deny place and the void, there cannot be local motion. Consequently, some believed that the void is a cause of motion in the way that place is, i.e., as that in which motion takes place.
Deinde cum dicit: neque una autem necessitas est etc., excludit rationes ponentium vacuum esse. Et non intendit hic rationes praemissas vera solutione solvere; sed instantiam dare ex qua ex ipso aspectu apparet, quod rationes non ex necessitate concludunt. Primo ergo excludit rationes ponentium vacuum separatum; secundo ponentium vacuum in corporibus, ibi: contingit autem densari et cetera. 515. Then [356] he rejects the arguments of those who posit existence of the void. He does not, however, intend here to give a true solution to the aforesaid arguments, but to bring an objection which at a glance shows that their arguments do not conclude with necessity. First therefore he rejects the reasons given by those who posit a separated void; Secondly, the arguments of those who posit a void existing in bodies, at no. 517.
Primam autem rationem excludit dupliciter. Primo quidem, quia non est necessarium si motus sit quod vacuum sit. Et si loquamur universaliter de qualibet specie motus, manifeste apparet quod nequaquam est necessarium. Nihil enim prohibet id quod est plenum, alterari: solus enim motus localis excludi videtur si vacuum non ponatur. Et hoc latuit Melissum, dum credidit remoto vacuo omnem speciem motus auferri. 516. He rejects the first reason in two ways: First, because even though motion exists, it does not necessarily follow that the void exists. And if we speak generally of any species of motion, it is clear that the void is not necessary at all. For nothing prevents the full from being altered [i.e., having motion in quality], since only local motion seems to be excluded if the void is not posited. Yet Melissus did not see this, for he believed that if there were no void, no motion of any kind could exist.
Secundo excludit eandem rationem per hoc quod neque motus localis tollitur, si vacuum non sit. Dato enim quod nullum spatium separabile sit praeter corpora quae moventur, potest motus localis esse per hoc quod corpora subintrent se invicem per modum inspissationis, et sic aliquid in plenum movetur, et non in vacuum. Et hoc apparet manifeste in generationibus corporum continuorum, et praecipue in humidis, sicut videtur in aqua. Si enim proiiciatur lapis in aliquam magnam latitudinem aquae, manifeste apparet fieri quasdam circulationes circa locum percussionis, quousque pars aquae depulsae commoveat aliam et subintret ipsam: unde quia modica pars aquae subintrat per quandam diffusionem in maiorem aquam, circulationes praedictae a parvo in maius procedunt, quousque totaliter deficiant. Secondly, he rejects the same reason on the ground that not even local motion is destroyed, if there is no void. For, assuming that there is no separable space over and above moving bodies, local motion can take place, if bodies make room for one another by contracting: thus they would be moving into the full rather than into the empty. This is evident in the generations of continuous bodies, especially in liquids, such as water. For if a stone is thrown into a large surface of water, circles appear around the place of entry as long as one part of the moving water agitates another part and enters it. Hence, because a small portion of water by a process of diffusion enters a larger section, the circles grow from small to large until they cease entirely.
Deinde cum dicit: contingit autem densari etc., excludit rationes ponentium vacuum in corporibus. Et primo rationem quae procedebat ex condensatione. Et dicit quod contingit corpora condensari, et partes corporis subintrare sibi invicem, non propter hoc quod pars subintrans vadat in locum vacuum; sed ideo quia erant aliqua foramina, plena aliquo corpore subtiliori, quod facta condensatione elabitur: sicut quando aqua colliditur et inspissatur, aer qui intus erat, excluditur. Et haec maxime apparent in spongia, et in huiusmodi corporibus porosis. Haec igitur solutio non ostendit causam condensationis, quam inferius ponit: sed ostendit quod etiam per hunc modum manifeste excludi potest necessitas vacui. 517. Then [357] he rejects the reasons given by those who posit a void in bodies. And first of all the reason based an condensation. And he says that bodies happen to become condensed, and parts of a body mutually penetrate, not because the invading part is entering an empty place but because there were certain openings, full of a more subtle body which escapes under condensation, just when water is compressed and contracted, the air that was present is expelled. This takes place manifestly in a sponge and other like porous bodies. Therefore this solution does not give the reason for condensation (he will give this later [L.14]: but it does show that also in this way, the need of a void can be clearly eliminated.
Secundo ibi: et augmentari etc., excludit rationem quae procedit ex augmento. Et dicit quod augmentum contingit esse non solum per additionem alicuius corporis ingredientis in corpus augmentatum, ut sic necesse sit esse vacuum, sed etiam per alterationem: sicut cum ex aqua fit aer, maior fit quantitas aeris quam erat aquae. Et haec etiam non est vera solutio rationis inductae: sed solum instantia quaedam, ne sit necesse ponere vacuum. Vera autem solutio ponitur in libro de generatione, ubi ostenditur quod alimentum non sic transit in id quod augetur, quasi sit aliud corpus ab ipso; sed quia convertitur in substantiam eius, sicut ligna apposita igni, convertuntur in ignem. 518. Secondly [358] he rejects the argument based on growth. And he says that growth occurs not only by the addition of some body invading the growing body so as to make the void necessary but also by alteration, as, when air comes to be from water, the quantity of air becomes greater than the quantity of water. This too is not the true solution of their argument but merely an objection showing that it is not necessary to posit a void. The true solution is given in the book “ De Generatione, where it is shown that food does not pass into that which grows as to be a body distinct from it; rather it is converted into its substance, as wood added to fire is converted into fire.
Tertio ibi: omnino autem et quae est de augmento etc., excludit simul et rationem de augmento et rationem de aqua effusa in cinerem: et dicit quod utraque ratio impedit seipsam. Quod sic patet. Est enim circa augmentum haec dubitatio. Videtur enim vel quod non totum augeatur; vel quod augmentum non fiat per additionem corporis, sed per additionem alicuius incorporei; aut quod contingat duo corpora esse in eodem loco. Hanc igitur dubitationem, quae communiter videtur esse tam contra ponentes vacuum, quam contra non ponentes, volunt solvere. Sed tamen non demonstrant quod vacuum sit; vel oportet eos dicere, si augmentum sit propter vacuum, quod totum corpus sit vacuum, cum totum corpus augeatur. 519. Thirdly [351] he rejects together both the argument about increase [in growth] and that about water poured on ashes and says that each of these arguments blocks the other. This is evident as follows. For there is in respect to increase this difficulty: it seems either that the whole body is not being increased, or that increase does not come about by the addition of body but by the addition of something incorporeal, or that two bodies can be in the same place. Now it is this difficulty, which seems to be against both these who posit a void and against those who do not, that they wish to solve. But they do not show that the void exists, or, if increase is due to the void, then they would have to say that the whole body is a void, since the whole body is increased.
Et similiter dicendum est de cinere: quia si vas plenum cinere recipit tantum de aqua quantum vacuum, oportet dicere quod totum sit vacuum. Non est igitur hoc propter vacuitatem: sed propter commixtionem in aqua. Aqua enim commixta cineri condensatur, et aliqua pars eius exhalat; et iterum partes cineris magis inspissantur humefactione: cuius signum est, quod non potest extrahi tantum de aqua, quantum prius fuit. Likewise, in regard to the ashes: for if a vessel full of ashes can take as much water as the empty vessel, then one has to say that the whole container must be a void. Therefore this is not due to empty space but to being mixed in with the water. For when water is mixed with ashes it condenses and part of it evaporates; moreover, parts of the ash are condensed on account of the moisture, and a sign of this is that not as much water can be recovered as was put in.
Ultimo autem concludit quod manifestum est, quod facile est solvere ea ex quibus demonstrant vacuum esse. Finally, he concludes that it is clearly easy to solve the arguments by which they prove the existence of a void.

Lecture 11
From motion there is shown to be no separated void
Lectio 11
Chapter 8
Ὅτι δ' οὐκ ἔστιν κενὸν οὕτω κεχωρισμένον, ὡς ἔνιοί φασι, λέγωμεν πάλιν. εἰ γὰρ ἔστιν ἑκάστου φορά τις τῶν ἁπλῶν σωμάτων φύσει, οἷον τῷ πυρὶ μὲν ἄνω τῇ δὲ γῇ κάτω καὶ πρὸς τὸ μέσον, δῆλον ὅτι οὐκ ἂν τὸ κενὸν αἴτιον εἴη τῆς φορᾶς. τίνος οὖν αἴτιον ἔσται τὸ κενόν; δοκεῖ γὰρ αἴτιον εἶναι κινήσεως τῆς κατὰ τόπον, ταύτης δ' οὐκ ἔστιν. Let us explain again that there is no void existing separately, as some maintain. If each of the simple bodies has a natural locomotion, e.g. fire upward and earth downward and towards the middle of the universe, it is clear that it cannot be the void that is the condition of locomotion. What, then, will the void be the condition of? It is thought to be the condition of movement in respect of place, and it is not the condition of this.
ἔτι εἰ ἔστιν τι οἷον τόπος ἐστερημένος σώματος, ὅταν ᾖ κενόν, ποῦ οἰσθήσεται τὸ εἰστεθὲν εἰς αὐτὸ σῶμα; οὐ γὰρ δὴ εἰς ἅπαν. ὁ δ' αὐτὸς λόγος καὶ πρὸς τοὺς τὸν τόπον οἰομένους εἶναί τι κεχωρισμένον, εἰς ὃν φέρεται· πῶς γὰρ οἰσθήσεται τὸ ἐντεθὲν ἢ μενεῖ; καὶ περὶ τοῦ ἄνω καὶ κάτω καὶ περὶ τοῦ κενοῦ ὁ αὐτὸς ἁρμόσει λόγος εἰκότως· τὸ γὰρ κενὸν τόπον ποιοῦσιν οἱ εἶναι φάσκοντες· καὶ πῶς δὴ ἐνέσται ἢ ἐν [τῷ] τόπῳ ἢ ἐν τῷ κενῷ; οὐ γὰρ συμβαίνει, ὅταν ὅλον τεθῇ ὡς ἐν κεχωρισμένῳ τόπῳ καὶ ὑπομένοντι σῶμά τι· τὸ γὰρ μέρος, ἂν μὴ χωρὶς τιθῆται, οὐκ ἔσται ἐν τόπῳ ἀλλ' ἐν τῷ ὅλῳ. ἔτι εἰ μὴ τόπος, οὐδὲ κενὸν ἔσται. Again, if void is a sort of place deprived of body, when there is a void where will a body placed in it move to? It certainly cannot move into the whole of the void. The same argument applies as against those who think that place is something separate, into which things are carried; viz. how will what is placed in it move, or rest? Much the same argument will apply to the void as to the 'up' and 'down' in place, as is natural enough since those who maintain the existence of the void make it a place. And in what way will things be present either in place—or in the void? For the expected result does not take place when a body is placed as a whole in a place conceived of as separate and permanent; for a part of it, unless it be placed apart, will not be in a place but in the whole. Further, if separate place does not exist, neither will void.
συμβαίνει δὲ τοῖς λέγουσιν εἶναι κενὸν ὡς ἀναγκαῖον, εἴπερ ἔσται κίνησις, τοὐναντίον μᾶλλον, ἄν τις ἐπισκοπῇ, μὴ ἐνδέχεσθαι μηδὲ ἓν κινεῖσθαι, ἐὰν ᾖ κενόν· ὥσπερ γὰρ οἱ διὰ τὸ ὅμοιον φάμενοι τὴν γῆν ἠρεμεῖν, οὕτω καὶ ἐν τῷ κενῷ ἀνάγκη ἠρεμεῖν· οὐ γὰρ ἔστιν οὗ μᾶλλον ἢ ἧττον κινηθήσεται· ᾗ γὰρ κενόν, οὐκ (215a.) ἔχει διαφοράν. If people say that the void must exist, as being necessary if there is to be movement, what rather turns out to be the case, if one the matter, is the opposite, that not a single thing can be moved if there is a void; for as with those who for a like reason say the earth is at rest, so, too, in the void things must be at rest; for there is no place to which things can move more or less than to another; since the void in so far as it is void admits no difference.
ἔπειθ' ὅτι πᾶσα κίνησις ἢ βίᾳ ἢ κατὰ φύσιν. ἀνάγκη δὲ ἄν περ ᾖ <�ἡ> βίαιος, εἶναι καὶ τὴν κατὰ φύσιν (ἡ μὲν γὰρ βίαιος παρὰ φύσιν, ἡ δὲ παρὰ φύσιν ὑστέρα τῆς κατὰ φύσιν)· ὥστ' εἰ μὴ κατὰ φύσιν ἔστιν ἑκάστῳ τῶν φυσικῶν σωμάτων κίνησις, οὐδὲ τῶν ἄλλων ἔσται κινήσεων οὐδεμία. ἀλλὰ μὴν φύσει γε πῶς ἔσται μηδεμιᾶς οὔσης διαφορᾶς κατὰ τὸ κενὸν καὶ τὸ ἄπειρον; ᾗ μὲν γὰρ ἄπειρον, οὐδὲν ἔσται ἄνω οὐδὲ κάτω οὐδὲ μέσον, ᾗ δὲ κενόν, οὐδὲν διάφορον τὸ ἄνω τοῦ κάτω (ὥσπερ γὰρ τοῦ μηδενὸς οὐδεμία ἔστι διαφορά, οὕτω καὶ τοῦ κενοῦ· τὸ γὰρ κενὸν μὴ ὄν τι καὶ στέρησις δοκεῖ εἶναι). ἡ δὲ φύσει φορὰ διάφορος, ὥστε ἔσται φύσει διάφορα. ἢ οὖν οὐκ ἔστι φύσει οὐδαμοῦ οὐδενὶ φορά, ἢ εἰ τοῦτ' ἔστιν, οὐκ ἔστι κενόν. The second reason is this: all movement is either compulsory or according to nature, and if there is compulsory movement there must also be natural (for compulsory movement is contrary to nature, and movement contrary to nature is posterior to that according to nature, so that if each of the natural bodies has not a natural movement, none of the other movements can exist); but how can there be natural movement if there is no difference throughout the void or the infinite? For in so far as it is infinite, there will be no up or down or middle, and in so far as it is a void, up differs no whit from down; for as there is no difference in what is nothing, there is none in the void (for the void seems to be a non-existent and a privation of being), but natural locomotion seems to be differentiated, so that the things that exist by nature must be differentiated. Either, then, nothing has a natural locomotion, or else there is no void.
ἔτι νῦν μὲν κινεῖται τὰ ῥιπτούμενα τοῦ ὤσαντος οὐχ ἁπτομένου, ἢ δι' ἀντιπερίστασιν, ὥσπερ ἔνιοί φασιν, ἢ διὰ τὸ ὠθεῖν τὸν ὠσθέντα ἀέρα θάττω κίνησιν τῆς τοῦ ὠσθέντος φορᾶς ἣν φέρεται εἰς τὸν οἰκεῖον τόπον· ἐν δὲ τῷ κενῷ οὐδὲν τούτων ὑπάρχει, οὐδ' ἔσται φέρεσθαι ἀλλ' ἢ ὡς τὸ ὀχούμενον. Further, in point of fact things that are thrown move though that which gave them their impulse is not touching them, either by reason of mutual replacement, as some maintain, or because the air that has been pushed pushes them with a movement quicker than the natural locomotion of the projectile wherewith it moves to its proper place. But in a void none of these things can take place, nor can anything be moved save as that which is carried is moved.
ἔτι οὐδεὶς ἂν ἔχοι εἰπεῖν διὰ τί κινηθὲν στήσεταί που· τί γὰρ μᾶλλον ἐνταῦθα ἢ ἐνταῦθα; ὥστε ἢ ἠρεμήσει ἢ εἰς ἄπειρον ἀνάγκη φέρεσθαι, ἐὰν μή τι ἐμποδίσῃ κρεῖττον. ἔτι νῦν μὲν εἰς τὸ κενὸν διὰ τὸ ὑπείκειν φέ ρεσθαι δοκεῖ· ἐν δὲ τῷ κενῷ πάντῃ ὁμοίως τὸ τοιοῦτον, ὥστε πάντῃ οἰσθήσεται. Further, no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way. Further, things are now thought to move into the void because it yields; but in a void this quality is present equally everywhere, so that things should move in all directions.
Positis opinionibus aliorum de vacuo, et quid significetur nomine vacui, hic incipit inquirere veritatem. Et primo ostendit vacuum non esse separatum; secundo ostendit vacuum non esse corporibus inditum, ibi: sunt autem quidam et cetera. 520. Having gone over others’ opinions about the void and having indicated what is meant by the word “void,” he now begins to search for the truth. First, he shows that the void does not have a separate existence; Secondly, that there is no void in bodies at no. 544 (L.14).
Circa primum duo facit: primo ostendit vacuum separatum non esse, ex parte motus; secundo ex consideratione qua ipsum vacuum consideratur secundum se, ibi: et per se autem et cetera. Concerning the first he does two things: First he used motion to show that a separate void does not exist; Secondly, by considering the void in itself, at no. 541.
Circa primum duo facit: primo ostendit vacuum non esse ex parte motus; secundo ex parte velocitatis et tarditatis in motu, ibi: amplius autem et ex his et cetera. As to the first he does two things: First, from the fact of motion he shows there is no void; Secondly from the fact of faster and slower motions, at no.527 (L.12).
Circa primum ponit sex rationes. Circa quarum primam dicit quod oportet iterum dicere quod non est vacuum separatum, sicut quidam dicunt. Ideo autem apponit iterum, quia hoc etiam aliqualiter ostensum est ex parte loci: si enim locus non sit spatium, sequitur quod vacuum nihil sit, ut supra dictum est. Sed nunc iterum idem ostendit ex parte motus: ponebant enim vacuum, ut dictum est, propter motum. Sed propter motum non est necessarium ponere vacuum. Maxime enim videtur quod esset causa motus localis: sed propter motum localem non oportet ponere vacuum, quia omnia corpora simplicia habent motus locales naturales, sicut motus naturalis ignis est sursum, et motus terrae est deorsum et ad medium. Et sic manifestum est quod natura uniuscuiusque corporis est causa motus localis, et non vacuum. Quod quidem esset, si propter necessitatem vacui aliqua corpora naturalia moverentur. Si autem non ponitur causa motus localis, nullius alterius motus causa poni potest, neque alterius rei. Frustra igitur vacuum esset. 521. In regard to the first point he gives six reasons. In regard to the first of which he says [360] that we must repeat that there is no separated void as some assert. He says “repeat,” because this was already somewhat proved from the notion of place: for if place is not space, it follows that the void is nothing, as was said above. But now he proves the same point again from motion: for void was posited, as we said, on account of motion. But motion does not necessarily require a void. For it would seem especially to be the cause of local motion. But it is not necessary to posit a void in order to explain local motion, because all simple bodies have natural local motions, as the natural motion of fire is upward and that of earth downward toward the center. Thus it is clear that it is the nature of each body that causes its local motion and not the void. The latter would be the cause if any natural bodies were moved due to the necessity of a void. But if it is not set down as the cause of local motion, it cannot be considered the cause of any other motion or of any other thing. The void therefore would exist without a purpose.
Secundam rationem ponit ibi: amplius, si est etc.: quae talis est. Si ponatur vacuum esse, non potest assignari causa motus naturalis et quietis naturalis. Manifestum est enim quod corpus naturale movetur ad locum suum naturalem et quiescit in eo naturaliter, propter convenientiam quam habet cum ipso, et quia non convenit cum loco a quo recedit. Sed vacuum non habet aliquam naturam per quam possit convenire vel disconvenire a corpore naturali. Si ergo ponatur aliquod vacuum, quasi quidam locus privatus corpore, non poterit assignari ad quam partem illud corpus naturaliter moveatur. Non enim potest dici quod feratur ad quamlibet partem, quia hoc videmus ad sensum esse falsum, quia ab una parte naturaliter recedit, et naturaliter accedit ad aliam. 522. He then gives the second reason [361]. If a void be postulated, no reason can be assigned for natural motion and rest. For it is clear that a natural body is moved toward its own natural place and rests there naturally on account of the kinship it has with its place and because it has no kinship to the place from which it departs. But the void has no nature by which it could be akin or hostile to a natural body. Therefore, it there were a void, considered as a certain place without a body in it, one could not assign any part to which the body would be naturally moved. For we cannot say that it would be borne to just any part, because observation shows that this is wrong, for a body naturally goes from one place and naturally approaches another.
Et haec eadem ratio valet contra eos qui ponunt locum esse quoddam spatium separatum, in quod corpus mobile fertur. Non enim erit assignare quomodo corpus positum in tali loco, vel moveatur vel quiescat: quia dimensiones spatii nullam habent naturam per quam possit attendi similitudo vel dissimilitudo ad corpus naturale. Et merito congruit eadem ratio de vacuo et de sursum et deorsum, idest de loco, cuius partes sunt sursum et deorsum. Quia illi qui ponunt vacuum, dicunt ipsum esse locum. This same reason is valid against those who posit place as a separate space into which a mobile body is borne. For it would be impossible to explain how a body in such a place could either be moved or be at rest: for the dimensions of space have no nature to which a natural body could be similar or dissimilar. Deservedly, then, the same argument applies to the void as to “up” and “down,” i.e., to place, whose parts are “up” and “down”; for those who posit a void call it place.
Et non solum ponentes vacuum, et ponentes locum esse spatium, non possunt assignare quomodo aliquid moveatur et quiescat secundum locum: sed etiam non possunt convenienter assignare quomodo aliquid sit in loco vel in vacuo. Si enim locus ponatur esse spatium, oportet quod totum corpus inferatur in illud spatium; et non sicut accidit apud ponentes locum esse terminum corporis continentis, quod locatum est in loco sicut in aliquo separato, et sicut in quodam corpore continente et sustentante. Et hoc videtur esse de ratione loci, quod aliquid sit in loco sicut in separato et seorsum existente: quia si pars alicuius corporis non ponatur seorsum ab ipso corpore, non erit in eo sicut in loco, sed sicut in toto. Est igitur de ratione loci et locati, quod locus seorsum sit a locato. Et hoc non accidit si spatium sit locus, in quod totum mergitur totum corpus. Non igitur spatium est locus. Et si spatium non est locus, manifestum est quod vacuum non est. Moreover, not only are those who posit a void and those who posit place to be space unable to explain how something is moved and at rest In respect to place, but also how something exists in place or in the void. For if place is supposed to be space, then the whole body would have to be enclosed inside that space, and not as happens with those who agree that place is the boundary of the containing body and that a thing is in place as in something separate and as in a body that contains and sustains it. Indeed, it seems to be of the very nature of place that something be in place as in something separated and existing apart from it: for if any part of a body is not laid down as separated from the body, it will exist in that body not as in a place but as in the whole. Therefore, it pertains to the very nature of place and of the thing in place that one be separated from the other. But this does not happen if place is space into whose entirety the entice body is immersed. Therefore space is not place. And if space is not place it is clear that no void is place.
Tertiam rationem ponit ibi: accidit autem dicentibus et cetera. Et dicit quod, cum antiqui philosophi ponerent quod necesse est vacuum esse si est motus, e converso accidit: quia si est vacuum, non est motus. Et hoc probat per quoddam simile. Quidam enim dixerunt quod terra quiescit in medio propter similitudinem partium circumferentiae undique: et sic terra, cum non habeat quare moveatur magis versus unam partem circumferentiae quam versus aliam, quiescit. Et eadem ratione necesse est in vacuo quiescere. Non enim est assignare quare magis moveatur, ad unam partem quam ad aliam: quia vacuum, inquantum huiusmodi, non habet differentias in suis partibus; non entis enim non sunt differentiae. 523. He gives the third reason [362] saying that, whereas the early philosophers claimed that the void had to be, if motion existed, the very opposite is the case: for if there were a void there would be no motion. And this he proves by a simile. For some have said that earth comes to rest at the center on account of the likeness of the parts on the whole circumference: consequently, earth, having no reason to be moved toward one part of the circumference more than another, rests. The same reason would cause rest in a void. For there would be no reason for earth to be moved to one part rather than to another, since the void, as such, does not have differences among its parts—for non-being does not possess differences.
Quartam rationem ponit ibi: deinde quoniam omnis motus etc.: quae talis est. Motus naturalis est prior violento, cum motus violentus non sit nisi quaedam declinatio a motu naturali. Remoto ergo motu naturali, removetur omnis motus; cum remoto priori, removeatur posterius. Sed posito vacuo, removetur motus naturalis; quia tollitur differentia partium loci, ad quas est motus naturalis, sicut et posito infinito, ut supra dictum est. 524. He gives the fourth reason [363]as follows. Natural motion is prior to compulsory since compulsory motion is only a departure from natural motion. Therefore, remove natural motion and all other motion is removed; for when the prior is removed, all that follows is removed. But if the void is posited, natural motion is removed; because the differences among the parts of place would be taken away and it is toward such parts that natural motions tend The same holds if the infinite be posited, as we said above.
Sed hoc interest inter vacuum et infinitum, quia posito infinito, nullo modo potest poni neque sursum neque deorsum neque medium, ut in tertio dictum est: posito autem vacuo, possunt haec quidem poni, sed non quod ad invicem differant; quia nullius et non entis, et per consequens vacui, cum sit non ens et privatio, non est aliqua differentia. Sed loci mutatio naturalis requirit locorum differentiam, quia diversa corpora ad diversa loca moventur. Unde oportet loca naturalia differre ad invicem. Si igitur ponatur vacuum, nullius erit naturalis loci mutatio. Et si non est loci mutatio naturalis, nulla loci mutatio erit. Unde si est aliqua loci mutatio, oportet quod vacuum non sit. There is, however, this difference between the void and the infinite, that after granting the infinite there is no way of positing “up” or “down” or “center,” as we pointed out in Book III; but after granting a void, these places could be posited, but it would not be because they were mutually different: for no difference can be assigned in the realm of nothing and non-being and, consequently, of the void, which is a non-being and a privation. Yet natural changes of place do require difference of place, because diverse bodies are moved to diverse places. Consequently, natural places must be different one from the other. Therefore, if a void be posited, nothing could undergo a natural change of place; and if there is no natural change of place, there will be no change of place of any sort. Hence, if there is any change of place, there can be no void.
Quintam rationem ponit ibi: amplius, nunc quidem proiecta et cetera. Circa quam considerandum est quod solet esse quaedam dubitatio circa ea quae proiiciuntur: oportet enim movens et motum simul esse, ut infra in septimo probatur; et tamen illud quod proiicitur, invenitur moveri etiam postquam separatum est a proiiciente, sicut apparet in lapide proiecto, et sagitta emissa per arcum. Nunc igitur supposito quod vacuum non sit, solvitur ista dubitatio ex parte aeris, quo medium repletur. Et hoc dupliciter. Dicunt enim quidam quod ea quae proiiciuntur, moventur etiam postquam non tanguntur a proiiciente, propter antiperistasim, idest repercussionem vel contra-resistentiam: aer enim motus repercutitur ad alium aerem, et ille ad alium, et sic deinceps; et per talem repercussionem aeris ad aerem movetur lapis. 525. The fifth reason is then given [364]. in regard to this it should be considered that some question exists about projectiles: for the mover and the thing moved must be always together, as will be proved below in Book VII (1-3). Yet a projectile is found to be in motion even after it is separated from the projector, as is evident in the case of a stone that is thrown, or of an arrow shot from a bow. Now on the supposition that there is no void this difficulty is solved by attending to the air with which the medium [the field of trajectory] is filled. And it is solved in two ways. For some assert that projectiles remain in motion even after they are no longer contact with what gave them impulse on account of antiperistasis, i.e., repercussion or counter-resistence: for the air that has been pushed, pushes against other air, and that against other air, and so on, and it is on account of this impact of air against air that the stone is moved.
Alii vero dicunt quod hoc ideo est, quia aer, qui continuus existens a proiiciente impellitur, velocius impellit corpus proiectum, quam sit motus quo corpus proiectum fertur naturaliter in proprium locum. Unde propter velocitatem motus aeris non permittitur corpus proiectum, ut puta lapis vel aliud huiusmodi, cadere deorsum; sed fertur secundum impulsionem aeris. The other explanation is that the continuum of air that received the impact from the projector pushes the impelled body with more speed than the speed of the motion by which the projectile is naturally borne to its proper place. Hence the speed of the air movement prevents the projectile, for example, the stone, or some other such, from falling downward; but it is carried along by the impulse of the air.
Nulla autem istarum causarum posset poni, si esset vacuum; et ita corpus proiectum nullo modo ferretur nisi quandiu veheretur, puta a manu proiicientis, sed statim emissus a manu caderet; cuius contrarium videmus. Non ergo est vacuum. Now neither of these explanations could be alleged if there were a void; consequently, a projectile could be moved only as long as it was carried, for example, in the hand of the one casting it: but as soon as it was released from the hand it would fall. But it is the opposite that happens. Therefore, there is not a void.
Sextam rationem ponit ibi: amplius nullus utique etc.: quae talis est. Si motus sit in vacuo, nullus poterit assignare causam propter quid illud quod movetur, alicubi stat. Non enim est ratio quare magis quiescat in una parte vacui quam in alia; neque in his quae moventur naturaliter, cum non sit differentia in partibus vacui, ut supra dictum est; neque in his quae moventur motu violento. Nunc enim dicimus quod cessat motus violentus, ubi deficit repercussio vel impulsio aeris, secundum duas causas assignatas. Oportebit ergo quod vel quiescat omne corpus, et nihil moveatur; aut si aliquid moveatur, quod movetur in infinitum, nisi occurrat ei aliquod corpus maius, quod violentum motum eius impediat. 526. He then gives the sixth reason [365]. If motion were in a void, no one could give a reason why the moving object should stop anywhere. For there is no reason why it should stop at one part of the void rather than another. This is true both in the case of objects that are moved naturally, because there is no difference among the parts of the void, as we have said, and in the case of objects moved by a compulsory motion. For now we say that a violent compulsory motion ceases when repercussions or impulsions of the air are lacking, on account of the two reasons already given. Therefore it will have to be admitted either that every body is at rest and nothing in motion or that, if anything be in motion, it will remain In motion to infinity unless it runs into a more powerful body that could impede its compulsory motion.
Ad confirmationem autem huius rationis, subiungit causam quare ponunt aliqui motum fieri in vacuo; quia scilicet vacuum cedit, et non resistit mobili; unde cum vacuum similiter cedit ex omni parte, feretur in infinitum ex qualibet parte. In support of this reasoning, he gives the reason why some posit motion in the void. It is because the void yields to and does not resist the mobile; hence since the void yields in the same way, in all directions, a mobile thing should be moved in all directions ad infinitum.

Lecture 12
From the fastness and slowness of motion, a separated void is disproved
Lectio 12
Chapter 8 cont.
ἔτι δὲ καὶ ἐκ τῶνδε φανερὸν τὸ λεγόμενον. ὁρῶμεν γὰρ τὸ αὐτὸ βάρος καὶ σῶμα θᾶττον φερόμενον διὰ δύο αἰτίας, ἢ τῷ διαφέρειν τὸ δι' οὗ, οἷον δι' ὕδατος ἢ γῆς ἢ δι' ὕδατος ἢ ἀέρος, ἢ τῷ διαφέρειν τὸ φερόμενον, ἐὰν τἆλλα ταὐτὰ ὑπάρχῃ, διὰ τὴν ὑπεροχὴν τοῦ βάρους ἢ τῆς κουφότητος. Further, the truth of what we assert is plain from the following considerations. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, as between water, air, and earth, or because, other things being equal, the moving body differs from the other owing to excess of weight or of lightness.
τὸ μὲν οὖν δι' οὗ φέρεται αἴτιον, ὅτι ἐμποδίζει μάλιστα μὲν ἀντιφερόμενον, ἔπειτα καὶ μένον· μᾶλλον δὲ τὸ μὴ εὐδιαίρετον· τοιοῦτο δὲ τὸ παχύτερον. τὸ δὴ ἐφ' οὗ (215b.) Α οἰσθήσεται διὰ τοῦ Β τὸν ἐφ' ᾧ Γ χρόνον, διὰ δὲ τοῦ Δ λεπτοτέρου ὄντος τὸν ἐφ' ᾧ Ε, εἰ ἴσον τὸ μῆκος τὸ τοῦ Β τῷ Δ, κατὰ τὴν ἀναλογίαν τοῦ ἐμποδίζοντος σώματος. ἔστω γὰρ τὸ μὲν Β ὕδωρ, τὸ δὲ Δ ἀήρ· ὅσῳ δὴ λεπτότερον ἀὴρ ὕδατος καὶ ἀσωματώτερον, τοσούτῳ θᾶττον τὸ Α διὰ τοῦ Δ οἰσθήσεται ἢ διὰ τοῦ Β. ἐχέτω δὴ τὸν αὐτὸν λόγον ὅνπερ διέστηκεν ἀὴρ πρὸς ὕδωρ, τὸ τάχος πρὸς τὸ τάχος. ὥστε εἰ διπλασίως λεπτόν, ἐν διπλασίῳ χρόνῳ τὴν τὸ Β δίεισιν ἢ τὴν τὸ Δ, καὶ ἔσται ὁ ἐφ' ᾧ Γ χρόνος διπλάσιος τοῦ ἐφ' ᾧ Ε. καὶ ἀεὶ δὴ ὅσῳ ἂν ᾖ ἀσωματώτερον καὶ ἧττον ἐμποδιστικὸν καὶ εὐδιαιρετώτερον δι' οὗ φέρεται, θᾶττον οἰσθήσεται. Now the medium causes a difference because it impedes the moving thing, most of all if it is moving in the opposite direction, but in a secondary degree even if it is at rest; and especially a medium that is not easily divided, i.e. a medium that is somewhat dense. A, then, will move through B in time G, and through D, which is thinner, in time E (if the length of B is egual to D), in proportion to the density of the hindering body. For let B be water and D air; then by so much as air is thinner and more incorporeal than water, A will move through D faster than through B. Let the speed have the same ratio to the speed, then, that air has to water. Then if air is twice as thin, the body will traverse B in twice the time that it does D, and the time G will be twice the time E. And always, by so much as the medium is more incorporeal and less resistant and more easily divided, the faster will be the movement.
τὸ δὲ κενὸν οὐδένα ἔχει λόγον ᾧ ὑπερέχεται ὑπὸ τοῦ σώματος, ὥσπερ οὐδὲ τὸ μηδὲν πρὸς ἀριθμόν. εἰ γὰρ τὰ τέτταρα τῶν τριῶν ὑπερέχει ἑνί, πλείονι δὲ τοῖν δυοῖν, καὶ ἔτι πλείονι τοῦ ἑνὸς ἢ τοῖν δυοῖν, τοῦ δὲ μηδενὸς οὐκέτι ἔχει λόγον ᾧ ὑπερέχει· ἀνάγκη γὰρ τὸ ὑπερέχον διαιρεῖσθαι εἴς τε τὴν ὑπεροχὴν καὶ τὸ ὑπερεχόμενον, ὥστε ἔσται τὰ τέτταρα ὅσῳ τε ὑπερέχει καὶ οὐδέν. διὸ οὐδὲ γραμμὴ στιγμῆς ὑπερέχει, εἰ μὴ σύγκειται ἐκ στιγμῶν. ὁμοίως δὲ καὶ τὸ κενὸν πρὸς τὸ πλῆρες οὐδένα οἷόν τε ἔχειν λόγον, ὥστε οὐδὲ τὴν κίνησιν, Now there is no ratio in which the void is exceeded by body, as there is no ratio of 0 to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more than it exceeds 2, still there is no ratio by which it exceeds 0; for that which exceeds must be divisible into the excess + that which is exceeded, so that will be what it exceeds 0 by + 0. For this reason, too, a line does not exceed a point unless it is composed of points! Similarly the void can bear no ratio to the full, and therefore neither can movement through the one to movement through the other,
ἀλλ' εἰ διὰ τοῦ λεπτοτάτου ἐν τοσῳδὶ τὴν τοσήνδε φέρεται, διὰ τοῦ κενοῦ παντὸς ὑπερβάλλει λόγου. but if a thing moves through the thickest medium such and such a distance in such and such a time, it moves through the void with a speed beyond any ratio.
ἔστω γὰρ τὸ Ζ κενόν, ἴσον δὲ [τῷ μεγέθει] τοῖς Β καὶ Δ. τὸ δὴ Α εἰ δίεισι καὶ κινηθήσεται ἐν τινὶ μὲν χρόνῳ, τῷ ἐφ' οὗ Η, ἐν ἐλάττονι δὲ τοῦ ἐφ' οὗ Ε, τοῦτον ἕξει τὸν λόγον τὸ κενὸν πρὸς τὸ πλῆρες. ἀλλ' ἐν τοσούτῳ χρόνῳ ὅσος ἐφ' οὗ τὸ Η, τοῦ Δ τὸ Α δίεισι τὴν τὸ Θ. δίεισι δέ γε κἂν ᾖ τι λεπτότητι διαφέρον τοῦ ἀέρος ἐφ' ᾧ τὸ Ζ ταύτην τὴν ἀναλογίαν ἣν ἔχει ὁ χρόνος ἐφ' ᾧ Ε πρὸς τὸν ἐφ' ᾧ Η. ἂν γὰρ ᾖ τοσούτῳ λεπτότερον τὸ ἐφ' ᾧ Ζ σῶμα τοῦ Δ, ὅσῳ ὑπερέχει τὸ Ε τοῦ Η, ἀντεστραμμένως δίεισι τῷ (216a.) τάχει ἐν τῷ τοσούτῳ ὅσον τὸ Η, τὴν τὸ Ζ τὸ ἐφ' οὗ Α, ἐὰν φέρηται. ἐὰν τοίνυν μηδὲν ᾖ σῶμα ἐν τῷ Ζ, ἔτι θᾶττον. ἀλλ' ἦν ἐν τῷ Η. ὥστ' ἐν ἴσῳ χρόνῳ δίεισι πλῆρές τε ὂν καὶ κενόν. ἀλλ' ἀδύνατον. φανερὸν τοίνυν ὅτι, εἰ ἔστι χρόνος ἐν ᾧ τοῦ κενοῦ ὁτιοῦν οἰσθήσεται, συμβήσεται τοῦτο τὸ ἀδύνατον· ἐν ἴσῳ γὰρ ληφθήσεται πλῆρές τε ὂν διεξιέναι τι καὶ κενόν· ἔσται γάρ τι ἀνάλογον σῶμα ἕτερον πρὸς ἕτερον ὡς χρόνος πρὸς χρόνον. For let Z be void, equal in magnitude to B and to D. Then if A is to traverse and move through it in a certain time, H, a time less than E, however, the void will bear this ratio to the full. But in a time equal to H, A will traverse the part O of A. And it will surely also traverse in that time any substance Z which exceeds air in thickness in the ratio which the time E bears to the time H. For if the body Z be as much thinner than D as E exceeds H, A, if it moves through Z, will traverse it in a time inverse to the speed of the movement, i.e. in a time equal to H. If, then, there is no body in Z, A will traverse Z still more quickly. But we supposed that its traverse of Z when Z was void occupied the time H. So that it will traverse Z in an equal time whether Z be full or void. But this is impossible. It is plain, then, that if there is a time in which it will move through any part of the void, this impossible result will follow: it will be found to traverse a certain distance, whether this be full or void, in an equal time; for there will be some body which is in the same ratio to the other body as the time is to the time.
ὡς δ' ἐν κεφαλαίῳ εἰπεῖν, δῆλον τὸ τοῦ συμβαίνοντος αἴτιον, ὅτι κινήσεως μὲν πρὸς κίνησιν πάσης ἔστι λόγος (ἐν χρόνῳ γάρ ἐστι, χρόνου δὲ παντὸς ἔστι πρὸς χρόνον, πεπερασμένων ἀμφοῖν), κενοῦ δὲ πρὸς πλῆρες οὐκ ἔστιν. To sum the matter up, the cause of this result is obvious, viz. that between any two movements there is a ratio (for they occupy time, and there is a ratio between any two times, so long as both are finite), but there is no ratio of void to full.
ᾗ μὲν οὖν διαφέρουσι δι' ὧν φέρονται, ταῦτα συμβαίνει, These are the consequences that result from a difference in the media;
κατὰ δὲ τὴν τῶν φερομένων ὑπεροχὴν τάδε· ὁρῶμεν γὰρ τὰ μείζω ῥοπὴν ἔχοντα ἢ βάρους ἢ κουφότητος, ἐὰν τἆλλα ὁμοίως ἔχῃ [τοῖς σχήμασι], θᾶττον φερόμενα τὸ ἴσον χωρίον, καὶ κατὰ λόγον ὃν ἔχουσι τὰ μεγέθη πρὸς ἄλληλα. ὥστε καὶ διὰ τοῦ κενοῦ. ἀλλ' ἀδύνατον· διὰ τίνα γὰρ αἰτίαν οἰσθήσεται θᾶττον; ἐν μὲν γὰρ τοῖς πλήρεσιν ἐξ ἀνάγκης· θᾶττον γὰρ διαιρεῖ τῇ ἰσχύϊ τὸ μεῖζον· ἢ γὰρ σχήματι διαιρεῖ, ἢ ῥοπῇ ἣν ἔχει τὸ φερόμενον ἢ τὸ ἀφεθέν. ἰσοταχῆ ἄρα πάντ' ἔσται. ἀλλ' ἀδύνατον. the following depend upon an excess of one moving body over another. We see that bodies which have a greater impulse either of weight or of lightness, if they are alike in other respects, move faster over an equal space, and in the ratio which their magnitudes bear to each other. Therefore they will also move through the void with this ratio of speed. But that is impossible; for why should one move faster? (In moving through plena it must be so; for the greater divides them faster by its force. For a moving thing cleaves the medium either by its shape, or by the impulse which the body that is carried along or is projected possesses.) Therefore all will possess equal velocity. But this is impossible.
ὅτι μὲν οὖν εἰ ἔστι κενόν, συμβαίνει τοὐναντίον ἢ δι' ὃ κατασκευάζουσιν οἱ φάσκοντες εἶναι κενόν, φανερὸν ἐκ τῶν εἰρημένων. οἱ μὲν οὖν οἴονται τὸ κενὸν εἶναι, εἴπερ ἔσται ἡ κατὰ τόπον κίνησις, ἀποκεκριμένον καθ' αὑτό· τοῦτο δὲ ταὐτόν ἐστι τῷ τὸν τόπον φάναι εἶναί τι κεχωρισμένον· τοῦτο δ' ὅτι ἀδύνατον, εἴρηται πρότερον. It is evident from what has been said, then, that, if there is a void, a result follows which is the very opposite of the reason for which those who believe in a void set it up. They think that if movement in respect of place is to exist, the void cannot exist, separated all by itself; but this is the same as to say that place is a separate cavity; and this has already been stated to be impossible.
Hic ostendit vacuum non esse, ex parte velocitatis et tarditatis in motu. 527. Here the Philosopher, arguing from the fast and slow in motion, shows that the void does not exist.
Et circa hoc duo facit: primo assignat causas propter quas velocitas et tarditas est in motu; secundo ex illis causis argumentatur ad propositum, ibi: hoc igitur per quod fertur et cetera. About this he does two things: First he assigns the causes of fastness and slowness in motion; Secondly, he uses these reasons to argue to his point, at no. 529.
Dicit ergo primo quod unum et idem corpus grave, et quodcumque aliud, utpote lapis vel aliquid huiusmodi, propter duas causas velocius fertur; aut propter differentiam medii per quod fertur, ut per aerem vel terram vel aquam; aut propter differentiam ipsius mobilis, quia est vel gravius vel levius, caeteris paribus. He says therefore first that one and the same heavy body, and any other thing, for example, a stone or something of this sort, is in faster motion for two reasons: either on account of the medium in which it is being moved, e.g., air or earth or water; or on account of differences in the object, namely, that it is heavier or lighter, all other things being equal.
Deinde cum dicit: hoc igitur per quod fertur etc., ex praemissis causis argumentatur ad propositum. Et primo ex differentia medii; secundo ex differentia mobilis, ibi: secundum autem eorum et cetera. 528. Then [367] he argues to his point from the aforesaid causes. First from the differences of the medium; Secondly, from the differences in the mobile object, at no. 539,
Circa primum duo facit: primo ponit rationem; secundo eam recapitulando recolligit, ibi: sed sicut in capitulo et cetera. As to the first he does two things: First he gives an argument; Secondly, he recapitulates, at no. 533.
