It is necessary that whatever is moved, be moved by another.
Chapter 1 1 Ἅπαν τὸ κινούμενον ὑπό τινος ἀνάγκη κινεῖσθαι· εἰ μὲν γὰρ ἐν ἑαυτῷ μὴ ἔχει τὴν ἀρχὴν τῆς κινήσεως, φανερὸν ὅτι ὑφ' ἑτέρου κινεῖται (ἄλλο γὰρ ἔσται τὸ κινοῦν)· εἰ δ' ἐν αὑτῷ, ἔστω [τὸ] εἰλημμένον ἐφ' οὗ τὸ ΑΒ ὃ κινεῖται καθ' αὑτό, ἀλλὰ μὴ <�τῷ τῶν> τούτου τι κινεῖσθαι. πρῶτον μὲν οὖν τὸ ὑπολαμβάνειν τὸ ΑΒ ὑφ' ἑαυτοῦ κινεῖσθαι διὰ τὸ ὅλον τε κινεῖσθαι καὶ ὑπ' οὐδενὸς τῶν ἔξωθεν ὅμοιόν ἐστιν ὥσπερ εἰ τοῦ ΚΛ κινοῦντος τὸ ΛΜ καὶ αὐτοῦ κινουμένου εἰ μὴ φάσκοι τις τὸ ΚΜ κινεῖσθαι ὑπό τινος, διὰ τὸ μὴ φανερὸν εἶναι πότερον τὸ κινοῦν καὶ πότερον τὸ κινούμενον· Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else that moves it. If on the other hand it has the source of its motion in itself, let AB be taken to represent that which is in motion essentially of itself and not in virtue of the fact that something belonging to it is in motion. Now in the first place to assume that Ab, because it is in motion as a whole and is not moved by anything external to itself, is therefore moved by itself—this is just as if, supposing that KL is moving LM and is also itself in motion, we were to deny that KM is moved by anything on the ground that it is not evident which is the part that is moving it and which the part that is moved. εἶτα τὸ μὴ ὑπό τινος κινούμενον (242a.) οὐκ ἀνάγκη παύσασθαι κινούμενον τῷ ἄλλο ἠρεμεῖν, ἀλλ' εἴ τι ἠρεμεῖ τῷ ἄλλο πεπαῦσθαι κινούμενον, ἀνάγκη ὑπό τινος αὐτὸ κινεῖσθαι. τούτου δ' εἰλημμένου πᾶν τὸ κινούμενον κινήσεται ὑπό τινος. ἐπεὶ γὰρ εἴληπται [τὸ] κινούμενον ἐφ' ᾧ τὸ ΑΒ, ἀνάγκη διαιρετὸν αὐτὸ εἶναι· πᾶν γὰρ τὸ κινούμενον διαιρετόν. διῃρήσθω δὴ κατὰ τὸ Γ. τοῦ δὴ ΓΒ μὴ κινουμένου οὐ κινηθήσεται τὸ ΑΒ. εἰ γὰρ κινήσεται, δῆλον ὅτι τὸ ΑΓ κινοῖτ' ἂν τοῦ ΓΒ ἠρεμοῦντος, ὥστε οὐ καθ' αὑτὸ κινηθήσεται καὶ πρῶτον. ἀλλ' ὑπέκειτο καθ' αὑτὸ κινεῖσθαι καὶ πρῶτον. ἀνάγκη ἄρα τοῦ ΓΒ μὴ κινουμένου ἠρεμεῖν τὸ ΑΒ. ὃ δὲ ἠρεμεῖ (45) μὴ κινουμένου τινός, ὡμολόγηται ὑπό τινος κινεῖσθαι, ὥστε πᾶν ἀνάγκη τὸ κινούμενον ὑπό τινος κινεῖσθαι· ἀεὶ γὰρ ἔσται τὸ κινούμενον διαιρετόν, τοῦ δὲ μέρους μὴ κινουμένου ἀνάγκη καὶ τὸ ὅλον ἠρεμεῖν. In the second place that which is in motion without being moved by anything does not necessarily cease from its motion because something else is at rest, but a thing must be moved by something if the fact of something else having ceased from its motion causes it to be at rest. Thus, if this is accepted, everything that is in motion must be moved by something. For AB, which has been taken to represent that which is in motion, must be divisible since everything that is in motion is divisible. Let it be divided, then, at G. Now if GB is not in motion, then AB will not be in motion: for if it is, it is clear that AG would be in motion while BG is at rest, and thus AB cannot be in motion essentially and primarily. But ex hypothesi AB is in motion essentially and primarily. Therefore if GB is not in motion AB will be at rest. But we have agreed that that which is at rest if something else is not in motion must be moved by something. Consequently, everything that is in motion must be moved by something: for that which is in motion will always be divisible, and if a part of it is not in motion the whole must be at rest.
Postquam philosophus in praecedentibus libris determinavit de motu secundum se, et de consequentibus ad ipsum, et de partibus eius, hic incipit determinare de motu per comparationem ad motores et mobilia. Et dividitur in partes duas. In prima ostendit esse primum motum et primum motorem. In secunda inquirit qualis sit motus primus et primus motor; et hoc in octavo libro, ibi: utrum autem factus sit aliquando et cetera. 884. After discussing motion in itself, and the concomitants of motion, and the division of motion into parts, in the preceding books, the Philosopher now begins to treat of motion in its relationship to movers and things moved, i.e., the mobiles. The treatment falls into two parts; In the first he shows that there is a first motion and a first mover; In the second he investigates the properties of the first motion and of the first mover, in Book VIII. Prima autem pars dividitur in partes duas. In prima parte ostendit esse primum motum et primum motorem. Et quia ea quae sunt unius ordinis, habent aliquam comparationem ad invicem, ideo in secunda parte