Circa primum duo facit: primo ponit rationem; secundo ostendit conclusionem sequi ex praemissis, ibi: sit enim z vacuum et cetera. Concerning the first he does two things: First he gives his argument; Secondly, he shows that the conclusion follows from the premises, at no. 532.
Ponit ergo primo talem rationem. Proportio motus ad motum in velocitate est sicut proportio medii ad medium in subtilitate; sed spatii vacui ad spatium plenum nulla est proportio; ergo motus per vacuum non habet proportionem ad motum qui sit per plenum. 529. Therefore, he first gives this argument: The ratio of motion to motion in regard to speed is equal to the ration of medium to medium in respect of subtlety. But there is no ratio between empty space and full space. Therefore, motion in a void has no ratio to motion in the full.
Primo ergo manifestat primam propositionem huius rationis. Et dicit quod medium per quod aliquid fertur, est causa velocitatis et tarditatis, quia impedit corpus quod movetur. Et maxime quidem impedit quando medium fertur in contrarium, ut patet in navi, cuius motus impeditur a vento. Secundario autem impedit, si etiam quiescat: quia si simul moveretur cum mobili, non impediret, sed magis iuvaret, sicut fluvius qui defert navem inferius. Sed inter ea quae impediunt, magis impedit illud quod non facile dividitur; et tale est corpus magis grossum. Et hoc manifestat per exemplum. Sit enim corpus quod movetur a; spatium per quod movetur, sit b; et tempus in quo a movetur per b, sit c. Ponamus autem aliud spatium quod sit d, aequalis longitudinis cum b; sed tamen d sit plenum subtiliori corpore quam b, secundum aliquam analogiam, idest proportionem, corporis medii, quod impedit motum corporis; ut puta quod spatium b sit plenum aqua, spatium vero d sit plenum aere. Quanto ergo aer est subtilior aqua et minus spissus, tanto mobile quod est a, citius movebitur per spatium d, quam per spatium b. Quae est ergo proportio aeris ad aquam in subtilitate, eadem est proportio velocitatis ad velocitatem: et quanto est maior velocitas, tanto est minus tempus; quia velocior motus dicitur, qui est in minori tempore per aequale spatium, ut in sexto dicetur. Unde, si aer est in duplo subtilior quam aqua, sequetur quod tempus in quo a movetur per b, quod est plenum aqua, sit duplum tempore in quo pertransit d, quod est plenum aere: et ita tempus c, in quo pertransit spatium b, erit duplum tempore quod est e, in quo pertransit spatium d. Et sic poterimus universaliter accipere, quod in quacumque proportione medium, per quod aliquid fertur, est subtilius et minus impeditivum et facilius divisibile, in eadem proportione erit motus velocior. First of all he explains the first proposition of this argument. And he says that the medium through which a body is in motion is the cause of its fastness or slowness because it acts as an obstacle to the body in motion. The greatest obstacle occurs when the medium is in a contrary motion, as is evident in the case of a ship whose movement is impeded by the wind. The medium is an obstacle in a secondary way even if it is not in motion, because if it were in motion with the object it would not be an obstacle but a help, as the water which carries a ship downstream. But among obstacles a greater impediment is offered by things that are not easy to divide, such as the grosser bodies. He explains this by an example. Let the body in motion be A, and let the space through which it is being moved be B, and the time in which A is being moved through B be C. Let us posit another space, D, of the same length as B, but let D be full of a subtler body than the one in B, so that a certain analogy, i.e., ratio, exists between the bodies which impede the motion (for example, let B be full of water and D full of air). Now to the extent that air is subtler than water and less condensed, to that extent will the mobile A be more quickly moved through D than through B. Therefore the ratio of the velocities will equal the ratio of the subtlety of air to the subtlety of water. And the greater the velocity, the less the time: because that motion is faster which covers the same interval in less time, as will be shown in Book VI (L.3). Hence if air is twice as subtle as water, the time it takes A to be moved through B (full of’ water) will be twice the time for A to pass through D (full of air). Consequently, the time C in which it travels the distance B will be twice the time it takes E to pass through D. Therefore, we can take it as a general rule that in whatever ratio the medium (in which something is in motion) is subtler and less resistant and more easily divisible, in that ratio will the motion be faster.
Deinde cum dicit: vacuum autem nullam etc., manifestat secundam propositionem: et dicit quod vacuum non exceditur a pleno secundum aliquam proportionem. Et hoc probat per hoc, quod numerus non excedit nihil secundum aliquam proportionem, sed solum attenditur proportio aliqua numeri ad numerum, vel ad unitatem: sicut quatuor excedunt tria in uno, et adhuc in pluri excedunt duo, et adhuc in pluri unum. Unde dicitur maior proportio quatuor ad unum, quam ad duo vel tria. Sed quatuor non excedunt nihil secundum aliquam proportionem. 530. Then [368] he explains the second proposition, and says that the void is not exceeded by the full according to some certain ratio. And he proves this by the fact that a number does not exceed nothing [zero] by any ratio, for ratios can exist only between one number and another, or between a number and unity; as four exceeds three by one, and exceeds two by more yet, and one by still more. Hence there is said to be a greater ratio existing between four and one, than between four and two, or four and three. But four does not exceed nothing according to any ratio.
Et hoc ideo quia necesse est quod omne excedens dividatur in id quod exceditur, et in excedentiam, idest in id in quo excedit: sicut quatuor dividitur in tria, et in unum in quo excedit tria. Si ergo quatuor excedunt nihil, sequetur quod quatuor dividantur in aliquot et nihil: quod est inconveniens. Unde etiam non potest dici, quod linea excedat punctum, nisi componeretur ex punctis, et divideretur in ea. Et similiter non potest dici quod vacuum habeat aliquam proportionem ad plenum: quia vacuum non cadit in compositionem pleni. This is so because anything exceeding is necessarily divided into that which is exceeded and into the excess, i.e., that in which it exceeds; for example, four can be divided into three, and into one, which latter is the amount by which four exceeds 3. But if four exceeds nothing, it will follow that four can be divided into so much and nothing; which is unacceptable. For a same reason one could not say that a line exceeds a point unless it were composed of points and divided into points. In like manner, it cannot be said that the void has any ratio to the full; because the void is not a part of the full.
Deinde cum dicit: ergo neque motum etc., ponit conclusionem, concludens quod non est possibile esse proportionem inter motum qui fit per vacuum, et motum qui fit per plenum; sed si aliquod corpus fertur per quodcumque subtilissimum in tanto spatio talique tempore, motus qui est per vacuum transcendet omnem proportionem datam. 531. Then [369] he concludes that there can be no ratio between a motion in the void and a motion in the full: but that if any body is in motion in the subtlest of mediums over such and such a distance for such and such a time, the motion in the void will exceed any given ratio.
Deinde cum dicit: sit enim z vacuum etc., quia praedictam conclusionem ostensive ex principiis suppositis deduxerat, ne qua dubitatio oriatur de principiis praemissis, ut certior sit processus, probat eandem conclusionem deducendo ad impossibile. 532. Then [370], because he had deduced the above conclusion in direct line from the assumed principles, he now, lest any doubt arise about those principles, and to make the process more certain, proves the same conclusion by deducing to the impossible.
Si enim dicatur quod motus qui est per vacuum, habet aliquam proportionem velocitatis ad motum qui est per plenum, ponatur ergo quod spatium vacuum sit z, quod quidem sit aequale secundum magnitudinem, spatio b quod est plenum aqua, et spatio d quod est plenum aere. For if it be claimed that the speed of a motion taking place in the void has a ratio to the speed of a motion taking place in the full, then let the empty space be Z, which shall be equal in magnitude to the space B, full of water, and to the space D, full of air.
Si autem detur quod motus qui est per z, habeat aliquam proportionem secundum velocitatem ad motus qui sunt per b et d, oportet dicere quod motus qui est per z, quod est vacuum, sit in aliquo determinato tempore: quia velocitates distinguuntur secundum quantitates temporum, ut supra dictum est. Si ergo dicatur quod mobile quod est a, transeat per spatium vacuum quod est z, in aliquo tempore; sit illud tempus I, quod oportet esse minus quam tempus e, in quo pertransit spatium d, quod est plenum aere; et sic haec erit proportio motus per vacuum ad motum per plenum, quae est proportio temporis e ad tempus I. Sed necesse erit ponere quod in tanto tempore quantum est I, mobile quod est a, pertranseat quoddam spatium plenum subtiliori corpore ipsius d, idest ipso d. Et hoc quidem continget, si inveniatur aliquod corpus quod differat in subtilitate ab aere, quo ponebatur plenum spatium d, secundum illam proportionem quam habet tempus e ad tempus I; ut puta si dicatur illud corpus esse ignis, quo ponatur plenum spatium z, quod prius ponebatur vacuum: quia si corpus quo ponitur plenum spatium z, est tanto subtilius corpore quo ponitur plenum spatium d, quantum tempus e excedat tempus I, sequetur quod mobile quod est a, si feratur per z, quod est spatium plenum subtilissimo corpore, et per d, quod est spatium plenum aere, transibit per z e converso in maiori velocitate in tanto tempore, quantum est I. Si ergo nullum corpus sit in quo est z, sed ponatur hoc spatium vacuum, sicut et primo; adhuc debebit velocius moveri. Sed hoc est contra id quod fuit positum. Positum enim erat quod motus fieret per spatium z, quod est vacuum, in tempore I; et sic cum in tempore I transeat idem spatium, cum est plenum subtilissimo corpore, sequitur quod in eodem tempore transibit idem mobile unum et idem spatium, cum est vacuum et cum est plenum. Now if it is supposed that a motion through Z has a certain ratio in respect of speed to the motions through B and D, then it must be admitted that the motion through Z (the void) takes place in some definite portion of time, because velocities are distinguished according to the quantities of the times consumed, as was said above. If therefore we say the object A passes through the empty space Z in a definite time, let that time be I, which must be less than the time E required for A to pass through D, which is full of air. Then the ratio of the motion through the empty to the motion through the full will equal the ratio of time E to time I. But during time I, the mobile A will pass through a definite space that is full of a subtler body than exists in D, i.e., than D. And this will happen, if one can find a body which differs in subtlety from air (of which D is full) in the ratio that the time E has to the time I. For example, say the space Z, which had been originally empty space, is now full of fire. If the body of which Z is full is subtler than the body of which D is full, in the amount that the time E exceeds the time I, it will follow that the mobile A, if it is in motion through Z (which is the space now full of a most subtle body), and through D (which is the space full of air), it will pass through Z conversely at a greater speed in a time I. If therefore no body exists in Z but it is again considered to be empty space, as previously, it will have to move even faster. But this is against what was laid down, namely, that the motion through Z (empty space) required time I. Consequently, since in time I it passes over the same space when it is full of the most subtle of bodies, it follows that during the same time the same mobile passes through one and the same space, when that space is empty and when it is full.
Manifestum est ergo, quod si fuerit aliquod tempus, in quo mobile feratur per quodcumque spatium vacuum, sequetur hoc impossibile, quod in aequali tempore transibit plenum et vacuum: quia erit accipere aliquod corpus quod habebit proportionem ad aliud corpus, sicut habet proportionem tempus ad tempus. It is clear therefore that if it took a definite time for the mobile to pass through an empty space, the impossibility follows that in equal time it will pass through full and empty space, because there will be some body having the same ratio to some other body as one time has to another time.
Deinde cum dicit: sed sicut in capitulo est dicere etc., summatim colligit ea, in quibus virtus consistit praemissae rationis. Et dicit quod sicut contingit recapitulando dicere, manifesta est causa, quare praedictum inconveniens accidat: quia scilicet quilibet motus est proportionatus cuilibet motui secundum velocitatem: quia omnis motus est in tempore, et qualibet duo tempora, si sint finita, habent proportionem ad invicem. Sed vacui ad plenum non est proportio, ut probatum est. Unde si ponatur motus fieri per vacuum, necesse est quod sequatur inconveniens. 533. Then [371] he summarized that in which the force of the previous reasoning consists. And he says that we can now say in recapitulation that the reason why the conflict mentioned in the above occurs is clear: it is because every motion has a ratio to every other motion in respect to speed. For every motion requires time, and any two periods of time, if they are finite, have a ratio one to the other. But there is no ratio between the empty and the full, as we proved. Hence the supposition that motion occurs in the void leads to the conflict mentioned.
Ultimo autem epilogans concludit, quod praedicta inconvenientia accidunt, si accipiantur diversae velocitates motuum secundum differentiam mediorum. In a final summary [372] he concludes that the above mentioned conflicts occur if the different species of motion are taken according to differences of the media.
Sed contra hanc rationem Aristotelis insurgunt plures difficultates. Quarum quidem prima est, quod non videtur sequi, si fiat motus per vacuum, quod non habeat proportionem in velocitate ad motum qui fit per plenum. Quilibet enim motus habet determinatam velocitatem ex proportione potentiae motoris ad mobile, etiam si nullum sit impedimentum. Et hoc patet per exemplum et per rationem. Per exemplum quidem in corporibus caelestibus, quorum motus a nullo impeditur; et tamen eorum est determinata velocitas, secundum determinatum tempus. Per rationem autem, quia ex hoc ipso quod in magnitudine, per quam transit motus, est accipere prius et posterius, contingit etiam accipere prius et posterius in motu; ex quo sequitur motum esse in determinato tempore. Sed verum est quod huic velocitati potest aliquid subtrahi ex aliquo impediente. Non igitur oportet quod proportio motus ad motum in velocitate, sit sicut proportio impedimenti ad impedimentum, ita quod si non sit aliquod impedimentum, quod motus fiat in non tempore: sed oportet quod secundum proportionem impedimenti ad impedimentum, sit proportio retardationis ad retardationem. 534. But several difficulties arise against this reasoning of Aristotle. The first is that it does not seem to follow that if motion takes place in the void that it has no ratio to motion in the full. For every motion has its definite velocity from the ratio of the motive energy to the mobile, even if no obstacle exists. And this is evident both from an example and from reason. From an example, indeed, in the heavenly bodies, whose motion encounters no obstacle and yet they have a definite velocity depending on the amount of time. From reason also: for, since it is possible to point out a “before” and “after” in the magnitude through which the motion takes place, so also one can take a “before” and “after” in the motion from which it follows that motion is in a determined time. But it is true that this velocity can be diminished on account of an obstacle. Yet it is not necessary therefore to make the ratio of motion to motion in respect of velocity be as the ratio of obstacle to obstacle, so as to make the motion occur in no time, if there be no obstacle; rather, the ratio of one slowing up to another slowing up must correspond to the ratio of obstacle to obstacle.
Unde posito quod motus sit per vacuum, sequitur quod nulla retardatio accidat supra velocitatem naturalem; et non sequitur quod motus qui est per vacuum, non habeat proportionem ad motum qui fit per plenum. Hence on the assumption that motion takes place in the void, it follows that no slowing up happens to the natural speed, but it does not follow that a motion in the void will have no ratio to motion in the full.
Huic autem obiectioni Averroes in commento suo resistere conatur. Et primo quidem conatur ostendere hanc obiectionem ex falsa imaginatione procedere. Dicit enim quod ponentes praedictam obiectionem imaginantur additionem in tarditate motus fieri, sicut fit additio in magnitudine lineae, quod pars addita sit alia a parte cui additur. Ita enim videtur praedicta obiectio procedere, ac si tardatio fiat per hoc, quod aliquis motus addatur alteri motui, ita quod subtracto illo motu addito per impedimentum retardans, remaneat quantitas motus naturalis. Sed hoc dicit non esse simile: quia cum retardatur motus, quaelibet pars motus fit tardior; non autem quaelibet pars lineae fit maior. 535. Averroes attempts to counter this objection in his commentary. First he tries to show that this objection proceeds from false imagination. For he says that those who make the above objection imagine that an addition in slowness of motion occurs just like an addition in the magnitude of a line, where the added part is distinct from the part to which the addition is made. For the above objection seems to proceed as though slowing up takes place by adding one motion to another motion in such a way that if you were to subtract the motion that was added through the obstacle which slows, the quantity of natural motion would then be left. But this is not the case, because when a motion is slowed up, each part of the motion becomes slower, whereas each part of a line does not become larger.
Deinde ostendere nititur, quomodo ratio Aristotelis necessitatem habeat. Et dicit quod velocitas vel tarditas motus consurgit quidem ex proportione motoris ad mobile; sed oportet mobile esse aliquo modo resistens motori, sicut patiens quodammodo est contrarium agenti. Quae quidem resistentia potest esse ex tribus. Primo quidem ex ipso situ mobilis: ex hoc enim ipso quod movens intendit transferre mobile ad aliquod ubi, ipsum mobile in alio ubi existens repugnat intentioni motoris; secundo ex natura mobilis, sicut apparet in motibus violentis, ut cum grave proiicitur sursum; tertio ex parte medii. Omnia enim haec tria accipienda sunt simul ut unum resistens, ad hoc quod causetur una causa tarditatis in motu. Quando igitur mobile, seorsum consideratum secundum quod differt a movente, est aliquid ens actu, potest inveniri resistentia mobilis ad motorem, vel ex parte mobilis tantum, sicut accidit in corporibus caelestibus, vel ex parte mobilis et medii simul, sicut accidit in corporibus animatis quae sunt hic. Sed in gravibus et levibus, subtracto eo quod mobile habet a movente, scilicet forma, quae est principium motus, quam dat generans, quod est movens, non remanet nisi materia, ex cuius parte nulla resistentia potest considerari ad movens; unde relinquitur in talibus sola resistentia ex parte medii. Sic igitur in corporibus caelestibus est differentia velocitatis solum secundum proportionem motoris ad mobile; in corporibus vero animatis secundum proportionem motoris ad mobile et ad medium resistens simul. Et in talibus procederet obiectio praedicta, quod remota retardatione quae est ex parte medii impedientis, adhuc remanet determinata quantitas temporis in motu, secundum proportionem motoris ad mobile. Sed in gravibus et levibus non potest esse retardatio velocitatis, nisi secundum resistentiam medii; et in talibus procedit ratio Aristotelis. Then he attempts to show how Aristotle’s argument concludes with necessity. And he says that the speed or slowness of a motion does indeed arise from the proportion of the mover to the mobile; but the mobile must in some manner resist the mover, as the patient is in a certain way contrary to the agent. This resistance can arise from three sources: First, from the situs of the mobile; for from the very fact that the mover intends to transfer the mobile to some certain place, the mobile, existing in some other place, resists the intention of the mover. Secondly, from the nature of the mobile, as is evident in compulsory motions, as when a heavy object is thrown upwards. Thirdly, from the medium. All three are taken together as one resistance, to constitute one cause of slowing up in the motion. Therefore when the mobile, considered in isolation as different from the mover, is a being in act, the resistance of the mobile to the mover can be traced either to the mobile only, as happens in the heavenly bodies, or to the mobile and medium together, as happens in the case of animate bodies on this earth. But in heavy and light objects, if you take away what the mobile receives from the mover, viz., the form which is the principle of motion given by the generator, i.e., by the mover, nothing remains but the matter which can offer no resistance to the mover. Hence in light and heavy objects the only source of resistance is the medium. Consequently, in heavenly bodies differences in velocity arise only on account of the ratio between mover and mobile; in animate bodies from the proportion of the mover to the mobile and to the resisting medium—both together. And it is in these latter cases that the given objection would have effect, viz., that if you remove the slowing up caused by the impeding medium, there still remains a definite amount of time in the motion, according to the proportion of the mover to the mobile. But in heavy and light bodies, there can be no slowing up of speed, except what the resistance of the medium causes—and in such cases Aristotle’s argument applies.
Sed haec omnino videntur esse frivola. Primo quidem, quia licet quantitas tarditatis non sit secundum modum quantitatis continuae, ut addatur motus motui, sed secundum modum quantitatis intensivae, sicut cum aliquid est altero albius; tamen quantitas temporis ex qua Aristoteles argumentatur, est secundum modum quantitatis continuae, et fit tempus maius per additionem temporis ad tempus; unde subtracto tempore quod additur ex impediente, remanet tempus naturalis velocitatis. 536. But all this seems quite frivolous. First, because, although the quantity of slowing up is not parallel to the mode of continuous quantity, so that motion is added to motion, but parallel to the mode of intensive quantity, as when something is whiter than something else, yet the quantity of time from which Aristotle argues is parallel to the manner of continuous quantity—and time becomes greater by the addition of time to time. Hence if you subtract the time which was added on account of the obstacle, the time of the natural velocity remains.
Deinde quia in gravibus et levibus remota forma, quam dat generans, remanet per intellectum corpus quantum; quod ex hoc ipso quod quantum est, in opposito situ existens, habet resistentiam ad motorem; non enim potest intelligi alia resistentia in corporibus caelestibus ad suos motores. Unde nec etiam in gravibus et levibus sequetur ratio Aristotelis, secundum quod ipse dicit. Then, because if you remove the form which the generator gives to light and heavy bodies there still remains in the understanding “quantified body,” which from the very fact that it is a quantified body existing in an opposite situs offers resistance to the mover. For we cannot suppose in heavenly bodies any other resistance to their movers. Hence, as he [Averroes] presents the case, even in the case of heavy and light bodies the reasoning of Aristotle would not follow.
Et ideo melius et brevius dicendum est, quod ratio Aristotelis inducta, est ratio ad contradicendum positioni, et non ratio demonstrativa simpliciter. Ponentes autem vacuum, hac de causa ipsum ponebant, ut non impediretur motus: et sic secundum eos causa motus erat ex parte medii, quod non impedit motum. Et ideo contra eos Aristoteles argumentatur, ac si tota causa velocitatis et tarditatis esset ex parte medii; sicut etiam et supra evidenter hoc ostendit dicens, quod si natura est causa motus simplicium corporum, non oportet ponere vacuum ut causam motus eorum: per quod dat intelligere quod totam causam motus ponebant ex parte medii, et non ex natura mobilis. Therefore it is better and briefer to say that the argument brought forward by Aristotle is an argument aimed at contradicting his opponent’s position and not a demonstrative argument in the absolute sense. For those who posited a void did so in order that motion be not prevented. Thus, according to them, the cause of motion was on the part of a medium which did not impede motion. And therefore Aristotle argued against them as though the total cause of fastness and slowness derived from the medium, as he clearly shows above when he says that if nature is the cause of the motion of simple bodies, it is not necessary to posit the void as the cause of their motion. In this way he gives us to understand that they supposed the total cause of the motion to depend on the medium and not on the nature of the mobile.
Secunda autem dubitatio contra rationem praedictam est, quia si medium quod est plenum, impedit, ut ipse dicit, sequitur quod non sit in hoc medio inferiori aliquis motus purus non impeditus, quod videtur inconveniens. Et ad hoc Commentator praedictus respondet, quod hoc impedimentum quod est ex medio, requirit motus naturalis gravium et levium, ut possit esse resistentia mobilis ad motorem, saltem ex parte medii. 537. The second difficulty against [Aristotle’s] argument is that if the medium which is full impedes, as he says it does, then it follows that there will not be any pure unimpeded motion in this lower medium—and this seems unfitting. To this the Commentator replies that the impediment that arises from the medium is required by the natural motion of heavy and light bodies, so that there can be resistance of the mobile to the mover, at least on the side of the medium.
Sed melius dicendum est quod omnis motus naturalis incipit a loco non naturali, et tendit in locum naturalem. Unde quandiu ad locum naturalem perveniat, non est inconveniens si aliquid non naturale ei coniungatur. Paulatim enim recedit ab eo quod est contra naturam, et tendit in id quod est secundum naturam: et propter hoc motus naturalis in fine intenditur. But it is better to say that every natural motion begins from a place that is not natural and tends to a natural place. Hence until it reaches its natural place it is not unfitting if something unnatural be attached to it. For it gradually departs from what is against its nature and tends to what is in keeping with its nature. And for this reason a natural motion accelerates as it nears its end.
Tertia obiectio est, quia cum in corporibus naturalibus sit determinatus terminus raritatis, non videtur quod semper sit accipere corpus rarius et rarius secundum quamlibet proportionem temporis ad tempus. 538. The third objection is that since in natural bodies there is a fixed limit of rarity, it does not seem that one can keep supposing a rarer and rarer body according to any given proportion of time to time.
Sed dicendum est, quod hoc quod sit determinata raritas in rebus naturalibus, non est ex natura corporis mobilis inquantum est mobile, sed ex natura determinatarum formarum, quae requirunt determinatas raritates vel densitates. In hoc autem libro agitur de corpore mobili in communi: et ideo frequenter utitur Aristoteles in hoc libro in suis rationibus, quibusdam, quae sunt falsa, si considerentur naturae determinatae corporum; possibilia autem, si consideretur natura corporis in communi. In reply it should be said that a fixed rarity in natural things is not due to the nature of the mobile body insofar as it is mobile, but to the nature of specific forms that require specific rareness and density. But in this book we are dealing with mobile body in general, and therefore Aristotle frequently uses in his arguments things which are false if the specific natures of bodies are considered, but possible if the nature of body in general is considered.
Vel potest dici, quod hic etiam procedit secundum opinionem antiquorum philosophorum, qui ponebant rarum et densum prima principia formalia; secundum quos raritas et densitas in infinitum augeri poterant, cum non sequerentur alias priores formas, secundum quarum exigentiam determinarentur. Or it can be replied that he is here also proceeding according to the opinion of the earlier philosophers who posited the rare and the dense as the first formal principles. According to them, rarity and density could be increased ad infinitum since these did not depend on other previous forms according to whose exigencies they would be determined.
Deinde cum dicit: secundum autem eorum etc., ostendit non esse vacuum separatum, ex velocitate et tarditate motus, secundum quod omnino causa sumitur ex parte mobilis. 539. Then [373] he shows there is no separated void, arguing from the speed and slowness of motion, insofar as the cause is taken entirely from the viewpoint of the mobile.
Et dicit quod haec quae dicentur consequuntur, si consideretur differentia velocitatis et tarditatis, secundum quod mobilia quae feruntur se invicem excellunt; quia videmus quod per aequale spatium finitum, citius feruntur ea quae habent maiorem inclinationem aut secundum gravitatem aut secundum levitatem; sive sint maiora in quantitate, aequaliter gravia vel levia existentia, sive sint aequalia in quantitate, et sint magis gravia vel levia. Et hoc dico si similiter se habeant secundum figuras: nam corpus latum tardius movetur, si deficiat in gravitate vel magnitudine, quam corpus acutae figurae. Et secundum proportionem quam habent magnitudines motae ad invicem vel in gravitate vel in magnitudine, est proportio velocitatis. Unde et oportebit ita esse etiam si sit motus per vacuum, scilicet quod corpus gravius seu levius aut magis acutum velocius feratur per medium vacuum. Sed hoc non potest esse: quia non est assignare aliquam causam propter quam unum corpus alio velocius feratur. Si enim motus fiat per spatium plenum aliquo corpore, potest assignari causa maioris vel minoris velocitatis, secundum aliquam praedictarum causarum: hoc enim est, quia illud quod movetur maius existens, ex sua fortitudine velocius dividit medium; vel propter aptitudinem figurae, quia acutum est penetrabilius, aut propter inclinationem maiorem, quam habet vel ex gravitate vel ex levitate, vel etiam propter violentiam prohibentis. Vacuum autem dividi non potest citius vel tardius: unde sequetur quod omnia aequali velocitate movebuntur per vacuum. Sed hoc manifeste apparet impossibile. And he says that what he is about to say will follow logically, if we attend to the difference of speed and slowness insofar as bodies in motion exceed one another. For we see that over a given equal space, greater speed is shown by bodies having a greater inclination due either to heaviness or lightness, whether they are greater in quantity but equally heavy or light, or whether they are equal in quantity but unequal in heaviness or lightness. And I say this if they are similar in shape. For a wide body is moved more slowly if it be deficient in heaviness or size than a body with a pointed shape. And the ratio of the velocity corresponds to the ratio which the moving magnitudes have to one another in respect to their weight or in respect to their magnitude. And this will have to be true also if the motion occurs in the void, namely, that a heavier body or a lighter body or a more pointed body will be moved faster through an empty medium. But this cannot be, since it is impossible to explain why one body would be moved faster than another. For if the motion takes place within a space filled with some body, an explanation for the greater or lesser speed can be given—it will be due to any of the aforesaid causes. The explanation is that a greater body will on account of its strength divide the medium more quickly, either an account of its shape, because what is sharp has greater penetrating power; or on account of a greater inclination traceable either to the heaviness or lightness of the body; or even to the force imparted by that which projects it. But the void cannot be cleaved faster or slower. Hence it will be moved through a void with equal speed. But this clearly appears as impossible.
Patet igitur ex ipsa velocitate motus, quod vacuum non est. And so from a consideration of the velocity of motion, it is evident that the void does not exist.
Attendendum est autem quod in processu huius rationis est similis difficultas sicut et in prima. Videtur enim supponere, quod differentia velocitatis in motibus non sit nisi propter differentiam divisionis medii: cum tamen in corporibus caelestibus sint diversae velocitates, in quibus non est aliquod plenum medium resistens, quod dividi oporteat per motum corporis caelestis. Sed solvenda est haec dubitatio sicut et prius. It should be observed that in this reasoning process there exists the same difficulty as in the first one. For he seems to suppose that difference in velocity in motions is due only to the different ways in which the medium can be cleaved, whereas the fact is that there are differences of velocity among the heavenly bodies in which there is no full medium resisting which has to be cleaved by the motion of the heavenly body. But this difficulty should be solved as the above one was.
Ultimo, autem epilogando concludit manifestum esse ex dictis, quod si ponatur vacuum esse, accidit contrarium eius quod supponebant probantes esse vacuum. Illi enim procedebant, ac si motus esse non possit, si vacuum non sit. Sed ostensum est contrarium: scilicet, si vacuum sit, quod motus non est. Sic igitur praemissi philosophi opinantur vacuum esse quoddam discretum et separatum secundum se, scilicet quoddam spatium habens dimensiones separatas: et huiusmodi vacuum opinantur necesse esse, si sit motus secundum locum. Ponere autem sic vacuum separatum, idem est quod dicere locum esse quoddam spatium distinctum a corporibus; quod est impossibile, ut supra ostensum est in tractatu de loco. 540. Finally [347] he summarizes, and concludes that from the foregoing it is clear that in regard to the philosophers who posit a void, the contrary of what they supposed as a reason for proving it occurs. For they proceeded on the assumption that motion could not take place unless there was a void. But the contrary has been proved; namely, that if there be a void, there is no motion. Thus, therefore, those philosophers believe that the void is some distinct and separate thing—a space having separate dimensions—and they believed it was such a space that had to exist if local motion were to be possible. However, to posit such a separated void is the same as saying that place is a kind of space distinct from bodies—which is impossible, as was shown in the treatise on place.

Lecture 13
Non-existence of the void from the void itself
Lectio 13
Chapter 8 cont.
καὶ καθ' αὑτὸ δὲ σκοποῦσιν φανείη ἂν τὸ λεγόμενον κενὸν ὡς ἀληθῶς κενόν. ὥσπερ γὰρ ἐὰν ἐν ὕδατι τιθῇ τις κύβον, ἐκστήσεται τοσοῦτον ὕδωρ ὅσος ὁ κύβος, οὕτω καὶ ἐν ἀέρι· ἀλλὰ τῇ αἰσθήσει ἄδηλον. καὶ αἰεὶ δὴ ἐν παντὶ σώματι ἔχοντι μετάστασιν, ἐφ' ὃ πέφυκε μεθίστασθαι, ἀνάγκη, ἂν μὴ συμπιλῆται, μεθίστασθαι ἢ κάτω αἰεί, εἰ κάτω ἡ φορὰ ὥσπερ γῆς, ἢ ἄνω, εἰ πῦρ, ἢ ἐπ' ἄμφω, [ἢ] ὁποῖον ἄν τι ᾖ τὸ ἐντιθέμενον· ἐν δὲ δὴ τῷ κενῷ τοῦτο μὲν ἀδύνατον (οὐδὲν γὰρ σῶμα), διὰ δὲ τοῦ κύβου τὸ ἴσον διάστημα διεληλυθέναι, ὅπερ ἦν καὶ πρότερον (216b.) ἐν τῷ κενῷ, ὥσπερ ἂν εἰ τὸ ὕδωρ μὴ μεθίστατο τῷ ξυλίνῳ κύβῳ μηδ' ὁ ἀήρ, ἀλλὰ πάντῃ διῄεσαν δι' αὐτοῦ. ἀλλὰ μὴν καὶ ὁ κύβος γε ἔχει τοσοῦτον μέγεθος, ὅσον κατέχει κενόν· ὃ εἰ καὶ θερμὸν ἢ ψυχρόν ἐστιν ἢ βαρὺ ἢ κοῦφον, οὐδὲν ἧττον ἕτερον τῷ εἶναι πάντων τῶν παθημάτων ἐστί, καὶ εἰ μὴ χωριστόν· λέγω δὲ τὸν ὄγκον τοῦ ξυλίνου κύβου. ὥστ' εἰ καὶ χωρισθείη τῶν ἄλλων πάντων καὶ μήτε βαρὺ μήτε κοῦφον εἴη, καθέξει τὸ ἴσον κενὸν καὶ ἐν τῷ αὐτῷ ἔσται τῷ τοῦ τόπου καὶ τῷ τοῦ κενοῦ μέρει ἴσῳ ἑαυτῷ. τί οὖν διοίσει τὸ τοῦ κύβου σῶμα τοῦ ἴσου κενοῦ καὶ τόπου; καὶ εἰ δύο τοιαῦτα, διὰ τί οὐ καὶ ὁποσαοῦν ἐν τῷ αὐτῷ ἔσται; ἓν μὲν δὴ τοῦτο ἄτοπον καὶ ἀδύνατον. But even if we consider it on its own merits the so-called vacuum will be found to be really vacuous. For as, if one puts a cube in water, an amount of water equal to the cube will be displaced; so too in air; but the effect is imperceptible to sense. And indeed always in the case of any body that can be displaced, must, if it is not compressed, be displaced in the direction in which it is its nature to be displaced—always either down, if its locomotion is downwards as in the case of earth, or up, if it is fire, or in both directions—whatever be the nature of the inserted body. Now in the void this is impossible; for it is not body; the void must have penetrated the cube to a distance equal to that which this portion of void formerly occupied in the void, just as if the water or air had not been displaced by the wooden cube, but had penetrated right through it. But the cube also has a magnitude equal to that occupied by the void; a magnitude which, if it is also hot or cold, or heavy or light, is none the less different in essence from all its attributes, even if it is not separable from them; I mean the volume of the wooden cube. So that even if it were separated from everything else and were neither heavy nor light, it will occupy an equal amount of void, and fill the same place, as the part of place or of the void equal to itself. How then will the body of the cube differ from the void or place that is equal to it? And if there can be two such things, why cannot there be any number coinciding? This, then, is one absurd and impossible implication of the theory.
ἔτι δὲ φανερὸν ὅτι τοῦτο ὁ κύβος ἕξει καὶ μεθιστάμενος, ὃ καὶ τὰ ἄλλα σώματα πάντ' ἔχει. ὥστ' εἰ τοῦ τόπου μηδὲν διαφέρει, τί δεῖ ποιεῖν τόπον τοῖς σώμασιν παρὰ τὸν ἑκάστου ὄγκον, εἰ ἀπαθὲς ὁ ὄγκος; οὐδὲν γὰρ συμ βάλλεται, εἰ ἕτερον περὶ αὐτὸν ἴσον διάστημα τοιοῦτον εἴη. It is also evident that the cube will have this same volume even if it is displaced, which is an attribute possessed by all other bodies also. Therefore if this differs in no respect from its place, why need we assume a place for bodies over and above the volume of each, if their volume be conceived of as free from attributes? It contributes nothing to the situation if there is an equal interval attached to it as well.
[ἔτι δεῖ δῆλον εἶναι οἷον κενὸν ἐν τοῖς κινουμένοις. νῦν δ' οὐδαμοῦ ἐντὸς τοῦ κόσμου· ὁ γὰρ ἀὴρ ἔστιν τι, οὐ δοκεῖ δέ γε—οὐδὲ τὸ ὕδωρ, εἰ ἦσαν οἱ ἰχθύες σιδηροῖ· τῇ ἁφῇ γὰρ ἡ κρίσις τοῦ ἁπτοῦ.] ὅτι μὲν τοίνυν οὐκ ἔστι κεχωρισμένον κενόν, ἐκ τούτων ἐστὶ δῆλον. [Further it ought to be clear by the study of moving things what sort of thing void is. But in fact it is found nowhere in the world. For air is something, though it does not seem to be so—nor, for that matter, would water, if fishes were made of iron; for the discrimination of the tangible is by touch.] It is clear, then, from these considerations that there is no separate void.
Hic ostendit vacuum non esse, rationibus acceptis ex parte ipsius vacui, absque consideratione motus: et hoc ostendit tribus rationibus. Dicit ergo primo: quod etiam considerantibus vacuum per se, absque motu, videbitur quod ita sit dictum ab aliquibus vacuum esse, sicut vere sonat nomen vacui. Nam vacuum sonat aliquid inane et quod non est; et inaniter et absque ratione et veritate dictum est, quod vacuum sit. Et hoc quidem sic ostendit. 541. Now the Philosopher taking his arguments from the void itself, without any mention of motion, shows that the void does not exist. He shows this by three reasons. He says therefore first [375] that even considering the void on its own merits, without motion, it will be seen that the void spoken of by some is just what the name “void” implies. For “void” means something empty and non-existent—and the claim that it exists is vain and without reason and truth. And he shows this as follows.
Quia si aliquis ponat in aqua aliquod corpus cubicum (scilicet quod habet sex superficies quadratas), oportet quod tanta quantitas aquae recedat a loco suo, quanta est quantitas cubi. Et sicut est de aqua, ita est et de aere; licet non sit ita manifestum, eo quod aqua est magis sensibilis quam aer. Eadem igitur ratione, quandocumque aliquid immittitur in aliquod corpus, quod natum est transmutari in aliquam partem, necesse est quod, nisi partes cohaereant per condensationem aut subintrationem partium in invicem, quod transmutetur: vel secundum conditionem corporis cedentis (quando habet exitum liberum), utpote quod corpus grave, ut terra, cedat deorsum, et corpus leve, ut ignis, cedat sursum, et corpus quod est respectu alicuius grave et respectu alicuius leve, cedat in utramque partem, sicut aer et aqua: vel quod corpus cedat secundum conditionem corporis impositi, quando scilicet corpus cedens coarctatur a corpore imposito, ut non possit moveri secundum suam exigentiam, sed secundum exigentiam corporis impositi. Universaliter tamen hoc verum est, quod oportet corpus cedere in quod alterum corpus immittitur, ne sint duo corpora simul. If anyone places a cubic body in water (i.e., a body having six square surfaces) an amount of water equal to the quantity of the cube must be displaced. And what is true of water is true of air, although it is not so evident, because water is more perceptible to sense than air. By the same reasoning applied to the case of any body that can be displaced, in some part, it must, if the parts are not compressed, or enter into each other, be dislodged either (1) according to the state of a yielding body (when it has free exit); for example, if it is a heavy body such as earth it will yield downwards, and if it is a light body such as fire it will yield upwards, and if it is a body which is light in relation to one body and heavy in relation to another, it will yield in both directions, such as do air and water; or (2) because the body yields on account of the condition of the newly imposed body, i.e., when the yielding body is prevented by the imposed body, i.e., when the yielding body is prevented by the imposed body from being moved according to its demands but is moved according to the demands of the imposed body. And in general it can be held as true that a body must yield to an inserted one, lest two bodies be in the same place.
Sed hoc non potest dici de vacuo, quod cedat corpori immisso: quia vacuum non est aliquod corpus; omne autem quod movetur quocumque modo, est corpus. Sed si sit aliquod spatium vacuum, et aliquod corpus immittatur in illud spatium, oportet quod corpus impositum transeat per illud spatium, quod prius erat vacuum, scilicet simul cum eo existens; sicut si aqua non cederet ligneo cubo neque aer, sed ista corpora transirent per ipsum corpus ligneum cubicum, ita quod aer et aqua subintrarent ipsum corpus cubicum, et essent simul cum eo. But this will not be true in the case of the void, i.e., that it must yield to the inserted body, since the void is not a body, whereas whatever is moved in any manner whatsoever is a body. But if there be empty space and a body inserted therein, then the inserted body must pass through that space which previously was empty and cohabit the same space as the void—just as if water or air were not to yield to a wooden cube, but were to pass into the cube in such a way that the air and water would penetrate that cubic body and cohabit with it.
Sed hoc est impossibile, scilicet quod corpus cubicum ligneum sit simul cum spatio vacuo: quia corpus cubicum ligneum habet tantam magnitudinem, quantam habet vacuum, quod ponitur quoddam spatium dimensionatum sine corpore sensibili. Et quamvis corpus ligneum cubicum sit calidum vel frigidum, aut grave vel leve, nihilominus tamen ipsum corpus cubicum alterum est secundum rationem ab omnibus passionibus sensibilibus sibi accidentibus: quamvis non sit separabile ab eis secundum rem. Hoc autem quod est secundum rationem alterum a passionibus, est ipsum corpus lignei cubi, idest quod pertinet ad corporeitatem eius. Si ergo separetur hoc corpus ab omnibus quae sunt alia ab ipso secundum rationem, ita quod non sit neque grave neque leve, sequitur quod contineat vel occupet de spatio vacuo aliquid aequale sibi. Et sic in eadem parte sibi aequali, quae est pars loci et vacui, erit simul corpus lignei cubi. But it is impossible for a wooden cube to exist with empty space; for the wooden cube has the same magnitude as the empty space, which is supposed to be a certain dimensional space without a sensible body. And even though the wooden cube be hot or cold, heavy or light, nevertheless the cubic body is other in notion from all the sensible qualities, that are its accidents, although it be not separable from them in reality. Now what is in conception distinct from the qualities is the body of a wooden cube, i.e., that which pertains to its corporeity. Now if this body be separated from whatever is distinct from it in notion, so that it is neither heavy nor light, it follows that it will occupy a volume of empty space equal to itself. Thus in the same part equal to it, which is part of the place and of the void, the body of the wooden cube will be.
Quo supposito, non videtur quod sit assignare differentiam inter corpus cubi, et dimensiones loci vel vacui. Nam sicut dimensiones loci vel vacui sunt sine qualitatibus sensibilibus, ita et dimensiones corporis cubici, ad minus secundum rationem, sunt aliae ab huiusmodi passionibus. Duae autem magnitudines aequalis quantitatis non possunt differre, nisi secundum situm. Non enim potest imaginari quod haec linea sit alia ab illa sibi aequali, nisi inquantum imaginamur utramque in alio et alio situ. Unde si ponantur duae magnitudines simul, non videtur quod possint differre: et sic si duo corpora aequalia dimensionata sint simul, sive sint cum passionibus sensibilibus sive non, sequitur quod duo corpora sint unum. Vel si adhuc corpus cubicum, et spatium quod est locus vel vacuum, remaneant duo et simul sint, non potest assignari ratio quare non quaecumque alia corpora simul possint esse in eodem. Et ita, sicut corpus cubicum simul est cum spatio loci aut vacui, ita etiam simul cum utroque poterit adhuc esse aliud tertium vel etiam quartum corpus: quod est impossibile. Non enim potest dici quod simul cum corpore cubico ligneo non possit esse simul aliud corpus sensibile, propter materiam: quia corpori non debetur locus ratione materiae, nisi secundum quod materia continetur sub dimensionibus. Unde quod duo corpora non possint esse simul, non est ex parte materiae vel passionum sensibilium, sed solum ex ratione dimensionum, in quibus non potest esse diversitas si sint aequales, nisi secundum situm, ut dictum est. Unde cum dimensiones sint in spatio vacuo sicut in corpore sensibili, sicut duo corpora sensibilia non possunt esse simul, ita nec corpus sensibile simul cum spatio vacuo. Hoc est igitur unum inconveniens et impossibile, quod sequitur ex praemissa positione, quod duo corpora sunt simul. On this assumption it does not seem possible to find a difference between the body of the cube and the dimensions of the place or void. For just as the dimensions of the place or void exist without sensible qualities, so too the dimensions of the cubic body, at least according to notion, are distinct from its sensible qualities. But two magnitudes of equal quantity can differ only in situs. For we cannot imagine one line as distinct from another of equal length, unless we imagine one in one situs and the other in another. Hence, if two magnitudes are imagined together, it does not seem that they can differ: consequently, if two bodies of equal dimensions are together, whether accompanied by their sensible qualities or not, it follows that two bodies are one, or if the cubic body and the space which is the place or void remain two, but are still together, there is no reason why any number of bodies cannot be there. In that case, just as the cubic body is together with the space of the place or void, along with both a third or even a fourth body ought to be able to be inserted. This, of course, is impossible. For we cannot say that it is because of matter that some other sensible body cannot exist together with the wooden cubic body, for place does not belong to a body because of its matter, except in the sense that the matter is contained under dimensions. Hence the impossibility for two bodies to be together is not on account of the matter or of the sensible qualities, but only on account of the dimensions, in which no diversity can be found if they are equal except a diversity based on situs, as was said. Wherefore since there are dimensions in empty space just as there are in a sensible body, then, just as two sensible bodies cannot be together, so neither can a sensible body be together with empty space. So this is one unacceptable result and impossibility that follows from the aforementioned premise: namely, that two bodies would be in the same place.
Secundam rationem ponit ibi: amplius autem manifestum est et cetera. Et dicit manifestum esse quod cubus, qui transmutatur et ponitur in spatium vacuum, habet hoc quod habent omnia alia corpora, scilicet dimensiones. Si ergo dimensiones corporis cubici non differunt a dimensionibus loci secundum rationem, quare oportet facere aliquem locum corporibus extra proprium corpus uniuscuiusque, si locus nihil aliud est quam corpus impassibile, idest absque passionibus sensibilibus? Ex quo enim corpus habet proprias dimensiones, ad nihil videtur esse necessarium quod ponantur circa ipsum aliquae aliae dimensiones spatii aequalis suis dimensionibus. Accidit igitur, si ponatur vacuum vel locus esse quoddam spatium separatum, quod non est necessarium corpora esse in loco. 542. He then gives the second reason [376], saying that it is clear that a cube which is transferred to an empty space has what all other bodies have, namely, dimensions. If therefore the dimensions of the cube do not differ from the dimensions of the place according to conception, why is it necessary to find for a body a place distinct from its own body, if place is nothing more than “impossible body,” i.e., a body without sensible qualities? In view of the fact that a body has its own dimensions, there seems to be no necessity for it to be surrounded by other dimensions of a space equal to its own dimensions. Consequently if the void is presumed, or place as a certain separated space, it follows that bodies do not have to be in place.
Tertiam rationem ponit ibi: amplius oportet etc.; et dicit quod si aliquid esset vacuum, oporteret quod manifestaretur in istis mobilibus. Sed nunquam apparet aliquid vacuum infra mundum: quia plenum aere, quod videtur vacuum, non est vacuum. Aer enim est aliquid, licet visu non percipiatur. Quia si etiam pisces essent ferrei, et haberent similem apparentiam cum aqua, non posset aqua discerni ab eis per visum; nec tamen sequeretur quod aqua non esset, vel etiam pisces: quia non solum visu, sed etiam tactu discernitur illud quod tangitur. Et sic patet aerem aliquid esse: quia tactu percipitur calidus vel frigidus. 543. He gives the third reason [377] when he says that if there were a void, it would have to be evident in mobile things. But there is no evidence of a void anywhere in the world, because what is full of air seems to be a void, though it to not. For air is something, although not perceptible to sight. Now if fish were made of iron and had the same appearance as water, our sight would not be able to distinguish them from water; but it would not follow that the water, or even the fish, were non-existent: for it is not only by sight but also by touch that we can discern what is touched. Consequently, it is evident that water is something, because touch can perceive whether it be hot or cold.
Ex his igitur apparet quod vacuum non sit aliquod spatium separatum, neque infra mundum neque extra mundum. From all this it appears that there is no separate void either within or outside the universe.

Lecture 14
There is no void within bodies
Lectio 14
Chapter 9
Εἰσὶν δέ τινες οἳ διὰ τοῦ μανοῦ καὶ πυκνοῦ οἴονται φανερὸν εἶναι ὅτι ἔστι κενόν. εἰ μὲν γὰρ μὴ ἔστι μανὸν καὶ πυκνόν, οὐδὲ συνιέναι καὶ πιλεῖσθαι οἷόν τε· εἰ δὲ τοῦτο μὴ εἴη, ἢ ὅλως κίνησις οὐκ ἔσται, ἢ κυμανεῖ τὸ ὅλον, ὥσπερ ἔφη Ξοῦθος, ἢ εἰς ἴσον ἀεὶ <�δεῖ> μεταβάλλειν ἀέρα καὶ ὕδωρ (λέγω δὲ οἷον εἰ ἐξ ὕδατος κυάθου γέγονεν ἀήρ, ἅμα ἐξ ἴσου ἀέρος ὕδωρ τοσοῦτον γεγενῆσθαι), ἢ κενὸν εἶναι ἐξ ἀνάγκης· συμπιλεῖσθαι γὰρ καὶ ἐπεκτείνεσθαι οὐκ ἐνδέχεται ἄλλως. There are some who think that the existence of rarity and density shows that there is a void. If rarity and density do not exist, they say, neither can things contract and be compressed. But if this were not to take place, either there would be no movement at all, or the universe would bulge, as Xuthus said, or air and water must always change into equal amounts (e.g. if air has been made out of a cupful of water, at the same time out of an equal amount of air a cupful of water must have been made), or void must necessarily exist; for compression and expansion cannot take place otherwise.
εἰ μὲν οὖν τὸ μανὸν λέγουσι τὸ πολλὰ κενὰ κεχωρισμένα ἔχον, φανερὸν ὡς εἰ μηδὲ κενὸν ἐνδέχεται εἶναι χωριστὸν ὥσπερ μηδὲ τόπον ἔχοντα διάστημα αὑτοῦ, οὐδὲ μανὸν οὕτως· Now, if they mean by the rare that which has many voids existing separately, it is plain that if void cannot exist separate any more than a place can exist with an extension all to itself, neither can the rare exist in this sense.
εἰ δὲ μὴ χωριστόν, ἀλλ' ὅμως ἐνεῖναί τι κενόν, ἧττον μὲν ἀδύνατον, συμβαίνει δὲ πρῶτον μὲν οὐ πάσης κινήσεως αἴτιον τὸ κενόν, ἀλλὰ τῆς ἄνω (τὸ γὰρ μανὸν κοῦφον, διὸ (217a.) καὶ τὸ πῦρ μανὸν εἶναί φασιν), But if they mean that there is void, not separately existent, but still present in the rare, this is less impossible, yet, first, the void turns out not to be a condition of all movement, but only of movement upwards (for the rare is light, which is the reason why they say fire is rare);
ἔπειτα κινήσεως αἴτιον οὐχ οὕτω τὸ κενὸν ὡς ἐν ᾧ, ἀλλ' ὥσπερ οἱ ἀσκοὶ τῷ φέρεσθαι αὐτοὶ ἄνω φέρουσι τὸ συνεχές, οὕτω τὸ κενὸν ἄνω φέρει. καίτοι πῶς οἷόν τε φορὰν εἶναι κενοῦ ἢ τόπον κενοῦ; κενοῦ γὰρ γίγνεται κενόν, εἰς ὃ φέρεται. second, the void turns out to be a condition of movement not as that in which it takes place, but in that the void carries things up as skins by being carried up themselves carry up what is continuous with them. Yet how can void have a local movement or a place? For thus that into which void moves is till then void of a void.
ἔτι δὲ πῶς ἐπὶ τοῦ βαρέος ἀποδώσουσιν τὸ φέρεσθαι κάτω; Again, how will they explain, in the case of what is heavy, its movement downwards?
καὶ δῆλον ὅτι εἰ ὅσῳ ἂν μανότερον καὶ κενώτερον ᾖ ἄνω οἰσθήσεται, εἰ ὅλως εἴη κενόν, τάχιστ' ἂν φέροιτο. ἴσως δὲ καὶ τοῦτ' ἀδύνατον κινηθῆναι· λόγος δ' ὁ αὐτός, ὥσπερ ὅτι ἐν τῷ κενῷ ἀκίνητα πάντα, οὕτω καὶ τὸ κενὸν ὅτι ἀκίνητον· ἀσύμβλητα γὰρ τὰ τάχη. And it is plain that if the rarer and more void a thing is the quicker it will move upwards, if it were completely void it would move with a maximum speed! But perhaps even this is impossible, that it should move at all; the same reason which showed that in the void all things are incapable of moving shows that the void cannot move, viz. the fact that the speeds are incomparable.
ἐπεὶ δὲ κενὸν μὲν οὔ φαμεν εἶναι, τὰ ἄλλα δ' ἠπόρηται ἀληθῶς, ὅτι ἢ κίνησις οὐκ ἔσται, εἰ μὴ ἔσται πύκνωσις καὶ μάνωσις, ἢ κυμανεῖ ὁ οὐρανός, ἢ αἰεὶ ἴσον ὕδωρ ἐξ ἀέρος ἔσται καὶ ἀὴρ ἐξ ὕδατος (δῆλον γὰρ ὅτι πλείων ἀὴρ ἐξ ὕδατος γίγνεται· ἀνάγκη τοίνυν, εἰ μὴ ἔστι πίλησις, ἢ ἐξωθούμενον τὸ ἐχόμενον τὸ ἔσχατον κυμαίνειν ποιεῖν, ἢ ἄλλοθί που ἴσον μεταβάλλειν ἐξ ἀέρος ὕδωρ, ἵνα ὁ πᾶς ὄγκος τοῦ ὅλου ἴσος ᾖ, ἢ μηδὲν κινεῖσθαι· ἀεὶ γὰρ μεθισταμένου τοῦτο συμβήσεται, ἂν μὴ κύκλῳ περιίστηται· οὐκ ἀεὶ δ' εἰς τὸ κύκλῳ ἡ φορά, ἀλλὰ καὶ εἰς εὐθύ)· οἱ μὲν δὴ διὰ ταῦτα κενόν τι φαῖεν ἂν εἶναι, Since we deny that a void exists, but for the rest the problem has been truly stated, that either there will be no movement, if there is not to be condensation and rarefaction, or the universe will bulge, or a transformation of water into air will always be balanced by an equal transformation of air into water (for it is clear that the air produced from water is bulkier than the water): it is necessary therefore, if compression does not exist, either that the next portion will be pushed outwards and make the outermost part bulge, or that somewhere else there must be an equal amount of water produced out of air, so that the entire bulk of the whole may be equal, or that nothing moves. For when anything is displaced this will always happen, unless it comes round in a circle; but locomotion is not always circular, but sometimes in a straight line. These then are the reasons for which they might say that there is a void;
ἡμεῖς δὲ λέγομεν ἐκ τῶν ὑποκειμένων ὅτι ἔστιν ὕλη μία τῶν ἐναντίων, θερμοῦ καὶ ψυχροῦ καὶ τῶν ἄλλων τῶν φυσικῶν ἐναντιώσεων, καὶ ἐκ δυνάμει ὄντος ἐνεργείᾳ ὂν γίγνεται, καὶ οὐ χωριστὴ μὲν ἡ ὕλη, τὸ δ' εἶναι ἕτερον, καὶ μία τῷ ἀριθμῷ, εἰ ἔτυχε, χροιᾶς καὶ θερμοῦ καὶ ψυχροῦ. our statement is based on the assumption that there is a single matter for contraries, hot and cold and the other natural contrarieties, and that what exists actually is produced from a potential existent, and that matter is not separable from the contraries but its being is different, and that a single matter may serve for colour and heat and cold.
ἔστι δὲ καὶ σώματος ὕλη καὶ μεγάλου καὶ μικροῦ ἡ αὐτή. δῆλον δέ· ὅταν γὰρ ἐξ ὕδατος ἀὴρ γένηται, ἡ αὐτὴ ὕλη οὐ προσλαβοῦσά τι ἄλλο ἐγένετο, ἀλλ' ὃ ἦν δυνάμει, ἐνεργείᾳ ἐγένετο, καὶ πάλιν ὕδωρ ἐξ ἀέρος ὡσαύτως, ὁτὲ μὲν εἰς μέγεθος ἐκ μικρότητος, ὁτὲ δ' εἰς μικρό τητα ἐκ μεγέθους. ὁμοίως τοίνυν κἂν ὁ ἀὴρ πολὺς ὢν ἐν ἐλάττονι γίγνηται ὄγκῳ καὶ ἐξ ἐλάττονος μείζων, ἡ δυνάμει οὖσα ὕλη γίγνεται ἄμφω. The same matter also serves for both a large and a small body. This is evident; for when air is produced from water, the same matter has become something different, not by acquiring an addition to it, but has become actually what it was potentially, and, again, water is produced from air in the same way, the change being sometimes from smallness to greatness, and sometimes from greatness to smallness. Similarly, therefore, if air which is large in extent comes to have a smaller volume, or becomes greater from being smaller, it is the matter which is potentially both that comes to be each of the two.
ὥσπερ γὰρ καὶ ἐκ ψυχροῦ θερμὸν καὶ ἐκ θερμοῦ ψυχρὸν ἡ αὐτή, ὅτι ἦν δυνάμει, οὕτω καὶ ἐκ θερμοῦ (217b.) μᾶλλον θερμόν, οὐδενὸς γενομένου ἐν τῇ ὕλῃ θερμοῦ ὃ οὐκ ἦν θερμὸν ὅτε ἧττον ἦν θερμόν, ὥσπερ γε οὐδ' ἡ τοῦ μείζονος κύκλου περιφέρεια καὶ κυρτότης ἐὰν γίγνηται ἐλάττονος κύκλου, <�ἢ> ἡ αὐτὴ οὖσα ἢ ἄλλη, ἐν οὐθενὶ ἐγγέγονε τὸ κυρτὸν ὃ ἦν οὐ κυρτὸν ἀλλ' εὐθύ (οὐ γὰρ τῷ διαλείπειν τὸ ἧττον ἢ τὸ μᾶλλον ἔστιν)· οὐδ' ἔστι τῆς φλογὸς λαβεῖν τι μέγεθος ἐν ᾧ οὐ καὶ θερμότης καὶ λευκότης ἔνεστιν. οὕτω τοίνυν καὶ ἡ πρότερον θερμότης <�πρὸς> τὴν ὕστερον. ὥστε καὶ τὸ μέγεθος καὶ ἡ μικρότης τοῦ αἰσθητοῦ ὄγκου οὐ προσλαβούσης τι τῆς ὕλης ἐπεκτείνεται, ἀλλ' ὅτι δυνάμει ἐστὶν ὕλη ἀμφοῖν· ὥστ' ἐστὶ τὸ αὐτὸ πυκνὸν καὶ μανόν, καὶ μία ὕλη αὐτῶν. For as the same matter becomes hot from being cold, and cold from being hot, because it was potentially both, so too from hot it can become more hot, though nothing in the matter has become hot that was not hot when the thing was less hot; just as, if the arc or curve of a greater circle becomes that of a smaller, whether it remains the same or becomes a different curve, convexity has not come to exist in anything that was not convex but straight (for differences of degree do not depend on an intermission of the quality); nor can we get any portion of a flame, in which both heat and whiteness are not present. So too, then, is the earlier heat related to the later. So that the greatness and smallness, also, of the sensible volume are extended, not by the matter's acquiring anything new, but because the matter is potentially matter for both states; so that the same thing is dense and rare, and the two qualities have one matter.
ἔστι δὲ τὸ μὲν πυκνὸν βαρύ, τὸ δὲ μανὸν κοῦφον. [ἔτι ὥσπερ ἡ τοῦ κύκλου περιφέρεια συναγομένη εἰς ἔλαττον οὐκ ἄλλο τι λαμβάνει τὸ κοῖλον, ἀλλ' ὃ ἦν συνήχθη, καὶ τοῦ πυρὸς ὅ τι ἄν τις λάβῃ πᾶν ἔσται θερμόν, οὕτω καὶ τὸ πᾶν συναγωγὴ καὶ διαστολὴ τῆς αὐτῆς ὕλης.] δύο γὰρ ἔστιν ἐφ' ἑκατέρου, τοῦ τε πυκνοῦ καὶ τοῦ μανοῦ· τό τε γὰρ βαρὺ καὶ τὸ σκληρὸν πυκνὰ δοκεῖ εἶναι, καὶ τἀναντία μανὰ τό τε κοῦφον καὶ τὸ μαλακόν· διαφωνεῖ δὲ τὸ βαρὺ καὶ τὸ σκληρὸν ἐπὶ μολίβδου καὶ σιδήρου. The dense is heavy, and the rare is light. [Again, as the arc of a circle when contracted into a smaller space does not acquire a new part which is convex, but what was there has been contracted; and as any part of fire that one takes will be hot; so, too, it is all a question of contraction and expansion of the same matter.] There are two types in each case, both in the dense and in the rare; for both the heavy and the hard are thought to be dense, and contrariwise both the light and the soft are rare; and weight and hardness fail to coincide in the case of lead and iron.
ἐκ δὴ τῶν εἰρημένων φανερὸν ὡς οὔτ' ἀποκεκριμένον κενὸν ἔστιν, οὔθ' ἁπλῶς οὔτ' ἐν τῷ μανῷ, οὔτε δυνάμει, εἰ μή τις βούλεται πάντως καλεῖν κενὸν τὸ αἴτιον τοῦ φέρεσθαι. οὕτω δ' ἡ τοῦ βαρέος καὶ κούφου ὕλη, ᾗ τοιαύτη, εἴη ἂν τὸ κενόν· τὸ γὰρ πυκνὸν καὶ τὸ μανὸν κατὰ ταύτην τὴν ἐναντίωσιν φορᾶς ποιητικά, κατὰ δὲ τὸ σκληρὸν καὶ μαλακὸν πάθους καὶ ἀπαθείας, καὶ οὐ φορᾶς ἀλλ' ἑτεροιώσεως μᾶλλον. καὶ περὶ μὲν κενοῦ, πῶς ἔστι καὶ πῶς οὐκ ἔστι, διωρίσθω τὸν τρόπον τοῦτον. From what has been said it is evident, then, that void does not exist either separate (either absolutely separate or as a separate element in the rare) or potentially, unless one is willing to call the condition of movement void, whatever it may be. At that rate the matter of the heavy and the light, qua matter of them, would be the void; for the dense and the rare are productive of locomotion in virtue of this contrariety, and in virtue of their hardness and softness productive of passivity and impassivity, i.e. not of locomotion but rather of qualitative change. So much, then, for the discussion of the void, and of the sense in which it exists and the sense in which it does not exist.
Postquam philosophus ostendit non esse vacuum separatum, hic ostendit non esse vacuum corporibus inditum. Et circa hoc tria facit: primo ponit rationem ponentium sic vacuum; secundo improbat eorum positionem, ibi: si igitur rarum dicunt etc.; tertio solvit rationem ipsorum, ibi: quoniam autem vacuum et cetera. 544. Having shown that there is no separated void, the Philosopher here shows that there is no void inherent in bodies. As to this he does three things: First he gives the reason proposed by those who posit such a void; Secondly, he disproves their position, at no. 546; Thirdly, he dissolves their argument, at no. 551.
Dicit ergo primo quod quidam philosophi fuerunt, qui opinati sunt quod vacuum sit in corporibus, accipientes rationem ex raro et denso. Videbatur enim eis quod rarefactio et condensatio fieret propter vacuum intrinsecum corporibus. Si vero non esset sic rarum et densum, dicebant quod non erat possibile ut partes alicuius corporis coirent, idest subintrarent ad invicem, et quod aliquod corpus calcaretur, idest comprimeretur per condensationem. Si autem hoc non sit, ducebant ad inconveniens, et ex parte motus localis, et ex parte motus generationis et corruptionis, sive alterationis. 545. He says therefore first [347] that there have been some philosophers who believed that there is a void in bodies, basing their argument on the existence of rarity and density. For they believed that rarefaction and condensation took place on account of a void inhering in bodies. If rarity and density did not exist, they say, the parts of bodies could not “go in,” i.e., enter each other, and “harden,” i.e., be compressed by condensation. But if this does not take place, they deduced certain difficulties both in respect to local motion, and in respect to the motions of generation and corruption, or alteration.
Ex parte quidem motus localis, quia oportebit dicere vel quod omnino motus non sit, vel quod uno moto moveatur totum universum, sicut dixit Xuthus philosophus. Et hoc ideo, quia si aliquod corpus movetur localiter, cum accedit ad locum plenum alio corpore, oportet quod illud corpus inde expellatur, et tendat in alium locum, et iterum corpus ibi inventum in alium: et nisi fiat condensatio corporum, oportebit quod omnia corpora moveantur. In respect to local motion, because it would be necessary to admit either that motion does not exist at all, or that the whole universe is moved with one motion, as says Xuthus, a philosopher. This would be because if a body were moved locally, when it approached a place full of another body, this body would have to be expelled, and tend toward another place and the body found there would have to go to yet another place, so that, unless there were condensation of bodies, all bodies would have to be in motion.
Ex parte vero generationis sive alterationis sequitur hoc inconveniens, quod semper fiat aequalis mutatio ex aere in aquam, et ex aqua in aerem: ut puta, si ex aqua unius cyathi generatus est aer, oportet quod ex tanto aere quantus est aer generatus, alibi generetur aqua. Et hoc ideo, quia maior quantitas est aeris quam aquae ex qua generatur. Occupat igitur aer generatus maiorem locum quam aqua ex qua generatur. Et sic oportet quod vel totum corpus universi occuparet maiorem locum; vel quod alibi tantumdem de aere convertatur in aquam: vel oportet dicere quod sit aliquid vacuum intra corpora, ad hoc quod fiat condensatio corporum; quia non opinabantur quod aliter contingeret condensari et rarefieri corpora, nisi vacuo in eis existente. In regard to generation or alteration, this difficulty arises that there would also be an equal change of air into water and of water into air: for example, if air be generated from one cupful of water, it would be necessary that from a same amount of air as was generated, an amount of water be generated somewhere else. The reason is that there is now a greater amount [i.e. volume] of air than there previously was of water from which it was generated. The generated air therefore occupies a greater place than the water from which it was generated. Consequently, either the whole body of the universe would have to occupy a greater place, or else as much air in some other place would have to be converted into water, or else finally, it must be admitted that there is a void within bodies to allow them to be condensed, because these philosophers supposed that bodies could not become condensed and rarefied unless there was a void existing in them.
Deinde cum dicit: si igitur rarum etc., destruit positionem praedictam. Et primo secundum unum intellectum; secundo secundum alium, ibi: si autem non est separabile et cetera. 546. Then [379] he rejects this position: First according to one interpretation; Secondly, according to another interpretation, at no.547.
Dicit ergo primo quod illi qui dicunt vacuum esse in corporibus, dupliciter possunt hoc intelligere; uno modo quod in quolibet corpore sint multa quasi foramina vacua, quae sint separata secundum situm ab aliis partibus plenis, sicut est videre in spongia vel in pumice vel in aliquo alio huiusmodi: alio modo quod vacuum non sit separatum secundum situm ab aliis partibus corporis, utpote si dicamus quod dimensiones, quas dicebant esse vacuum, subintrent omnes partes corporis. He says therefore that those who posit a void within bodies can give this two interpretations: the first is that in each body there are, as it were, many empty openings, each existing separate in respect to situs from the other full parts, as can be seen in a sponge or in pumice or things of this sort. The second interpretation is that the void is not separate in respect to situs from the other parts of the body; as if we should say that the dimensions, which they said were the void would penetrate all the parts of the body.
Si autem primo modo dicant vacuum esse in corporibus, patet reprobatio huius ex praemissis. Per quam enim rationem ostenditur, quod non est aliquod vacuum separatum extra corpora, nec aliquis locus habens aliquod tale spatium proprium praeter dimensiones corporum; per eandem rationem probari potest, quod non est aliquod corpus hoc modo rarum, quod habeat intra se aliqua spatia vacua, distincta ab aliis partibus corporis. The refutation of their claim as to the first way of the void’s being in bodies is evident from what went before. For the very argument that shows there is not a separate void outside of bodies nor any place having such a space proper to itself over and above the dimensions of bodies. The same argument can be used to prove that there is no body so rarefied that it would have within itself any empty spaces distinct from the other parts of the body.
Deinde cum dicit: si autem non est separabile etc., improbat praedictam positionem quantum ad secundum intellectum, quatuor rationibus. Dicit ergo quod si vacuum non est sic in corporibus sicut separabile et distinctum ab aliis partibus, sed tamen inest aliquod vacuum in corporibus, minus quidem est impossibile, quia non sequuntur inconvenientia supra posita contra vacuum separatum; sed tamen ad hoc etiam sequuntur quaedam inconvenientia. Primo quidem quod vacuum non erit causa omnis motus localis, ut ipsi intendebant, sed solum motus qui est in sursum: quia vacuum secundum eos est causa raritatis, rarum autem invenitur esse leve, ut patet in igne, leve autem est quod movetur sursum; unde vacuum erit causa solum motus sursum. 547. He then [380] disproves the aforesaid position as to the second interpretation and gives four reasons for rejecting it. He says, therefore, that if the void is not in bodies in such a way as to be separable and distinct from the other parts but is nevertheless present in bodies, the situation is less impossible, because the difficulties mentioned above against a separate void do not arise; yet against this also certain discrepancies do arise. First of all, the void will not be the cause of every local motion, as the maintained, but only of upward motion—for the void, according to them, is the cause of rarity, and the rare in turn is found to be light, as is evident in fire, and what is light travels upwards; consequently, the void will be the cause only of upward motion.
Secundam rationem ponit ibi: postea motus causa et cetera. Et dicit quod secundum istos qui ponunt vacuum in corporibus, vacuum est causa motus, non sicut in quo aliquid movetur, ut ponebant causam motus vacuum qui dicebant vacuum spatium separatum; sed eo modo ponunt vacuum causam motus, in quantum ipsum vacuum intrinsecum defert corpora; sicut si dicamus quod utres inflati, in eo quod feruntur ipsi sursum propter levitatem, deferunt sursum quidquid eis continuatur. Et sic vacuum inditum corporibus fert secum corpus in quo est. 548. He gives the second reason [381] when he says that according to those who posit a void in bodies the void is the cause of motion, not as that in which something is moved (in the way that those who held for a separate empty space posited the void as a cause of motion), but as the cause of motion in such a way that the empty space within the bodies transports them: it is analogous to the case of inflated wine-skins, which, due to the fact that they are carried upward on account of their lightness, also carry upward whatever is attached to them. And in this way the void inherent in bodies carries with it the body in which it is.
Sed hoc videtur esse impossibile: quia tunc oporteret quod vacuum movetur, et quod esset aliquis locus vacui; et eum vacuum et locus sint idem, sequetur quod vacui interioris erit vacuum exterius, in quod fertur; quod est impossibile. But this seems impossible: because then it would follow that the void would have to be subject to motion and that there would exist a certain place for the void. And since the void and place are the same, it will follow that of an interior void there will be an exterior void into which it is transported—which is impossible.
Tertiam rationem ponit ibi: amplius quomodo et cetera. Et dicit quod si motus sursum causa est vacuum, deferens corpus sursum, cum nihil sit assignare quod deferat corpus deorsum, non erit assignare quare gravia deorsum ferantur. 549. The third reason [382] is given when he says that if the cause of upward motion is the void carrying a body upward, then since there is nothing to carry the body down, there would be no explanation of why heavy bodies are carried downwards.
Quartam rationem ponit ibi: et manifestum est et cetera. Et dicit quod si rarum causat motum sursum propter vacuitatem, oportebit quod quanto aliquid est rarius et magis vacuum, tanto velocius feratur sursum: et si sit omnino vacuum, velocissime feretur. 550. Be then gives the fourth reason [833], and says that if the rare causes upward motion on account of emptiness, then the rarer and more empty a thing is, the faster it should be carried upward. And if it were completely empty, it should move with a maximum speed.
Sed hoc est impossibile, quia quod est omnino vacuum non potest moveri, eadem ratione qua supra ostensum est quod in spatio vacuo non potest esse motus; quia non esset comparare velocitates vacui et pleni, neque ex parte spatii neque ex parte mobilis, secundum aliquam determinatam proportionem, eo quod pleni ad vacuum nulla est proportio. Non ergo vacuum potest esse causa motus sursum. But this is impossible, because what is completely empty cannot be moved, for the same reason by which it was shown above that motion is impossible in an empty space; for there is no way to compare the speeds of the empty and of the full (whether you consider the space or the mobile) according to some definite ratio, because there is no ratio between the full and the empty. Therefore the void cannot be the cause of upward motion.
Deinde cum dicit: quoniam autem vacuum etc., solvit praemissam rationem. Et primo repetit eam, magis ipsam explanans; secundo solvit eam, ibi: nos autem dicimus et cetera. 551. Then [385] be answers a previous argument: First he repeats it, explaining it more extensively; Secondly, he solves it, at no. 552.
Dicit ergo primo, quod quia non dicimus esse vacuum, neque in corporibus neque extra, oportet solvere quae ab aliis inducuntur, quia vere ingerunt dubitationem. He says therefore first that because we do not admit a void either in bodies or outside of them, we must answer the arguments of our opponents, because they present a real difficulty.
Et primo ex parte motus localis: quia aut non erit omnino motus localis, nisi sit raritas et densitas, quam non intelligebant fieri nisi per vacuum; aut oportebit dicere quod ad motum cuiuslibet corporis etiam ipsum caelum in sursum feratur, vel aliqua pars eius, quod vocat turbationem caeli. First of all on the side of local motion: either (1) local motion will not be if there is not rarity and density, which they believed could not be produced without the void; or (2) we will be forced to say that whenever a body is moved, the very heavens or some part of them are borne outward, which he calls the “bulging” of the heavens.
Aut iterum ex parte generationis et corruptionis, oportebit quod semper aequalis aqua fiat ex aere, et alibi aer ex aqua: quia cum plus de aere generetur ex aqua, necesse est, nisi fiat condensatio, quam non credebant posse fieri sine vacuo, aut quod corpus quod habetur ultimum secundum communem opinionem, scilicet corpus caeleste, depellatur per exuberantiam inferiorum corporum; aut quod alibi in quocumque loco tantumdem de aere convertatur in aquam, ad hoc quod totum corpus universi inveniatur semper aequale. Secondly, from the viewpoint of generation and corruption a transformation of water into air will always have to be balanced by an equal transformation of air into water somewhere else; for since more air is generated from water it is required (unless condensation takes place which they thought impossible without a void) either (1) that the body which was held to be outermost according to common opinion, namely, the heavenly body, be pushed outward by the swelling of lower bodies; or (2) that somewhere else there must be an equal amount of air converted into water, so that the entire bulk of the universe remain always equal.
Sed quia ad hoc quod dixerat de motu locali, posset quodammodo obviari, iterum repetit ut excludat illud: et dicit quod aut sequitur quod nihil moveatur: quia secundum praedicta, tumultuatio caeli accidet quocumque transmutato. Sed hoc est verum, nisi intelligatur motus fieri circulariter; ut puta quod a moveatur ad locum b, et b ad locum c, et c ad locum d, et iterum d ad locum a. Sic enim non oportebit, posita circulari latione, quod uno moto, totum universum turbetur. Sed nos non videmus quod omnis loci mutatio naturalium corporum sit in circulum, sed multae sunt in rectum. Unde adhuc sequetur tumultuatio caeli, nisi ponatur condensatio et vacuum. But because one could in a certain way elude what he had said about local motion, he mentions this [evasion] again in order to exclude it. Thus he repeats, “Or it follows that nothing is moved.” Now according to the foregoing a disturbance of the heavens occurs whenever anything is transmuted. And this is true unless the motion is rotational: for example, let A be in motion to place B, and B to place C, and C to place D, and again D to place A. In this case, on the assumption of rotational motion, it will not be necessary, if one thing moves, that the whole universe be disturbed. But we do not see every local motion of natural bodies to be rotational, but many are in a straight line. Hence, there will be still disturbance of the heavens, unless condensation and the void be admitted.
Haec est igitur ratio propter quam aliqui ponebant esse vacuum. This then is the argument which prompted some to posit the void.
Deinde cum dicit: nos autem dicimus etc., solvit praemissam rationem. Tota autem vis praemissae rationis in hoc consistit, quod rarefactio et condensatio fiat per vacuum. Unde hic obviat Aristoteles ostendens quod contingit rarefieri et condensari sine vacuo. Et primo ostendit propositum; secundo inducit conclusionem principaliter intentam, ibi: ex dictis igitur manifestum est et cetera. 552. Then 385] he answers this argument. Now the entire force of this argument consists in this, that rarefaction and condensation take place by means of the void. Accordingly, Aristotle meets this by showing that rarefaction and condensation can take place without a void. First, he reveals his proposition; Secondly, he introduces the conclusion be mainly intends, at no. 557.
Circa primum tria facit: primo manifestat propositum per rationem; secundo per exempla, ibi: sicut enim ex frigido fit calidum etc.; tertio per effectus rari et densi, ibi: est autem densum quidem et cetera. As to the first he does three things: First he explains his proposition by an argument; Secondly, by examples, at no. 555; Thirdly, by the effects of rarity and density, at no. 556.
Circa primum duo facit: primo praemittit quaedam necessaria ad propositum; secundo probat propositum, ibi: est igitur et corporis et cetera. As to the first he does two things: First he premises certain things necessary for his proposition; Secondly, he proves his proposition, at no. 554.
Praemittit autem quatuor, quae accipit ex subiectis, id est ex his quae supponuntur in scientia naturali, et supra etiam manifestata sunt in primo huius libri. Quorum primum est, quod una est materia contrariorum, ut calidi et frigidi, vel cuiuscumque alterius naturalis contrarietatis: contraria enim nata sunt fieri circa idem. Secundum est, quod omne quod in actu est, necessario fit ex eo quod est in potentia. Tertium est, quod materia non est separabilis a contrariis, ita ut sit absque eis: sed tamen secundum rationem materia est aliud a contrariis. Quartum est, quod materia per hoc quod nunc est sub uno contrario et postea sub alio, non est alia et alia, sed eadem numero. 553. Now [385] he lays down four preliminary statements which he takes from the “subjects,” i.e., the presuppositions of natural science, and which were already explained in Book I.
  • The first of these is that the matter of contraries is one; for example, of the hot and the cold, or of any other natural contrariety—for contraries are apt to affect the same thing.
  • The second is that whatever is in act had to come into being from what was in potency.
  • The third is that matter is not separable from contraries so as to exist without them—but yet, according to motion, the matter is distinct from the contraries.
  • The fourth is that matter is not, by virtue of being, now under one contrary, now under another, other and other, but numerically one.
Deinde cum dicit: est igitur et corporis materia etc., ex praemissis ostendit propositum in hunc modum. Eadem numero est materia contrariorum: magnum autem et parvum sunt contraria circa quantitatem: ergo eadem numero est materia magni et parvi. 554. Then [386] from these preliminaries he proves his point in this way: The matter of contraries is one in number. But the large and the small are contraries in respect of quantity. Therefore the matter of the large and the small to numerically the same.
Et hoc manifestum est in transmutatione substantiali. Cum enim generatur aer ex aqua, eadem materia quae prius erat sub aqua, facta est sub aere, non accipiendo aliquid quod prius non haberet, sed illud quod prius erat in potentia in materia, reductum est in actum. Et similiter est cum e converso ex aere generatur aqua. Sed hoc interest, quod cum ex aqua generatur aer, fit mutatio ex parvo in magnum; quia maior est quantitas aeris generati, quam aquae ex qua generatur; cum autem ex aere fit aqua, fit e converso transmutatio a magnitudine in parvitatem. Ergo et cum aer multus existens reducitur ad minorem quantitatem per condensationem, vel ex minori in maiorem per rarefactionem, eadem materia est quae fit utrumque in actu, scilicet magnum et parvum, prius existens ad haec in potentia. And this is clear in substantial transmutation. For when air is generated from water, the same matter which previously was under the water, came to be under air, not receiving anything that it previously lacked, but rather that which was previously in potency in the matter was reduced to act. And the same is true in reverse, when from air water is generated. But there is this difference: when air is generated from water, there is a change from small to large; because the quantity of air generated is larger than the quantity of water from which it was generated. But when, from air, water is made, there is produced contrariwise a transmutation from largeness to smallness. Therefore when a large amount of air is reduced to a smaller amount by condensation, or from a small amount to a larger amount by rarefaction, it is the same matter which becomes both in act, namely, large and small, while being previously in potency to them.
Non ergo condensatio fit per hoc quod aliquae aliae partes subintrando adveniant; vel rarefactio per hoc quod partes inhaerentes extrahantur, ut existimabant ponentes vacuum inter corpora; sed per hoc quod materia earundem partium accipit nunc maiorem, nunc minorem quantitatem: ut sic rarefieri nihil aliud sit, quam materiam recipere maiores dimensiones per reductionem de potentia in actum; condensari autem e converso. Sicut autem materia est in potentia ad determinatas formas, ita etiam est in potentia ad determinatam quantitatem. Unde rarefactio et condensatio non procedit in rebus naturalibus in infinitum. Therefore condensation does not take place by certain parts moving into others, or rarefaction by inhering parts being extracted, as those thought who posited a void within bodies. Rather it is because the matter of the same parts now has greater, now lesser, quantity: hence, to become rare is nothing other than for matter to receive greater dimensions by being reduced from potency to act; and the opposite for becoming dense. For just as matter is in potency to definite forms, so it is in potency to definite quantity. Hence rarefaction and condensation do not proceed ad infinitum in natural things.
Deinde cum dicit: sicut enim ex frigido fit calidum etc., manifestat idem per exempla. Et quia rarefactio et condensatio pertinet ad motum alterationis, ponit exemplum de aliis alterationibus. 555. Then [387] he makes the same thing clear from examples. And because rarefaction and condensation pertain to the motion of alteration, [i.e., change in quality] he gives an example of other alterations.
Et dicit quod sicut eadem materia mutatur ex frigido in calidum et ex calido in frigidum, propter hoc quod utrumque istorum erat in potentia in materia; sic etiam et aliquid fit ex calido magis calidum, non propter hoc quod aliqua pars materiae fiat calida quae prius non erat calida, cum esset minus calidum; sed quia tota materia reducitur in actum magis vel minus calidi. And he says that just as the same matter is changed from cold to hot and from hot to cold, because both were in the matter potentially, so also something passes from hot to hotter, not because some part of the matter previously not hot becomes hot which was not so when It was less hot, but because the entire matter is reduced into the act of being more or less hot.
Aliud etiam exemplum ponit de qualitate circa quantitatem. Et dicit quod si circumferentia et convexitas maioris circuli restringatur ad minorem circulum, manifestum est quod fit magis curvum: non tamen ista ratione, quod ambitus, id est circularitas, facta sit in aliqua parte quae primo non fuisset curvata sed recta; sed per hoc quod idem ipsum quod prius erat minus curvatum, magis curvatur. He gives another example of a quality in the matter of quantity. And he says that if the circumference and convexity of a larger circle are brought in to that of a smaller circle, they become more curved. This happens not because an “ambit,” or curvature, begins to exist in some part that previously was not curved but straight, but because the same that was previously less curved, becomes more curved.
Non enim in huiusmodi alterationibus fit aliquid magis vel minus deficiendo, id est per subtractionem, neque etiam per additionem; sed per unius et eiusdem transmutationem de perfecto ad imperfectum, aut e converso. Et hoc patet per hoc quod in eo quod est simpliciter et uniformiter aliquale, non est invenire aliquam partem quae sit sine tali qualitate; sicut non est accipere in scintilla ignis aliquam partem in qua non sit caliditas et albedo, id est claritas. Sic igitur et prior calor advenit posteriori, non per hoc quod aliqua pars quae non erat calida, sit facta calida; sed per hoc quod illud quod erat minus calidum, fit magis calidum. For in alterations of this sort things do not become more and less by “defect,” i.e., by subtraction, or addition but by the transmutation of one and the same thing from perfect to imperfect, or from imperfect to perfect. This is evident in the case of what is absolutely and uniformly “such and such”: it is impossible to find in it any part lacking that quality, just as it is impossible in a flame to find any part lacking heat and “whiteness,” i.e., clarity. So also prior heat comes to a later heat, not because a part previously not hot became hot, but because what was less hot became hotter.
Unde et magnitudo et parvitas sensibilis corporis non extenditur vel ampliatur in rarefactione et condensatione per hoc, quod materia aliquid superadditum accipiat; sed quia materia, quae prius erat in potentia ad magnum et parvum, transmutatur de uno in alterum. Et ideo rarum et densum non fit per additionem partium subintrantium, vel per subtractionem earundem; sed per hoc quod una est materia rari et densi. So too the largeness and smallness of a sensible body is not extended or increased in rarefaction and condensation by the matter receiving some addition, but by the matter which was previously in potency to large and small being transmuted from one to the other. Therefore the rare and the dense are not produced by the addition of penetrating parts or by their removal, but by there being one matter of the rare and of the dense.
Deinde cum dicit: est autem densum etc., manifestat propositum per effectus rari et densi. Ex differentia enim raritatis et densitatis consequitur differentia aliarum qualitatum, scilicet gravis et levis, duri et mollis. Et sic patet quod rarum et densum diversificant qualitates et non quantitates. 556. Then [388] he manifests his proposition by the effects of the rare and of the dense. For from a difference in rarity and density there follows a difference in other qualities; namely, in heaviness and lightness, hardness and softness. Consequently, rarity and density diversify qualities and not quantities.
Dicit ergo quod ad raritatem sequitur levitas, et ad densitatem sequitur gravitas. Et hoc rationabiliter: quia rarum est ex hoc, quod materia recipit maiores dimensiones; densum autem ex hoc, quod materia recipit minores dimensiones: et sic si accipiantur diversa corpora aequalis quantitatis, unum rarum et aliud densum, densum habet plus de materia. Dictum est autem supra in tractatu de loco, quod corpus contentum comparatur ad continens sicut materia ad formam: et sic grave, quod tendit versus medium contentum, rationabiliter est magis densum, habens plus de materia. Sicut ergo circumferentia circuli maioris reducta ad minorem circulum, non recipit concavitatem in aliqua sui parte, in qua non erat prius, sed quod prius erat concavum, reducitur ad maiorem concavitatem; et sicut quaecumque pars ignis quam quis receperit, est calida: ita et totum corpus fit rarum et densum conductione, id est contractione, et distensione unius et eiusdem materiae, secundum quod movetur ad maiorem vel minorem dimensionem. He says therefore, that lightness follows rarity, and heaviness density. And with good reason: for rarity arises from matter receiving greater dimensions, density from matter receiving lesser dimensions. Consequently, if you take diverse bodies of equal quantity, one being rare and the other dense, then the dense has more matter. Now it was said above in the treatise on place that the contained body is related to the container, as is matter to form; consequently, a heavy body which tends toward the middle [i.e., center]contained is with good reason more dense because it has more matter. Just as, therefore, the circumference of a larger circle, when it is restricted to a smaller circle does not receive concavity in a part not previously concave, but rather a part previously concave was reduced to a greater concavity, and just as any part of fire that anyone may take will be hot, so also it is the whole body that becomes rare or dense by the “conduction,” i.e., contraction, or expansion of one and the same matter, accordingly as it is moved to greater or smaller dimensions.