determinat de comparatione motuum ad invicem, ibi: dubitabit autem utique et cetera. The first part is divided into two sections: In the first he shows that there is a first motion and a first mover. And because things that belong to one order are mutually related, therefore in the second part he compares the various types of motion (L-7). Circa primum tria facit: primo praemittit quoddam quo indiget ad propositum ostendendum; secundo ostendit propositum, ibi: quoniam autem omne quod movetur etc.; tertio manifestat quoddam quod supposuerat, ibi: primum autem movens et cetera. About the first he does three things: First he mentions the pre-notes needed for proving the proposition; Secondly, he proves the proposition (L. 2). Thirdly, he proves something he took for granted (L. 3) Proponit ergo primo quod necesse est omne quod movetur, ab aliquo alio moveri. Quod quidem in aliquibus est manifestum. Sunt enim quaedam quae non habent in seipsis principium sui motus, sed principium motus ipsorum est ab extrinseco, sicut in his quae per violentiam moventur. Si ergo aliquid sit quod non habeat in seipso principium sui motus, sed principium sui motus est ab extrinseco, manifestum est quod ab alio movetur. Si vero sit aliquod mobile quod habeat in seipso principium sui motus, circa hoc potest esse dubium an ab alio moveatur. Et ideo circa hoc instat, ad ostendendum quod ab alio movetur. Si ergo aliquid tale ponatur non moveri ab alio, accipiatur mobile ab, cui quidem moveri conveniat secundum se et primo, non autem ex eo quod aliqua pars eius movetur. Sic enim non moveretur secundum se, sed secundum partem; oportet autem, si aliquid movet seipsum non motum ab altero, quod sit primo et per se motum; sicut si aliquid est calidum non ab alio, oportet quod sit primo et per se calidum. 885. He proposes therefore first (676) that everything that is being moved is necessarily being moved by some other. In some cases this is indeed evident, for there are some things which do not possess in themselves the principle of their motion; rather the principle of their motion is from without, as in things which are being moved by compulsion. Therefore, if there is anything that does not have in itself the principle of its own motion but its principle of motion is from without, it is clear that it is being moved by some other. However, if there is a mobile which does have in itself the principle of its own motion, there could be doubt whether it too is being moved by some other. Accordingly, he devotes himself to showing that this type of mobile is being moved by some other. Therefore, if it is supposed that such a mobile is not being moved by some other, let AB be a mobile capable of being moved primarily and according to itself and not in the sense that some part of it is being moved; for then it would not be being moved according to itself, but according to a part. Now it is necessary that if something moves itself without having been moved by some other, that it be moved primarily and per se; for example, if something is hot not from some other source, it must be primarily and per se hot. Hoc ergo dato, procedit ad propositum ostendendum dupliciter: primo quidem excludendo illud, unde maxime videri posset quod aliquid non ab alio moveatur; secundo directe ostendendo quod nihil potest a seipso moveri, ibi: amplius quod a seipso movetur et cetera. With this in mind, he proceeds to prove his proposition in two ways: First by excluding the most evident case in which it would appear that something is not being moved by some other; Secondly, by proving directly that nothing can be moved by itself, at 886. Id autem ex quo maxime videtur quod aliquid non moveatur ab alio, est quia non movetur ab aliquo exteriori, sed ab interiori principio. The most evident reason why it seems that something is not being moved by some other is that it is not being moved by something outside itself but by an intrinsic principle. Dicit ergo primo, quod opinari quod ab moveatur a seipso propter hoc quod totum movetur, et non movetur ab aliquo exteriori, simile est ac si aliquis diceret quod mobile, cuius una pars movetur et alia movet, moveat seipsum, propter hoc quod non discernitur quae pars sit movens, et quae sit mota; sicut si huiusmodi mobilis quod est dez, pars quae est de, moveat partem quae est ez, et non videatur quae pars earum sit movens et quae sit mota. He says therefore first (676 bis) that to believe that AB is being moved by itself because the whole is being moved, and this without being moved by anything outside of it, is like saying that, when one part of a whole is being moved and another part causes it to be moved, it is moving itself, because it is not evident which part is the mover and which is being moved. Such would be the case if a mobile DEZ is such that one part DE moves the part EZ and it is not seen which part moves the other, and which is being moved. Vult autem per primum mobile ab, quod totum movetur et a principio interiori movente, intelligi aliquod corpus animatum, quod totum movetur ab anima: per mobile autem dez vult intelligi corpus aliquod quod non totum movetur, sed una pars eius corporalis est movens, et alia mota; in quo quidem mobili manifestum est quod id quod movetur, ab alio movetur. Et ex hoc vult simile ostendere de corpore animato, quod videtur movere seipsum. Hoc enim ei convenit inquantum una pars aliam movet, scilicet anima corpus, ut in octavo plenius ostendetur. When he speaks of the first mobile AB as being moved as a whole by an intrinsic principle of motion, he means a living body which is, as a whole, being moved by the soul; but when he speaks of the mobile DEZ he means some body that is not being moved as a whole but one bodily part of it is the mover and another the moved. In this latter case, it is evident that what is being moved is being moved by some other. From this latter case he wants to prove of a living body that seems to move itself that it too is being moved by some other. For it seems to move itself inasmuch as one part moves another, i.e., as the soul moves the body, as will be more fully explained in Book VIII. Deinde cum dicit: amplius quod etc., ostendit directe quod omne quod movetur ab alio movetur, tali ratione. Omne quod movetur a seipso, non quiescit a suo motu per quietem cuiuscumque alterius mobilis. Et hoc accipit quasi per se notum. Ex hoc autem ulterius concludit, quod si aliquod mobile quiescit ad quietem alterius, quod hoc movetur ab altero. Hoc autem supposito, concludit quod necesse est omne quod movetur ab aliquo alio moveri. Et quod hoc sequatur ex praemissis, sic probat. 886. Then at (677) he proves directly that whatever is being moved is being moved by some other. This is his argument: Nothing that is being moved by itself rests from its motion on account of some other mobile’s resting. (He takes this as per se evident). From this he further concludes that if a mobile rests on account of the rest of another, then the mobile is moved by another. On this ground he concludes that. necessarily whatever is being moved is being moved by some other. And that this follows from the premises, he now proves. Illud mobile quod supposuimus a seipso moveri, scilicet ab, oportet divisibile esse, quia omne quod movetur est divisibile, ut supra probatum est. Quia ergo divisibile est, nullum inconveniens sequitur si dividatur. Dividatur ergo in puncto c, ita quod una pars eius sit bc, et alia ac. Si ergo bc est pars eius quod est ab, necesse est quod quiescente bc parte, quiescat totum ab. Si ergo non quiescat totum, quiescente parte, accipiatur quod totum moveatur, et una pars quiescat: sed quia una pars ponitur quiescere, non poterit poni totum moveri, nisi ratione alterius partis. Sic ergo bc quiescente, quod est una pars, movetur ac, quod est alia pars. Sed nullum totum cuius una sola pars movetur, movetur primo et per se. Non ergo movebitur ab primo et per se, quod erat suppositum. Ergo oportet quod bc quiescente, quiescat totum ab. Et sic illud quod movetur pausabit, idest desinet moveri, ad quietem alterius. Sed supra habitum est, quod si aliquid quiescit et desinit moveri ad quietem alterius, hoc ab altero movetur. Ergo ab ab altero movetur. That mobile which we have supposed as being moved by itself, i.e., ABI must be divisible, for whatever is being moved is divisible, as was proved above. Hence, because it is divisible, nothing prevents it from being divided. Therefore, let it be divided at the point C so that one part of it is PC and the other part AC. Now, if PC is part, of AB, then when the part BC rests, the entire AB must rest. But if upon the part resting, the whole