Et hoc patet per ea quae sequuntur ex raro et denso, quae sunt qualitates. Nam ad densum sequitur grave et durum. Et de gravi quidem ratio assignata est; de duro autem ratio manifesta est: quia durum dicitur quod magis resistit pulsui vel divisioni; quod autem habet plus de materia, minus est divisibile, quia minus obedit agenti, propter hoc quod est magis remotum ab actu. E converso autem, ad rarum sequitur leve et molle. This is clear from what follows from rarity and density, namely, qualities. For the heavy and the hard follow from density. Why heaviness follows density has already been explained. Why hardness follows is easy to explain: that is hard which is better able to resist both pressure and cleavage; but what has more matter is less divisible, because it is less obedient to something acting upon it, on account of its being more remote from actuality. Contrariwise, lightness and softness follow upon rarity.
Sed grave et durum in aliquibus dissonant, sicut in ferro et plumbo: nam plumbum est gravius, sed ferrum est durius. Et huius ratio est, quia plumbum habet plus de terrestri: sed id quod est aquae in eo, est imperfectius congelatum et digestum. But the heavy and the hard fail to coincide in some things: for lead is heavier, but iron is harder. The reason for this is that lead has more of the element “earth” in it, but what there is of “water” in it is less perfectly congealed and distributed.
Deinde cum dicit: ex dictis igitur manifestum est etc., concludit principale propositum. Et dicit manifestum esse ex dictis, quod non est vacuum aliquod spatium separatum; neque simpliciter est extra corpus existens; neque existens in raro secundum aliqua foramina vacua; neque etiam existens est in potentia in corpore raro, secundum illos qui non ponebant vacuum quod est in corporibus separatum a pleno. Et sic nullo modo est vacuum, nisi aliquis penitus velit vocare vacuum materiam, quae quodammodo est causa gravitatis et levitatis, et sic est causa motus secundum locum. Densum enim et rarum sunt causa motus secundum contrarietatem gravis et levis; sed secundum contrarietatem duri et mollis, sunt causa passibile et impassibile: nam molle est id quod facile patitur divisionem, durum autem e contra, ut dictum est. Sed hoc non pertinet ad loci mutationem, sed magis ad alterationem. 557. Then [389] he concludes his chief proposition. And he says it is clear from the foregoing that there is no separate empty space: it is not anything existing absolutely outside a body; or in a rarefied thing after the manner of empty holes; or in potency in a rarefied body, according to those who did not posit a void that exists in bodies as something separated from the fullness of the body. Consequently, in no way is there a void, unless someone simply wants to call matter the void, since it is somehow the cause of heaviness and lightness, and consequently the cause of motion in respect of place. For density and rarity are causes of motion according to the contrariety of heavy and light; but in regard to the contrariety of hard and soft, passible and non-passible are the causes: for the soft is that which easily suffers division and the hard contrariwise, as was said. However, this does not pertain to local motion but rather to [the motion called] “alteration.”
Et sic concludit determinatum esse de vacuo, quomodo sit, et quomodo non sit. And so he concludes that it has been determined in what way the void exists and in what way it does not.

Lecture 15
Does time exist, and is there the same “now” in the whole of time?
Lectio 15
Chapter 10
Ἐχόμενον δὲ τῶν εἰρημένων ἐστὶν ἐπελθεῖν περὶ χρόνου· πρῶτον δὲ καλῶς ἔχει διαπορῆσαι περὶ αὐτοῦ καὶ διὰ τῶν ἐξωτερικῶν λόγων, πότερον τῶν ὄντων ἐστὶν ἢ τῶν μὴ ὄντων, εἶτα τίς ἡ φύσις αὐτοῦ. Next for discussion after the subjects mentioned is Time. The best plan will be to begin by working out the difficulties connected with it, making use of the current arguments. First, does it belong to the class of things that exist or to that of things that do not exist? Then secondly, what is its nature?
ὅτι μὲν οὖν ἢ ὅλως οὐκ ἔστιν ἢ μόλις καὶ ἀμυδρῶς, ἐκ τῶνδέ τις ἂν ὑποπτεύσειεν. τὸ μὲν γὰρ αὐτοῦ γέγονε καὶ οὐκ ἔστιν, τὸ δὲ μέλλει καὶ οὔπω ἔστιν. (218a.) ἐκ δὲ τούτων καὶ ὁ ἄπειρος καὶ ὁ ἀεὶ λαμβανόμενος χρόνος σύγκειται. τὸ δ' ἐκ μὴ ὄντων συγκείμενον ἀδύνατον ἂν εἶναι δόξειε μετέχειν οὐσίας. To start, then: the following considerations would make one suspect that it either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and is not yet. Yet time—both infinite time and any time you like to take—is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality.
πρὸς δὲ τούτοις παντὸς μεριστοῦ, ἄνπερ ᾖ, ἀνάγκη, ὅτε ἔστιν, ἤτοι πάντα τὰ μέρη εἶναι ἢ ἔνια· τοῦ δὲ χρόνου τὰ μὲν γέγονε τὰ δὲ μέλλει, ἔστι δ' οὐδέν, ὄντος μεριστοῦ. τὸ δὲ νῦν οὐ μέρος· μετρεῖ τε γὰρ τὸ μέρος, καὶ συγκεῖσθαι δεῖ τὸ ὅλον ἐκ τῶν μερῶν· ὁ δὲ χρόνος οὐ δοκεῖ συγκεῖσθαι ἐκ τῶν νῦν. Further, if a divisible thing is to exist, it is necessary that, when it exists, all or some of its parts must exist. But of time some parts have been, while others have to be, and no part of it is though it is divisible. For what is 'now' is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of 'nows'.
ἔτι δὲ τὸ νῦν, ὃ φαίνεται διορίζειν τὸ παρελθὸν καὶ τὸ μέλλον, πότερον ἓν καὶ ταὐτὸν ἀεὶ διαμένει ἢ ἄλλο καὶ ἄλλο, οὐ ῥᾴδιον ἰδεῖν. Again, the 'now' which seems to bound the past and the future—does it always remain one and the same or is it always other and other? It is hard to say.
εἰ μὲν γὰρ αἰεὶ ἕτερον καὶ ἕτερον, μηδὲν δ' ἐστὶ τῶν ἐν τῷ χρόνῳ ἄλλο καὶ ἄλλο μέρος ἅμα (ὃ μὴ περιέχει, τὸ δὲ περιέχεται, ὥσπερ ὁ ἐλάττων χρόνος ὑπὸ τοῦ πλείονος), τὸ δὲ νῦν μὴ ὂν πρότερον δὲ ὂν ἀνάγκη ἐφθάρθαι ποτέ, καὶ τὰ νῦν ἅμα μὲν ἀλλήλοις οὐκ ἔσται, ἐφθάρθαι δὲ ἀνάγκη ἀεὶ τὸ πρότερον. ἐν αὑτῷ μὲν οὖν ἐφθάρθαι οὐχ οἷόν τε διὰ τὸ εἶναι τότε, ἐν ἄλλῳ δὲ νῦν ἐφθάρθαι τὸ πρότερον νῦν οὐκ ἐνδέχεται. ἔστω γὰρ ἀδύνατον ἐχόμενα εἶναι ἀλλήλων τὰ νῦν, ὥσπερ στιγμὴν στιγμῆς. εἴπερ οὖν ἐν τῷ ἐφεξῆς οὐκ ἔφθαρται ἀλλ' ἐν ἄλλῳ, ἐν τοῖς μεταξὺ [τοῖς] νῦν ἀπείροις οὖσιν ἅμα ἂν εἴη· τοῦτο δὲ ἀδύνατον. (1) If it is always different and different, and if none of the parts in time which are other and other are simultaneous (unless the one contains and the other is contained, as the shorter time is by the longer), and if the 'now' which is not, but formerly was, must have ceased-to-be at some time, the 'nows' too cannot be simultaneous with one another, but the prior 'now' must always have ceased-to-be. But the prior 'now' cannot have ceased-to-be in itself (since it then existed); yet it cannot have ceased-to-be in another 'now'. For we may lay it down that one 'now' cannot be next to another, any more than point to point. If then it did not cease-to-be in the next 'now' but in another, it would exist simultaneously with the innumerable 'nows' between the two—which is impossible.
ἀλλὰ μὴν οὐδ' αἰεὶ τὸ αὐτὸ διαμένειν δυνατόν· οὐδενὸς γὰρ διαιρετοῦ πεπερασμένου ἓν πέρας ἔστιν, οὔτε ἂν ἐφ' ἓν ᾖ συνεχὲς οὔτε ἂν ἐπὶ πλείω· τὸ δὲ νῦν πέρας ἐστίν, καὶ χρόνον ἔστι λαβεῖν πεπερασμένον. Yes, but (2) neither is it possible for the 'now' to remain always the same. No determinate divisible thing has a single termination, whether it is continuously extended in one or in more than one dimension: but the 'now' is a termination, and it is possible to cut off a determinate time.
ἔτι εἰ τὸ ἅμα εἶναι κατὰ χρόνον καὶ μήτε πρότερον μήτε ὕστερον τὸ ἐν τῷ αὐτῷ εἶναι καὶ ἑνὶ [τῷ] νῦν ἐστιν, εἰ τά τε πρότερον καὶ τὰ ὕστερον ἐν τῷ νῦν τῳδί ἐστιν, ἅμα ἂν εἴη τὰ ἔτος γενόμενα μυριοστὸν τοῖς γε νομένοις τήμερον, καὶ οὔτε πρότερον οὔτε ὕστερον οὐδὲν ἄλλο ἄλλου. περὶ μὲν οὖν τῶν ὑπαρχόντων αὐτῷ τοσαῦτ' ἔστω διη πορημένα· Further, if coincidence in time (i.e. being neither prior nor posterior) means to be 'in one and the same "now"', then, if both what is before and what is after are in this same 'now', things which happened ten thousand years ago would be simultaneous with what has happened today, and nothing would be before or after anything else. This may serve as a statement of the difficulties about the attributes of time.
Postquam determinavit de loco et vacuo, nunc determinat de tempore. Et primo dicit de quo est intentio, et quo ordine procedendum sit; secundo prosequitur propositum, ibi: quod quidem igitur et cetera. 558. Having arrived at conclusions concerning Place and the Void, the Philosopher now concluded concerning Time. First he tells what his intention is and the order he will follow; Secondly, he carries out his proposal, at no. 559.
Dicit ergo primo quod consequens est ad praedicta, aggredi de tempore; in quo designat difficultatem considerationis. Et sicut de praemissis, ita et de tempore primo oportet opponendo procedere per rationes extraneas, idest ab aliis positas vel sophisticas: utrum scilicet sit tempus vel non; et si est, quae est natura eius. He says therefore first [390] that our plan now calls for us to “attack” time, by which he signifies how difficult the subject is. And as in previous discussions, so in the case of time one must begin by presenting extraneous reasons, i.e., the opinions of others, as well as sophistical arguments, dealing with the question of whether time exists or not and, if it does, what is its nature.
Deinde cum dicit: quod quidem igitur omnino non sit etc., prosequitur de tempore: et primo opponendo; secundo determinando veritatem, ibi: accipiendum autem et cetera. Then [391] he begins the discussion of time: First by arguing against [existence of time]; Secondly, by presenting the truth, at no. 571 (L.17).
Circa primum duo facit: primo opponendo inquirit an tempus sit; secundo quid sit, ibi: quid autem sit tempus et cetera. In regard to the first he does two things: First he inquires whether time exists, arguing against it; Secondly, what it is, at no. 565 (L.16).
Circa primum duo facit: primo ponit duas rationes ad ostendendum tempus non esse; secundo inquirit de nunc, utrum sit unum nunc in toto tempore vel plura, ibi: amplius autem ipsum nunc et cetera. As to the first he does two things: First he gives two reasons which show that time does not exist; Secondly, he inquires about the “now”: asking whether there is one “now” in the whole of time or several, at no. 561.
Dicit ergo primo quod ex his duabus rationibus potest aliquis concipere, quod tempus vel omnino non sit, vel sit aliquid quod vix et obscure percipi possit. Prima ergo ratio talis est. Omne compositum ex his quae non sunt, impossibile est esse, vel habere aliquam substantiam. Sed tempus componitur ex his quae non sunt; quia temporis est aliquid praeteritum, et iam non est, aliud est futurum, et nondum est, et ex his duobus componitur totum tempus, infinitum et perpetuum positum. Ergo impossibile est tempus aliquid esse. 559. He says then [391] that two reasons could lead us to suppose either that time does not exist at all or that it is something that can scarcely and only in an obscure way be conceived. Here is the first reason: anything that is composed of things which do not exist cannot have any existence or any substance; but time is composed of what does not exist—for part of time is the past which no longer exists, and the rest is the future, which does not yet exist (and these two things comprise the whole of time considered as infinite and everlasting). Therefore, it is impossible for time to be anything.
Secundam rationem ponit ibi: adhuc autem omnis etc.: quae talis est. Cuiuslibet divisibilis existentis necesse est esse, dum est, aliquam partem eius, aut aliquas. Sed tempus non est huiusmodi; quia quaedam partes temporis sunt iam praeteritae, aliae vero sunt futurae, et nihil temporis quod sit divisibile est in actu. Ipsum vero nunc, quod est in actu, non est pars temporis: quia pars est quae mensurat totum, ut binarius senarium; vel saltem ex qua componitur totum, sicut quaternarius est pars senarii, non mensurans ipsum, sed quia ex ipso et binario componitur senarius; tempus autem non componitur ex ipsis nunc, ut infra probabitur. Tempus igitur non est aliquid. 560. The second reason [392] is as follows: As long as any divisible thing is existing there must exist some part of it or a number of parts. But time does not meet these requirements—for some parts of time are already past and others are in the future, so that no divisible part of time is actually existing. And the “now” which is actual is not a part of time: for a part is either a measure of a whole, as two is the measure of six, or at least it is a component of the whole, as four is a part of six (although not its measure) since from it and two, six is composed. Time however does not have “nows” as its parts, as will be proved later (Book VI). Therefore, time is not anything.
Deinde cum dicit: amplius autem ipsum nunc etc., inquirit utrum sit idem nunc in toto tempore. Et circa hoc tria facit: primo movet quaestionem; secundo obiicit ad unam partem, ibi: si quidem enim nunc etc.; tertio ad alteram, ibi: at vero neque nunc et cetera. 561. Then [393] he inquires whether there be the same “now” through the whole of time. About this he does three things: First, he raises the question; Secondly, he objects to one side of the question, at no. 562; Thirdly, he objects to the opposite side, at no. 563.
Dicit ergo primo quod non est facile scire, utrum nunc, quod videtur distinguere inter praeteritum et futurum, semper maneat idem in toto tempore, an sit aliud et aliud. He says therefore first that it is not easy to be certain whether the “now” which is seen to distinguish the past from the future always remains identical with itself throughout the whole of time or whether it is other and other.
Deinde cum dicit: si quidem enim nunc etc., ostendit quod non sit aliud et aliud nunc, tali ratione. Duae partes temporis quae sunt aliae ab invicem, non possunt simul esse, nisi una contineat aliam, sicut maius tempus continet minus, ut annus mensem, et mensis diem (simul enim est et dies et mensis, et mensis et annus). Sed unum nunc, cum sit indivisibile, non continet alterum: si ergo est accipere in tempore duo nunc, necesse est quod illud nunc quod prius fuit et modo non est, aliquando corrumpatur, et quod nunquam duo nunc sint simul. Omne autem corruptum necesse est in aliquo nunc corrumpi. Non autem potest dici quod prius nunc sit corruptum in ipso nunc priori, quia tunc erat ipsum nunc, et nihil corrumpitur dum est. Similiter etiam non potest dici, quod prius nunc corrumpatur in posteriori: quia impossibile est sic se habere duo nunc ad invicem, quod sint habita, idest immediate se consequentia, sicut etiam impossibile est de duobus punctis. Et hoc nunc supponatur, quia in sexto probabitur. Sic igitur inter quaelibet duo nunc sunt infinita nunc. Si ergo prius nunc corrumpatur in aliquo posteriori nunc, sequitur quod illud nunc quod est ante, simul sit cum omnibus nunc intermediis; quod est impossibile, ut dictum est. Impossibile est igitur esse aliud et aliud nunc. 562. Then [394] he gives a reason to show that the “now” is not other and other. Two parts of time which are not the same cannot be existing together unless one contains the other, as a greater period of time contains a smaller, e.g., as a year contains the month and the month the day (for the day and the month and the year exist together). But one “now,” since it is indivisible, does not contain another. If, therefore, we are to accept two “now’s” in time, then that “now” which existed before the present one and no longer exists, ceased to be sometime, and so two “now’s” are never together. However, anything that ceased to be, did so in some “now.” But it cannot be that the prior “now” ceased to be in that prior “now,” because the prior “now” was existing then, and nothing ceases to be while it is. Likewise, it cannot be said that the prior “now” ceases to be in a later one: for it is impossible to have two “now’s” together as “had,” i.e., so as to follow immediately one upon the other, just as the same thing is impossible in the case of two points. (This is supposed now, but will be proved in Book VI). Thus, between any two “now’s” there are an infinity of “nows.” If, therefore, that prior “now” ceases to be in some later “now,” it follows that the prior “now” was existing along with all the intermediate “now’s”—which is impossible, as we have said. It is impossible, therefore, that the “now” be other and other.
Deinde cum dicit: at vero neque etc., ostendit quod non possit esse unum et idem nunc, duabus rationibus. Quarum prima talis est. Nullius divisibilis finiti potest esse unus terminus tantum; neque si sit continuum secundum unam dimensionem tantum, ut linea; neque si secundum plures, ut superficies et corpus. Nam unius lineae finitae termini sunt duo puncta, et superficiei plures lineae, et corporis plures superficies. Sed ipsum nunc est terminus temporis. Cum igitur sit accipere aliquod tempus finitum, necesse est ponere plura nunc. 563. Then [395] he gives two reasons to show that there cannot be just one “now.” The first is that no finite divisible thing can have just one boundary; whether it be a divisible of one dimension, as a line; or of more than one dimension, as a plane or a solid. For the boundaries of one finite line are two points and of a surface the boundaries are several lines, and of a body several planes. But the “now” is a boundary of time. Since therefore it is possible to conceive of a finite time there must be more than one “now.”
Secundam rationem ponit ibi: amplius si simul esse etc.: quae talis est. Illa dicuntur esse simul secundum tempus, et nec prius nec posterius, quae sunt in eodem nunc: si igitur est idem nunc permanens in toto tempore, sequitur quod illa quae fuerunt ante mille annos, sint simul cum his quae sunt hodie. 564. He gives a second reason [396].Those things are said to be together in time, and neither previously nor later, which are in the same “now.” If therefore it is the same “now” that persevere throughout time, it follows that things which existed a thousand years ago are together with things that exist today.
Ultimo autem epilogando concludit, tot opposita esse de ipsis nunc, quae sunt in tempore. Summarizing, he concludes that these are the conflicting opinions about the “now’s” which exist in time.

Lecture 16
Dialectical inquiry into what time is, and how related to motion
Lectio 16
Chapter 10 cont.
τί δ' ἐστὶν ὁ χρόνος καὶ τίς αὐτοῦ ἡ φύσις, ὁμοίως ἔκ τε τῶν παραδεδομένων ἄδηλόν ἐστιν, καὶ περὶ ὧν τυγχάνομεν διεληλυθότες πρότερον. οἱ μὲν γὰρ τὴν τοῦ ὅλου (218b.) κίνησιν εἶναί φασιν, οἱ δὲ τὴν σφαῖραν αὐτήν. As to what time is or what is its nature, the traditional accounts give us as little light as the preliminary problems which we have worked through. Some assert that it is (1) the movement of the whole, others that it is (2) the sphere itself.
καίτοι τῆς περιφορᾶς καὶ τὸ μέρος χρόνος τίς ἐστι, περιφορὰ δέ γε οὔ· μέρος γὰρ περιφορᾶς τὸ ληφθέν, ἀλλ' οὐ περιφορά. (1) Yet part, too, of the revolution is a time, but it certainly is not a revolution: for what is taken is part of a revolution, not a revolution.
ἔτι δ' εἰ πλείους ἦσαν οἱ οὐρανοί, ὁμοίως ἂν ἦν ὁ χρόνος ἡ ὁτουοῦν αὐτῶν κίνησις, ὥστε πολλοὶ χρόνοι ἅμα. Besides, if there were more heavens than one, the movement of any of them equally would be time, so that there would be many times at the same time.
ἡ δὲ τοῦ ὅλου σφαῖρα ἔδοξε μὲν τοῖς εἰποῦσιν εἶναι ὁ χρόνος, ὅτι ἔν τε τῷ χρόνῳ πάντα ἐστὶν καὶ ἐν τῇ τοῦ ὅλου σφαίρᾳ· ἔστιν δ' εὐηθικώτερον τὸ εἰρημένον ἢ ὥστε περὶ αὐτοῦ τὰ ἀδύνατα ἐπισκοπεῖν. (2) Those who said that time is the sphere of the whole thought so, no doubt, on the ground that all things are in time and all things are in the sphere of the whole. The view is too naive for it to be worth while to consider the impossibilities implied in it.
ἐπεὶ δὲ δοκεῖ μάλιστα κίνησις εἶναι καὶ μεταβολή τις ὁ χρόνος, τοῦτ' ἂν εἴη σκεπτέον. ἡ μὲν οὖν ἑκάστου μεταβολὴ καὶ κίνησις ἐν αὐτῷ τῷ μεταβάλλοντι μόνον ἐστίν, ἢ οὗ ἂν τύχῃ ὂν αὐτὸ τὸ κινούμενον καὶ μεταβάλλον· ὁ δὲ χρόνος ὁμοίως καὶ πανταχοῦ καὶ παρὰ πᾶσιν. But as time is most usually supposed to be (3) motion and a kind of change, we must consider this view. Now (a) the change or movement of each thing is only in the thing which changes or where the thing itself which moves or changes may chance to be. But time is present equally everywhere and with all things.
ἔτι δὲ μεταβολὴ μέν ἐστι θάττων καὶ βραδυτέρα, χρόνος δ' οὐκ ἔστιν· τὸ γὰρ βραδὺ καὶ ταχὺ χρόνῳ ὥρισται, ταχὺ μὲν τὸ ἐν ὀλίγῳ πολὺ κινούμενον, βραδὺ δὲ τὸ ἐν πολλῷ ὀλίγον· ὁ δὲ χρόνος οὐχ ὥρισται χρόνῳ, οὔτε τῷ ποσός τις εἶναι οὔτε τῷ ποιός. ὅτι μὲν τοίνυν οὐκ ἔστιν κίνησις, φανερόν· μηδὲν δὲ διαφερέτω λέγειν ἡμῖν ἐν τῷ παρόντι κίνησιν ἢ μεταβολήν. Again, (b) change is always faster or slower, whereas time is not: for 'fast' and 'slow' are defined by time—'fast' is what moves much in a short time, 'slow' what moves little in a long time; but time is not defined by time, by being either a certain amount or a certain kind of it. Clearly then it is not movement. (We need not distinguish at present between 'movement' and 'change'.)
Chapter 11
Ἀλλὰ μὴν οὐδ' ἄνευ γε μεταβολῆς· ὅταν γὰρ μηδὲν αὐτοὶ μεταβάλλωμεν τὴν διάνοιαν ἢ λάθωμεν μεταβάλλοντες, οὐ δοκεῖ ἡμῖν γεγονέναι χρόνος, καθάπερ οὐδὲ τοῖς ἐν Σαρδοῖ μυθολογουμένοις καθεύδειν παρὰ τοῖς ἥρωσιν, ὅταν ἐγερθῶσι· συνάπτουσι γὰρ τῷ πρότερον νῦν τὸ ὕστερον νῦν καὶ ἓν ποιοῦσιν, ἐξαιροῦντες διὰ τὴν ἀναισθησίαν τὸ μεταξύ. ὥσπερ οὖν εἰ μὴ ἦν ἕτερον τὸ νῦν ἀλλὰ ταὐτὸ καὶ ἕν, οὐκ ἂν ἦν χρόνος, οὕτως καὶ ἐπεὶ λανθάνει ἕτερον ὄν, οὐ δοκεῖ εἶναι τὸ μεταξὺ χρόνος. εἰ δὴ τὸ μὴ οἴεσθαι εἶναι χρόνον τότε συμβαίνει ἡμῖν, ὅταν μὴ ὁρίσωμεν μηδεμίαν μεταβολήν, ἀλλ' ἐν ἑνὶ καὶ ἀδιαιρέτῳ φαίνηται ἡ ψυχὴ μένειν, ὅταν δ' αἰσθώμεθα καὶ ὁρίσωμεν, τότε φαμὲν γεγονέναι χρόνον, φανερὸν ὅτι οὐκ ἔστιν ἄνευ κινήσεως καὶ μεταβολῆς (219a.) χρόνος. ὅτι μὲν οὖν οὔτε κίνησις οὔτ' ἄνευ κινήσεως ὁ χρόνος ἐστί, φανερόν· But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed, any more than those who are fabled to sleep among the heroes in Sardinia do when they are awakened; for they connect the earlier 'now' with the later and make them one, cutting out the interval because of their failure to notice it. So, just as, if the 'now' were not different but one and the same, there would not have been time, so too when its difference escapes our notice the interval does not seem to be time. If, then, the non-realization of the existence of time happens to us when we do not distinguish any change, but the soul seems to stay in one indivisible state, and when we perceive and distinguish we say time has elapsed, evidently time is not independent of movement and change. It is evident, then, that time is neither movement nor independent of movement.
Postquam inquisivit an tempus sit, hic disputative inquirit quid sit. Et primo improbat positiones aliorum; secundo inquirit quomodo se habeat tempus ad motum, qui tempori propinquissimus videtur, ibi: quoniam autem videtur maxime et cetera. 565. After inquiring whether time exists, the Philosopher now inquires dialectically what it is. First he disproves the opinions of others; Secondly, he inquires how time is related to motion, which seems to be something most akin to time, at no. 568.
Circa primum duo facit: primo ponit opiniones aliorum de tempore; secundo improbat eas, ibi: quamvis circulationis et cetera. About the first he does two things: First he gives various opinions of others about time; Secondly, he disproves them, at no. 566.
Dicit ergo primo quod quid sit tempus, et quid sit natura eius, non potest esse manifestum ex his quae tradita erant de tempore ab antiquioribus, neque per aliqua quibus attingi possit quid ipsi circa hoc determinaverint. Quidam enim dixerunt quod tempus est motus caeli; quidam vero quod est ipsa sphaera caelestis. He says therefore first that what time is and what is the nature of time cannot be gathered from what is handed down from the earlier philosophers nor from any piecing together of what they concluded about it. For some said that time is a motion of the heavens; others that it is a heavenly sphere itself.
Deinde cum dicit: quamvis circulationis etc., improbat positas opiniones: et primo primam; secundo secundam, ibi: totius autem sphaera et cetera. 566. Then [398] he disproves their opinions, first of all, the first; then the second, at no. 567.
Circa primum ponit duas rationes: quarum prima talis est. Si circulatio est tempus, oportet quod pars circulationis sit circulatio, quia pars temporis tempus est: sed pars circulationis non est circulatio: ergo tempus non est circulatio. In regard to the first opinion he gives two counter-arguments, of which the first is: If a circular revolution in time then part of that revolution is a circular revolution, because a part of time is time. But part of a circular revolution is not a circular revolution. Therefore time is not a circular revolution.
Secundam rationem ponit ibi: amplius autem etc., quae talis est. Motus multiplicatur secundum multitudinem mobilium: si ergo plures essent caeli, plures essent circulationes eorum; et sic, si circulatio sit tempus, sequeretur quod essent multa tempora simul: quod est impossibile. Non enim est accipere duas partes temporis simul, nisi una contineat aliam, ut supra dictum est. Movebantur tamen hi ad ponendum tempus esse circulationem, quia videbant tempora circulo quodam reiterari. Then [399] he gives a second argument: The number of motions corresponds to the number of mobiles; if therefore there are many heavens, there are many circular revolutions. And thus if a circular revolution is time, there are many times together—which is impossible. For no two parts of time are together unless one contains the other, as we have said. (Those who posited time as a circular revolution were led to do so because they observed that times occur over and over in a kind of cycle.
Deinde cum dicit: totius autem sphaera etc., excludit secundam opinionem. Et dicit quod quibusdam visum est quod sphaera caeli esset tempus, propter hoc quod omnia sunt in tempore, et etiam omnia sunt in sphaera totius, quia caelum continet omnia: unde concludere volebant, quod sphaera caeli esset tempus. In qua quidem ratione duplex erat defectus: primo quidem quia non univoce dicitur esse aliquid in tempore et in loco; secundo quia argumentabantur in secunda figura ex duabus affirmativis. Et ideo dicit quod ista positio est magis stulta, quam quod oporteat considerare impossibilia quae ad ipsam consequuntur. Manifestum est enim quod omnes partes sphaerae sunt simul, non autem temporis. 567. Then [400] he rejects the second opinion. And he says that some thought the sphere of the heavens in time, because all things are in time and all things are also in the sphere of the whole, because the heavens contain all things. Hence they wished to conclude that the sphere of the heavens is time. But there were two things wrong in their reasoning: first, because something is not said univocally as being in time and in place; secondly, because they were using two affirmative premises in a Second Figure syllogism. Therefore he says that their position is too foolish to consider the impossibilities that follow upon it. For it is clear that all the parts of the sphere exist simultaneously, whereas the parts of time do not.
Deinde cum dicit: quoniam autem videtur etc., inquirit quomodo se habeat tempus ad motum. Et primo ostendit quod tempus non est motus; secundo quod non est sine motu, ibi: at vero neque sine motu et cetera. 568. Then [401] he inquires how time is related to motion. First he shows that time is not motion; Secondly that time does not exist independently of motion, at no. 570.
Circa primum ponit duas rationes ad ostendendum quod tempus non sit motus aut mutatio, quod posset maxime videri. Quia omnis mutatio et motus vere est solum in ipso transmutato, vel etiam in loco ubi est transmutatum et transmutans. Quorum primum dicitur propter motum in substantia et quantitate et qualitate; secundum autem dicitur propter motum in ubi, qui dicitur motus in loco. Sed tempus est ubique et apud omnia: ergo tempus non est motus. In regard to the first he gives two reasons to show that time is not a motion or a change (for it certainly seems to be such). Here is his reason: Every change and motion is certainly only in the thing being changed or in the place where the changer and changed are. The first of these is mentioned because of motion in substance and quantity and quality; the second because of motion in the predicament “where,” called motion in place.” But time is everywhere and exists among all things. Therefore time is not a motion.
Secundam rationem ponit ibi: amplius autem mutatio etc.: quae talis est. Omnis mutatio et motus est velox aut tardus: sed tempus non est huiusmodi: ergo tempus non est motus vel mutatio. Mediam sic probat. Tardum et velox determinantur ex tempore: quia velox dicitur quod movetur per multum spatium in pauco tempore; tardum autem quod e converso per paucum spatium in multo tempore. Sed tempus non determinatur tempore, neque secundum suam quantitatem, neque secundum suam qualitatem; quia idem non est mensura sui ipsius. Ergo tempus non est neque velox neque tardum. Et quia proposuerat quod mutatio est velox aut tarda, non facta mentione de motu, subiungit quod quantum ad praesens, non differt dicere motum aut mutationem: in quinto enim ostendetur eorum differentia. 569. He gives the second reason [402]: Every change and motion is either slow or fast; but time is not either. Therefore time is neither a motion nor a change. He explains the minor premise thus: Slow and fast are determined by time—because that is fast which is moved a great distance in a short time and that is slow which is moved a short distance in much time. But time is not determined by either according to its quantity or its quality, because nothing is its own measure. Therefore, time is neither slow nor fast. And since he had proposed that change is fast or slow, without mention of motion, he adds that for the present it does not matter whether one says “motion” or “change.” Their difference will be shown in Book V.
Deinde cum dicit: at vero, neque sine motu etc., ostendit quod tempus non est sine motu: quia quando homines non mutantur secundum suam apprehensionem, aut, si mutantur, tamen latet eos, tunc non videtur eis quod pertranseat aliquod tempus. Sicut patet in iis qui in Sardo, quae est civitas Asiae, dicuntur fabulose dormire apud heroas, idest apud deos. Animas enim bonorum et magnorum heroas vocabant, et quasi deos colebant, ut Herculis et Bacchi et similium. Per incantationes enim aliquas, aliqui insensibiles reddebantur, quos dicebant dormire apud heroas; quia excitati, quaedam mirabilia se vidisse dicebant, et futura quaedam praenunciabant. Tales autem ad se redeuntes, non percipiebant tempus quod praeterierat dum ipsi sic absorpti erant; quia illud instans primum, in quo dormire coeperant, copulabant posteriori nunc in quo excitabantur, ac si essent unum; medium enim tempus non percipiebant. Sicut igitur, si non esset aliud et aliud nunc, sed idem et unum, non esset tempus medium; sic et quando latet diversitas duorum nunc, non videtur tempus esse medium. Si ergo tunc accidit non opinari tempus, cum non percipimus aliquam mutationem, sed homini videtur quod sit in uno indivisibili nunc; tunc autem percipimus fieri tempus, quando sentimus et determinamus, id est numeramus, motum aut mutationem; manifeste sequitur quod tempus non sit sine motu, neque sine mutatione. 570. Then [403] he shows that although time is not motion, it is not independent of motion: for when men are not changing according to what they apprehend, they are changing without being aware of it, then it does not seem to them that time is passing. This is clear in the fable about the city in Asia called Sardo. In Sardo certain people were said to sleep among the Heroes, i.e., among the gods. For they called the souls of the good and the great “Heroes,” and worshipped them as gods, as in the case of Hercules and Bacchus and the like. Certain ones were rendered insensible by means of incantations and said to sleep among the gods, because then they awoke they claimed to have seen marvelous things and foretold future events. These persons, returning to themselves, were not aware of the time which elapsed while they were thus absorbed; because that first instant in which they began to sleep they joined to the instant in which they awoke, as if it were one instant—but the time that elapsed escaped them. Therefore just as there would be no intervening time between “now’s,” if the “now” of time were always the same and not other and other, so also when two “now’s” are fused in our apprehension, the elapsed time is not apprehended, and there seems to have been no intervening time. If, then, we are apt to think that no time has elapsed when we do not perceive any changes, and that we are in one and the same indivisible “now,” but we then perceive time to be elapsing when we sense and determine, i.e., motion and change, it clearly follows that time is not independent of motion and change.
Ultimo ergo concludit quod tempus non sit motus, neque sit sine motu. In summary he concludes that time is not motion, nor is it without motion.

Lecture 17
The definition of time, given and explained
Lectio 17
Chapter 11 cont.
ληπτέον δέ, ἐπεὶ ζητοῦμεν τί ἐστιν ὁ χρόνος, ἐντεῦθεν ἀρχομένοις, τί τῆς κινήσεώς ἐστιν. ἅμα γὰρ κινήσεως αἰσθανόμεθα καὶ χρόνου· καὶ γὰρ ἐὰν ᾖ σκότος καὶ μηδὲν διὰ τοῦ σώματος πάσχωμεν, κίνησις δέ τις ἐν τῇ ψυχῇ ἐνῇ, εὐθὺς ἅμα δοκεῖ τις γεγονέναι καὶ χρόνος. ἀλλὰ μὴν καὶ ὅταν γε χρόνος δοκῇ γεγονέναι τις, ἅμα καὶ κίνησίς τις δοκεῖ γεγονέναι. ὥστε ἤτοι κίνησις ἢ τῆς κινήσεώς τί ἐστιν ὁ χρόνος. ἐπεὶ οὖν οὐ κίνησις, ἀνάγκη τῆς κινήσεώς τι εἶναι αὐτόν. We must take this as our starting-point and try to discover—since we wish to know what time is—what exactly it has to do with movement. Now we perceive movement and time together: for even when it is dark and we are not being affected through the body, if any movement takes place in the mind we at once suppose that some time also has elapsed; and not only that but also, when some time is thought to have passed, some movement also along with it seems to have taken place. Hence time is either movement or something that belongs to movement. Since then it is not movement, it must be the other.
ἐπεὶ δὲ τὸ κινούμενον κινεῖται ἔκ τινος εἴς τι καὶ πᾶν μέγεθος συνεχές, ἀκολουθεῖ τῷ μεγέθει ἡ κίνησις· διὰ γὰρ τὸ τὸ μέγεθος εἶναι συνεχὲς καὶ ἡ κίνησίς ἐστιν συνεχής, διὰ δὲ τὴν κίνησιν ὁ χρόνος· ὅση γὰρ ἡ κίνησις, τοσοῦτος καὶ ὁ χρόνος αἰεὶ δοκεῖ γεγονέναι. But what is moved is moved from something to something, and all magnitude is continuous. Therefore the movement goes with the magnitude. Because the magnitude is continuous, the movement too must be continuous, and if the movement, then the time; for the time that has passed is always thought to be in proportion to the movement.
τὸ δὴ πρότερον καὶ ὕστερον ἐν τόπῳ πρῶτόν ἐστιν. ἐνταῦθα μὲν δὴ τῇ θέσει· ἐπεὶ δ' ἐν τῷ μεγέθει ἔστι τὸ πρότερον καὶ ὕστερον, ἀνάγκη καὶ ἐν κινήσει εἶναι τὸ πρότερον καὶ ὕστερον, ἀνάλογον τοῖς ἐκεῖ. ἀλλὰ μὴν καὶ ἐν χρόνῳ ἔστιν τὸ πρότερον καὶ ὕστερον διὰ τὸ ἀκολουθεῖν ἀεὶ θατέρῳ θάτερον αὐτῶν. The distinction of 'before' and 'after' holds primarily, then, in place; and there in virtue of relative position. Since then 'before' and 'after' hold in magnitude, they must hold also in movement, these corresponding to those. But also in time the distinction of 'before' and 'after' must hold, for time and movement always correspond with each other.
ἔστι δὲ τὸ πρότερον καὶ ὕστερον ἐν τῇ κινήσει ὃ μέν ποτε ὂν κίνησις [ἐστιν]· τὸ μέντοι εἶναι αὐτῷ ἕτερον καὶ οὐ κίνησις. The 'before' and 'after' in motion is identical in substratum with motion yet differs from it in definition, and is not identical with motion.
ἀλλὰ μὴν καὶ τὸν χρόνον γε γνωρίζομεν ὅταν ὁρίσωμεν τὴν κίνησιν, τῷ πρότερον καὶ ὕστερον ὁρίζοντες· καὶ τότε φαμὲν γεγονέναι χρόνον, ὅταν τοῦ προτέρου καὶ ὑστέρου ἐν τῇ κινήσει αἴσθησιν λάβωμεν. But we apprehend time only when we have marked motion, marking it by 'before' and 'after'; and it is only when we have perceived 'before' and 'after' in motion that we say that time has elapsed.
ὁρίζομεν δὲ τῷ ἄλλο καὶ ἄλλο ὑπολαβεῖν αὐτά, καὶ μεταξύ τι αὐτῶν ἕτερον· ὅταν γὰρ ἕτερα τὰ ἄκρα τοῦ μέσου νοήσωμεν, καὶ δύο εἴπῃ ἡ ψυχὴ τὰ νῦν, τὸ μὲν πρότερον τὸ δ' ὕστερον, τότε καὶ τοῦτό φαμεν εἶναι χρόνον· τὸ γὰρ ὁριζόμενον τῷ νῦν χρόνος εἶναι δοκεῖ· καὶ ὑποκείσθω. ὅταν μὲν οὖν ὡς ἓν τὸ νῦν αἰσθανώμεθα, καὶ μὴ ἤτοι ὡς πρότερον καὶ ὕστερον ἐν τῇ κινήσει ἢ ὡς τὸ αὐτὸ μὲν προτέρου δὲ καὶ ὑστέρου τινός, οὐ δοκεῖ χρόνος γεγονέναι οὐδείς, ὅτι οὐδὲ κίνησις. ὅταν δὲ τὸ πρότερον (219b.) καὶ ὕστερον, τότε λέγομεν χρόνον· τοῦτο γάρ ἐστιν ὁ χρόνος, ἀριθμὸς κινήσεως κατὰ τὸ πρότερον καὶ ὕστερον. οὐκ ἄρα κί νησις ὁ χρόνος ἀλλ' ᾗ ἀριθμὸν ἔχει ἡ κίνησις. Now we mark them by judging that A and B are different, and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the 'nows' are two, one before and one after, it is then that we say that there is time, and this that we say is time. For what is bounded by the 'now' is thought to be time—we may assume this. When, therefore, we perceive the 'now' one, and neither as before and after in a motion nor as an identity but in relation to a 'before' and an 'after', no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do perceive a 'before' and an 'after', then we say that there is time. For time is just this—number of motion in respect of 'before' and 'after'. Hence time is not movement, but only movement in so far as it admits of enumeration.
σημεῖον δέ· τὸ μὲν γὰρ πλεῖον καὶ ἔλαττον κρίνομεν ἀριθμῷ, κίνησιν δὲ πλείω καὶ ἐλάττω χρόνῳ· ἀριθμὸς ἄρα τις ὁ χρόνος. A proof of this: we discriminate the more or the less by number, but more or less movement by time. Time then is a kind of number.
ἐπεὶ δ' ἀριθμός ἐστι διχῶς (καὶ γὰρ τὸ ἀριθμούμενον καὶ τὸ ἀριθμητὸν ἀριθμὸν λέγομεν, καὶ ᾧ ἀριθμοῦμεν), ὁ δὴ χρόνος ἐστὶν τὸ ἀριθμούμενον καὶ οὐχ ᾧ ἀριθμοῦμεν. (Number, we must note, is used in two senses—both of what is counted or the countable and also of that with which we count. Time obviously is what is counted, not that with which we count: there are different kinds of thing.)
Postquam philosophus disputative inquisivit de tempore, hic incipit determinare veritatem. Et primo determinat veritatem de tempore; secundo movet quasdam dubitationes circa veritatem determinatam, et solvit eas, ibi: dignum autem et cetera. 571. After treating of time dialectically, the Philosopher here begins to determine the truth. First, he determines the truth concerning time; Secondly, he brings up and solves some objections concerning the truth determined, at no. 625 (L.23).
Circa primum duo facit: primo determinat de tempore secundum se; secundo per comparationem ad ea quae tempore mensurantur, ibi: quoniam autem est tempus et cetera. In regard to the first he does two things: First he determines concerning time absolutely. Secondly, in relation to things measured by time, at no. 600 (L.20).
Circa primum tria facit: primo manifestat quid sit tempus; secundo quid sit nunc temporis, ibi: et sicut motus semper etc.; tertio ex definitione motus assignata, assignat rationes eorum quae dicuntur de tempore, ibi: quod quidem igitur tempus et cetera. As to the first he does three things: First he makes clear what time is; Secondly, what the “now” of time is, at no. 582 (L.18); Thirdly, from the definition he gives of time, he explains the things said about time, at no. 593 (L.19).
Circa primum duo facit: primo ponit definitionem temporis; secundo manifestat eam, ibi: signum est autem et cetera. About the first he does two things: First he gives the definition of time; Secondly, he explains it, at no. 581.
Prima pars dividitur in tres, secundum tres particulas definitionis temporis quas investigat; secunda pars incipit ibi: quoniam autem quod movetur etc.; tertia ibi: determinamus autem et cetera. The first point is divided into three parts according to the three parts which he investigates of the definition; The second part begins at no. 575; The third part at no. 580.