does not rest, let us grant that the whole is being moved and one part is at rest. But because we have assumed that one part is resting, the whole could not be granted as being moved except by reason of the other part. Therefore, when BC (which is one part) is at rest, the other part AC is being moved. But no whole of which one part only is being moved is being moved primarily and se. Therefore AB is not being moved primarily and per se, as we originally assumed. Therefore while BC is at rest, the entire AB must be at rest. Thus, what is being moved ceases to be moved upon the occasion of something else resting. But above we held that if something rests and ceases to be moved on the occasion of another’s resting, it is being moved by that other. Therefore, AB is being moved by some other. Et eadem ratio est de quolibet alio mobili: quia omne quod movetur est divisibile, et eadem ratione oportet quod quiescente parte, quiescat totum. Manifestum est ergo quod omne quod movetur, ab aliquo alio movetur. The same argument applies to any other mobile, for whatever is being moved is divisible and, for the same reason, if the part rests the whole rests. Therefore, it is clear that whatever is moved is moved by some other. Contra istam autem Aristotelis probationem multipliciter obiicitur. Obiicit enim Galenus contra hoc quod dicit Aristoteles, quod si una tantum pars eius mobilis moveatur et reliqua quiescat, quod totum non per se movetur: dicens hoc esse falsum; quia ea quae moventur secundum partem, per se moventur. 887. Many objections are leveled against this argument of Aristotle. For Galen objects against the statement that if just one part of a mobile is being moved and the others are at rest, then the whole is not being moved per se. Galen says this is false, because things that are being moved according to a part are moved per se. Sed deceptus est Galenus ex aequivocatione eius quod est per se. Per se enim quandoque sumitur secundum quod opponitur ei tantum quod est per accidens; et sic quod movetur secundum partem, movetur per se, ut Galenus intellexit. Quandoque vero sumitur secundum quod opponitur simul ei quod est per accidens, et ei quod est secundum partem; et hoc dicitur non solum per se, sed etiam primo. Et sic accipit per se Aristoteles hic: quod patet quia, cum conclusisset non ergo movetur per se ab, subiungit: sed concessum est per seipsum moveri primum. But Galen was deceived by playing on the phrase “ per se ”. For sometimes it is taken in opposition to per accidens, and then it is true that what is being moved according to a part is being moved per se, as Galen said. But sometimes per se is taken in opposition both to per accidens and to what is according to a part: and in this sense something is said to be not only per se, but also primarily so. And this is the sense in which it was being used by Aristotle in his proof. That he does so is clear, because after concluding, “therefore AB is not being moved per se,” he adds, “whereas it had been assumed that it was being moved primarily and per se.” Sed magis urget obiectio Avicennae, qui obiicit contra hanc rationem, dicens eam procedere ex suppositione impossibili, ex quo sequitur impossibile, et non ex eo quod ponitur aliquid a seipso moveri. Si enim ponamus aliquod mobile a seipso moveri primo et per se, naturale est ei quod moveatur et secundum totum et secundum partes. Si ergo ponatur quod aliqua pars eius quiescat, erit positio impossibilis. Et ex hac positione sequitur impossibile ad quod Aristoteles inducit, scilicet quod totum moveatur non primo et per se, ut positum est. 888. But a more serious objection is that of Avicenna who says against the argument that it proceeds from an impossible assumption, from which the impossible follows, and not from the assumption that something is being moved by itself. For if we assume that a mobile is being moved first and per se, it is natural that it be moved both according to the whole and according to the parts. Therefore, if it is then assumed that a part is at rest, that is the same as assuming what is impossible. And it is from this added assumption that there follows the impossibility which Aristotle deduces, namely, that the whole is not being moved first and per se, as was assumed. Huic autem obiectioni posset aliquis obviare dicendo, quod