Primo ergo investigat hanc particulam, quod tempus est aliquid motus. Unde dicit quod quia inquirimus quid sit tempus, hinc incipiendum est, ut accipiamus quid motus sit tempus. Et quod tempus sit aliquid motus, per hoc manifestum est, quod simul sentimus motum et tempus. Contingit enim quandoque quod percipimus fluxum temporis, quamvis nullum motum particularem sensibilem sentiamus; utpote si simus in tenebris, et sic visu non sentimus motum alicuius corporis exterioris. Et si nos non patiamur aliquam alterationem in corporibus nostris ab aliquo exteriori agente, nullum motum corporis sensibilis sentiemus: et tamen si fiat aliquis motus in anima nostra, puta secundum successionem cogitationum et imaginationum, subito videtur nobis quod fiat aliquod tempus. Et sic percipiendo quemcumque motum, percipimus tempus: et similiter e converso, cum percipimus tempus, simul percipimus motum. Unde cum non sit ipse motus, ut probatum est, relinquitur quod sit aliquid motus. 572. First [404] therefore he investigates this part: that time is “something of motion.” He says that since we are investigating what time is, we must begin by understanding what aspect of motion time is. That time is something of motion is manifested by the very fact that we sense motion and time together. For it happens that we perceive the flow of time even though we are not sensing any particular sensible motion; for example, if we are in the dark and do not see any external object moving. And if while we are in this situation, we are not undergoing any bodily changes brought about by an external agent, then we are not sensing any motion of a sensible body. Yet if there is a motion within our soul, such as a succession of thoughts and imaginings, suddenly it appears to us that some time is elapsing. Thus by perceiving any sort of motion we perceive time and, vice-versa, when we perceive time we are simultaneously perceiving a motion. Hence, although time is not a motion, as we have already shown, yet it is somehow connected with motion.
Habet autem dubitationem quod hic dicitur de perceptione temporis et motus. Si enim tempus consequatur aliquem motum sensibilem extra animam existentem, sequitur quod qui non sentit illum motum, non sentiat tempus; cuius contrarium hic dicitur. Si autem tempus consequatur motum animae, sequetur quod res non comparentur ad tempus nisi mediante anima; et sic tempus erit non res naturae, sed intentio animae, ad modum intentionis generis et speciei. Si autem consequatur universaliter omnem motum, sequetur quod quot sunt motus, tot sint tempora: quod est impossibile, quia duo tempora non sunt simul, ut supra habitum est. 573. What has been just said about the perceiving of time and of motion raises a difficulty. For if time follows upon some sensible motion outside the mind, it follows that whosoever does not sense that motion, does not sense time; whereas the opposite of that is said here. And if time depends upon some motion of the mind, it follows that things are not connected to time except through the medium of the mind: thus time will not be a thing of nature but a notion in the mind like the intention of genus and species. But if time follows upon any and every motion, then there are as many times as there are motions—which is impossible, for there cannot be two times together as we said above.
Ad huius igitur evidentiam sciendum est, quod est unus primus motus, qui est causa omnis alterius motus. Unde quaecumque sunt in esse transmutabili, habent hoc ex illo primo motu, qui est motus primi mobilis. Quicumque autem percipit quemcumque motum, sive in rebus sensibilibus existentem, sive in anima, percipit esse transmutabile, et per consequens percipit primum motum quem sequitur tempus. Unde quicumque percipit quemcumque motum, percipit tempus: licet tempus non consequatur nisi unum primum motum, a quo omnes alii causantur et mensurantur: et sic remanet tantum unum tempus. 574. In order to clear up this difficulty it must be remembered that there is one first motion which is the cause of every other motion. Hence whatever is in a transmutable state possesses that state on account of the first motion, which is the motion of the first mobile being. Whosoever, therefore, perceives any motion, whether it exists in sensible things or in the mind, is perceiving transmutable being and consequently is perceiving the first motion, which time follows. Thus anyone who perceives any motion whatsoever is perceiving time, although time follows upon just the one first motion by which all other motions are caused and measured. Consequently, there remains only one time.
Deinde cum dicit: quoniam autem quod movetur etc., investigat secundam particulam positam in definitione temporis. Supposito enim quod tempus sit aliquid motus, consequens scilicet ipsum, restat investigandum secundum quid tempus consequatur motum, quia secundum prius et posterius. Circa hoc ergo tria facit: primo ostendit quomodo in motu inveniatur prius et posterius; secundo quomodo prius et posterius se habeant ad motum, ibi: est autem prius et posterius etc.; tertio quod tempus sequitur motum secundum prius et posterius, ibi: at vero et tempus et cetera. 575. Then [405] he investigates the second particle placed in the definition of time. For supposing that time is something of motion, namely, that it follows upon motion, there still remains the task of investigating according to what does time follow upon motion; the answer being that it follows upon motion “according to before and after.” As to this then he does three things: First he shows how “before and after” are found in motion; Secondly, how they are related to motion, at no. 578; Thirdly, he shows that time follows motion according to “before and after,” at no. 579.
Circa primum duo facit: primo ostendit quod continuitas est in tempore ex motu et magnitudine; secundo quod etiam prius et posterius, ibi: prius autem et posterius et cetera. About the first he does two things: First he shows that the continuity of time is due to the continuity of motion and magnitude; Secondly, that the same is true of the “before and after” of time, at no.577.
Dicit ergo primo quod omne quod movetur, movetur ex quodam in quiddam. Sed inter alios motus, primus est motus localis, qui est a loco in locum secundum aliquam magnitudinem. Primum autem motum consequitur tempus; et ideo ad investigandum de tempore oportet accipere motum secundum locum. Quia ergo motus secundum locum, est secundum magnitudinem ex quodam in quiddam et omnis magnitudo est continua; oportet quod motus consequatur magnitudinem in continuitate, ut, quia magnitudo continua est, et motus continuus sit. Et per consequens etiam tempus continuum est: quia quantus est motus primus, tantum videtur fieri tempus. Non autem tempus mensuratur secundum quantitatem cuiuscumque motus, quia tardum movetur secundum paucum spatium in multo tempore, velox autem e converso; sed solum quantitatem primi motus sequitur tempus. 576. He says therefore first that everything that is being moved is being moved. from something to something. But of motions the first is local motion, which is from place to place along a magnitude. But it is the first motion that time follows upon, and therefore, to investigate time, one must take local motion. Since, then, motion according to place is motion according to a magnitude from one place to another, and since every magnitude is continuous, motion must follow magnitude in regard to its continuity, so that, just as magnitude is continuous, so also is motion. Consequently time also is continuous: for the quantity of the first motion and the quantity of time correspond. For time is not measured according to the quantity of just any motion, since something is being moved over a small distance In a large amount of time, and a fast object, vice-versa. Time however corresponds only to the quantity of the first motion.
Deinde cum dicit: prius autem et posterius etc., ostendit etiam, quod idem ordo consideratur in priori et posteriori: et dicit quod prius et posterius sunt prius in loco sive in magnitudine. Et hoc ideo, quia magnitudo est quantitas positionem habens: de ratione autem positionis est prius et posterius: unde ex ipsa positione, locus habet prius et posterius. Et quia in magnitudine est prius et posterius, necesse est quod in motu sit prius et posterius proportionaliter his quae sunt ibi, scilicet in magnitudine et in loco. Et per consequens etiam in tempore est prius et posterius; quia motus et tempus ita se habent, quod semper alterum eorum sequitur ad alterum. 577. Then [406] he shows that the same order prevails in respect to “before and after,” saying that “before and after” are first of all in a place or in a magnitude. This is so, because a magnitude is a quantity having position; position, however, implies “before and after.” Hence from its position place has “before and after.” And because there is “before and after” in magnitude, it follows that there is a “before and after” in motion corresponding to the things which are there, i.e., in magnitude and place. Consequently, there is a prior and subsequent also in time: for motion and time are so related that the one always follows the other.
Deinde cum dicit: est autem prius et posterius ipsorum etc., ostendit quomodo prius et posterius se habeant ad motum. Et dicit quod prius et posterius ipsorum, scilicet temporis et motus, quantum ad id quod est, motus est: tamen secundum rationem est alterum a motu, et non est motus. De ratione enim motus est, quod sit actus existentis in potentia: sed quod in motu sit prius et posterius, hoc contingit motui ex ordine partium magnitudinis. Sic igitur prius et posterius sunt idem subiecto cum motu, sed differunt ratione. Unde restat inquirendum, cum tempus sequatur motum, sicut supra ostensum est, utrum sequatur ipsum inquantum est motus, an inquantum habet prius et posterius. 578. Then [407] he shows how “before and after” are related to motion. And he says that the “before and after” of these, namely, of time and of motion is, as to what it is, motion; yet in conception, it is distinct from motion and not motion. For it is the notion of motion that it be the act of a being in potency; but that there be in motion a “before and after” occurs in it by reason of the order of the parts of the magnitude. Accordingly, “before and after” are the same as motion as to subject but they differ from it as to notion. Hence the task remains to inquire, since time follows motion, whether it follows upon it inasmuch as it is motion, or inasmuch as it has a “before and after.”
Deinde cum dicit: at vero et tempus cognoscimus etc., ostendit quod tempus sequatur motum ratione prioris et posterioris. Propter hoc enim ostensum est quod tempus sequitur motum, quia simul cognoscimus tempus et motum. Secundum illud ergo tempus sequitur motum, quo cognito in motu cognoscitur tempus: sed tunc cognoscimus tempus, cum distinguimus motum determinando prius et posterius; et tunc dicimus fieri tempus, quando accipimus sensum prioris et posterioris in motu. Relinquitur ergo quod tempus sequitur motum secundum prius et posterius. 579. Then [408] he shows that motion follows upon time by reason of “before and after.” For it has been shown that the reason why time follows motion is that we recognize both simultaneously. Therefore time follows motion according to that which, when it is perceived in motion, time is perceived. But it is then that we perceive time, when we distinguish a “before” and “after” in motion; and it is then that we say time is passing when we have a sense of the “before” and “after” in motion. Consequently time follows motion according to “before and after.”
Deinde cum dicit: determinamus autem etc., ostendit quid motus tempus sit, quia numerus motus: et hoc etiam ostendit eodem medio, scilicet per cognitionem temporis et motus. Manifestum est enim quod tunc esse tempus determinamus, cum accipimus in motu aliud et aliud, et accipimus aliquid medium inter ea. Cum enim intelligimus extrema diversa alicuius medii, et anima dicat illa esse duo nunc, hoc prius, illud posterius, quasi numerando prius et posterius in motu, tunc hoc dicimus esse tempus. Tempus enim determinari videtur ipso nunc. Et hoc supponatur ad praesens, quia postea erit magis manifestum. Quando igitur sentimus unum nunc, et non discernimus in motu prius et posterius; vel quando discernimus in motu prius et posterius, sed accipimus idem nunc ut finem prioris et principium posterioris; non videtur fieri tempus, quia neque est motus. Sed cum accipimus prius et posterius et numeramus ea, tunc dicimus fieri tempus. Et hoc ideo, quia tempus nihil aliud est quam numerus motus secundum prius et posterius: tempus enim percipimus, ut dictum est, cum numeramus prius et posterius in motu. Manifestum est ergo quod tempus non est motus, sed sequitur motum secundum quod numeratur. Unde est numerus motus. 580. Then [409] he shows what aspect of motion time is, and says that it is “the number of motion.” He explains this by using the same means as before, namely, our knowledge of time and motion. For it is clear that when we take in motion something different from something other and understand that there is something between them, then it is that we determine that time exists. For when we perceive the differing boundaries of something and the mind calls them two “now’s,” one being before and the other after, as though the mind were counting the “before’s” and “after’s” in a motion, that is what we call time. For time seems to be determined by the “now.” (This statement is taken for granted at present, but later it will be explained). When therefore we sense one “now” but do not discern a “before” and “after” of motion, or when we in discerning a “before” and “after” take the same “now” as the end of the prior and the beginning of the subsequent, no time seems to exist because no motion seemed to exist. But when we discern a “before” and “after” and count them, then we say that time is produced. This is so because time is nothing less than “the numbering of motion according to before and after”: for we perceive time, as was said, when we count the “before and after” of motion. it is clear there fore that time is not motion, but accompanies motions inasmuch as it is counted. Hence time is the number of motion.
Si quis autem obiiciat contra praedictam definitionem, quod prius et posterius tempore determinantur, et sic definitio est circularis, dicendum est quod prius et posterius ponuntur in definitione temporis, secundum quod causantur in motu ex magnitudine, et non secundum quod mensurantur ex tempore. Et ideo supra Aristoteles ostendit quod prius et posterius prius sunt in magnitudine quam in motu, et in motu quam in tempore, ut haec obiectio excludatur. But if someone objects against this definition and says that “before and after” are determined by time, and consequently, that the definition is circular, he should remember that “before and after” are placed in the definition of time inasmuch as they are caused in motion by magnitude, and not inasmuch as they are measured out of time. That is why Aristotle had previously shown that “before and after” are present in magnitude before they are so in motion, and they are in motion before they are in time, to exclude this objection.
Deinde cum dicit: signum est autem etc., manifestat praedictam definitionem dupliciter. Primo quidem quodam signo. Id enim quo aliquid iudicamus plus et minus, est numerus eius: sed motum iudicamus plurem et minorem tempore: tempus igitur est numerus. 581. Then [410] he clarifies the aforesaid definition in two ways, and first by a sign. Now that which is a standard of judging something to be more and less is a number of it. But the standard for judging whether a motion is greater or smaller is time. Therefore, time is a number.
Secundo ibi: quoniam autem numerus etc., manifestat quod dictum est per distinctionem numeri; et dicit quod numerus dicitur dupliciter. Uno modo id quod numeratur actu, vel quod est numerabile, ut puta cum dicimus decem homines aut decem equos; qui dicitur numerus numeratus, quia est numerus applicatus rebus numeratis. Alio modo dicitur numerus quo numeramus, idest ipse numerus absolute acceptus, ut duo, tria, quatuor. Tempus autem non est numerus quo numeramus, quia sic sequeretur quod numerus cuiuslibet rei esset tempus: sed est numerus numeratus, quia ipse numerus prioris et posterioris in motu tempus dicitur; vel etiam ipsa quae sunt prius et posterius numerata. Secondly, [411] he makes clearer what has been stated by distinguishing number, saying there are two. First there is that which is actually numbered which can be, as when we say ten men or 100 horses, and this is called “number numbered,” because it is a number applied to the things that are numbered. Then there is the number by which we count, i.e., number considered absolutely, such as two, three, four [the counting numbers]. Now time is not a counting number; otherwise the number of anything would be time; rather it is a number numbered, because it is the number of before and after in motion that we call “time,” or else the things that are counted before and after.
Et ideo, licet numerus sit quantitas discreta, tempus tamen est quantitas continua, propter rem numeratam; sicut decem mensurae panni quoddam continuum est, quamvis denarius numerus sit quantitas discreta. Therefore, although number is discrete quantity, time is nevertheless a continuous quantity on account of the thing counted, just as ten measures of cloth is a continuous quantity, even though ten is a discrete quantity.

Lecture 18
How the same “now” is or is not in a whole time
Lectio 18
Chapter 11 cont.
ἔστι δ' ἕτερον ᾧ ἀριθμοῦμεν καὶ τὸ ἀριθμούμενον. καὶ ὥσπερ ἡ κίνησις αἰεὶ ἄλλη καὶ ἄλλη, καὶ ὁ χρόνος (ὁ δ' ἅμα πᾶς χρόνος ὁ αὐτός· τὸ γὰρ νῦν τὸ αὐτὸ ὅ ποτ' ἦν—τὸ δ' εἶναι αὐτῷ ἕτερον—τὸ δὲ νῦν τὸν χρόνον ὁρίζει, ᾗ πρότερον καὶ ὕστερον). Just as motion is a perpetual succession, so also is time. But every simultaneous time is self-identical; for the 'now' as a subject is an identity, but it accepts different attributes. The 'now' measures time, in so far as time involves the 'before and after'.
τὸ δὲ νῦν ἔστι μὲν ὡς τὸ αὐτό, ἔστι δ' ὡς οὐ τὸ αὐτό· ᾗ μὲν γὰρ ἐν ἄλλῳ καὶ ἄλλῳ, ἕτερον (τοῦτο δ' ἦν αὐτῷ τὸ νῦν <�εἶναι>, ὃ δέ ποτε ὄν ἐστι τὸ νῦν, τὸ αὐτό. The 'now' in one sense is the same, in another it is not the same. In so far as it is in succession, it is different (which is just what its being was supposed to mean), but its substratum is an identity:
ἀκολουθεῖ γάρ, ὡς ἐλέχθη, τῷ μὲν μεγέθει ἡ κίνησις, ταύτῃ δ' ὁ χρόνος, ὥς φαμεν· καὶ ὁμοίως δὴ τῇ στιγμῇ τὸ φερόμενον, ᾧ τὴν κίνησιν γνωρίζομεν καὶ τὸ πρότερον ἐν αὐτῇ καὶ τὸ ὕστερον. τοῦτο δὲ ὃ μέν ποτε ὂν τὸ αὐτό (ἢ στιγμὴ γὰρ ἢ λίθος ἤ τι ἄλλο τοιοῦτόν ἐστι), τῷ λόγῳ δὲ ἄλλο, ὥσπερ οἱ σοφισταὶ λαμβάνουσιν ἕτερον τὸ Κορίσκον ἐν Λυκείῳ εἶναι καὶ τὸ Κορίσκον ἐν ἀγορᾷ. καὶ τοῦτο δὴ τῷ ἄλλοθι καὶ ἄλλοθι εἶναι ἕτερον· τῷ δὲ φερομένῳ ἀκολουθεῖ τὸ νῦν, ὥσπερ ὁ χρόνος τῇ κινήσει (τῷ γὰρ φερομένῳ γνωρίζομεν τὸ πρότερον καὶ ὕστερον ἐν κινήσει, ᾗ δ' ἀριθμητὸν τὸ πρότερον καὶ ὕστερον, τὸ νῦν ἔστιν)· ὥστε καὶ ἐν τούτοις ὃ μέν ποτε ὂν νῦν ἐστι, τὸ αὐτό (τὸ πρότερον γὰρ καὶ ὕστερόν ἐστι τὸ ἐν κινήσει), τὸ δ' εἶναι ἕτερον (ᾗ ἀριθμητὸν γὰρ τὸ πρότερον καὶ ὕστερον, τὸ νῦν ἔστιν). for motion, as was said, goes with magnitude, and time, as we maintain, with motion. Similarly, then, there corresponds to the point the body which is carried along, and by which we are aware of the motion and of the 'before and after' involved in it. This is an identical substratum (whether a point or a stone or something else of the kind), but it has different attributes as the sophists assume that Coriscus' being in the Lyceum is a different thing from Coriscus' being in the market-place. And the body which is carried along is different, in so far as it is at one time here and at another there. But the 'now' corresponds to the body that is carried along, as time corresponds to the motion. For it is by means of the body that is carried along that we become aware of the 'before and after' the motion, and if we regard these as countable we get the 'now'. Hence in these also the 'now' as substratum remains the same (for it is what is before and after in movement), but what is predicated of it is different; for it is in so far as the 'before and after' is numerable that we get the 'now'.
καὶ γνώριμον δὲ μάλιστα τοῦτ' ἔστιν· καὶ γὰρ ἡ κίνησις διὰ τὸ κινούμενον καὶ ἡ φορὰ διὰ τὸ φερόμενον· τόδε γάρ τι τὸ φερόμενον, ἡ δὲ κίνησις οὔ. ἔστι μὲν οὖν ὡς τὸ αὐτὸ τὸ νῦν αἰεί, ἔστι δ' ὡς οὐ τὸ αὐτό· καὶ γὰρ τὸ φερόμενον. This is what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is carried. what is carried is a real thing, the movement is not. Thus what is called 'now' in one sense is always the same; in another it is not the same: for this is true also of what is carried.
φανερὸν δὲ καὶ ὅτι εἴτε χρόνος μὴ εἴη, τὸ νῦν οὐκ ἂν (220a.) εἴη, εἴτε τὸ νῦν μὴ εἴη, χρόνος οὐκ ἂν εἴη· ἅμα γὰρ ὥσπερ τὸ φερόμενον καὶ ἡ φορά, οὕτως καὶ ὁ ἀριθμὸς ὁ τοῦ φερομένου καὶ ὁ τῆς φορᾶς. Clearly, too, if there were no time, there would be no 'now', and vice versa. just as the moving body and its locomotion involve each other mutually, so too do the number of the moving body and the number of its locomotion. For the number of the locomotion is time, while the 'now' corresponds to the moving body, and is like the unit of number.
χρόνος μὲν γὰρ ὁ τῆς φορᾶς ἀριθμός, τὸ νῦν δὲ ὡς τὸ φερόμενον, οἷον μονὰς ἀριθμοῦ. καὶ συνεχής τε δὴ ὁ χρόνος τῷ νῦν, καὶ διῄρηται κατὰ τὸ νῦν· ἀκολουθεῖ γὰρ καὶ τοῦτο τῇ φορᾷ καὶ τῷ φερομένῳ. καὶ γὰρ ἡ κίνησις καὶ ἡ φορὰ μία τῷ φερομένῳ, ὅτι ἕν (καὶ οὐχ ὅ ποτε ὄν—καὶ γὰρ ἂν διαλίποι—ἀλλὰ τῷ λόγῳ)· καὶ ὁρίζει δὲ τὴν πρότερον καὶ ὕστερον κίνησιν τοῦτο. Time, then, also is both made continuous by the 'now' and divided at it. For here too there is a correspondence with the locomotion and the moving body. For the motion or locomotion is made one by the thing which is moved, because it is one—not because it is one in its own nature (for there might be pauses in the movement of such a thing)—but because it is one in definition: for this determines the movement as 'before' and 'after'.
ἀκολουθεῖ δὲ καὶ τοῦτό πως τῇ στιγμῇ· καὶ γὰρ ἡ στιγμὴ καὶ συνέχει τὸ μῆκος καὶ ὁρίζει· ἔστι γὰρ τοῦ μὲν ἀρχὴ τοῦ δὲ τελευτή. ἀλλ' ὅταν μὲν οὕτω λαμβάνῃ τις ὡς δυσὶ χρώμενος τῇ μιᾷ, ἀνάγκη ἵστασθαι, εἰ ἔσται ἀρχὴ καὶ τελευτὴ ἡ αὐτὴ στιγμή· τὸ δὲ νῦν διὰ τὸ κινεῖσθαι τὸ φερόμενον αἰεὶ ἕτερον. ὥσθ' ὁ χρόνος ἀριθμὸς οὐχ ὡς τῆς αὐτῆς στιγμῆς, ὅτι ἀρχὴ καὶ τελευτή, ἀλλ' ὡς τὰ ἔσχατα τῆς γραμμῆς μᾶλλον—καὶ οὐχ ὡς τὰ μέρη, διά τε τὸ εἰρημένον (τῇ γὰρ μέσῃ στιγμῇ ὡς δυσὶ χρήσεται, ὥστε ἠρεμεῖν συμβήσεται), Here, too there is a correspondence with the point; for the point also both connects and terminates the length—it is the beginning of one and the end of another. But when you take it in this way, using the one point as two, a pause is necessary, if the same point is to be the beginning and the end. The 'now' on the other hand, since the body carried is moving, is always different. Hence time is not number in the sense in which there is 'number' of the same point because it is beginning and end, but rather as the extremities of a line form a number, and not as the parts of the line do so, both for the reason given (for we can use the middle point as two, so that on that analogy time might stand still),
καὶ ἔτι φανερὸν ὅτι οὐδὲν μόριον τὸ νῦν τοῦ χρόνου, οὐδ' ἡ διαίρεσις τῆς κινήσεως, ὥσπερ οὐδ' ἡ στιγμὴ τῆς γραμμῆς· αἱ δὲ γραμμαὶ αἱ δύο τῆς μιᾶς μόρια. ᾗ μὲν οὖν πέρας τὸ νῦν, οὐ χρόνος, ἀλλὰ συμβέβηκεν· ᾗ δ' ἀριθμεῖ, ἀριθμός · τὰ μὲν γὰρ πέρατα ἐκείνου μόνον ἐστὶν οὗ ἐστιν πέρατα, ὁ δ' ἀριθμὸς ὁ τῶνδε τῶν ἵππων, ἡ δεκάς, καὶ ἄλλοθι. and further because obviously the 'now' is no part of time nor the section any part of the movement, any more than the points are parts of the line—for it is two lines that are parts of one line. In so far then as the 'now' is a boundary, it is not time, but an attribute of it; in so far as it numbers, it is number; for boundaries belong only to that which they bound, but number (e.g. ten) is the number of these horses, and belongs also elsewhere.
Postquam philosophus ostendit quid est tempus, hic determinat de nunc. Et primo ostendit utrum sit idem nunc in toto tempore, vel aliud et aliud: quod supra in dubitatione positum fuit; secundo ex hoc ulterius assignat rationem eorum quae dicuntur de nunc, ibi: manifestum est autem et cetera. 582. After explaining what time is, the Philosopher here explains the “now.” First he determines whether the “now” in a whole time is always the same or other and other, which was brought up as a problem above; Secondly, after settling this he gives the reason for what is said above the “now,” at no. 588.
Circa primum tria facit: primo ponit quod nunc quodammodo est idem, et quodammodo non est idem; secundo exponit quod dixerat, ibi: ipsum autem nunc etc.; tertio probat, ibi: sequitur enim sicut dictum est et cetera. As to the first he does three things: First, he declares that the “now” is somehow always the same and somehow not; Secondly, he explains this, at no. 584; Thirdly, he proves it, at no. 585.
Dicit ergo primo quod cum tempus sit numerus motus, sicut partes motus sunt semper aliae et aliae, ita et partes temporis: sed illud quod simul existit de toto tempore est idem, scilicet ipsum nunc. Quod quidem secundum id quod est, idem est: sed ratione est alterum, secundum quod est prius et posterius: et sic nunc mensurat tempus, non secundum quod est idem subiecto, sed secundum quod ratione est alterum et alterum, et prius et posterius. 583. He says therefore first [412] that since time is the number of motion, then, just as the parts of motion are always other and other, so also the parts of time. But that which always exists throughout the whole of time is the same, namely, the “now,” which as to its nature is always the same. While in conception it varies accordingly as it is prior and subsequent. Thus the “now” measures time, not inasmuch as it is always the same thing, but inasmuch as in conception it is other and other, and “before” and “after”.
Deinde cum dicit: ipsum autem nunc etc., exponit quod dixerat: et dicit quod ipsum nunc quodammodo semper est idem, et quodammodo non idem. Inquantum enim semper consideratur ut in alio et alio secundum successionem temporis et motus, sic est alterum et non idem. Et hoc est quod supra diximus, quod ipsi est esse alterum. Nam hoc est esse ipsi nunc, idest secundum hoc accipitur ratio ipsius, ut consideratur in decursu temporis et motus. Sed inquantum ipsum nunc est quoddam ens, sic est idem subiecto. 584. Then [413] he explains what he had just said and declares that the “now” is somehow always the same and somehow not. For insofar as it is always being considered as being in something other and other in the succession of time and of motion, in that sense it is other and not always the same. And this is what we stated above, namely, that “it is other in motion.” for this is the esse of the “now,” i.e., it is according to this that its notion is taken, namely, as considered in the succession of time and motion. But insofar as the “now” is a certain being, from that viewpoint it is always the same thing.
Deinde cum dicit: sequitur enim sicut dictum est etc., probat quod dixerat. Et primo probat quod nunc est idem subiecto, sed alterum et alterum ratione; secundo quod ipsum nunc mensuret tempus, ibi: et notum autem maxime et cetera. 585. Then [414] he proves what he has just said. First he proves that the “now” is always the same as to subject but other and other in conception; secondly, that it is the “now” that measures time, at no. 587.
Dicit ergo primo quod sicut supra dictum est, motus quantum ad continuitatem et prius et posterius, sequitur magnitudinem, et tempus motum. Imaginemur igitur secundum geometras, quod punctus motus faciat lineam: similiter oportebit esse aliquid idem in tempore, sicut est aliquid idem in motu. Si autem punctum suo motu faciat lineam, ipsum punctum quod fertur, est quo cognoscimus motum, et prius et posterius in ipso. Non enim motus percipitur nisi ex hoc, quod mobile aliter et aliter se habet: et secundum id quod pertinet ad praecedentem dispositionem mobilis, iudicamus prius in motu: secundum autem id quod pertinet ad sequentem dispositionem mobilis, iudicamus posterius in motu. Hoc ergo quod movetur, quo motum cognoscimus, et discernimus prius et posterius in ipso, sive sit punctum, sive sit lapis, sive quodcumque aliud, ex ea parte qua est quoddam ens, quodcumque sit, est idem, scilicet subiecto, sed ratione est alterum. Et hoc modo sophistae utuntur altero, cum dicunt Coriscum alterum esse in theatro et in foro, sic arguentes secundum sophisma accidentis: esse in foro est aliud ab eo quod est esse in theatro; sed Coriscus est nunc in foro, nunc in theatro; ergo est alius a se. Sic igitur patet quod id quod movetur est alterum secundum rationem, in eo quod est alibi et alibi, licet sit idem subiecto. He says therefore, first that, as was said above, in respect of continuity and in respect of “before” and “after”, motion follows upon magnitude and time upon motion. Let us imagine, therefore, after the manner of geometers, that a point in motion is making a line: then, just as there is something that remains identical in this motion, so there must be something that remains identical throughout time. If the moving point should make a line, it is by the moving point that we discern the motion and the “before” and “after” in it. For motion is perceived only because the mobile thing is in other and other states: according to what pertains to the previous position of the mobile, we judge something as “before” in motion, and according to what pertains to a subsequent position, we judge something as “after” in motion. Therefore this thing which is being moved, by which we recognize that there is motion and by which we discern a “before” and “after” in it, whether it be a point or a stone or anything else, insofar as it is a certain being, whatever it may be, is the same, namely as to subject—but in conception it is other. And this is the way the Sophists use the term “other” when they say that Coriscus in the forum is other than Coriscus in the theater, arguing thus: according to the fallacy of accident: to be in the forum is other than to be in the theater; but Coriscus is now in the forum and now in the theater; therefore he is other than himself. In like manner, it is plain that that which is being moved is other according to conception insofar as it is now here, now there—while remaining the same as to subject.
Sed sicut tempus sequitur ad motum, ita ipsum nunc sequitur ad id quod fertur. Et hoc probat, quia per mobile cognoscimus prius et posterius in motu. Cum enim invenimus mobile in aliqua parte magnitudinis per quam movetur, iudicamus quod motus qui fuit per unam partem magnitudinis, prius praeteriit, et per aliam partem magnitudinis post sequetur. Et similiter in numeratione motus, quae fit per tempus, id quod distinguit prius et posterius temporis, est ipsum nunc, quod est terminus praeteriti et principium futuri. Sic igitur se habet nunc ad tempus, sicut mobile ad motum: ergo secundum commutatam proportionem, sicut tempus ad motum, ita et nunc ad mobile. Unde si mobile in toto motu est idem subiecto, sed differt ratione, oportebit ita esse et in nunc, quod sit idem subiecto et aliud et aliud ratione: quia illud quo discernitur in motu prius et posterius, est idem subiecto, sed alterum ratione, scilicet mobile; et id secundum quod numeratur prius et posterius in tempore est ipsum nunc. Now just as time follows upon motion, so the “now” follows that which is being moved. This is so because it is through the mobile that we know the “before” and “after” in motion. For when we see the mobile in some certain part of a magnitude through which it is being moved, we judge that the motion which passed through one part of the magnitude has ceased to be before and that motion through another part will follow after. In like manner, in the counting of motion (which counting is done by time), that which distinguishes the “before.” and “after” of time is the “now,” which is the end of the past and the beginning of the future. Thus the “now” is related to time as the mobile in to motion. Therefore also, by commuting the proportion, we get that time is to motion as the “now” is to the mobile. Hence, if the mobile remains the same as to subject throughout the entire motion—though differing in conception—the same will be true of the “now”: it too will remain the same as to subject but will be other and other in conception. For that by which “before” and “after” are discerned in a motion is the same as to subject but differing in conception, the mobile; and that according to which “before” and “after” are counted in time is the “now.”
Ex hac autem consideratione de facili potest accipi intellectus aeternitatis. Ipsum enim nunc, inquantum respondet mobili se habenti aliter et aliter, discernit prius et posterius in tempore, et suo fluxu tempus facit, sicut punctus lineam. Sublata igitur alia et alia dispositione a mobili, remanet substantia semper eodem modo se habens. Unde intelligitur nunc ut semper stans, et non ut fluens, nec habens prius et posterius. Sicut igitur nunc temporis intelligitur ut numerus mobilis, ita nunc aeternitatis intelligitur ut numerus, vel potius ut unitas rei semper eodem modo se habentis. 586. This train of thought makes easy an understanding of eternity. For the. “now,” insofar as it corresponds to a mobile that is continually other and other, distinguishes the “before” and “after” in time and by its flow makes time, just as a point makes a line. But if that varying status of the mobile be removed, the substance remains always in the same state; whence the “now” is then understood as always standing still and not as flowing nor as having a “before” and “after.” Therefore, just as the “now” of time is understood as the number of the mobile, so the “now” of eternity is understood as the number, or rather the unity of a thing always remaining in the same state.
Deinde cum dicit: et notum etc., ostendit unde habeat nunc mensurare tempus. Et dicit quod hoc ideo est, quia id quod est maxime notum in tempore, nunc est; et unumquodque mensuratur per id quod est maxime notum sui generis, ut dicitur in X Metaphys. Et hoc etiam ostendit ex habitudine motus ad mobile: quia motus cognoscitur per id quod movetur, et loci mutatio per id quod localiter fertur, quasi minus notum per magis notum. Quod ideo est, quia id quod movetur est hoc aliquid, idest res quaedam per se stans; quod non convenit motui. Unde mobile est notius motu, et per mobile cognoscitur motus: et similiter tempus per ipsum nunc. Et sic concludit conclusionem principaliter intentam, quod id quod dicitur nunc, semper est idem quodammodo, et quodammodo non; quia similiter est de mobili, ut dictum est. 587. Then [415] he shows whence the “now” derives its function of measuring time. And he says it is because that which is best known in time is the “now”, and what is best known in any genus is the measure of everything in that genus, as is said in Metaphysics X. He also shows this from the relation of motion to the mobile: for motion is perceived through something being moved and local motion is perceived through observing something being moved locally; after the manner of the better known manifesting the less known. This is so because that which is being moved is “this something,” i.e., a certain thing stable in itself—a characteristic which does not belong to motion. Hence the mobile is more known by us than the motion, and motion is known through the mobile object. In like manner., time is made known through the “now.” Thus, he reaches the conclusion principally intended: that what is called the “now” is always the same in one way, and in another way not, because it is similar to the mobile, as was said.
Deinde cum dicit: manifestum est autem etc., assignat rationem eorum quae dicuntur de nunc; et primo eius quod dicitur, quod nihil est temporis nisi nunc; secundo eius quod dicitur, quod nunc dividit et continuat temporis partes, ibi: et continuum iam etc.; tertio eius quod dicitur, quod nunc non sit pars temporis, ibi: et adhuc manifestum et cetera. 588. Then [416] he explains the reason for the things which are said of the “now”: First, why it is said that nothing of time exists but the “now”; Secondly, why the “now” is said to separate and continue the parts, of time, at no. 590; Thirdly, why it is said that the “now” is not a part of time, at no. 592.
Dicit ergo primo manifestum esse, quod si non sit tempus, non erit nunc; et si non erit nunc, non erit tempus. Et hoc ex habitudine motus ad mobile. Sicut enim loci mutatio et id quod fertur, sunt simul; sic et numerus eius quod fertur, simul est cum numero localis motus: sed tempus est numerus loci mutationis, ipsum autem nunc comparatur ad id quod fertur, non quidem sicut numerus (quia nunc indivisibile est), sed sicut unitas numeri. Relinquitur igitur quod tempus et nunc non sunt sine invicem. Attendendum est autem quod tempus semper comparatur loci mutationi, qui est primus motuum: tempus enim est numerus primi motus, ut dictum est. 589. He says therefore first that it is plain that if there is no time, there will be no “now,” and if no “now,” no time. This is explained by the relation of motion to the mobile. For just as the change of place and that which is being changed are together, so the count of that which is being changed accompanies the count of the change of place. But time is the number of a local motion, while the “now” is related to what is being moved, not as its number (since the “now” is indivisible), but as the unit of number. It follows therefore that time and the “now” are not one without the other. Notice that time is always compared to a local motion, which is the first of all motions: for time is the number of the first motion, as was said.
Deinde cum dicit: et continuum iam tempus etc., assignat rationem eius quod dicitur, quod tempus continuatur et dividitur secundum nunc. Et primo ex parte motus et mobilis; secundo ex parte lineae et puncti, ibi: sequitur autem et hoc et cetera. 590. Then [417] he explains why it is said that time is continued and, divided according to the “now.” First he explains it by considering motion and the mobile; Secondly, by considering a line and a point, at no. 591.
Dicit ergo primo quod iam ex praedictis patet, quod tempus est continuum ipsi nunc, idest per ipsum nunc, et dividitur secundum ipsum. Et hoc etiam consequens est ad id quod invenitur in loci mutatione, cuius numerus est tempus, et in eo quod fertur secundum locum, cui respondet ipsum nunc. Manifestum est enim quod omnis motus habet unitatem ab eo quod movetur: quia scilicet illud quod movetur est unum et idem manens in toto motu; et non est indifferenter id quod movetur, uno motu manente, quodcumque ens, sed illud idem ens quod prius incepit moveri: quia si esset aliud ens quod postea moveretur, deficeret primus motus, et esset alius motus alterius mobilis. Et sic patet quod mobile dat unitatem motui, quae est eius continuitas. He says therefore first that what we have already said makes clear that time is made continuous with the “now,” i.e., by the “now,” and is divided by the “now.” This fact also follows from what is found in local motion (the number of which is time) and in the object that is being moved according to place which corresponds to the ‘how”). For it is clear that every motion derives its unity from the object being moved, since that which is being moved remains one and the same throughout the whole course of the motion. And it is not a matter of indifference whether that which is moved, in the course of one motion, be any being at all, but rather it must be that same being which first began to be moved, for if it were another being that was later moved, the former motion would have failed and there would now be another motion of another mobile. So it is clear that it to the mobile that gives unity to the motion, which unity constitutes its continuity.
Sed verum est quod mobile est aliud et aliud secundum rationem. Et per hunc modum distinguit priorem et posteriorem partem motus: quia secundum quod consideratur in una ratione vel dispositione, cognoscitur quod quaecumque dispositio fuit in mobili ante istam signatam, pertinebat ad priorem partem motus; quaecumque autem post hanc erit, pertinebit ad posteriorem. Sic igitur mobile et continuat motum et distinguit ipsum. Et eodem modo se habet nunc ad tempus. But it to true that the mobile is other and other according to conception. And it to in this way that it distinguishes the prior and the subsequent part of motion: because insofar as the mobile is considered under one aspect or disposition it is recognized that whatever disposition was in the mobile previous to its present state pertained to the prior part of the motion; whatever disposition will come after this state will pertain to the subsequent part of the motion. Thus it is that the mobile both continues the motion and distinguishes its parts. And the same holds for the “now” in relation to time.
Deinde cum dicit: sequitur autem et hoc etc., assignat eiusdem rationem ex parte lineae et puncti. Et dicit quod hoc quod dictum est de tempore et nunc, consequitur quodammodo ad id quod invenitur in linea et puncto: quia punctum continuat lineam, et distinguit ipsam inquantum est principium unius partis et finis alterius. 591. Then [418] he explains a case of the same in the matter of line and point. And he says that the conclusion drawn about time and the “now” in the preceding section follows in a way from what is found in a line and a point; for the point continues the line and distinguishes its parts, inasmuch as it is the beginning of one part and the end of another.
Sed tamen differenter se habet in linea et puncto, et tempore et nunc. Quia punctum est quoddam stans, et linea similiter: unde potest homo accipere idem punctum bis, et uti eo ut duobus, ut scilicet principio et ut fine. Et cum sic utimur puncto ut duobus, accidit quies; sicut patet in motu reflexo, in quo id quod erat finis primi motus est principium secundi motus reflexi. Et propter hoc probatur infra in octavo, quod motus reflexus non est continuus, sed intercidit quies media. But there is a difference in the case of line and point, and in the case of time and the “now”. For both the point and the line are something stationary; whence a person can consider the same point twice and use it as two [give it two interpretations] namely, as both a beginning and an end. When we thus use the point as two, rest occurs, as is evident in a reflex motion, in which that which was the and of the first motion is the beginning of the second and reflected motion. It is on this basis that we shall prove in Book VIII that a reflex motion is not continuous but that an intermediate pause occurs.
Sed ipsum nunc non est stans, propter id quod respondet mobili, quod semper fertur durante motu; et propter hoc oportet nunc esse semper alterum et alterum secundum rationem, ut supra dictum est. Et ideo, cum tempus sit numerus motus, non hoc modo numerat motum, quod aliquid idem temporis accipiatur ut principium unius et finis alterius; sed magis numerat motum accipiendo duo ultima temporis, scilicet duo nunc, quae tamen non sunt partes eius. But the “now” is not stationary, because it corresponds to the mobile which is always being carried along during the motion—which also accounts for the “now” having to be always other and other in conception as was said above. Therefore since time is the number of motion, it does not number motion in the sense that some same time is taken as the beginning of one and the end of another, but rather it numbers motion by taking two boundaries of time, namely, two “nows,” which are nevertheless not parts of time.
Et quare competat iste modus numerandi in tempore magis quam alius, quo per punctum numerantur partes lineae, inquantum est principium et finis, ratio est quae dicta est, quia secundum hunc modum utitur aliquis puncto ut duobus; et sic accidit quies media, quae non potest esse in tempore et in motu. Non tamen intelligendum est per id quod dicitur, quod idem nunc non sit principium futuri et finis praeteriti, sed quod non percipimus tempus numerando motum per unum nunc, sed magis per duo, ut dictum est: quia sequeretur quod in numeratione motus idem nunc sumeretur bis. The reason why this method of counting is used in numbering time, rather than the method used when a point numbers the parts of a line (where the same point is considered both a beginning and an end), is that, as was stated, in the latter method we use the point as two things and this brings about an intermediate pause, which cannot exist in time or in motion. Now this does not mean that the same “‘now” is not the beginning of the future and the end of the past, but that we do not perceive time by counting motion in terms of one “now” but in terms of two, as was said; otherwise, in our counting of motion the same “now” would be employed twice.
Deinde cum dicit: et adhuc manifestum quod nulla pars etc., assignat rationem eius quod dicitur, quod nunc non est pars temporis. Et dicit manifestum esse quod nunc non est pars temporis, sicut neque id per quod distinguitur motus, est pars motus, scilicet aliqua dispositio signata in mobili; sicut etiam nec puncta sunt partes lineae. Duae enim lineae sunt partes unius lineae. 592. Then [419] he explains why it is said that the “now” is not a part of time. And he says it is plain that the “now” is not a part of time, just as what distinguishes a motion is not a part of the motion, namely, some disposition in the mobile itself, just as points are not parts of a line. For two lines are the parts of a line.
Manifestat autem proprietates ipsius temporis ex motu et linea: quia, sicut dictum est supra, motus est continuus propter magnitudinem, et tempus propter motum. Now he manifests the properties of time from the properties of motion and of line because, as was said above, motion is continuous on account of the magnitude, and time on account of the motion.
Concludit ergo finaliter, quod ipsum nunc secundum quod est terminus quidam, non est tempus, sed accidit tempori, ut terminus terminato: sed secundum quod tempus vel nunc numerat alia, sic etiam nunc est numerus aliorum quam temporis. Et huius ratio est, quia terminus non est nisi eius cuius est terminus; sed numerus potest esse diversorum, sicut numerus decem equorum numerus est et aliarum rerum. Sic igitur nunc est terminus solius temporis, sed est numerus omnium mobilium quae moventur in tempore. He concludes, therefore, finally that the “now,” insofar as it is a certain boundary, is not time but it happens to time, as a boundary does to that which is bounded; but insofar as time or the “now” numbers other things, the “now” is the number of things other than time. The reason is because a boundary can only be of that of which it is the boundary; but a number can be applied to various thing, as the number of ten horses is also that of other things. Thus therefore the “now” is the boundary only of time, but it is the number of all mobiles that are being moved in time.

Lecture 19
From the definition of time certain things are clarified
Lectio 19
Chapter 11 cont.
ὅτι μὲν τοίνυν ὁ χρόνος ἀριθμός ἐστιν κινήσεως κατὰ τὸ πρότερον καὶ ὕστερον, καὶ συνεχής (συνεχοῦς γάρ), φανερόν. It is clear, then, that time is 'number of movement in respect of the before and after', and is continuous since it is an attribute of what is continuous.
Chapter 12
Ἐλάχιστος δὲ ἀριθμὸς ὁ μὲν ἁπλῶς ἐστὶν ἡ δυάς· τὶς δὲ ἀριθμὸς ἔστι μὲν ὡς ἔστιν, ἔστι δ' ὡς οὐκ ἔστιν, οἷον γραμμῆς ἐλάχιστος πλήθει μέν ἐστιν αἱ δύο ἢ ἡ μία, μεγέθει δ' οὐκ ἔστιν ἐλάχιστος· ἀεὶ γὰρ διαιρεῖται πᾶσα γραμμή. ὥστε ὁμοίως καὶ χρόνος· ἐλάχιστος γὰρ κατὰ μὲν ἀριθμόν ἐστιν ὁ εἷς ἢ οἱ δύο, κατὰ μέγεθος δ' οὐκ ἔστιν. The smallest number, in the strict sense of the word 'number', is two. But of number as concrete, sometimes there is a minimum, sometimes not: e.g. of a 'line', the smallest in respect of multiplicity is two (or, if you like, one), but in respect of size there is no minimum; for every line is divided ad infinitum. Hence it is so with time. In respect of number the minimum is one (or two); in point of extent there is no minimum.
φανερὸν (220b.) δὲ καὶ ὅτι ταχὺς μὲν καὶ βραδὺς οὐ λέγεται, πολὺς δὲ καὶ ὀλίγος καὶ μακρὸς καὶ βραχύς. ᾗ μὲν γὰρ συνεχής, μακρὸς καὶ βραχύς, ᾗ δὲ ἀριθμός, πολὺς καὶ ὀλίγος. It is clear, too, that time is not described as fast or slow, but as many or few and as long or short. For as continuous it is long or short and as a number many or few, but it is not fast or slow—any more than any number with which we number is fast or slow.
ταχὺς δὲ καὶ βραδὺς οὐκ ἔστιν· οὐδὲ γὰρ ἀριθμὸς ᾗ ἀριθμοῦμεν ταχὺς καὶ βραδὺς οὐδείς. καὶ ὁ αὐτὸς δὲ πανταχοῦ ἅμα· πρότερον δὲ καὶ ὕστερον οὐχ ὁ αὐτός, ὅτι καὶ ἡ μεταβολὴ ἡ μὲν παροῦσα μία, ἡ δὲ γεγενημένη καὶ ἡ μέλλουσα ἑτέρα, ὁ δὲ χρόνος ἀριθμός ἐστιν οὐχ ᾧ ἀριθμοῦμεν ἀλλ' ὁ ἀριθμούμενος, οὗτος δὲ συμβαίνει πρότερον καὶ ὕστερον ἀεὶ ἕτερος· τὰ γὰρ νῦν ἕτερα. ἔστι δὲ ὁ ἀριθμὸς εἷς μὲν καὶ ὁ αὐτὸς ὁ τῶν ἑκατὸν ἵππων καὶ ὁ τῶν ἑκατὸν ἀνθρώπων, ὧν δ' ἀριθμός, ἕτερα, οἱ ἵπποι τῶν ἀνθρώπων. Further, there is the same time everywhere at once, but not the same time before and after, for while the present change is one, the change which has happened and that which will happen are different. Time is not number with which we count, but the number of things which are counted, and this according as it occurs before or after is always different, for the 'nows' are different. And the number of a hundred horses and a hundred men is the same, but the things numbered are different—the horses from the men.
ἔτι ὡς ἐνδέχεται κίνησιν εἶναι τὴν αὐτὴν καὶ μίαν πάλιν καὶ πάλιν, οὕτω καὶ χρόνον, οἷον ἐνιαυτὸν ἢ ἔαρ ἢ μετόπωρον. Further, as a movement can be one and the same again and again, so too can time, e.g. a year or a spring or an autumn.
οὐ μόνον δὲ τὴν κίνησιν τῷ χρόνῳ μετροῦμεν, ἀλλὰ καὶ τῇ κινήσει τὸν χρόνον διὰ τὸ ὁρίζεσθαι ὑπ' ἀλλήλων· ὁ μὲν γὰρ χρόνος ὁρίζει τὴν κίνησιν ἀριθμὸς ὢν αὐτῆς, ἡ δὲ κίνησις τὸν χρόνον. καὶ λέγομεν πολὺν καὶ ὀλίγον χρόνον τῇ κινήσει μετροῦντες, καθάπερ καὶ τῷ ἀριθμητῷ τὸν ἀριθμόν, οἷον τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμόν. τῷ μὲν γὰρ ἀριθμῷ τὸ τῶν ἵππων πλῆθος γνωρίζομεν, πάλιν δὲ τῷ ἑνὶ ἵππῳ τὸν τῶν ἵππων ἀριθμὸν αὐτόν. ὁμοίως δὲ καὶ ἐπὶ τοῦ χρόνου καὶ τῆς κινήσεως· τῷ μὲν γὰρ χρόνῳ τὴν κίνησιν, τῇ δὲ κινήσει τὸν χρόνον μετροῦμεν. Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is its number, and the movement the time. We describe the time as much or little, measuring it by the movement, just as we know the number by what is numbered, e.g. the number of the horses by one horse as the unit. For we know how many horses there are by the use of the number; and again by using the one horse as unit we know the number of the horses itself. So it is with the time and the movement; for we measure the movement by the time and vice versa.
καὶ τοῦτ' εὐλόγως συμβέβηκεν· ἀκολουθεῖ γὰρ τῷ μὲν μεγέθει ἡ κίνησις, τῇ δὲ κινήσει ὁ χρό νος, τῷ καὶ ποσὰ καὶ συνεχῆ καὶ διαιρετὰ εἶναι· διὰ μὲν γὰρ τὸ τὸ μέγεθος εἶναι τοιοῦτον ἡ κίνησις ταῦτα πέπονθεν, διὰ δὲ τὴν κίνησιν ὁ χρόνος. καὶ μετροῦμεν καὶ τὸ μέγεθος τῇ. κινήσει καὶ τὴν κίνησιν τῷ μεγέθει· πολλὴν γὰρ εἶναί φαμεν τὴν ὁδόν, ἂν ἡ πορεία πολλή, καὶ ταύτην πολλήν, ἂν ἡ ὁδὸς [ᾖ] πολλή· καὶ τὸν χρόνον, ἂν ἡ κίνησις, καὶ τὴν κίνησιν, ἂν ὁ χρόνος. It is natural that this should happen; for the movement goes with the distance and the time with the movement, because they are quanta and continuous and divisible. The movement has these attributes because the distance is of this nature, and the time has them because of the movement. And we measure both the distance by the movement and the movement by the distance; for we say that the road is long, if the journey is long, and that this is long, if the road is long—the time, too, if the movement, and the movement, if the time.
Postquam philosophus definivit tempus, hic ex definitione data reddit rationem eorum quae dicuntur de tempore. Et circa hoc quatuor facit: primo ostendit quomodo in tempore invenitur minimum, et quomodo non; secundo quare tempus dicitur multum et paucum, breve et longum, non autem velox et tardum, ibi: manifestum est autem propter quid etc.; tertio quomodo tempus sit idem, et quomodo non, ibi: et idem autem ubique etc.; quarto quomodo tempus cognoscitur motu et e converso, ibi: non solum autem motum et cetera. 593. Having defined time, the Philosopher now, in the light of the definition which he has given, gives an explanation of those things that are said about time. About which he does four things: First, he shows in what sense there to found in time a smallest part, and in what sense there is not; Secondly, why time is said to be “much” and “little,” “short” and “long”, but not “fast” and “slow,” at no. 595; Thirdly, in what sense time is the saw, and in what sense it is not [ever the same again] at no. 596; Fourthly, how time to known through motion and vice-versa, at no. 597.
Dicit ergo primo quod manifestum est ex definitione temporis prius data, quod tempus est numerus motus secundum prius et posterius, ut supra expositum est; et iterum manifestum est ex praemissis, quod tempus est quoddam continuum. Licet enim non habeat continuitatem ex eo quod est numerus, habet tamen continuitatem ex eo cuius est numerus: quia est numerus continui, scilicet motus, ut etiam supra dictum est. Non enim est tempus numerus simpliciter, sed numerus numeratus. 594. He says therefore first [420] that the previously given definition of time makes clear that time is “the number of motion according to before and after,” as was expounded above, and that time is a type of continuum, as is likewise manifest from what has gone before. For although it does not have continuity insofar as it is a number, yet it has continuity by reason of that of which it is the number: for it is the number of a continuum, namely, of motion, as was said above. For time to not a number absolutely but a number of something numbered.
In numero autem simpliciter est omnino invenire aliquem minimum numerum, scilicet dualitatem. Sed si accipiamus numerum quendam, scilicet numerum alicuius rei continuae, quodammodo est invenire minimum, et quodammodo non; quia secundum multitudinem est invenire minimum, non autem secundum magnitudinem. Sicut in multis lineis secundum multitudinem quidem est minimum, ut una linea vel duae lineae; una quidem si accipiatur id quod est minimum simpliciter in numero; duae autem si accipiatur id quod est minimum in genere numeri, habens rationem numeri. Sed in lineis non est invenire minimum secundum magnitudinem, ut sit scilicet aliqua linea minima; quia semper est dividere quamcumque lineam. Among absolute numbers there is unequivocally a least to be found, namely, two. But if we consider owe certain number, namely, the number of something that is continuous, then there is in one sense a minimum and in one sense no minimum, because in the order of multitude [plurality] there is a least, but not in the order of magnitude. For example, in a plurality of lines there is a minimum according to plurality, i.e., one line or two lines (one if you consider what is the minimum in number absolutely; two if you mean that which is least in the genus of number, having the notion of number). But in respect of magnitude there is no minimum in lines, so that there would be namely, some smallest lines—because it is always possible to divide any line whatsoever.
Et similiter dicendum est de tempore: quia est invenire in eo minimum secundum multitudinem, scilicet unum vel duo, ut puta aut unum annum aut duos annos, aut duos dies aut horas. Sed minimum secundum magnitudinem non est invenire in tempore; quia cuiuslibet temporis dati est accipere partes in quas dividitur. A parallel situation is found in time, for there is a minimum according to multitude, namely, one or two, for example, one year or two years or two days or two hours. But in the order of magnitude there is no minimum, because of any given time there are parts into which it may be divided.
Deinde cum dicit: manifestum est autem etc., assignat rationem quare tempus non dicitur tardum aut velox, sed dicitur multum et paucum, breve et longum. Iam enim ostensum est quod tempus et numerus est, et continuum est. Inquantum ergo est continuum, dicitur tempus et longum et breve, sicut et linea; inquantum autem numerus est, dicitur et multum et paucum. Esse autem velox et tardum, nullo modo competit numero: neque numero simpliciter, ut manifestum est; neque etiam potest convenire numero alicuius rei. Nam esse velox vel tardum, dicitur de aliquo secundum quod est numeratum: dicitur enim velox motus, eo quod parvo tempore numeratur; tardum autem e converso. Unde manifestum est quod tempus nullo modo potest dici velox vel tardum. 595. Then [421] he gives a reason why time is not said to be slow or fast, but great and small, short and long. For it has already been shown that time is both a number and a continuum. Insofar, therefore, as it is the latter, time, is said to be “long” and “short”, insofar as it is a number, it is said to be “great” and “small.” But to be “fast” and “slow” in no wise belongs to number, neither to number absolutely, as is plain, not to the number of some things. For to be “fast” or “slow” is said of something accordingly as it is numbered: for a motion is called “fast” insofar as it is counted off in a short time—and “slow” conversely. Hence it is clear that in no sense can time be called “fast” or “slow.”
Deinde cum dicit: et idem autem etc., ostendit quomodo tempus sit idem, et quomodo non idem. 596. Then [422] he shows how time is the same and how not the same. First, how it is the same or not the same absolutely; Secondly, how it is the same in a certain respect, at no. 597.
Et primo quomodo sit idem vel non idem simpliciter; secundo quomodo sit idem secundum quid, ibi: amplius sicut contingit et cetera. Dicit ergo primo quod tempus simul existens, est idem ubique, idest respectu omnium quae moventur ubicumque. Non enim diversificatur secundum diversa mobilia; sed diversificatur secundum diversas partes eiusdem motus. Et ideo tempus prius et tempus posterius non est idem. Et hoc ideo, quia prima mutatio praesens, cuius primo et principaliter numerus tempus est, una est; sed huius mutationis altera pars est, quae iam facta est et pertransiit, et altera, quae futura est. Unde et tempus alterum est quod prius fuit, et alterum quod futurum est. Et hoc ideo, quia tempus non est numerus simpliciter, sed numerus alicuius rei numeratae, scilicet prioris et posterioris in motu; et huic numero semper accidit esse alterum, et prius et posterius, propter hoc quod ipsa nunc, secundum quod se habent prius et posterius, semper sunt altera. Si autem esset numerus simpliciter, tunc esset idem tempus et mutationis quae praeteriit, et eius quae futura est; quia numerus simpliciter est unus et idem diversorum numeratorum, ut centum equorum et centum hominum. Sed numerus numeratus est alius diversorum: centum enim equi sunt aliud quid a centum hominibus. Et quia tempus est numerus prioris et posterioris in motu; quia alia sunt quae in motu se habent prius et posterius secundum id quod praeteriit de motu, et alia secundum id quod sequitur; propter hoc est aliud tempus praeteritum, et aliud futurum. He says therefore first that the time existing at a given moment is the same everywhere, i.e., it is the same in respect to everything that is being moved anywhere. For it is not diversified by reason of the diverse mobiles, but by reason of the diverse parts of the same motion. For which reason a prior time and a later time are not the same. Why? Because the first and present motion, of which time is primarily and principally the number, is one; but one part of this motion has already taken place and is past, and another will be in the future. Hence there is one time which is past, and another time which is future. This is so because time is not number absolutely but the number of something numbered; namely, of the “before” and “after” in motion. And this number always varies and is “before” and “after,” because the “now’s,” as before and after, are always other. But if time were number absolutely, then the time corresponding to the change which is past and the time corresponding to the change which is to come would be the same, for number absolutely is one and the same of different things counted as, for example, in the case of 100 horses and 100 men. But number numbered varies with different things. For 100 horses are not the same as 100 men. Since time is the number of “before’s and “after” in motion; and since the “before” and “after” of a past motion are not the same as those of that which follow, therefore the past time and the future time are other and other.
Deinde cum dicit: amplius sicut contingit etc., ostendit quomodo tempus reiteratur idem secundum quid. Et dicit quod sicut reiterari unum et eundem motum contingit, sic contingit reiterari unum et idem tempus. Reiteratur enim unus et idem motus specie, sed non numero: quia ab eodem signo arietis, a quo primo movebatur sol, et postea movebitur; et ideo sicut fuit hiems aut ver aut aestas aut autumnus, ita erit, non quidem unum numero, sed specie. 597. Then [423] he shows how the same time returns in a certain respect. And he says that in the same way that one and the same motion may be repeated, so may one and the same time. For one and the same motion can be duplicated specifically, but not numerically; for it is from the same sign of the Ram that the sun first moves [at the vernal equinox] and later will move the following year; therefore, just as there has been winter or spring or summer or fall, so also there will be, not, indeed, the same one in number, but in species.
Deinde cum dicit: non solum autem motum tempore etc., ostendit quod sicut motum cognoscimus tempore, ita et tempus motu: et hoc primo ex ratione numeri et numerati; secundo ex similitudine magnitudinis et motus, ibi: et hoc rationabiliter et cetera. 598. Then [424] he shows that just as we know motion from time, so also time from motion. First, by reason of number and the thing numbered; Secondly, from the likeness existing between magnitude and motion, at no. 599.
Dicit ergo primo quod non solum mensuramus motum per tempus, sed etiam mensuramus tempus per motum, propter hoc quod ad invicem definiuntur. Oportet enim accipere quantitatem unius secundum quantitatem alterius. Quod enim tempus determinet motum, ex hoc contingit, quia est numerus ipsius; sed e converso motus determinat tempus quoad nos. Percipimus enim interdum quantitatem temporis ex motu, utpote cum dicimus tempus esse multum vel paucum, secundum mensuram motus nobis certam: quia et ipsum numerum aliquando per numerabilia cognoscimus, et e converso. Cognoscimus enim numero equorum multitudinem, et iterum uno equo cognoscimus numerum equorum. Non enim sciremus quot sunt milliaria, nisi sciremus quid est milliare. Et similiter est in tempore et motu. Quia cum est nobis certa quantitas temporis, quantitas autem motus ignota, tunc tempore mensuramus motum; e converso autem, quando motus est notus et tempus ignotum. He says therefore first that we not only measure time by motion but motion by time, because each is defined in terms of the other. For one must take the quantity of the one according to the quantity of the other. Now that time should determine motion comes about because it is the number of motion; but conversely, as to us, motion determines time. For we sometimes perceive a quantity of time by means of motion, as when we declare a time to be long or short according to a measure of motion, certain to us; because sometimes we know a number through the things that can be counted, and conversely. For we know by this number a multitude of horses and likewise by one horse we know the number of horses. For we would not know how many thousands there were unless we know what a thousand was. The same holds for time and motion. For when a quantity of time is certain to us, but the quantity of motion unknown, then by the time we measure the motion; but we do the opposite when the motion is known and the time unknown.
Deinde cum dicit: et hoc rationabiliter etc., ostendit idem ex comparatione motus ad magnitudinem. Et dicit quod rationabiliter accidit quod dictum est de tempore et motu: quia sicut motus magnitudinem imitatur in quantitate et continuitate et divisibilitate, ita et tempus imitatur motum; haec enim in motu inveniuntur propter magnitudinem, et in tempore propter motum. Mensuramus autem et magnitudinem per motum, et motum per magnitudinem. Dicimus enim multam esse viam, quando percipimus motum nostrum fuisse multum: et e converso, quando consideramus magnitudinem viae, dicimus motum nostrum fuisse multum. Et ita etiam est de tempore et motu, ut supra dictum est. 599. Then [425] he shows the same thing by comparing motion and magnitude. And he says that what has been just said of time and motion happens reasonably because just as motion imitates magnitude in quantity and continuity and divisibility, so also does time imitate motion; for the latter [quantity, continuity and divisibility] are found in motion on account of their presence in magnitude, and they are found in time on account of their presence in motion. For we measure magnitude by means of motion, and motion by means of magnitude. For we say that a road is long when we notice that our motion over it was long; and conversely, when we consider the magnitude of the road, we say that our motion was long. The same holds when relating time and motion, “ we said above.

Lecture 20
How things are, and are not, in time
Lectio 20
Chapter 12 cont.
ἐπεὶ δ' ἐστὶν ὁ χρόνος μέτρον (221a.) κινήσεως καὶ τοῦ κινεῖσθαι, μετρεῖ δ' οὗτος τὴν κίνησιν τῷ ὁρίσαι τινὰ κίνησιν ἣ καταμετρήσει τὴν ὅλην (ὥσπερ καὶ τὸ μῆκος ὁ πῆχυς τῷ ὁρίσαι τι μέγεθος ὃ ἀναμετρήσει τὸ ὅλον), καὶ ἔστιν τῇ κινήσει τὸ ἐν χρόνῳ εἶναι τὸ μετρεῖσθαι τῷ χρόνῳ καὶ αὐτὴν καὶ τὸ εἶναι αὐτῆς (ἅμα γὰρ τὴν κίνησιν καὶ τὸ εἶναι τῆς κινήσεως μετρεῖ, καὶ τοῦτ' ἔστιν αὐτῇ τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῆς τὸ εἶναι), Time is a measure of motion and of being moved, and it measures the motion by determining a motion which will measure exactly the whole motion, as the cubit does the length by determining an amount which will measure out the whole. Further 'to be in time' means for movement, that both it and its essence are measured by time (for simultaneously it measures both the movement and its essence, and this is what being in time means for it, that its essence should be measured).
δῆλον ὅτι καὶ τοῖς ἄλλοις τοῦτ' ἔστι τὸ ἐν χρόνῳ εἶναι, τὸ μετρεῖσθαι αὐτῶν τὸ εἶναι ὑπὸ τοῦ χρόνου. τὸ γὰρ ἐν χρόνῳ εἶναι δυοῖν ἐστιν θάτερον, ἓν μὲν τὸ εἶναι τότε ὅτε ὁ χρόνος ἔστιν, ἓν δὲ ὥσπερ ἔνια λέγομεν ὅτι ἐν ἀριθμῷ ἐστιν. τοῦτο δὲ σημαίνει ἤτοι ὡς μέρος ἀριθμοῦ καὶ πάθος, καὶ ὅλως ὅτι τοῦ ἀριθμοῦ τι, ἢ ὅτι ἔστιν αὐτοῦ ἀριθμός. ἐπεὶ δ' ἀριθμὸς ὁ χρόνος, τὸ μὲν νῦν καὶ τὸ πρότερον καὶ ὅσα τοιαῦτα οὕτως ἐν χρόνῳ ὡς ἐν ἀριθμῷ μονὰς καὶ τὸ περιττὸν καὶ ἄρτιον (τὰ μὲν γὰρ τοῦ ἀριθμοῦ τι, τὰ δὲ τοῦ χρόνου τί ἐστιν)· τὰ δὲ πράγματα ὡς ἐν ἀριθμῷ τῷ χρόνῳ ἐστίν. εἰ δὲ τοῦτο, περιέχεται ὑπὸ χρόνου ὥσπερ <�καὶ τὰ ἐν ἀριθμῷ ὑπ' ἀριθμοῦ> καὶ τὰ ἐν τόπῳ ὑπὸ τόπου. φανερὸν δὲ καὶ ὅτι οὐκ ἔστιν τὸ ἐν χρόνῳ εἶναι τὸ εἶναι ὅτε ὁ χρόνος ἔστιν, ὥσπερ οὐδὲ τὸ ἐν κινήσει εἶναι οὐδὲ τὸ ἐν τόπῳ ὅτε ἡ κίνησις καὶ ὁ τόπος ἔστιν. εἰ γὰρ ἔσται τὸ ἔν τινι οὕτω, πάντα τὰ πράγματα ἐν ὁτῳοῦν ἔσται, καὶ ὁ οὐρανὸς ἐν τῇ κέγχρῳ· ὅτε γὰρ ἡ κέγχρος ἔστιν, ἔστι καὶ ὁ οὐρανός. ἀλλὰ τοῦτο μὲν συμβέβηκεν, ἐκεῖνο δ' ἀνάγκη παρακολουθεῖν, καὶ τῷ ὄντι ἐν χρόνῳ εἶναί τινα χρόνον ὅτε κἀκεῖνο ἔστιν, καὶ τῷ ἐν κινήσει ὄντι εἶναι τότε κίνησιν. Clearly then 'to be in time' has the same meaning for other things also, namely, that their being should be measured by time. 'To be in time' is one of two things: (1) to exist when time exists, (2) as we say of some things that they are 'in number'. The latter means either what is a part or mode of number—in general, something which belongs to number—or that things have a number. Now, since time is number, the 'now' and the 'before' and the like are in time, just as 'unit' and 'odd' and 'even' are in number, i.e. in the sense that the one set belongs to number, the other to time. But things are in time as they are in number. If this is so, they are contained by time as things in place are contained by place. Plainly, too, to be in time does not mean to co-exist with time, any more than to be in motion or in place means to co-exist with motion or place. For if 'to be in something' is to mean this, then all things will be in anything, and the heaven will be in a grain; for when the grain is, then also is the heaven. But this is a merely incidental conjunction, whereas the other is necessarily involved: that which is in time necessarily involves that there is time when it is, and that which is in motion that there is motion when it is.
ἐπεὶ δέ ἐστιν ὡς ἐν ἀριθμῷ τὸ ἐν χρόνῳ, ληφθήσεταί τις πλείων χρόνος παντὸς τοῦ ἐν χρόνῳ ὄντος· διὸ ἀνάγκη πάντα τὰ ἐν χρόνῳ ὄντα περιέχεσθαι ὑπὸ χρόνου, ὥσπερ καὶ τἆλλα ὅσα ἔν τινί ἐστιν, οἷον τὰ ἐν τόπῳ ὑπὸ τοῦ τόπου. Since what is 'in time' is so in the same sense as what is in number is so, a time greater than everything in time can be found. So it is necessary that all the things in time should be contained by time, just like other things also which are 'in anything', e.g. the things 'in place' by place.
καὶ πάσχει δή τι ὑπὸ τοῦ χρόνου, καθάπερ καὶ λέγειν εἰώθαμεν ὅτι κατατήκει ὁ χρόνος, καὶ γηράσκει πάνθ' ὑπὸ τοῦ χρόνου, καὶ ἐπιλανθάνεται διὰ τὸν χρόνον, ἀλλ' (221b.) οὐ μεμάθηκεν, οὐδὲ νέον γέγονεν οὐδὲ καλόν· φθορᾶς γὰρ αἴτιος καθ' ἑαυτὸν μᾶλλον ὁ χρόνος· ἀριθμὸς γὰρ κινήσεως, ἡ δὲ κίνησις ἐξίστησιν τὸ ὑπάρχον· A thing, then, will be affected by time, just as we are accustomed to say that time wastes things away, and that all things grow old through time, and that there is oblivion owing to the lapse of time, but we do not say the same of getting to know or of becoming young or fair. For time is by its nature the cause rather of decay, since it is the number of change, and change removes what is.
ὥστε φανερὸν ὅτι τὰ αἰεὶ ὄντα, ᾗ αἰεὶ ὄντα, οὐκ ἔστιν ἐν χρόνῳ· οὐ γὰρ περιέχεται ὑπὸ χρόνου, οὐδὲ μετρεῖται τὸ εἶναι αὐτῶν ὑπὸ τοῦ χρόνου· Hence, plainly, things which are always are not, as such, in time, for they are not contained time, nor is their being measured by time.
σημεῖον δὲ τούτου ὅτι οὐδὲ πάσχει οὐδὲν ὑπὸ τοῦ χρόνου ὡς οὐκ ὄντα ἐν χρόνῳ. A proof of this is that none of them is affected by time, which indicates that they are not in time.
ἐπεὶ δ' ἐστὶν ὁ χρόνος μέτρον κινήσεως, ἔσται καὶ ἠρεμίας μέτρον [κατὰ συμβεβηκός]· πᾶσα γὰρ ἠρεμία ἐν χρόνῳ. Since time is the measure of motion, it will be the measure of rest too—indirectly. For all rest is in time.
οὐ γὰρ ὥσπερ τὸ ἐν κινήσει ὂν ἀνάγκη κινεῖσθαι, οὕτω καὶ τὸ ἐν χρόνῳ· οὐ γὰρ κίνησις ὁ χρόνος, ἀλλ' ἀριθμὸς κινήσεως, ἐν ἀριθμῷ δὲ κινήσεως ἐνδέχεται εἶναι καὶ τὸ ἠρεμοῦν. For it does not follow that what is in time is moved, though what is in motion is necessarily moved. For time is not motion, but 'number of motion': and what is at rest, also, can be in the number of motion.
οὐ γὰρ πᾶν τὸ ἀκίνητον ἠρεμεῖ, ἀλλὰ τὸ ἐστερημένον κινήσεως πεφυκὸς δὲ κινεῖσθαι, καθάπερ εἴρηται ἐν τοῖς πρότερον. τὸ δ' εἶναι ἐν ἀριθμῷ ἐστιν τὸ εἶναί τινα ἀριθμὸν τοῦ πράγματος, καὶ μετρεῖσθαι τὸ εἶναι αὐτοῦ τῷ ἀριθμῷ ἐν ᾧ ἐστιν, ὥστ' εἰ ἐν χρόνῳ, ὑπὸ χρόνου. Not everything that is not in motion can be said to be 'at rest'—but only that which can be moved, though it actually is not moved, as was said above. 'To be in number' means that there is a number of the thing, and that its being is measured by the number in which it is. Hence if a thing is 'in time' it will be measured by time.
μετρήσει δ' ὁ χρόνος τὸ κινούμενον καὶ τὸ ἠρεμοῦν, ᾗ τὸ μὲν κινούμενον τὸ δὲ ἠρεμοῦν· τὴν γὰρ κίνησιν αὐτῶν μετρήσει καὶ τὴν ἠρεμίαν, πόση τις. ὥστε τὸ κινούμενον οὐχ ἁπλῶς ἔσται μετρητὸν ὑπὸ χρόνου, ᾗ ποσόν τί ἐστιν, ἀλλ' ᾗ ἡ κίνησις αὐτοῦ ποσή. But time will measure what is moved and what is at rest, the one qua moved, the other qua at rest; for it will measure their motion and rest respectively. Hence what is moved will not be measurable by the time simply in so far as it has quantity, but in so far as its motion has quantity.
ὥστε ὅσα μήτε κινεῖται μήτ' ἠρεμεῖ, οὐκ ἔστιν ἐν χρόνῳ· τὸ μὲν γὰρ ἐν χρόνῳ εἶναι τὸ μετρεῖσθαί ἐστι χρόνῳ, ὁ δὲ χρόνος κινήσεως καὶ ἠρεμίας μέτρον. Thus none of the things which are neither moved nor at rest are in time: for 'to be in time' is 'to be measured by time', while time is the measure of motion and rest.
φανερὸν οὖν ὅτι οὐδὲ τὸ μὴ ὂν ἔσται πᾶν ἐν χρόνῳ, οἷον ὅσα μὴ ἐνδέχεται ἄλλως, ὥσπερ τὸ τὴν διάμετρον εἶναι τῇ πλευρᾷ σύμμετρον. ὅλως γάρ, εἰ μέτρον μέν ἐστι κινήσεως ὁ χρόνος καθ' αὑτό, τῶν δ' ἄλλων κατὰ συμβεβηκός, δῆλον ὅτι ὧν τὸ εἶναι μετρεῖ, τούτοις ἅπασιν ἔσται τὸ εἶναι ἐν τῷ ἠρεμεῖν ἢ κινεῖσθαι. ὅσα μὲν οὖν φθαρτὰ καὶ γενητὰ καὶ ὅλως ὁτὲ μὲν ὄντα ὁτὲ δὲ μή, ἀνάγκη ἐν χρόνῳ εἶναι (ἔστιν γὰρ χρόνος τις πλείων, ὃς ὑπερέξει τοῦ τε εἶναι αὐτῶν καὶ τοῦ μετροῦντος τὴν οὐσίαν αὐτῶν)· τῶν δὲ μὴ ὄντων ὅσα μὲν περιέχει ὁ χρόνος, τὰ μὲν ἦν, οἷον Ὅμηρός ποτε (222a.) ἦν, τὰ δὲ ἔσται, οἷον τῶν μελλόντων τι, ἐφ' ὁπότερα περιέχει· καὶ εἰ ἐπ' ἄμφω, ἀμφότερα [καὶ ἦν καὶ ἔσται]· ὅσα δὲ μὴ περιέχει μηδαμῇ, οὔτε ἦν οὔτε ἔστιν οὔτε ἔσται. ἔστι δὲ τὰ τοιαῦτα τῶν μὴ ὄντων, ὅσων τἀντικείμενα αἰεὶ ἔστιν, οἷον τὸ ἀσύμμετρον εἶναι τὴν διάμετρον ἀεὶ ἔστι, καὶ οὐκ ἔσται τοῦτ' ἐν χρόνῳ. οὐ τοίνυν οὐδὲ τὸ σύμμετρον· διὸ αἰεὶ οὐκ ἔστιν, ὅτι ἐναντίον τῷ αἰεὶ ὄντι. ὅσων δὲ τὸ ἐναντίον μὴ αἰεί, ταῦτα δὲ δύναται καὶ εἶναι καὶ μή, καὶ ἔστιν γένεσις καὶ φθορὰ αὐτῶν. Plainly, then, neither will everything that does not exist be in time, i.e. those non-existent things that cannot exist, as the diagonal cannot be commensurate with the side. Generally, if time is directly the measure of motion and indirectly of other things, it is clear that a thing whose existence is measured by it will have its existence in rest or motion. Those things therefore which are subject to perishing and becoming—generally, those which at one time exist, at another do not—are necessarily in time: for there is a greater time which will extend both beyond their existence and beyond the time which measures their existence. Of things which do not exist but are contained by time some were, e.g. Homer once was, some will be, e.g. a future event; this depends on the direction in which time contains them; if on both, they have both modes of existence. As to such things as it does not contain in any way, they neither were nor are nor will be. These are those nonexistents whose opposites always are, as the incommensurability of the diagonal always is—and this will not be in time. Nor will the commensurability, therefore; hence this eternally is not, because it is contrary to what eternally is. A thing whose contrary is not eternal can be and not be, and it is of such things that there is coming to be and passing away.
Postquam philosophus determinavit de tempore secundum se, hic determinat de tempore per comparationem ad ea quae sunt in tempore. Et circa hoc duo facit: primo comparat tempus ad ea quae sunt in tempore; secundo ad ea quae sunt in nunc, ibi: ipsum autem nunc et cetera. 600. After determining the question of time in itself, the Philosopher now discusses it in relation to things that are in time. As to this, he does two things: First he compares time with things that exist in time; Secondly, with things that exist in the “now,” at no. 612 (L.21).
Circa primum duo facit: primo comparat tempus ad motum; secundo ad alia quae sunt in tempore, ibi: manifestum autem quod et cetera. Concerning the first he does two things: First he compares time to motion; Secondly to other things that are in time, at no. 602.
Circa primum considerandum est quod alio modo comparatur motus ad tempus, et alio modo res aliae. Motus enim mensuratur tempore et secundum illud quod est, et secundum suam durationem sive secundum esse suum. Res autem aliae, utpote homo aut lapis, mensurantur tempore secundum suum esse sive secundum suam durationem, prout habent esse transmutabile: secundum autem id quod sunt, non mensurantur tempore, sed magis eis respondet nunc temporis, ut supra dictum est. 601. In regard to the first, note that motion is related to time in a way different from the way other things are related to it. For motion is measured by time both as to what it is and as to its duration i.e., its existence. But other things, such as a man or a stone, are measured by time as to their existence or their duration insofar as they have a changeable existence; but as to what they are in themselves, they are not measured by time; rather it is the “now” of time that here corresponds, as was said above (L. 18).
Dicit ergo quod tempus est mensura ipsius motus, et eius quod est moveri, per quod dat intelligere durationem motus. He says therefore [426] that time is the measure of motion itself, and “of being moved,” by which he means the duration of motion.
Mensurat autem tempus motum per hoc, quod tempore determinatur aliqua pars motus, quae mensurat totum. Et hoc necessarium est; quia unumquodque mensuratur per aliquid sui generis, ut dicitur in X metaphysicae. Et hoc apparet in mensuris magnitudinum. Cubitus enim mensurat totam longitudinem alicuius panni vel alicuius viae, per hoc quod determinat aliquam partem illius longitudinis, quae metitur totum. Et similiter per partem motus tempus mensurat totum motum: per motum enim unius horae mensuratur motus totius diei, et per motum diurnum mensuratur motus annuus. Quia igitur motus mensuratur tempore, nihil est aliud motum esse in tempore, quam mensurari a tempore, et secundum id quod est, et secundum suam durationem: quia secundum utrumque mensuratur a tempore, ut dictum est. Now time measures motion by a certain part of the motion’s being determined by time, which part then measures the whole motion. And this is necessary, because each thing is measured by something of the same genus, as is said in Metaphysics X. This is evident in the measures of lengths. For a cubit can measure the entire length of a piece of cloth or of a road, because the cubit determines some part of the length—which part then measures the whole. Likewise by means of a part of motion, time measures an entire motion: for by means of the motion of one hour, the motion of a whole day is measured, and by means of the daily motion the yearly motion is measured. Therefore, since motion is measured by times, for motion to be in time is, nothing more than for it to be measured by time, both as to what it is and as to its duration—because according to both aspects it is measured by time, as was said.
Deinde cum dicit: manifestum autem quod etc., ostendit quomodo se habeat ad alia. Et primo ostendit quomodo aliae res sint in tempore; secundo quibus rebus conveniat in tempore esse, ibi: quoniam autem est sicut et cetera. 602. Then [427] he shows how it is related to other things: First, how other things are in time; Secondly, what things belong in time, at no. 603.
Dicit ergo primo quod, quia motum esse in tempore est tempore mensurari et ipsum et esse eius, manifestum est quod etiam idem est alia in tempore esse et mensurari a tempore, non ipsa, sed esse eorum: motus enim per se mensuratur a tempore, sed alia secundum quod habent motum. He says therefore first [427] that since for motion to be in time is for it to be measured by time, both as to itself and as to its existence, it is clear that it is likewise the same for other things to exist in time and to be measured by time, i.e., not as to what they are, but as to their existence: for motion is essentially measured by time but other things only insofar as they have motion.
Et quod hoc sit rem esse in tempore, quod mensurari esse eius a tempore, sic ostendit: quia esse in tempore dupliciter potest intelligi; uno modo ut dicatur aliquid esse in tempore, quia est simul cum tempore; alio modo ut dicantur aliqua esse in tempore, sicut dicuntur aliqua esse in numero. Quod etiam dicitur dupliciter: in numero enim est aliquid sicut pars, sicut binarius est in quaternario; et aliquid est sicut propria passio eius, ut par et impar, vel quidquid aliud est ipsius numeri: alio vero modo dicitur aliquid esse in numero, non quia ipsum est aliquid numeri, sed quia numerus est eius ut numerati, sicut homines dicuntur esse in tali vel tali numero. He proves, in the following way, that for a thing to exist in time is to have its existence measured by time: To be in time can mean two things; first, as something is said to exist in time, because it co-exists with time; secondly, as something is said to exist in time in the way that things are said to exist in number. And this latter also has two meanings: for in a number something is present (1) as a part, as 2 is in 4; and as a property, such as even and odd, or whatever else that belongs to number; or (2) it can be there, not because it is anything pertaining to number, but because number belongs to it as numbered, as men may be said to be in such and such a number.
Sed quia tempus est numerus, utroque modo contingit aliquid esse in tempore. Nam nunc et prius et posterius et quaecumque sunt huiusmodi, hoc modo sunt in tempore, sicut sunt in numero unitas, quae est pars, et par et impar, quae sunt numeri passiones, et superfluum et perfectum. (Dicitur autem numerus perfectus, qui constat ex partibus mensurantibus ipsum; sicut numerus senarius, quem mensurant unitas, binarius et ternarius, quae simul iuncta constituunt senarium. Numerus autem superfluus dicitur, cuius partes mensurantes ipsum excedunt totum; sicut duodenarius, qui mensuratur unitate, binario, ternario, quaternario et senario, quae simul iuncta consurgunt in sexdecim). Et per hunc modum sunt aliqua in tempore, inquantum sunt aliquid temporis. Sed res quae non sunt aliquid temporis, dicuntur esse in tempore sicut numerata in numero. Unde oportet quod ea quae sunt in tempore, contineantur sub tempore sicut sub numero; sicut ea quae sunt in loco continentur sub loco sicut sub mensura. But because time is a number something can be present in time in both ways. For the “now,” and “before” and “after,” and things of this sort, exist in time as unity exists in number, of which it is a part, and as do even and odd, which are properties of number, and as do “superfluous” and “perfect.” (A number is called “perfect,” if the sum of the parts measuring it equals the number; for example, six is measured by one, two, and three, which, added together, equal six. A number is called “superfluous” if its divisors total up to a number which exceeds it: for example, 12 is measured by one, two, three, four, and six, which, when added together equal 16.) And that is the way in which some things exist in time, namely, as being something of time. But things that are not something of time are said to be in time as things numbered exist in number. Consequently these latter things that are in time must be contained under time as under a number, just as things in place are contained under place as under a measure.
Exponit etiam consequenter primum modum essendi aliquid in tempore. Et dicit manifestum esse quod non est idem esse in tempore, et esse quando tempus est; sicut etiam non est idem esse in motu et in loco, et esse quando est locus et motus: alioquin sequeretur quod omnes res essent in quolibet, ut puta quod caelum esset in grano milii, quia quando est milium, est caelum. Then he explains the very first way of something’s existing in time. And he says it is clear that it is not the same thing to exist in time, and to exist when time exists [i.e., to co-exist] just as it is not the same to be in motion and in place and to be in existence when place and motion exist. Otherwise, it would follow that all things would be in anything; for example, the heavens would be in a grain of millet, because when the millet exists, the heavens exist.
Est autem inter haec duo differentia: quia quando dicitur aliquid esse quando alterum est, accidit uni quod sit simul cum altero; sed illud in quo aliquid est sicut in mensura, ex necessitate consequitur; sicut tempus ex necessitate consequitur ei quod est in tempore, et motus ei quod est in motu, ut simul sint. There are two differences between these situations: for when something is said to be when something else exists, it is incidental to the one that it exists at the same time as the other; but that in which something exists as in a measure follows necessarily [upon that which is in it], as time necessarily follows upon that which is in time, and motion upon that which is in motion, so that they are together.
Deinde cum dicit: quoniam autem est, sicut est in numero etc., ostendit quibus conveniat esse in tempore. Et primo quod non omnia entia sunt in tempore; secundo quod non omnia non entia, ibi: manifestum igitur et cetera. 603. Then [428] he shows to what things it belongs to be in time; First he shows that not all beings exist in time; Secondly, that not all non-beings do, at no. 611.
Circa primum duo facit: primo ostendit quod ea quae sunt semper, non sunt in tempore; secundo quod nihilominus ea quae quiescunt, inquantum huiusmodi, sunt in tempore, ibi: quoniam autem tempus et cetera. As to the first he does two things: First he shows that things which are always do not exist in time; Secondly, that nevertheless things that are at rest are, as such, in time, at no. 606.
Circa primum duo facit: primo proponit ea ex quibus procedit ad propositum ostendendum; secundo concludit propositum, ibi: quare manifestum est, etc., proponit autem duo. Quorum primum est, quod cum aliquid sit in tempore sicut numeratum in numero, necesse est quod accipi possit aliquod tempus maius omni eo quod est in tempore; sicut potest accipi aliquis numerus maior omni eo quod est numeratum. Et propter hoc necesse est omnia quae sunt in tempore, totaliter contineri sub tempore et concludi sub ipso, sicut ea quae sunt in loco concluduntur sub loco. As to the first he does two things: First he mentions the facts from which he proceeds to the manifestation of his proposition; Secondly, he concludes to the proposition, at no. 605. Now he mentions two things. The first of these [428] is that, when something is in time as the numbered is in a number, then necessarily there is some time that can be taken larger than everything that exists in that time, just as it is possible to take a number larger than everything that is numbered. Consequently, all things that exist in time are of necessity contained under time and comprehended under it just as things in place are comprehended under place.
Secundum ponit ibi: et pati iam aliquid sub tempore etc.; et est quod omne quod est in tempore, aliquid patitur sub tempore, secundum quod passio pertinet ad defectum. Et hoc probat ex consueto modo locutionis. Consuevimus enim dicere quod longitudo temporis tabefacit, idest putrefacit et corrumpit; et iterum quod propter tempus omnia senescunt quae sunt in tempore; et quod propter tempus oblivio accidit: quae enim de recenti cognovimus, in memoria manent, sed per diuturnitatem temporis elabuntur. 604. The second thing is then mentioned [429] and it is that whatever exists in time suffers something under time in the sense of “suffering” (passio) which pertains to defect. And he proves this from the way people ordinarily speak. For we are wont to say that length of time “wastes things away,” i.e., decays and corrupts them, and again that on account of time all things that exist in time grow old, and that on account of time forgetting occurs - for things we have recently learned remain in the memory but with length of time they slip away.
Et ne aliquis dicat quod etiam perfectiones attribuuntur tempori sicut et passiones, hoc consequenter excludit; et ponit tria contra tria praemissa. And lest anyone should say that perfections also are attributed to time as well as defects, he subsequently forestalls this, giving, in effect, three reasons over and above the three aforesaid.
Contra id enim quod dixit, quod obliviscitur propter tempus, subdit, quod aliquis non addiscit propter tempus: si enim aliquis diu vivat otiosus a studio addiscendi, non propter hoc addiscit, sicut propter tempus obliviscitur. Complementing his statement that forgetting occurs on account of time, he add-s that no one learns on account of time; for if a person should neglect study for a long time, he does not on that account learn, while he does on account of time forget.