licet impossibile sit partem quiescere secundum determinatam naturam, inquantum est corpus talis speciei, ut puta caelum vel ignis, non est tamen impossibile, si ratio communis corporis consideretur: quia corpus, inquantum corpus, non prohibetur quiescere vel moveri. One might obviate this objection by countering that although it is impossible for a part to rest if you confine yourself to a body of a definite kind, for example, the heaven or fire, yet it is not impossible, if you consider the general definition of body, for body as body is not prevented from being at rest or in motion. Sed hanc responsionem excludit Avicenna dupliciter. Primo quidem quia pari ratione posset dici de toto corpore, quod non prohibetur quiescere ex hoc quod corpus est, sicut dicitur de parte; et ita superfluum fuit assumere ad probationem propositi divisionem mobilis et quietem partis. Secundo quia aliqua propositio simpliciter redditur impossibilis, si praedicatum repugnet subiecto ratione differentiae specificae, quamvis non repugnet ei ratione generis. Est enim impossibile quod homo sit irrationalis, quamvis non impediatur irrationalis esse ex hoc quod est animal. Sic igitur simpliciter impossibile est quod pars corporis moventis seipsum quiescat, quia hoc est contra rationem talis corporis, licet non sit contra rationem communem corporis. However, Avicenna forestalled such a response. First, because for the same reason it could be said of a whole body that it is not being prevented from resting just because it is a body, just as it is said of the part. Thus it was superfluous to assume, in order to prove the proposition, the division of the mobile and the rest of a part. Secondly, because some propositions are rendered impossible absolutely, if the predicate is repugnant to the subject by reason of its specific difference even though it be not repugnant to it by reason of its genus. For it is impossible for man to be non-rational, although he is not prevented from being non-rational from the fact of his being animal. Thus, therefore, it is impossible absolutely that a part of a body moving itself be at rest, for this is against the nature of any particular body, even though it be not against the common notion of body. Hac igitur responsione remota, Averroes aliter solvit: et dicit quod aliqua conditionalis potest esse vera, cuius antecedens est impossibile et consequens impossibile, sicut ista: si homo est asinus, est animal irrationale. Concedendum est ergo quod impossibile est quod, si aliquod mobile ponitur movere seipsum, quod vel totum vel pars eius quiescat; sicut impossibile est ignem non esse calidum, propter hoc quod est sibi ipsi causa caloris. Unde haec conditionalis est vera: si mobilis moventis seipsum pars quiescit, totum quiescit. Aristoteles autem, si verba eius diligenter considerentur, nunquam utitur quiete partis, nisi per locutionem habentem vim conditionalis propositionis. Non enim dicit quiescat bc, sed necesse est, bc quiescente, quiescere ab; et iterum, quiescente parte, quiescit totum: et ex hac conditionali vera, Aristoteles propositum demonstrat. 889. With this possible answer rejected, Avicenna solves it in another way. He says that a conditional whose antecedent is impossible and whose consequent is impossible can be true; for example, “If man is a horse, he is a non-rational animal.” It should be conceded, therefore, that it is an impossible assumption that mobile be moving itself and yet have the whole or a part of itself at rest, just as it is impossible for fire not to be hot, for fire is its own cause of its heat. Hence this conditional is true: “If a part of a mobile moving itself is at rest, the whole is at rest.” But Aristotle, if his words are carefully studied, does not speak of the rest of the part, except in a statement that has the force of a conditional. For he does not say, “Let BC be at rest,” but “If BC is at rest, AB must rest,” and “If the part rests, the whole rests”: and from this true conditional Aristotle proves his proposition. Sed dicit Averroes quod ista demonstratio non est de genere demonstrationum simpliciter, sed de genere demonstrationum quae dicuntur demonstrationes signi, vel demonstrationes quia, in quibus est usus talium conditionalium. But, says Averroes, that demonstration is not an absolute demonstration but