Contra hoc autem quod dixit, quod omnia senescunt sub tempore, subdit, quod non est aliquid factum novum propter tempus: non enim propter hoc solum aliquid innovatur quia longo tempore durat, sed magis antiquatur. In keeping with his statement that all things grow old in time, he adds that nothing becomes new on account of time; for a thing is not renewed on account of a long existence; rather, it becomes antiquated.
Contra illud vero quod dixerat, quod tempus tabefacit, subdit, quod tempus non facit bonum, idest integrum et perfectum, sed magis tabidum et corruptum. Et huius causa est, quia ex tempore aliqua corrumpuntur, etiam si non appareat aliquid aliud manifeste corrumpens: quod ex ipsa ratione temporis apparet. Est enim tempus numerus motus: de ratione autem motus est quod faciat distare id quod est, a dispositione in qua prius erat. Unde cum tempus sit numerus primi motus, ex quo in omnibus causatur mutabilitas, sequitur quod propter diuturnitatem temporis, omnia quae sunt in tempore removeantur a sua dispositione. To match his statement that time wastes things away, he adds that time does not make a thing good, i.e., whole, and perfect, but rather wasted and decayed. The reason for this is that time corrupts things even when there is no other manifest corrupting agents. All this is due to the very nature of time: for time is the number of motion—and it is of the nature of motion to put a distance between what now is and the condition it was in previously. Consequently, since time is the number of the first motion, which causes mutability in all things, it follows that length of time causes all things that exist to time to be removed from their former condition.
Deinde cum dicit: quare manifestum est etc., concludit propositum ex praemissis: et primo ex primo prius proposito. Ostensum est enim quod quaecumque sunt in tempore, continentur sub tempore: quae autem sunt semper, non continentur sub tempore quasi excedente; neque esse, idest duratio, ipsorum mensuratur sub tempore, cum in infinitum durent, infinitum autem non contingit mensurari: ergo illa quae sunt semper, non sunt in tempore. Sed hoc verum est secundum quod sunt semper. Corpora enim caelestia sunt semper secundum esse substantiae eorum, non autem secundum ubi; et ideo duratio eorum non mensuratur tempore, sed motus localis ipsorum tempore mensuratur. 605. Then [430] he concludes to his proposition from the foregoing premises, and first of all, from the first. For it has been shown that whatever exists in time is contained under time while whatever things are always, are not contained under time as exceeding time. Neither is the being, i.e., the duration, of such things measured under time, since they endure to infinity, and the infinite cannot be measured. Therefore those things that exist forever, are not in time. But this is true insofar as they exist always. For the heavenly bodies exist forever according to the being of their substance, but not in regard to “where” they are; consequently, their duration is not measured by time, yet their local motion is.
Secundo ibi: signum autem huius etc., probat idem ex secundo prius positorum. Et dicit quod signum huius, quod ea quae sunt semper non sunt in tempore, est, quod non patiuntur a tempore, quasi non existentia in tempore. Non enim tabescunt, neque senescunt, sicut dictum est de illis quae sunt in tempore. Secondly [431] he proves the same point from the second of the points laid down before. And he says that a sign that those things which exist forever do not exist in time is that they do not suffer from time, as though not existing in time. For they neither waste away nor grow old, as was said of things that exist in time.
Deinde cum dicit: quoniam autem tempus etc., quia ostenderat quod ea quae sunt semper non sunt in tempore, ea autem quae quiescunt, eodem modo se habent; posset aliquis credere quod quiescentia, inquantum huiusmodi, non mensurarentur tempore. Et ideo ad hoc excludendum, ostendit quod tempus est etiam quietis mensura. Et circa hoc quinque facit. 606. Then [432], because he had shown that those things which exist forever do not exist in time, while those things which are at rest also remain the same way someone might think that things at rest are, as such, not measured by time. Therefore to obviate this, he shows that time is also the measure of rest. And in regard to this he does five things:
Primo enim proponit quod intendit: et dicit quod quia tempus est mensura motus per se, erit etiam et per accidens mensura quietis; quia omnis quies est in tempore, sicut et omnis motus. First he proposes what he intends, and says that because time is the measure of motion per se, it will also be per accidens the measure of rest; for all rest is in time just as all motion is.
Secundo ibi: non enim sicut etc., excludit quoddam, per quod videri posset quod quies non mensuretur tempore. Quia enim tempus est mensura motus, posset aliquis credere quod quiescens, quia non est in motu, non sit in tempore. Et ideo ad hoc excludendum dicit, quod non est necesse moveri omne quod est in tempore, sicut necesse est moveri omne quod est in motu: quia tempus non est motus, sed numerus motus. Contingit autem esse in numero motus non solum quod movetur, sed etiam quod quiescit. 607. Secondly [433] he excludes something that might lead one to think that rest is not measured by time. For since time is the measure of motion, someone might suppose that a thing at rest, because it is not in motion, is not in time. Consequently, to exclude this, he says that not everything in time need be in motion, in the same way that everything in motion has necessarily to be moved. For time is not a motion but the number of motion. Now it occurs that not only what is being moved, but also what is at rest, may be in the number of motion.
Tertio ibi: non enim omne immobile etc., probat propositum, scilicet quod quiescens sit in numero motus, ita quod tempore mensuretur. Et ad hoc probandum inducit, quod non omne immobile, idest non omne quod non movetur, quiescit; sed quiescens est privatum motu, quod tamen aptum natum est moveri; sicut supra dictum est in tertio, quod movetur illud cuius immobilitas quies est; quies enim non est negatio motus, sed privatio ipsius. Et sic patet quod esse quiescentis est esse rei mobilis. Unde cum esse rei mobilis sit in tempore et mensuretur tempore, esse etiam rei quiescentis tempore mensuratur. Hic autem dicimus esse in tempore aliquid sicut in numero, quia est aliquis numerus ipsius rei, et quia esse ipsius mensuratur numero temporis. Unde manifestum est quod quiescens est in tempore, et mensuratur tempore, non inquantum est quiescens, sed inquantum est mobile. Et propter hoc praemisit quod tempus est mensura motus per se, quietis autem per accidens. 608. Thirdly [434] he proves the proposition that a thing at rest is in the number of motion, as to be measured by time. To do this, he adduces that not every immobile thing, i.e., not every thing that is not in motion, is at rest; rather, a thing at rest is something deprived of motion, but which is nevertheless by nature disposed to be moved, as it was said above in Book III that that is moved whose immobility is rest—for rest is not the negation of motion, but its privation. Consequently, it is evident that the being [existence] of a thing at rest is the being of a mobile being. Hence, since the being [existence] of a mobile being is in time and is measured by time, the being of a thing at rest is measured by time. Now here we are saying that a thing is in time as in a number, because there is some number for that thing, and because its existence is measured by the number of time. Thus it is clear that a thing at rest exists in time and is measured by time, no insofar as it is rest but insofar as it is a mobile being. That is why he said in the beginning that time is per se a measure of motion but per accidens a measure of rest.
Quarto ibi: mensurabit autem tempus etc., ostendit secundum quid mobile et quiescens mensurantur a tempore. Et dicit quod tempus mensurat illud quod movetur et quiescit, non inquantum est lapis vel homo, sed inquantum est motum et quiescens. Mensuratio enim proprie debetur quantitati: cuius ergo quantitas tempore mensuratur, illud proprie tempore mensuratur. Ex mensuratione autem temporis cognoscitur quantus sit motus, et quanta sit quies; non autem quantum sit id quod movetur. Unde quod movetur, non simpliciter mensuratur tempore secundum propriam quantitatem, sed secundum quantitatem sui motus. Ex quo patet quod tempus proprie sit mensura motus et quietis: sed motus per se, quietis autem per accidens. 609. Fourthly, [435] he shows in what sense a mobile and a thing at rest are measured by time. And he says that time measures what is moved and at rest not insofar as it is a stone or a man, but insofar as it is in motion and at rest. For measuring is properly due to quantity; therefore, time is properly the measure of that whose quantity is measured by time. Now, from the measuring done by time, are known both the quantity of motion and the quantity of rest, but not the quantity of the thing in motion. Hence the thing in motion is not measured by time according to its own proper quantity, but according to the quantity of its motion. From this it is clear that time properly is the measure of motion and of rest—of motion per se, but of rest per accidens.
Quinto ibi: quare quaecumque neque moventur etc., inducit quoddam corollarium ex praemissis. Si enim nihil mensuratur tempore nisi secundum quod movetur et quiescit, sequitur quod quaecumque non moventur neque quiescunt, ut substantiae separatae, non sunt in tempore: quia hoc est esse in tempore, mensurari a tempore. Tempus autem est mensura motus et quietis, ut ex dictis patet. 610. Fifthly, [436], he adduces a certain corollary from the foregoing. For if nothing is measured by time except insofar as it is in motion or at rest, it follows that whatsoever things are neither in motion nor at rest, e.g., the separated substances, are not in time; for this is to be in time, namely, to be measured by time. But time is the measure of motion and of rest, as is clear from the foregoing.
Deinde cum dicit: manifestum igitur quoniam etc., ostendit quod non omnia non entia sunt in tempore. Et dicit manifestum esse ex praemissis, quod neque etiam omne non ens est in tempore, sicut ea quae non contingit aliter esse, ut diametrum esse commensurabilem lateri quadrati: hoc enim est impossibile, quia nunquam contingit esse verum. Huiusmodi autem non mensurantur tempore. Et hoc sic probat. Tempus primo et per se est mensura motus, alia autem non mensurantur nisi per accidens: quaecumque ergo mensurantur tempore, eis contingit moveri et quiescere. Unde et generabilia et corruptibilia et omnia quae quandoque sunt et quandoque non sunt, quia sunt in moveri et quiescere, sunt in tempore: quia quoddam tempus est maius eis, quod excellit durationem ipsorum, et propter hoc mensurat substantias eorum, non secundum id quod sunt, sed secundum esse vel durationem ipsorum. 611. Then [473] he shows that not all non-beings are in time. He says it is clear from the foregoing that neither is every non-being in time, as in the case of things that cannot be otherwise [whose contradictory cannot be], e.g., that a diagonal be commensurate with the side of a square: for this is impossible, because it can never be true. Now such things are not measured by time. And he proves it in this way: Time is primarily and per se the measure of motion, and anything else is measured by time only per accidens. Consequently whatever is measured by time must be capable of motion and rest. Hence things generable and corruptible, and all things that sometimes exist and sometimes do not, since they are “in motion and rest,” exist in time, for same time can be found that is greater than they are and which exceeds their duration, and for that reason measures their substances, not in regard to the nature of the substances, but in regard to their existence or duration.
Sed inter ea quae non sunt, et tamen continentur a tempore, quaedam aliquando erant, ut Homerus; quaedam aliquando erunt, ut aliquod futurum; vel si continentur a tempore praeterito et futuro, erunt et erant. Ea vero quae nullo modo continentur a tempore, neque sunt neque fuerunt neque erunt. Et talia sunt ea quae semper non sunt, et quorum opposita semper sunt; sicut diametrum esse incommensurabilem lateri, semper est; unde non mensuratur tempore. Et propter hoc neque contrarium eius, quod est diametrum esse symmetrum, idest commensurabilem lateri, mensuratur tempore: ideo enim semper non est, quia est contrarium ei quod semper est. But among things that do not exist but are nevertheless contained by time, some things existed at one time, as Homer; others will exist, as some future event; or, if they are contained both by past and present time, they both will be and were. But things that are in no way contained by time neither are, nor were, nor will be. Such are things that forever are not, and whose opposites forever are; for example, that a diagonal be not commensurable to the side, forever is; whence it is not measured by time. And for this reason neither is its contrary measured by time, i.e. that the diagonal is symmetrical, i.e., commensurable. The reason why it forever is not, is that it is the contrary of what forever is.
Quorumcumque autem contrarium non semper est, haec possunt esse et non esse, et habent generationem et corruptionem: et talia mensurantur tempore. But of whatever things the contrary does not always exist, such things can exist and not exist, and are subject to generation and corruption; such things are measured by time.

Lecture 21
The meaning of “now” and related terms
Lectio 21
Chapter 13
Τὸ δὲ νῦν ἐστιν συνέχεια χρόνου, ὥσπερ ἐλέχθη· συνέχει γὰρ τὸν χρόνον τὸν παρεληλυθότα καὶ ἐσόμενον, καὶ πέρας χρόνου ἐστίν· ἔστι γὰρ τοῦ μὲν ἀρχή, τοῦ δὲ τελευτή. ἀλλὰ τοῦτ' οὐχ ὥσπερ ἐπὶ τῆς στιγμῆς μενούσης φανερόν. The 'now' is the link of time, as has been said (for it connects past and future time), and it is a limit of time (for it is the beginning of the one and the end of the other). But this is not obvious as it is with the point, which is fixed.
διαιρεῖ δὲ δυνάμει. καὶ ᾗ μὲν τοιοῦτο, αἰεὶ ἕτερον τὸ νῦν, ᾗ δὲ συνδεῖ, αἰεὶ τὸ αὐτό, ὥσπερ ἐπὶ τῶν μαθηματικῶν γραμμῶν (οὐ γὰρ ἡ αὐτὴ αἰεὶ στιγμὴ τῇ νοήσει· διαιρούντων γὰρ ἄλλη καὶ ἄλλη· ᾗ δὲ μία, ἡ αὐτὴ πάντῃ) —οὕτω καὶ τὸ νῦν τὸ μὲν τοῦ χρόνου διαίρεσις κατὰ δύναμιν, τὸ δὲ πέρας ἀμφοῖν καὶ ἑνότης· It divides potentially, and in so far as it is dividing the 'now' is always different, but in so far as it connects it is always the same, as it is with mathematical lines. For the intellect it is not always one and the same point, since it is other and other when one divides the line; but in so far as it is one, it is the same in every respect. So the 'now' also is in one way a potential dividing of time, in another the termination of both parts, and their unity.
ἔστι δὲ ταὐτὸ καὶ κατὰ ταὐτὸ ἡ διαίρεσις καὶ ἡ ἕνωσις, τὸ δ' εἶναι οὐ ταὐτό. τὸ μὲν οὖν οὕτω λέγεται τῶν νῦν, And the dividing and the uniting are the same thing and in the same reference, but in essence they are not the same. So one kind of 'now' is described in this way:
ἄλλο δ' ὅταν ὁ χρόνος ὁ τούτου ἐγγὺς ᾖ. ἥξει νῦν, ὅτι τήμερον ἥξει· ἥκει νῦν, ὅτι ἦλθε τήμερον. τὰ δ' ἐν Ἰλίῳ γέγονεν οὐ νῦν, οὐδ' ὁ κατακλυσμὸς [γέγονε] νῦν· καίτοι συνεχὴς ὁ χρόνος εἰς αὐτά, ἀλλ' ὅτι οὐκ ἐγγύς. another is when the time is near this kind of 'now'. 'He will come now' because he will come to-day; 'he has come now' because he came today. But the things in the Iliad have not happened 'now', nor is the flood 'now'—not that the time from now to them is not continuous, but because they are not near.
τὸ δὲ ποτέ χρόνος ὡρισμένος πρὸς τὸ πρότερον νῦν, οἷον ποτὲ ἐλήφθη Τροία, καὶ ποτὲ ἔσται κατακλυσμός· δεῖ γὰρ πεπεράνθαι πρὸς τὸ νῦν. ἔσται ἄρα ποσός τις ἀπὸ τοῦδε χρόνος εἰς ἐκεῖνο, καὶ ἦν εἰς τὸ παρελθόν. 'At some time' means a time determined in relation to the first of the two types of 'now', e.g. 'at some time' Troy was taken, and 'at some time' there will be a flood; for it must be determined with reference to the 'now'. There will thus be a determinate time from this 'now' to that, and there was such in reference to the past event.
εἰ δὲ μηδεὶς χρόνος ὃς οὔ ποτε, πᾶς ἂν εἴη χρόνος πεπερασμένος. ἆρ' οὖν ὑπολείψει; ἢ οὔ, εἴπερ αἰεὶ ἔστι κίνησις; ἄλλος οὖν ἢ ὁ αὐτὸς πολλάκις; δῆλον ὅτι ὡς ἂν ἡ κίνησις, οὕτω καὶ ὁ χρόνος· εἰ μὲν γὰρ ἡ αὐτὴ καὶ μία γίγνεταί ποτε, ἔσται καὶ χρόνος εἷς καὶ ὁ αὐτός, εἰ δὲ μή, οὐκ ἔσται. ἐπεὶ δὲ τὸ νῦν τελευτὴ (222b.) καὶ ἀρχὴ χρόνου, ἀλλ' οὐ τοῦ αὐτοῦ, ἀλλὰ τοῦ μὲν παρήκοντος τελευτή, ἀρχὴ δὲ τοῦ μέλλοντος, ἔχοι ἂν ὥσπερ ὁ κύκλος ἐν τῷ αὐτῷ πως τὸ κυρτὸν καὶ τὸ κοῖλον, οὕτως καὶ ὁ χρόνος ἀεὶ ἐν ἀρχῇ καὶ τελευτῇ. καὶ διὰ τοῦτο δοκεῖ ἀεὶ ἕτερος· οὐ γὰρ τοῦ αὐτοῦ ἀρχὴ καὶ τελευτὴ τὸ νῦν· ἅμα γὰρ ἂν καὶ κατὰ τὸ αὐτὸ τἀναντία ἂν εἴη. καὶ οὐχ ὑπολείψει δή· αἰεὶ γὰρ ἐν ἀρχῇ. But if there be no time which is not 'sometime', every time will be determined. Will time then fail? Surely not, if motion always exists. Is time then always different or does the same time recur? Clearly time is, in the same way as motion is. For if one and the same motion sometimes recurs, it will be one and the same time, and if not, not. Since the 'now' is an end and a beginning of time, not of the same time however, but the end of that which is past and the beginning of that which is to come, it follows that, as the circle has its convexity and its concavity, in a sense, in the same thing, so time is always at a beginning and at an end. And for this reason it seems to be always different; for the 'now' is not the beginning and the end of the same thing; if it were, it would be at the same time and in the same respect two opposites. And time will not fail; for it is always at a beginning.
τὸ δ' ἤδη τὸ ἐγγύς ἐστι τοῦ παρόντος νῦν ἀτόμου μέρος τοῦ μέλλοντος χρόνου (πότε βαδίζεις; ἤδη, ὅτι ἐγγὺς ὁ χρόνος ἐν ᾧ μέλλει), καὶ τοῦ παρεληλυθότος χρόνου τὸ μὴ πόρρω τοῦ νῦν (πότε βαδίζεις; ἤδη βεβάδικα). τὸ δὲ Ἴλιον φάναι ἤδη ἑαλωκέναι οὐ λέγομεν, ὅτι λίαν πόρρω τοῦ νῦν. 'Presently' or 'just' refers to the part of future time which is near the indivisible present 'now' ('When do you walk? 'Presently', because the time in which he is going to do so is near), and to the part of past time which is not far from the 'now' ('When do you walk?' 'I have just been walking'). But to say that Troy has just been taken—we do not say that, because it is too far from the 'now'.
καὶ τὸ ἄρτι τὸ ἐγγὺς τοῦ παρόντος νῦν [τὸ] μόριον τοῦ παρελθόντος. πότε ἦλθες; ἄρτι, ἐὰν ᾖ ὁ χρόνος ἐγγὺς τοῦ ἐνεστῶτος νῦν. πάλαι δὲ τὸ πόρρω. τὸ δ' ἐξαίφνης τὸ ἐν ἀναισθήτῳ χρόνῳ διὰ μικρότητα ἐκστάν· 'Lately', too, refers to the part of past time which is near the present 'now'. 'When did you go?' 'Lately', if the time is near the existing now. 'Long ago' refers to the distant past. 'Suddenly' refers to what has departed from its former condition in a time imperceptible because of its smallness;
Postquam philosophus ostendit quomodo se habeat tempus ad ea quae sunt in tempore, hic ostendit quomodo per comparationem ad nunc diversimode aliqua secundum tempus nominantur. Et circa hoc duo facit: primo ponit significationem ipsius nunc; secundo quorumdam aliorum quae determinantur secundum nunc, ibi: ipsum autem tunc et cetera. 612. After showing how time is related to things that exist in time, the Philosopher here shows how, in virtue of their relations to the “now,” certain words derived various meanings with respect to time. About this he does two things: First he explains the meaning of “now”; Secondly, the meaning of certain other words that are determined by the “now, “ at no. 615.
Circa primum duo facit: primo ponit propriam et principalem significationem ipsius nunc; secundo ponit secundariam significationem, ibi: aliud autem et cetera. As to the first be does two things: First be gives the proper and principal meaning of “now”; Secondly, be gives a secondary meaning, at no. 614.
Circa primum tria dicit de nunc. Quorum primum est, quod nunc continuat tempus praeteritum futuro, inquantum est terminus temporis, principium quidem futuri, finis autem praeteriti: licet hoc non sit sic manifestum in nunc, sicut in puncto. Nam punctum stans est; et ideo potest bis accipi, semel ut principium et semel ut finis: quod non accidit in nunc, ut supra dictum est. 613. In regard to the first be says three things about “now.” The first of these [438] is that the “now” joins past time to the future, insofar as it is the boundary of time—the beginning of the future and the end of the past, although this is not so evident in the “now” as in a point. For a point is stationary and therefore can be considered twice: once as a beginning, and once as an end. But this does not occur with the “now,” as was said above.
Secundo ibi: dividit autem potentia etc., dicit quod tempus etiam dividitur secundum nunc, sicut et linea dividitur secundum punctum. Sed tamen nunc dividit tempus inquantum consideratur ut multa in potentia: prout scilicet accipitur seorsum ut principium huius temporis, et seorsum ut finis alterius. Et inquantum sic accipitur, accipitur ut alterum et alterum nunc: sed secundum quod accipitur ut copulans tempus et continuans, accipitur ut idem. Et hoc manifestat per simile in lineis mathematicis, in quibus magis est manifestum. Non enim in lineis mathematicis punctum quod signatur in medio lineae, semper intelligitur ut idem: quia secundum quod dividitur linea, intelligitur aliud punctum quod est ultimum unius lineae, et aliud secundum quod est ultimum alterius; quia lineae secundum quod sunt divisae actu, intelliguntur ut contiguae, contigua autem sunt quorum ultima sunt simul. Sed secundum quod punctum continuat partes lineae, sic est unum et idem: quia continua sunt quorum terminus est idem. Et sic est etiam de nunc respectu temporis: quia uno modo potest accipi ut divisio temporis secundum potentiam; alio modo secundum quod est terminus communis duorum temporum, uniens et continuans ea. Secondly [439], he says that time is divided according to the “now” as a line is divided according to the point. But yet the “now” divides time insofar as it, the “now,” is considered to be many in potency, i.e., as it is, namely, taken separately as the beginning of this time, and separately as the end of that time. And insofar as it is taken in this way, the “now” is taken as other and other; but insofar as it is taken as linking time and giving it continuity, it to taken as one and the same. And he shows this from a similar situation in mathematical lines, in which it is more evident. For in mathematical lines the point in the middle of a line is not always taken as the same: for insofar as the line is divided, there is understood one point which is the end of one line, and one point which is the end of the other. For lines, insofar as they are actually divided, are considered as contiguous—and contiguous things are those whose boundaries are together. But insofar as the point continues the parts of the line, it is one and the same—for continuous things are those whose boundary is the same. And this is the situation with the “now” in respect of time: for it can be taken in one way as potentially dividing time; in another way, as the common boundary of two times, uniting them, and making them continuous.
Tertio ibi: est autem idem etc., dicit quod nunc dividens et continuans tempus est unum et idem subiecto, sed differt ratione, ut ex dictis patet. Uno igitur modo sic dicitur nunc. Thirdly [440], he says that the “now” that divides and continues time is one and the same as to subject, though differing in conception, as the foregoing has made clear. So much for the first meaning of “now.”
Deinde cum dicit: aliud autem, etc., ponit secundariam significationem ipsius nunc. Et dicit quod alio modo dicitur nunc, non terminus temporis continuans praeteritum futuro, sed ipsum tempus propinquum praesenti nunc, sive sit praeteritum sive sit futurum: sicut dicimus veniet nunc, quia veniet hodie, et veniet nunc, quia venit hodie. Sed non dicimus quod bellum Troianum sit factum nunc, neque quod diluvium factum sit nunc: quia licet totum tempus sit continuum, non tamen est propinquum praesenti nunc. 614. Then [441] he gives a secondary meaning of “now,” saying that “now” has another meaning, for it can be taken, not as the boundary of time continuing the past with the future, but as the time near to the present “now,” whether that time is past or future, as when we say, “He will come not,” because he will come today, or when we say, “He has come now,” because he came today. But we do not say that the Trojan war has happened “now,” nor that the Flood took place “now,” because, although the whole of the time is continuous [with the present] nevertheless it is not close to the present “now.”
Deinde cum dicit: ipsum autem tunc etc., exponit quaedam quae determinantur per nunc. Et primo quid significet ipsum tunc. Circa quod duo facit: primo ponit significationem eius; secundo movet quaestionem, ibi: si vero neque tempus et cetera. 615. Then [442] he explains certain things that are determined by the “now.” And first, what “then” signifies. About this he does two things: First he gives its meaning; Secondly, he raises a difficulty, at no. 616.
Dicit ergo primo quod hoc quod dico tunc, significat tempus determinatum per aliquod prius nunc, sive propinquum sive remotum. Possumus enim dicere quod tunc destructa est Troia, et tunc factum est diluvium. Oportet enim quod id quod dicitur factum tunc, includatur ad aliquod nunc vel instans praecedens. Oportebit enim dicere quod sit aliquod tempus determinatae quantitatis ab hoc tempore praesenti in illud nunc, quod erat in praeterito. Et sic patet quod hoc quod dico tunc, differt a secunda significatione nunc in duobus: quia tunc semper est ad praeteritum, et indifferenter se habet ad propinquum et remotum; sed nunc se habet ad propinquum, sed indifferenter ad praeteritum et futurum. He says therefore first (442) that “then” signifies a time determined by some previous “now,” whether near or remote. For we can say that Troy was destroyed “then,” and that the Deluge took place “then.” For what is said to have taken place “then” must be included between some preceding “now” or instant [and the present]. For it will be necessary to say that there is a time period of definite quantity from the present time to that “now” which was in the past. In this wise it to evident that “then” differs from the second meaning of “now” in two ways: first, because “then” always refers to the past and it matters not whether it to the near past or the remote past; but “now” refers to the near, and it matters not whether it be past or future.
Deinde cum dicit: si vero neque tempus est etc., movet quandam dubitationem ex praemissis, et solvit eam. Dixerat enim quod tempus quod dicitur tunc, includitur intra praeteritum nunc et praesens: unde omne tempus quod dicitur tunc oportet esse finitum: sed non est aliquod tempus, quod non possit dici tunc: ergo omne tempus erit finitum. Sed omne tempus finitum deficit: videtur ergo dicendum quod tempus deficiat. Sed si semper est motus, et tempus est numerus motus, sequitur quod tempus non deficiat. Oportebit igitur dicere, si omne tempus est finitum, quod vel semper sit aliud et aliud tempus, vel quod idem tempus multoties reiteretur. Et hoc oportet esse in tempore, sicut est in motu. Si enim unus sit semper et idem motus, oportebit unum et idem tempus esse. Si autem non est unus et idem motus, non erit unum et idem tempus. 616. Then [443] he raises a difficulty in the light of the foregoing and solves it. For he had said that the time which is called “then” is included within a past “now” and the present: hence all time called “then” must be finite. But there is no time which cannot be called “then.” Therefore all time is finite. Now all finite time runs out. It seems therefore that one must say that time runs out. But if motion is always and time is the measure of motion, it follows that time will not run out. Therefore, we shall be forced to say, if all time is finite, either that time is always other and other, or that the same time is repeated over and over. And this situation must exist in time just as it is in notion. For if there is some eternally one and the same motion, then there will have to be one and the same time; but if there is not one and the same motion, there will not be one and the same time.
Secundum igitur opinionem eius, motus nunquam incepit, neque deficiet, ut in octavo patebit; et ita reiteratur quidem unus et idem motus specie, sed non numero. Non enim eadem est circulatio quae nunc est, cum illa quae fuit, numero, sed specie. Et tamen totus motus est unus continuitate, quia una circulatio continuatur alteri, ut in octavo probabitur. Et similiter oportet esse de tempore sicut de motu. 617. According to his opinion, as will be clear in Book VIII, motion never had a beginning, and will never end. Thus one and the same motion is being repeated, not numerically but specifically. For it is not numerically the same revolution that is taking place now and which took place in the past, but it is specifically the same one. Nevertheless, the whole notion is one in continuity, because one revolution is continuous with the next, as will be proved in Book VIII. And what was said of motion must also apply to time.
Unde consequenter ostendit quod tempus nunquam deficiet. Patet enim ex praemissis, quod nunc est principium et finis, sed non respectu eiusdem; sed finis respectu praeteriti, et principium respectu futuri. Unde sic se habet de nunc, sicut se habet de circulo, in quo concavum et convexum sunt idem subiecto, sed differunt ratione per respectum ad diversa. Nam convexum circuli attenditur secundum comparationem ad exteriora, concavum autem per respectum ad interiora. Et quia nihil est accipere de tempore nisi nunc, ut supra dictum est, sequitur quod tempus semper sit in principio et in fine. Et propter hoc tempus videtur esse alterum et alterum: quia nunc non est principium et finis eiusdem temporis, sed diversorum temporum; alioquin opposita inessent eidem secundum idem. Principium enim et finis habent oppositas rationes: si ergo idem esset principium et finis respectu eiusdem, opposita inessent eidem secundum idem. From this he shows that time will never fail. For it is evident from the foregoing that the “now” is both a beginning and an end, although not in relation to the same thing; but it is an end with respect to the past and a beginning with respect to the future. Accordingly, the situation with respect to the “now” is like that of the circle, in which its concavity and convexity are the same thing in reality, but differ according as they are related to diverse things. For convexity is had in a circle with respect to things outside it, and concavity with respect to things inside it. And because nothing of time can be taken but the “now” (as was said above) it follows that time is always at a beginning and at an end. And for this reason time seems to be other and other, for the “now” is not the beginning and end of the same time, but of different times; otherwise, opposite things would be true of the same thing according to the same aspect. For “beginning” and “end” have opposite notions; consequently, if the same thing were a beginning and an end with respect to the same, opposites would exist in the same thing according to the same aspect.
Ulterius concludit ex praemissis, quod quia nunc est principium et finis temporis, tempus nunquam deficiet: quia tempus non potest accipi sine nunc, ut supra dictum est, et nunc est principium temporis: unde tempus semper est in sui principio. Quod autem est in sui principio non deficit: unde tempus non deficiet. Et eadem ratione potest probari quod tempus non incepit secundum quod nunc est finis temporis. He further concludes from the foregoing that since the “now” is both a beginning and an end of time, time will never fail: for time cannot be understood without a “now,” and the “now” is the beginning of a time: hence time is always existing in a beginning of itself. But what is at its beginning is not failing; therefore time will not fail. By the same reasoning it can be proved that time did not commence from the point of view of the “now” which is the end of time.
Sed haec ratio procedit supposito quod motus semper sit, ut ipse dicit. Hoc enim supposito, necesse est dicere quod quodlibet nunc temporis sit principium et finis. Si autem dicatur quod motus incepit aut finietur, sequetur quod aliquod nunc erit principium temporis et non finis, et aliquod erit finis et non principium, sicut et in linea accidit. Si enim esset linea infinita, quodlibet punctum signatum in ea, esset principium et finis. In linea autem finita est accipere aliquod punctum, quod est principium tantum vel finis tantum. Sed de hoc magis inquiretur in octavo. But this reasoning proceeds on the supposition that motion is always, as he says. On this supposition, one would have to say that any “now” of time is a beginning and an end. But if it be said that motion had a beginning, or that it will cease, it follows that some “now” will be a beginning of a period of time and not an end, and some “now” will be an end but not a beginning, as happens also in a line. For if there were an infinite line, any point designated in it would be a beginning and an and. But if the line is finite, some point in it is a beginning only, or an end only. But this will be investigated more in detail in Book VIII.
Deinde cum dicit: ipsum autem iam etc., ostendit quid significet hoc quod dico iam; et habet eandem significationem quam habet nunc, secundo modo acceptum. Illud enim dicitur iam, quod est propinquum praesenti indivisibili nunc, sive sit pars futuri, sive sit pars praeteriti. Pars quidem futuri, sicut cum dico, quando ibit? Iam; quia scilicet tempus in quo est hoc futurum, propinquum est. Pars autem praeteriti, sicut cum quaeritur, quando vadis? Et respondetur iam ivi. Sed de iis quae sunt procul, non dicimus iam; sicut non dicimus quod Troia iam sit destructa, quia hoc est multum remotum a praesenti nunc. 618. Then [444] he shows what is meant by the words “presently” or “just”; and that they have the same meaning of “now.” For “presently” and “just” refer to what is near the present indivisible “now”, whether it is part of the future or part of the past. It refers to a part of the future, when I say: “When will he leave?” “Presently”—because the time in which this will take place is close. It refers to the past when I say “When are you going?” and it is answered,—“I have just gone”. However in regard to events that are distant, we do not say “presently” or “just”; for example, we do not say that Troy has “just” been destroyed, because this is very remote from the present “now.”
Deinde cum dicit: ipsum autem modo prope etc., exponit quaedam alia ad tempus pertinentia. Et dicit quod hoc quod dico modo, significat quod praeteritum est propinquum praesenti nunc: sicut si quaeratur, quando venit talis? Respondetur modo, si tempus praeteritum sit proximum praesenti nunc. Sed olim dicimus, quando est remotum a praesenti nunc in praeterito. Repente autem aliquid fieri dicitur, quando tempus in quo fit, est insensibile propter parvitatem. 619. Then [445] he explains certain other words referring to time. And he says that “just now” [ modo ] signifies that a period of the past is near the present “now”, as when, if it is asked, “When did so-and-so come?” the answer is “just now,” if the past time is very close to the present. But we say “long ago”, when the time past is far from the present. Finally, we say that something occurs “suddenly”, when the time in which it takes place is imperceptibly small.

Lecture 22
How Corruption is attributed to Time—All Motion and Change are in Time.
Lectio 22
Chapter 13 cont.
μεταβολὴ δὲ πᾶσα φύσει ἐκστατικόν. ἐν δὲ τῷ χρόνῳ πάντα γίγνεται καὶ φθείρεται· διὸ καὶ οἱ μὲν σοφώτατον ἔλεγον, ὁ δὲ Πυθαγόρειος Πάρων ἀμαθέστατον, ὅτι καὶ ἐπιλανθάνονται ἐν τούτῳ, λέγων ὀρθότερον. δῆλον οὖν ὅτι φθορᾶς μᾶλλον ἔσται καθ' αὑτὸν αἴτιος ἢ γενέσεως, καθάπερ ἐλέχθη καὶ πρότερον (ἐκστατικὸν γὰρ ἡ μεταβολὴ καθ' αὑτήν), γενέσεως δὲ καὶ τοῦ εἶναι κατὰ συμβεβηκός. but it is the nature of all change to alter things from their former condition. In time all things come into being and pass away; for which reason some called it the wisest of all things, but the Pythagorean Paron called it the most stupid, because in it we also forget; and his was the truer view. It is clear then that it must be in itself, as we said before, the condition of destruction rather than of coming into being (for change, in itself, makes things depart from their former condition), and only incidentally of coming into being, and of being.
σημεῖον δὲ ἱκανὸν ὅτι γίγνεται μὲν οὐδὲν ἄνευ τοῦ κινεῖσθαί πως αὐτὸ καὶ πράττειν, φθείρεται δὲ καὶ μηδὲν κινούμενον. καὶ ταύτην μάλιστα λέγειν εἰώθαμεν ὑπὸ τοῦ χρόνου φθοράν. οὐ μὴν ἀλλ' οὐδὲ ταύτην ὁ χρόνος ποιεῖ, ἀλλὰ συμβαίνει ἐν χρόνῳ γίγνεσθαι καὶ ταύτην τὴν μεταβολήν. A sufficient evidence of this is that nothing comes into being without itself moving somehow and acting, but a thing can be destroyed even if it does not move at all. And this is what, as a rule, we chiefly mean by a thing's being destroyed by time. Still, time does not work even this change; even this sort of change takes place incidentally in time.
ὅτι μὲν οὖν ἔστιν ὁ χρόνος καὶ τί, καὶ ποσαχῶς λέγεται τὸ νῦν, καὶ τί τὸ ποτὲ καὶ τὸ ἄρτι καὶ τὸ ἤδη καὶ τὸ πάλαι καὶ τὸ ἐξαίφνης, εἴρηται. We have stated, then, that time exists and what it is, and in how many senses we speak of the 'now', and what 'at some time', 'lately', 'presently' or 'just', 'long ago', and 'suddenly' mean.
Chapter 14
Τούτων δ' ἡμῖν οὕτω διωρισμένων φανερὸν ὅτι πᾶσα μεταβολὴ καὶ ἅπαν τὸ κινούμενον ἐν χρόνῳ. τὸ γὰρ θᾶττον καὶ βραδύτερον κατὰ πᾶσάν ἐστιν μεταβολήν (ἐν πᾶσι γὰρ οὕτω φαίνεται)· λέγω δὲ θᾶττον κινεῖσθαι τὸ πρότερον (223a.) μεταβάλλον εἰς τὸ ὑποκείμενον κατὰ τὸ αὐτὸ διάστημα καὶ ὁμαλὴν κίνησιν κινούμενον (οἷον ἐπὶ τῆς φορᾶς, εἰ ἄμφω κατὰ τὴν περιφερῆ κινεῖται ἢ ἄμφω κατὰ τὴν εὐθεῖαν· ὁμοίως δὲ καὶ ἐπὶ τῶν ἄλλων). These distinctions having been drawn, it is evident that every change and everything that moves is in time; for the distinction of faster and slower exists in reference to all change, since it is found in every instance. In the phrase 'moving faster' I refer to that which changes before another into the condition in question, when it moves over the same interval and with a regular movement; e.g. in the case of locomotion, if both things move along the circumference of a circle, or both along a straight line; and similarly in all other cases.
ἀλλὰ μὴν τό γε πρότερον ἐν χρόνῳ ἐστί· πρότερον γὰρ καὶ ὕστερον λέγομεν κατὰ τὴν πρὸς τὸ νῦν ἀπόστασιν, τὸ δὲ νῦν ὅρος τοῦ παρήκοντος καὶ τοῦ μέλλοντος· ὥστ' ἐπεὶ τὰ νῦν ἐν χρόνῳ, καὶ τὸ πρότερον καὶ ὕστερον ἐν χρόνῳ ἔσται· ἐν ᾧ γὰρ τὸ νῦν, καὶ ἡ τοῦ νῦν ἀπόστασις. (ἐναντίως δὲ λέγεται τὸ πρότερον κατά τε τὸν παρεληλυθότα χρόνον καὶ τὸν μέλλοντα· ἐν μὲν γὰρ τῷ παρεληλυθότι πρότερον λέγομεν τὸ πορρώτερον τοῦ νῦν, ὕστερον δὲ τὸ ἐγγύτερον, ἐν δὲ τῷ μέλλοντι πρότερον μὲν τὸ ἐγγύτερον, ὕστερον δὲ τὸ πορρώτερον.) ὥστε ἐπεὶ τὸ μὲν πρότερον ἐν χρόνῳ, πάσῃ δ' ἀκολουθεῖ κινήσει τὸ πρότερον, φανερὸν ὅτι πᾶσα μεταβολὴ καὶ πᾶσα κίνησις ἐν χρόνῳ ἐστίν. But what is before is in time; for we say 'before' and 'after' with reference to the distance from the 'now', and the 'now' is the boundary of the past and the future; so that since 'nows' are in time, the before and the after will be in time too; for in that in which the 'now' is, the distance from the 'now' will also be. But 'before' is used contrariwise with reference to past and to future time; for in the past we call 'before' what is farther from the 'now', and 'after' what is nearer, but in the future we call the nearer 'before' and the farther 'after'. So that since the 'before' is in time, and every movement involves a 'before', evidently every change and every movement is in time.
Postquam philosophus comparavit tempus et nunc ad ea quae sunt in tempore, hic manifestat quaedam quae superius tacta sunt. Et primo quomodo corruptio attribuitur tempori; secundo quomodo omnis motus et mutatio sit in tempore, ibi: his autem nobis et cetera. 620. After comparing time and the “now” to things that exist in time, the Philosopher here explains some things that were touched upon above. First, how corruption is attributed to time; Secondly, how every motion and change exist in time, at no. 623.
Circa primum duo facit: primo manifestat propositum per rationem; secundo per signum, ibi: signum autem sufficiens et cetera. Concerning the first he does two things: First he makes his proposition clear by an argument; Secondly, by a sign, at no. 622.
Dicit ergo primo quod omnis mutatio de sui ratione removet rem quae mutatur, a naturali dispositione sua: sed tam generatio quam corruptio fit in tempore. Et ideo quidam attribuebant generationes rerum tempori, ut disciplinam et huiusmodi, dicentes tempus esse sapientissimum, propter hoc quod generatio scientiae fit in tempore. Sed quidam philosophus, Paro nomine, de secta Pythagoricorum, posuit e converso, quod tempus est penitus indisciplinabile, quia scilicet per longitudinem temporis accidit oblivio. Et in hoc rectius dixit: quia, ut prius dictum est, tempus per se magis est causa corruptionis quam generationis. Et hoc ideo, quia tempus est numerus motus: mutatio autem per se est destructiva et corruptiva. Sed causa generationis et ipsius esse non est nisi per accidens. Ex hoc enim ipso quod aliquid movetur, recedit a dispositione quam prius habebat. Sed quod perveniat ad aliquam dispositionem, hoc non importatur in ratione motus inquantum est motus, sed inquantum est finitus et perfectus: quam quidem perfectionem habet motus ex intentione agentis, quod movet ad determinatum finem. Et ideo corruptio magis potest attribui mutationi et tempori: sed generatio et esse agenti et generanti. 621. He says therefore first [446] that every change of its very nature removes from its natural disposition the thing that is changed: but both generation and corruption take place in time. And therefore some attributed generations in things to time, as in the case of learning and the like, saying that time is “very wise” because the generation of science takes place in time. But a certain philosopher by the name of Parus, a Pythagorean, claimed on the contrary that time was “wholly unteachable,” because with length of time comes forgetfulness. And he was more right: for, as was said above, time per se is more a cause of corruption than of generation. The reason is that time is the number of motion, and change is per se destructive and corruptive. It does not cause generation and existence except per accidens. For from the fact that something is moved, it departs from the state in which it was. But that it arrive at some disposition is not implied in the notion of motion insofar as it is motion but insofar as it is finished and perfect. And this perfection is brought about by motion on account of the intention of the agent which moves to a predetermined end. Therefore corruption is attributed rather to change and time, whereas generation and being attributed to the agent and generator.
Deinde cum dicit: signum autem sufficiens etc., manifestat idem per signum: et dicit signum sufficiens esse eius quod dictum est, quod nihil invenitur fieri, nisi appareat aliquid agens et movens ipsum; sed tamen aliquid corrumpitur, cum non appareat manifeste aliquid quod moveat ipsum ad corruptionem. Et talem corruptionem solemus attribuere tempori, sicut cum aliquis senio deficit ex causa intrinseca corrumpente non manifesta: cum autem aliquis occiditur gladio, corruptio eius non attribuitur tempori. In generatione autem semper est generans manifestum, quia nihil a seipso generatur: et ideo generatio non attribuitur tempori, sicut corruptio. Non tamen corruptio sic attribuitur tempori, quod tempus faciat ipsam: sed quia fit in tempore, et corrumpens latet. 622. Then [447] he explains the same point with a sign, and he says that a sufficient sign of his claim is that nothing is found to come into being independently of an agent and a mover, but that a thing can corrupt without any mover in evidence. And such corruption we are accustomed to attribute to time, as when someone fails through old age from a corrupting internal cause that is not apparent; but when someone is killed with a sword, his corruption is not attributed to time. However, in generation the generator is always evident, because nothing is generated by itself. That is why generation is not attributed to time, as is corruption. Nevertheless, corruption is not laid to time in such a way as that time should cause it; but rather as occurring in time, while the corrupting influence is latent.
Ultimo ibi: quod quidem igitur tempus etc., epilogat dictum esse quod tempus est, et quid sit, et quot modis dicitur nunc, et quid significet tunc et modo et iam et olim et repente. Finally [448], he asserts in a summary way that it has been explained that time exists, and what it is, and how “now” is used in various senses, and what are the meanings of “then” and “just now” and “presently” and “long ago” and “suddenly.”
Deinde cum dicit: his autem nobis sic determinatis etc., ostendit quod omnis mutatio sit in tempore, duabus rationibus. Quarum prima talis est. In omni mutatione invenitur velocius et tardius: haec autem determinantur tempore; quia velocius dicitur mutari, quod transmutatur prius ad determinatum terminum secundum idem spatium. Ita tamen quod eadem sit regula utriusque motus, ut in loci mutatione sit utraque mutatio circularis, aut utraque recta. Si autem una esset circularis et alia recta, non propter hoc velocius moveretur quod prius veniret ad terminum. Et similiter intelligendum in aliis generibus mutationum. Sequitur igitur quod omnis mutatio sit in tempore. 623. Then [449] he above by two arguments that all change occurs in time. The first of these is that in every change is found the distinction of “faster” and “slower.” But these are determined by time—because that is said to be changed “faster,” which is changed first to a designated term, over a same distance, provided that both motions are subject to the same rule; e.g., in the case of local motion, if both motions are circular, or both in a straight line. But if one were along a circle and the other straight, the fact that one reached its terminus before the other would be no reason for saying that one moved “faster” than the other. And the same is to be understood of other types of change. It follows, therefore, that every change exists in time.
Secundam rationem ponit ibi: at vero prius in tempore est etc.; et ad hoc probandum utitur tali propositione: prius et posterius sunt in tempore. Quod quidem manifestat hoc modo. Prius et posterius dicitur aliquid per distantiam ad ipsum nunc, quod est terminus praeteriti et futuri: sed ipsa nunc sunt in tempore: ergo et prius et posterius sunt in tempore; quia in eodem oportet quod sit nunc et distantia ipsius nunc, sicut in eodem est punctum et distantia quae accipitur per respectum ad punctum; utrumque enim est in linea. 624. He then gives a second reason [450], but in this proof he makes use of the proposition that “before” and “after” exist in time. He manifests this proposition in the following way. “Before” and “after” are said according to the distance from the “now,” which is the boundary of the past and of the future. Both “now’s” exist in time; therefore both “before” and “after” exist in time, because that in which the “now” is, and that in which the distance from the “now” is, must be the same; just as it is in the same thing that there are a point and the distance taken in relation to that point, for both are in a line.
Et quia dixerat quod prius et posterius determinantur per distantiam ad ipsum nunc, ostendit quomodo hoc sit e converso in praeteritis et futuris: quia in praeterito dicitur prius quod est remotius ab ipso nunc, posterius autem quod est propinquius; in futuro autem est e converso. Si ergo prius et posterius sunt in tempore, ad omnem autem motum sequitur prius et posterius, necesse est quod omnis motus sit in tempore. And because he had said that “before” and “after” are determined by the distance to the “now,” he shows how this occurs in a contrary manner with the past and the future. For in the past, that is “before” which is farther from the “now” but “after” which is nearer; but in the future it is just the opposite. If therefore “before” and “after” exist in time, and “before” and “after” follow upon every motion, then necessarily every motion exists in time.

Lecture 23
The Problems are Solved as to the Existence and Unity of Time.
Lectio 23
Chapter 14 cont.
ἄξιον δ' ἐπισκέψεως καὶ πῶς ποτε ἔχει ὁ χρόνος πρὸς τὴν ψυχήν, καὶ διὰ τί ἐν παντὶ δοκεῖ εἶναι ὁ χρόνος, καὶ ἐν γῇ καὶ ἐν θαλάττῃ καὶ ἐν οὐρανῷ. It is also worth considering how time can be related to the soul; and why time is thought to be in everything, both in earth and in sea and in heaven.
ἢ ὅτι κινήσεώς τι πάθος ἢ ἕξις, ἀριθμός γε ὤν, ταῦτα δὲ κινητὰ πάντα (ἐν τόπῳ γὰρ πάντα), ὁ δὲ χρόνος καὶ ἡ κίνησις ἅμα κατά τε δύναμιν καὶ κατ' ἐνέργειαν; Is because it is an attribute, or state, or movement (since it is the number of movement) and all these things are movable (for they are all in place), and time and movement are together, both in respect of potentiality and in respect of actuality?
πότερον δὲ μὴ οὔσης ψυχῆς εἴη ἂν ὁ χρόνος ἢ οὔ, ἀπορήσειεν ἄν τις. ἀδυνάτου γὰρ ὄντος εἶναι τοῦ ἀριθμήσοντος ἀδύνατον καὶ ἀριθμητόν τι εἶναι, ὥστε δῆλον ὅτι οὐδ' ἀριθμός. Whether if soul did not exist time would exist or not, is a question that may fairly be asked;
ἀριθμὸς γὰρ ἢ τὸ ἠριθμημένον ἢ τὸ ἀριθμητόν. εἰ δὲ μηδὲν ἄλλο πέφυκεν ἀριθμεῖν ἢ ψυχὴ καὶ ψυχῆς νοῦς, ἀδύνατον εἶναι χρόνον ψυχῆς μὴ οὔσης, for if there cannot be some one to count there cannot be anything that can be counted, so that evidently there cannot be number; for number is either what has been, or what can be, counted. But if nothing but soul, or in soul reason, is qualified to count, there would not be time unless there were soul,
ἀλλ' ἢ τοῦτο ὅ ποτε ὂν ἔστιν ὁ χρόνος, οἷον εἰ ἐνδέχεται κίνησιν εἶναι ἄνευ ψυχῆς. τὸ δὲ πρότερον καὶ ὕστερον ἐν κινήσει ἐστίν· χρόνος δὲ ταῦτ' ἐστὶν ᾗ ἀριθμητά ἐστιν. but only that of which time is an attribute, i.e. if movement can exist without soul, and the before and after are attributes of movement, and time is these qua numerable.
ἀπορήσειε δ' ἄν τις καὶ ποίας κινήσεως ὁ χρόνος ἀριθμός. One might also raise the question what sort of movement time is the number of.
ἢ ὁποιασοῦν; καὶ γὰρ γίγνεται ἐν χρόνῳ καὶ φθείρεται καὶ αὐξάνεται καὶ ἀλλοιοῦται καὶ φέρεται· ᾗ οὖν κίνησίς ἐστι, ταύτῃ ἐστὶν ἑκάστης κινήσεως ἀριθμός. διὸ κινήσεώς ἐστιν ἁπλῶς ἀριθμὸς (223b.) συνεχοῦς, ἀλλ' οὐ τινός. Must we not say 'of any kind'? For things both come into being in time and pass away, and grow, and are altered in time, and are moved locally; thus it is of each movement qua movement that time is the number. And so it is simply the number of continuous movement, not of any particular kind of it.
ἀλλ' ἔστι νῦν κεκινῆσθαι καὶ ἄλλο· ὧν ἑκατέρας τῆς κινήσεως εἴη ἂν ἀριθμός. ἕτερος οὖν χρόνος ἔστιν, καὶ ἅμα δύο ἴσοι χρόνοι ἂν εἶεν· But other things as well may have been moved now, and there would be a number of each of the two movements. Is there another time, then, and will there be two equal times at once?
ἢ οὔ; ὁ αὐτὸς γὰρ χρόνος καὶ εἷς ὁ ἴσος καὶ ἅμα· εἴδει δὲ καὶ οἱ μὴ ἅμα· εἰ γὰρ εἶεν κύνες, οἱ δ' ἵπποι, ἑκάτεροι δ' ἑπτά, ὁ αὐτὸς ἀριθμός. οὕτω δὲ καὶ τῶν κινήσεων τῶν ἅμα περαινομένων ὁ αὐτὸς χρόνος, ἀλλ' ἡ μὲν ταχεῖα ἴσως ἡ δ' οὔ, καὶ ἡ μὲν φορὰ ἡ δ' ἀλλοίωσις· ὁ μέντοι χρόνος ὁ αὐτός, εἴπερ καὶ [ὁ ἀριθμὸς] ἴσος καὶ ἅμα, τῆς τε ἀλλοιώσεως καὶ τῆς φορᾶς. καὶ διὰ τοῦτο αἱ μὲν κινήσεις ἕτεραι καὶ χωρίς, ὁ δὲ χρόνος πανταχοῦ ὁ αὐτός, ὅτι καὶ ὁ ἀριθμὸς εἷς καὶ ὁ αὐτὸς πανταχοῦ ὁ τῶν ἴσων καὶ ἅμα. Surely not. For a time that is both equal and simultaneous is one and the same time, and even those that are not simultaneous are one in kind; for if there were dogs, and horses, and seven of each, it would be the same number. So, too, movements that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration; still the time of the two changes is the same if their number also is equal and simultaneous; and for this reason, while the movements are different and separate, the time is everywhere the same, because the number of equal and simultaneous movements is everywhere one and the same.
ἐπεὶ δ' ἔστι φορὰ καὶ ταύτης ἡ κύκλῳ, ἀριθμεῖται δ' ἕκαστον ἑνί τινι συγγενεῖ, μονάδες μονάδι, ἵπποι δ' ἵππῳ, οὕτω <�δὲ> καὶ ὁ χρόνος χρόνῳ τινὶ ὡρισμένῳ, μετρεῖται δ', ὥσπερ εἴπομεν, ὅ τε χρόνος κινήσει καὶ ἡ κίνησις χρόνῳ (τοῦτο δ' ἐστίν, ὅτι ὑπὸ τῆς ὡρισμένης κινήσεως χρόνῳ μετρεῖται τῆς τε κινήσεως τὸ ποσὸν καὶ τοῦ χρόνου)— Now there is such a thing as locomotion, and in locomotion there is included circular movement, and everything is measured by some one thing homogeneous with it, units by a unit, horses by a horse, and similarly times by some definite time, and, as we said, time is measured by motion as well as motion by time (this being so because by a motion definite in time the quantity both of the motion and of the time is measured):
εἰ οὖν τὸ πρῶτον μέτρον πάντων τῶν συγγενῶν, ἡ κυκλοφορία ἡ ὁμαλὴς μέτρον μάλιστα, ὅτι ὁ ἀριθμὸς ὁ ταύτης γνωριμώτατος. ἀλλοίωσις μὲν οὖν οὐδὲ αὔξησις οὐδὲ γένεσις οὐκ εἰσὶν ὁμαλεῖς, φορὰ δ' ἔστιν. if, then, what is first is the measure of everything homogeneous with it, regular circular motion is above all else the measure, because the number of this is the best known. Now neither alteration nor increase nor coming into being can be regular, but locomotion can be.
διὸ καὶ δοκεῖ ὁ χρόνος εἶναι ἡ τῆς σφαίρας κίνησις, ὅτι ταύτῃ μετροῦνται αἱ ἄλλαι κινήσεις καὶ ὁ χρόνος ταύτῃ τῇ κινήσει. This also is why time is thought to be the movement of the sphere, viz. because the other movements are measured by this, and time by this movement.
διὰ δὲ τοῦτο καὶ τὸ εἰωθὸς λέγεσθαι συμβαίνει· φασὶν γὰρ κύκλον εἶναι τὰ ἀνθρώπινα πράγματα, καὶ τῶν ἄλλων τῶν κίνησιν ἐχόντων φυσικὴν καὶ γένεσιν καὶ φθοράν. τοῦτο δέ, ὅτι ταῦτα πάντα τῷ χρόνῳ κρίνεται, καὶ λαμβάνει τελευτὴν καὶ ἀρχὴν ὥσπερ ἂν εἰ κατά τινα περίοδον. καὶ γὰρ ὁ χρόνος αὐτὸς εἶναι δοκεῖ κύκλος τις· τοῦτο δὲ πάλιν δοκεῖ, διότι τοιαύτης ἐστὶ φορᾶς μέτρον καὶ μετρεῖται αὐτὸς ὑπὸ τοιαύτης. ὥστε τὸ λέγειν εἶναι τὰ γιγνόμενα τῶν πραγμάτων κύκλον τὸ λέγειν ἐστὶν τοῦ χρόνου εἶναί τινα κύκλον· τοῦτο δέ, ὅτι μετρεῖται τῇ κυκλοφορίᾳ· παρὰ γὰρ τὸ μέτρον οὐδὲν (224a.) ἄλλο παρεμφαίνεται τῷ μετρουμένῳ, ἀλλ' ἢ πλείω μέτρα τὸ ὅλον. This also explains the common saying that human affairs form a circle, and that there is a circle in all other things that have a natural movement and coming into being and passing away. This is because all other things are discriminated by time, and end and begin as though conforming to a cycle; for even time itself is thought to be a circle. And this opinion again is held because time is the measure of this kind of locomotion and is itself measured by such. So that to say that the things that come into being form a circle is to say that there is a circle of time; and this is to say that it is measured by the circular movement; for apart from the measure nothing else to be measured is observed; the whole is just a plurality of measures.
λέγεται δὲ ὀρθῶς καὶ ὅτι ἀριθμὸς μὲν ὁ αὐτὸς ὁ τῶν προβάτων καὶ τῶν κυνῶν, εἰ ἴσος ἑκάτερος, δεκὰς δὲ οὐχ ἡ αὐτὴ οὐδὲ δέκα τὰ αὐτά, ὥσπερ οὐδὲ τρίγωνα τὰ αὐτὰ τὸ ἰσόπλευρον καὶ τὸ σκαληνές, καίτοι σχῆμά γε ταὐτό, ὅτι τρίγωνα ἄμφω· ταὐτὸ γὰρ λέγεται οὗ μὴ διαφέρει διαφορᾷ, ἀλλ' οὐχὶ οὗ διαφέρει, οἷον τρίγωνον τριγώνου <�τριγώνου> διαφορᾷ διαφέρει· τοιγαροῦν ἕτερα τρίγωνα· σχήματος δὲ οὔ, ἀλλ' ἐν τῇ αὐτῇ διαιρέσει καὶ μιᾷ. σχῆμα γὰρ τὸ μὲν τοιόνδε κύκλος, τὸ δὲ τοιόνδε τρίγωνον, τούτου δὲ τὸ μὲν τοι όνδε ἰσόπλευρον, τὸ δὲ τοιόνδε σκαληνές. σχῆμα μὲν οὖν τὸ αὐτό, καὶ τοῦτο τρίγωνον, τρίγωνον δ' οὐ τὸ αὐτό. καὶ ἀριθμὸς δὴ ὁ αὐτός (οὐ γὰρ διαφέρει ἀριθμοῦ διαφορᾷ ὁ ἀριθμὸς αὐτῶν), δεκὰς δ' οὐχ ἡ αὐτή· ἐφ' ὧν γὰρ λέγεται, διαφέρει· τὰ μὲν γὰρ κύνες, τὰ δ' ἵπποι. καὶ περὶ μὲν χρόνου καὶ αὐτοῦ καὶ τῶν περὶ αὐτὸν οἰκείων τῇ σκέψει εἴρηται. It is said rightly, too, that the number of the sheep and of the dogs is the same number if the two numbers are equal, but not the same decad or the same ten; just as the equilateral and the scalene are not the same triangle, yet they are the same figure, because they are both triangles. For things are called the same so-and-so if they do not differ by a differentia of that thing, but not if they do; e.g. triangle differs from triangle by a differentia of triangle, therefore they are different triangles; but they do not differ by a differentia of figure, but are in one and the same division of it. For a figure of the one kind is a circle and a figure of another kind of triangle, and a triangle of one kind is equilateral and a triangle of another kind scalene. They are the same figure, then, that, triangle, but not the same triangle. Therefore the number of two groups also—is the same number (for their number does not differ by a differentia of number), but it is not the same decad; for the things of which it is asserted differ; one group are dogs, and the other horses. We have now discussed time—both time itself and the matters appropriate to the consideration of it.
Postquam philosophus determinavit de tempore, hic removet quasdam dubitationes circa tempus. Et primo circa existentiam temporis; secundo circa temporis unitatem, ibi: dubitabit autem aliquis et cetera. 625. After determining the truth about time, the Philosopher now settles certain doubts about time: First in regard to the existence of time; Secondly, in regard to the unity of time, at no. 630.
Circa primum duo facit: primo movet duas dubitationes; secundo solvit eas, ibi: aut quia motus et cetera. As to the first he does two things: First he raises the doubts; Secondly, he solves them, at no. 626.
Dicit ergo primo quod hae dubitationes indigent diligenti consideratione: scilicet quomodo tempus se habeat ad animam; et iterum quare tempus videatur esse ubique, scilicet in terra, in mari et in caelo. He says therefore first [451] that certain problems require diligent consideration: namely, that of how time is related to the soul; and that of how time seems to be everywhere, i.e., an earth, on the sea, and in the air.
Deinde cum dicit: aut quia motus etc., solvit praemissas quaestiones. Et primo secundam, quae facilior est; secundo primam, ibi: utrum autem cum non sit et cetera. 626. Then [452] he answers these questions: First he answers the second question, because it is easier; Secondly, he answers the first one, at no. 627.
Deinde cum dicit: utrum autem cum non sit anima etc., solvit primam quaestionem. Et circa hoc tria facit: primo movet dubitationem; secundo obiicit ad quaestionem, ibi: impossibile enim etc.; tertio solvit, ibi: sed aut hoc et cetera. Est ergo dubitatio, utrum non existente anima esset tempus, aut non. 627. Then [453] he answers the first question, and as to this he does three things: First he raises the question; Secondly, he gives an objection to the question, at no. 628; Thirdly, he resolves the question, at no. 629. The question, therefore, is this: Would time exist if no mind existed?
Dicit ergo quod tempus est quoddam accidens motus, quia est numerus eius (accidens autem consuevit nomine habitus et passionis nominari): unde ubicumque est motus oportet quod sit tempus. Omnia autem corpora sunt mobilia, etsi non aliis motibus, saltem motu locali; quia omnia sunt in loco. [72158] In Physic., lib. 4 l. 23 n. 3 He says therefore [452] that time is a certain accident of motion, because it is its number (an accident is wont to be called a “possession” [ habitus ] and “property” [ passio ]: hence, wherever there is motion, time must be. Now all bodies are mobile, if not with other motions, at least with respect to local motion, because all things are in place.
Et quia posset aliquis dicere quod licet sint mobilia, non tamen omnia moventur, sed quaedam quiescunt, et sic tempus non videtur in omnibus esse: ad hoc excludendum subiungit quod tempus est simul cum motu, sive motus accipiatur secundum actum sive secundum potentiam. Quaecumque enim sunt possibilia moveri et non moventur actu, quiescunt. Tempus autem non solum mensurat motum, sed etiam quietem, ut supra dictum est. Unde relinquitur quod ubicumque est motus, vel actu vel potentia, quod ibi sit tempus. And because someone could say that although they are mobile, they are not all being moved, but some are at rest, and thus time does not seem to be in all, to counter this he adds that time accompanies motion, whether motion be actual or potential. For things that are capable of motion, and are not actually being moved, are at rest. But time measures not only motion but rest as well, as was said above. Hence, wherever there is motion either actually or potentially, there time is.
Secundo ibi: impossibile enim cum sit etc., obiicit ad ostendendum quod non. Quia si impossibile esset esse aliquod potens numerare, impossibile esset esse aliquod numerabile, potens scilicet numerari. Sed si non est numerabile, non est numerus; quia numerus non est nisi in eo quod numeratur actu, vel quod est numerabile in potentia. Relinquitur ergo quod si non est aliquod potens numerare, quod non sit numerus. Sed nihil aliud natum est numerare quam anima, et inter partes animae non alia quam intellectus; quia numeratio fit per collationem numeratorum ad unam primam mensuram, conferre autem rationis est. Si igitur non est anima intellectiva, non est numerus. Tempus autem est numerus, ut dictum est. Si ergo non est anima intellectiva, non est tempus. 628. Secondly, [454] he objects, to say it would not. For if it were impossible for something able to count to exist, it would be impossible for some thing countable to exist, i.e., able to be counted. But if there is nothing countable, then there is no number, because number does not exist except in that which is being actually counted or which is potentially countable. Consequently, if there is no one able to count, there is no number. But only the soul is disposed by nature for counting, and among the parts of the soul only the intellect; for counting consists in comparing the things counted with one primary measure, and comparing is a function of reason. Consequently, if there is no intellective soul, there is no number. But time is a number, an was said. If therefore, there is no intellective soul, there is no time.
Deinde cum dicit: sed aut hoc etc., solvit dubitationem. Et dicit quod aut oportet dicere quod tempus non sit, si non est anima; aut oportet hoc dicere verius, quod tempus est utcumque ens sine anima, ut puta si contingit motum esse sine anima. Sicut enim ponitur motus, ita necesse est poni tempus: quia prius et posterius in motu sunt; et haec, scilicet prius et posterius motus, inquantum sunt numerabilia, sunt ipsum tempus. 629. Then [455] he answers the question. And he says that it is necessary to say either that time is not, if the soul is not; or to say what is truer, that time is still some sort of being even without the soul’s existing, similar to motion’s existing without the soul’s existing. For as motion is posited, so is it also necessary to posit time, because “before” and “after” exist in motion, and it is these things, namely, the “before” and “after” in motion, insofar as they are numberable, that are time.
Ad evidentiam autem huius solutionis considerandum est, quod positis rebus numeratis, necesse est poni numerum. Unde sicut res numeratae dependent a numerante, ita et numerus earum. Esse autem rerum numeratarum non dependet ab intellectu, nisi sit aliquis intellectus qui sit causa rerum, sicut est intellectus divinus: non autem dependet ab intellectu animae. Unde nec numerus rerum ab intellectu animae dependet: sed solum ipsa numeratio, quae est actus animae, ab intellectu animae dependet. Sicuti ergo possunt esse sensibilia sensu non existente, et intelligibilia intellectu non existente, ita possunt esse numerabilia et numerus, non existente numerante. To make this solution more evident it must be considered that once a series of numbered things is posited, it is necessary to posit number. Hence just as counted things depend on someone’s counting, so also their count [or number]. However, the existence of counted things does not depend on an intellect, unless it be an intellect which is the cause of things, as is the divine intellect, It does not depend on the intellect of the same. Hence neither does the number of things depend on the intellect in the human soul; only the counting of them, which counting is an act of the soul, depends on the intellect in the soul. Consequently, just as there can be things perceptible to sense even though no sense exists, and intelligible even though no intelligence exists, so there can exist both numberable [countable] things, and number even though no counter exist.
Sed forte conditionalis quam primo posuit, est vera, scilicet quod si est impossibile esse aliquem numerantem, impossibile est esse aliquod numerabile: sicut haec est vera, si impossibile est esse aliquem sentientem, impossibile est esse aliquid sensibile. Si enim est sensibile, potest sentiri, et si potest sentiri, potest esse aliquod sentiens; licet non sequatur quod si est sensibile, quod sit sentiens. Et similiter sequitur quod si est aliquid numerabile, quod possit esse aliquid numerans. Unde si impossibile est esse aliquod numerans, impossibile est esse aliquid numerabile: non tamen sequitur quod si non est numerans, quod non sit numerabile, ut obiectio philosophi procedebat. But perhaps the conditional he first mentioned is true, namely, that if no counter could exist, nothing countable could exist, just as the proposition is true that if there could be no one to sense, there could be nothing sensible. For if there is something sensible, it can be sensed, and if it can be sensed, there can be something to sense it—although it does not follow that if there is something sensible, there is something sensing. In like manner, it follows that if there is something countable, there can be someone to count. Consequently, if no one to count could exist, nothing countable could exist. However, it does not follow that if there is no one counting, there is nothing countable, which is the objection raised by the Philosopher.
Si ergo motus haberet esse fixum in rebus, sicut lapis vel equus, posset absolute dici quod sicut etiam anima non existente est numerus lapidum, ita etiam anima non existente esset numerus motus, qui est tempus. Sed motus non habet esse fixum in rebus, nec aliquid actu invenitur in rebus de motu, nisi quoddam indivisibile motus, quod est motus divisio: sed totalitas motus accipitur per considerationem animae, comparantis priorem dispositionem mobilis ad posteriorem. Sic igitur et tempus non habet esse extra animam, nisi secundum suum indivisibile: ipsa autem totalitas temporis accipitur per ordinationem animae numerantis prius et posterius in motu, ut supra dictum est. Et ideo signanter dicit philosophus quod tempus, non existente anima, est utcumque ens, idest imperfecte; sicut et si dicatur quod motum contingit esse sine anima imperfecte. Therefore, if motion had a fixed existence in reality, as a stone or a horse has, one could say unqualifiedly that, just as with no soul existing there exists a number of stones, so also with no soul existing, there would exist a number of motion, which is time. However, motion does not have a fixed existence in reality, nor is anything actual of motion found in things but a certain indivisible of motion which divides motion; indeed, the totality of motion comes to be on account of the mind considering and comparing a previous state of the mobile to a subsequent state. According to this, then, time also has no existence outside the soul except according to its indivisible; while the totality of time is had by an ordering process of the mind enumerating the prior and subsequent in motion [i.e., “before” and “after”], as was said above. And therefore the Philosopher said significantly that with no soul existing time is a being “of a sort,” i.e., imperfectly; this is similar to the statement that motion exists imperfectly without a soul existing.
Et per hoc solvuntur rationes supra positae ad ostendendum quod tempus non sit, quia componitur ex partibus non existentibus. Patet enim ex praedictis, quod non habet esse perfectum extra animam, sicut nec motus. So this answers the arguments mentioned earlier, to show that time does not exist on the ground that it is composed of parts that do not exist. For it is clear from the foregoing that like motion it does not have perfect existence outside the soul.
Deinde cum dicit: dubitabit autem aliquis etc., movet quaestionem de unitate temporis, sive de comparatione temporis ad motum. Et circa hoc tria facit: primo movet dubitationem; secundo solvit, ibi: aut cuiuslibet etc., tertio manifestat quoddam quod supposuerat, ibi: dicitur autem recte et cetera. 630. Then [456] he raises a question about the oneness of time, or about the relation of time to motion. As to this he does three things: First he raises the question; Secondly, he answers it, at no. 631; Thirdly, he explains something he took as a presupposition, at no. 637.
Dicit ergo primo quod dubitatio est, cum tempus sit numerus motus, cuius vel qualis motus sit numerus. Deinde cum dicit: aut cuiuslibet etc., solvit dubitationem. Et primo excludit falsam solutionem; secundo ponit veram, ibi: quoniam autem est loci mutatio et cetera. So he says first [456] that there is question, since time is the number of motion, of whose, or of what sort of, motion it is the number. Then [457] he answers the question. First he rejects a false solution; Secondly, he gives the true one, at no. 634;
Circa primum tria facit: primo ponit solutionem falsam; secundo improbat eam ducendo ad inconveniens, ibi: sed est nunc moveri etc.; tertio ostendit illud inconveniens esse impossibile, ibi: aut non: omne namque et cetera. In regard to the first he does three things: First he gives the false answer; Secondly he disproves it by leading to a discrepancy, at no. 632; Thirdly, he shows that this discrepancy is really an Impossibility, at no. 633.
Est ergo prima solutio, quod tempus sit numerus cuiuslibet motus. Et ad hoc probandum inducit quod omnis motus est in tempore; scilicet et generatio et augmentum et alteratio et loci mutatio. Quod autem convenit omni motui, convenit motui secundum quod ipsum: esse autem in tempore est numerari tempore. Sic igitur videtur quod quilibet motus, inquantum huiusmodi, habet numerum: unde cum tempus sit numerus motus, videtur sequi quod tempus sit numerus motus continui universaliter, et non alicuius determinati motus. 631. The first solution, therefore, is that time is the number of any motion whatsoever. To prove this he brings up that every motion exists in time; namely, generation, and increase, and alteration, and local motion. Now what is found in every motion belongs to motion as such. But to exist in time is to be numbered by time. Consequently, it seems that every motion as such has a number; hence, since time is the number of motion, it seems to follow that time is the number of each and every continuous motion and not of some definite motion.
Deinde cum dicit: sed est nunc moveri etc., improbat praedictam solutionem. Contingit enim aliqua duo simul moveri: si ergo cuiuslibet motus tempus sit numerus, sequetur quod duorum motuum simul existentium sit alterum et alterum tempus: et sic ulterius sequetur quod duo tempora aequalia sint simul, utpote duo dies vel duae horae. Duo autem tempora inaequalia simul esse, non est admirabile, ut diem et horam. 632. Then [458] he disproves this solution. For let us assume two things that are moving together: if, therefore, time to the number of any motion at all, it will follow that of two simultaneous motions each will have its own time, and so it will further follow that two equal times exist at once—e.g., two days or two hours. Now it is not strange for two unequal times to exist at once, e.g., a day and an hour.
Deinde cum dicit: aut non: omne namque tempus etc., ostendit hoc esse impossibile, scilicet duo tempora aequalia simul esse: quia omne tempus quod est simul et similiter, idest aequaliter, est unum tantum: sed tempus quod non est simul, non est unum numero; sed species eius est una, sicut dies cum die, et annus cum anno. 633. Then [459] he shows that it is impossible for two equal times to exist at once. For every time that is simultaneous and similar, i.e., equal, is one; but time that is not simultaneous is not numerically one, although it is one in species, as day with day and year with year.
Et hoc manifestat per simile in aliis numeratis. Si enim sunt septem equi et septem canes, non differunt secundum numerum, sed differunt secundum speciem rerum numeratarum. Et similiter omnium motuum qui simul terminantur et secundum principium et secundum finem, est idem tempus: sed motus differunt secundum proprias rationes, inquantum forte unus est velox et alius tardus, et unus est loci mutatio et alius alteratio. Sed tempus est idem, si alterationis et loci mutationis sit aequalis numerus, supposito quod sint simul. Et propter hoc oportet quod motus sint alteri et divisi ab invicem, sed tempus in omnibus est idem: quia unus et idem numerus est eorum quae sunt aequalia et simul, ubicumque sint. And he explains this by a similarity in other things that are numbered. For if there are seven horses and seven dogs, there is no difference so far as the number is concerned, but the difference is due to the species of the things counted. In like manner, for all motions which have simultaneous terms both as to their beginning and as to their end, there is the same time; yet the motions differ according to their proper notions, in that, perchance, one is fast and the other slow, one is local motion and the other alteration. But the time is the same if the number of the alteration and of the local motion is the same, supposing, of course, that they are simultaneous. Consequently, motions must be distinct from one another, but the time in all of them is the same— because there is one and the same number for all those that are equal and simultaneous, no matter where they occur.
Deinde cum dicit: quoniam autem est loci mutatio etc., ponit veram solutionem. Et circa hoc tria facit: primo praemittit, quaedam quae sunt necessaria ad solutionem; secundo ex praemissis solutionem concludit, ibi: si igitur quod primum etc.; tertio manifestat solutionem per dicta aliorum, ibi: unde et videtur et cetera. 634. Then [460] he gives the true solution. Concerning this he does three things: First he prefaces certain facts required for the solution; Secondly, from these he arrives at the solution, at no. 635; Thirdly, he makes the solution clear by appealing to the statements of others, at no. 636.
Circa primum praemittit tria. Quorum primum est, quod inter alios motus, primus et magis simplex et regularis est motus localis; et inter alios motus locales, motus circularis, ut in octavo probabitur. Secundum est quod unumquodque numeratur uno quodam proximo, idest sui generis, sicut unitates unitate, et equi equo, ut patet in X Metaphys.: unde oportet quod tempus quodam determinato tempore mensuretur, sicut videmus quod omnia tempora mensurantur per diem. Tertium quod praemittit est, quod tempus mensuratur motu et motus tempore, ut supra dictum est: et hoc ideo est, quia aliquo determinato motu, et aliquo determinato tempore, mensuratur quantitas cuiuslibet motus et temporis. In regard to the first he mentions three preliminary facts. The first of these is that among motions, the first and more simple and regular is local motion, and among these, circular motion, as will be proved in Book VIII. The second is that each thing is numbered by something near it, i.e., by something homogeneous with it, as units by a unit and horses by a horse, as is clear in Metaphysics X; hence time must be measured by some definite time, as we see that all times are measured by the day. The third presupposition is that time is measured by motion, and motion by time, as was said above. This is so because it is in terms of some definite motion and some definite time that the quantity of any motion and time is measured.
Deinde cum dicit: si igitur quod primum mensura est etc., concludit ex praemissis, quod si aliquid quod est primum, est mensura omnium proximorum, idest omnium quae sunt sui generis, necesse est quod circulatio, quae est maxime regularis, sit mensura omnium motuum. Dicitur autem motus regularis, qui est unus et uniformis. Haec autem regularitas non potest inveniri in alteratione et augmento, quia non sunt usquequaque continui nec aequalis velocitatis. Sed in loci mutatione inveniri potest regularitas, quia potest esse aliquis motus localis continuus et uniformis; et talis est solus motus circularis, ut in octavo probabitur. 635. Then [461] he concludes from the foregoing that if something that is first is the measure of all things that are near it, i.e., of all the things in its genus, it is necessary that circular motion, which is regular above all, be the measure of all motions. Now a motion is called “regular,” if it is one and uniform. But such regularity cannot be found in alteration and growth, because they are not incessantly continuous or of equal [constant] speed. But regularity can be found in change of place, because there can be a local motion that is continuous and uniform, and the only such motion is circular motion, as will be proved in Book VIII.
Et inter alios motus circulares, maxime uniformis et regularis est primus motus, qui revolvit totum firmamentum motu diurno: unde illa circulatio, tanquam prima et simplicior et regularior, est mensura omnium motuum. Oportet autem motum regularem esse mensuram seu numerum aliorum, quia omnis mensura debet esse certissima; et talia sunt quae uniformiter se habent. Ex hoc igitur colligere possumus, quod si prima circulatio mensurat omnem motum, et motus mensurantur a tempore, inquantum mensurantur quodam motu; necesse est dicere quod tempus sit numerus primae circulationis, secundum quam mensuratur tempus, et ad quem mensurantur omnes alii motus temporis mensuratione. Now among circular motions the most uniform and regular is the first motion which turns the whole firmament in a daily cycle; hence that revolution, as being the first and simplest and most regular, is the measure of all motions. But a regular motion must be the measure and number of the others, because every measure ought to be most certain—and those that are uniform are such. Consequently, from this we can gather that if the first circular motion measures every motion, and motions are measured by time insofar as they are measured by some motion, it has to be said that time is the number of the first circular motion, according to which time is measured, and in relation to which are measured all other motions that are timed.
Deinde cum dicit: unde et videtur tempus etc., approbat praedictam solutionem per opiniones aliorum. Et primo per opinionem errantium, qui moti fuerunt ad dicendum quod motus sphaerae caelestis sit tempus, propter hoc quod hoc motu mensurantur omnes alii motus, et tempus mensuratur hoc motu: manifestum est enim quod dicimus diem vel annum completum, attendentes ad motum caeli. 636. Then [462] he corroborates his solution by appealing to the opinions of others, and first of all by the opinion of those who were led to assert that the movement of the heavenly sphere is time, on the ground that all other motions, and time itself, are measured by that movement; for it is evident that we speak of a complete day or year by reckoning from the motion of the heavens.
Secundo ex usu communiter loquentium, ibi: propter hoc autem et cetera. Et dicit quod propter hoc, scilicet quod tempus est numerus circulationis primae, accidit quod consuevit dici, scilicet quod quidam circulus sit in rebus humanis, et in aliis quae moventur naturaliter et generantur et corrumpuntur. Quod ideo est, quia omnia huiusmodi mensurantur tempore, et accipiunt principium et finem in tempore, ac si tempus secundum quandam circulationem sit: quia et ipsum tempus videtur esse quidam circulus. Et hoc iterum videtur propter hoc, quod est mensura circulationis, et etiam a tali circulatione mensuratur. Et ideo dicere quod eorum quae fiunt in tempore, est quidam circulus, nihil est aliud quam dicere temporis esse quendam circulum; quod accidit propter hoc quod tempus mensuratur circulatione. Illud enim quod mensuratur, non videtur esse aliud quam mensura: sed multae mensurae videntur facere unum totum, sicut multae unitates unum numerum, et multae mensurae panni unam quantitatem panni. Et hoc verum est, quando accipitur mensura unius generis. Secondly [463] from a common saying. And he says that because of this, namely, that time is the number of the first circular movement, it comes about that people are want to say that there is a cycle in human affairs, and in other things that move naturally and come into being and pass away. This is so because all such things are measured by time, and have a beginning and an end in time, as if time moved in a circle, because time itself seems to be a certain circle. And this again seems to be so because time is a measure of circular movement and is also measured by such a circular movement. And therefore, to say that of things which take place in time there is a certain circle, is nothing other than to say that time is a certain circle—which occurs because time is measured by a circular movement. For that which is measured is not seen to be different from its measure: but rather many measures are seen to make one whole, as many units make one number, and many measures of cloth one quantity of cloth. And this is true when a homogeneous measure is taken.
Sic igitur patet quod tempus primo mensurat et numerat primum motum circularem, et per eum mensurat omnes alios motus. Unde est unum tempus tantum propter unitatem primi motus; et tamen quicumque sentit quemcumque motum, sentit tempus, eo quod ex primo motu causatur mutabilitas in omnibus mobilibus, ut supra dictum est. From all this it is clear that time first measures and numbers the first circular motion and through it measures all other motions. Consequently, there is but one time, due to the oneness of the first motion; and yet whoever perceives any motion whatever, perceives time, because from the first motion there is caused, mutability in all mobile- things, as was said above.
Deinde cum dicit: dicitur autem recte etc., manifestat quoddam, quod supra dixerat, qualiter sit intelligendum. Dixerat enim quod idem est numerus septem canum et septem equorum. Quomodo ergo hoc sit verum ostendit: et dicit quod recte potest dici, si aequalis est numerus aliquarum rerum diversarum, puta ovium et canum, quod idem sit numerus utrorumque, ut puta si tam oves quam canes sint decem. Sed non potest dici quod hoc ipsum quod est esse decem, sit idem canum et ovium: non enim eadem decem sunt decem canes et decem oves. Et hoc ideo, quia genus potest cum additione unitatis vel identitatis praedicari de pluribus individuis existentibus in una specie, et similiter genus remotum de pluribus speciebus existentibus sub uno genere propinquo; neque tamen species de individuis, neque genus propinquum de speciebus diversis potest praedicari cum additione unitatis vel identitatis. 637. Then [464] he explains how something he mentioned above is to be understood. For he said that the number of seven dogs and seven horses is the same number. How this is true he now explains. And he says that it is correct to say, if the number of certain different things is equal, for example, of sheep and dogs, that the number is the same—for example, if the sheep and the dogs are both 10. But it cannot be said that to be 10 is the same for the dogs and sheep, for 10 dogs are not the same 10 as 10 sheep. The reason for this is that a genus can be predicated, with the addition of unity or identity [i.e., as “one genus” or “the same genus”], of several individuals of the same species; and in like manner, the remote genus can be predicated of several species existing under one proximate genus; but neither can the species be predicated of individuals, nor the proximate genus of diverse species, with the addition of unity or identity.
Et huius consequenter ponit exemplum. Sunt enim duae species trianguli, scilicet aequilaterus, idest habens tria latera aequalia, et gradatus, idest habens tria latera inaequalia; figura autem est genus trianguli. Non ergo possumus dicere quod aequilaterus et gradatus sit idem triangulus; sed possumus dicere quod sunt eadem figura, quia utrumque continetur sub triangulo, qui est una species figurae. Et huius assignat rationem: quia cum idem et diversum seu differens opponantur, ibi possumus identitatem dicere, ubi differentia non invenitur; sed non possumus dicere identitatem, ubi invenitur differentia. Manifestum est autem quod aequilaterus et gradatus differunt ad invicem differentia trianguli, idest quae est proprie trianguli divisiva; et hoc ideo quia sunt diversae species trianguli. Sed aequilaterus et gradatus non differunt secundum differentiam figurae, sed sub una et eadem differentia divisiva figurae continentur. And he then gives an example of what he means. For there are two species of triangle, equilateral, i.e., having three equal sides, and scalene, i.e., having three unequal sides. Now “figure” is the genus for “triangle.” We therefore can not say that equilateral and scalene are the same “triangle,” but we can say that they are the same “figure,” because both are contained under “triangle” which is one species of “figure.” He gives the reason for this, which is that since “identical,” and “diverse” or “different,” are opposed, we can speak of identity whenever no difference is found, but we cannot speak of identity where there is a difference. But it is clear that equilateral and scalene differ mutually by reason of a difference that divides “triangle,” because they are diverse species of triangle. But “equilateral” and “scalene” do not differ in respect of the difference “figure”; rather, they are contained under one and the same difference that divides “figure.”
Et hoc sic patet. Si enim dividamus figuram in suas species, quae per differentias constituuntur, invenietur quod alia erit circulus, et alia triangulus, et sic de aliis speciebus figurae; sed si dividamus triangulum, inveniemus quod alia species eius est aequilaterus, et alia gradatus. Manifestum est igitur quod aequilaterus et gradatus sunt una figura, quia continentur sub una specie figurae, quae est triangulus: sed non sunt unus triangulus, quia sunt diversae trianguli species. And this is clear thus. If we divide “figure” into its species which are brought about by differences, it will be found that one species is a circle, another a triangle, and so on for the other species of figure. But if we divide “triangle,” we will find that one species is “equilateral,” another “scalene.” It is clear, therefore, that equilateral and scalene are one “figure,” because they are contained under the one species of “figure,” the species “triangle,” but they are not one “triangle,” because they are diverse species of “triangle.”
Et similiter est in proposito. Numerus enim dividitur in diversas species, quarum una est decem. Omnia ergo quae sunt decem, dicuntur habere unum numerum; quia non differunt ad invicem secundum speciem numeri, cum contineantur sub una numeri specie. Sed non potest dici quod sint eadem decem; quia ea quibus applicatur numerus denarius, differunt, cum quaedam horum sint canes et quaedam equi. The same thing applies to our proposition. For number is divided into diverse species, one of which is 10. Therefore all things that are 10 are said to have one number, because they do not differ from the other in regard to the species of their number, since they are contained under one and the same species of number. But we cannot say that they are the same 10, because the things being called “10” are different, since some are dogs and some horses.
Videtur autem hoc introduxisse Aristoteles, ne aliquis ad sustinendam unitatem temporis sit contentus eo quod dicitur unum numerum esse aequalium numero, licet diversorum: quia licet sit idem denarius vel ternarius propter unitatem speciei, non tamen est idem denarius vel ternarius propter diversitatem quae est secundum numerum ex parte materiae. Unde secundum istam rationem sequeretur quod tempus esset unum specie, sed non numero. Et ideo ad accipiendam veram temporis unitatem, oportet recurrere ad unitatem primi motus, qui primo mensuratur tempore, et quo etiam mensuratur tempus. Aristotle seems to have brought up this point so that no one, in trying to uphold the unity of time, would be content with saying that there is one number for things that are equal in number, even though the things be diverse; for although one might have a same 10 or 3 on account of a unity of species, yet it is not the same 10 or 3 on account of the diversity in number as based on matter. Hence, according to this reasoning, it would follow that time would be specifically, but not numerically, one. Therefore to get at the true unity of time, we must have recourse to the unity of the first motion, which is the first thing measured by time, and by which time itself is measured.
Ultimo autem epilogando concludit, dictum esse de tempore, et de iis quae sunt propria ad considerationem temporis. Finally, in summary, he concludes that we have finished with our consideration of time, and of the things that are proper to a consideration of time.