one of the type called “demonstrating by a sign” or a demonstration “quia”, in which such conditionals are used. Est autem haec solutio conveniens quantum ad hoc quod dicit de veritate conditionalis: sed videtur dicendum quod non sit demonstratio quia, sed propter quid; continet enim causam quare impossibile est aliquod mobile movere seipsum. However, this solution is agreeable in regard to what he says about the truth of a conditional but not in regard to the statement that it is a “quia” demonstration, for it seems to be a “propter quid’, because it contains the cause why it is impossible for a mobile to move itself. Ad cuius evidentiam sciendum est, quod aliquid movere seipsum nihil aliud est, quam esse sibi causa motus. Quod autem est sibi causa alicuius, oportet quod primo ei conveniat; quia quod est primum in quolibet genere, est causa eorum quae sunt post. Unde ignis, qui sibi et aliis est causa caloris, est primum calidum. Ostendit autem Aristoteles in sexto, quod in motu non invenitur primum, neque ex parte temporis, neque ex parte magnitudinis, neque etiam ex parte mobilis, propter horum divisibilitatem. Non ergo potest inveniri primum, cuius motus non dependeat ab aliquo priori: motus enim totius dependet a motibus partium, et dividitur in eos, ut in sexto probatum est. Sic ergo ostendit Aristoteles causam quare nullum mobile movet seipsum; quia non potest esse primum mobile, cuius motus non dependeat a partibus: sicut si ostenderem quod nullum divisibile potest esse primum ens, quia esse cuiuslibet divisibilis dependet a partibus: ut sic haec conditionalis sit vera: si pars non movetur, totum non movetur, sicut haec conditionalis est vera: si pars non est, totum non est. To see this, recall that to move oneself is nothing more than to be the cause of one’s own motion. Whatever is its own cause of something must possess it primarily, i.e., first, because what is first in any group is the cause of what comes after it. Hence fire, the cause of heat for itself and for other things, is the first hot thing. But, in Book VII Aristotle showed that there is no first in motion, whether on the side of time or the magnitude or the mobile—for they are all divisible. Therefore, it is impossible to find a first whose motion does not depend on a prior, for the motion of the whole depends on the motions of the parts and is divided into those motions, as was proved in Book VI. Aristotle, therefore, thus shows the cause why no mobile moves itself: it is because there cannot be a first mobile whose motion does not depend on its parts any more than the first being can be a divisible, for the existence of any divisible depends on the parts. Hence this conditional is true “If the part is not being moved, neither is the whole,” just as this one is true “If the part does not exist, the whole does not.” Unde et Platonici, qui posuerunt aliqua movere seipsa, dixerunt quod nullum corporeum aut divisibile movet seipsum; sed movere seipsum est tantummodo substantiae spiritualis, quae intelligit seipsam et amat seipsam: universaliter omnes operationes motus appellando; quia et huiusmodi operationes, scilicet sentire et intelligere, etiam Aristoteles in tertio de anima nominat motum, secundum quod motus est actus perfecti. Sed hic loquitur de motu secundum quod est actus imperfecti, idest existentis in potentia, secundum quem motum indivisibile non movetur, ut in sexto probatum est, et hic assumitur. Et sic patet quod Aristoteles, ponens omne quod movetur ab alio moveri, a Platone, qui posuit aliqua movere seipsa, non dissentit in sententia, sed solum in verbis. 890. Hence even the Platonists, who assumed that some things move themselves, said that no body or divisible thing moves itself; rather to move itself is a prerogative of a spiritual substance which understands and loves itself (here all operations are being called “motions,” just as Aristotle in Book III of On the Soul calls sensing and understanding by the name of “motions” in the sense that motion is the act of a perfect thing). However, in this Book VII he takes motion as the act of an imperfect thing, i.e., of a thing existing in potency. It is in this sense of motion that no indivisible is moved, as was proved in Book VI and is here taken for granted. And so it is clear that Aristotle, in stating that whatever is moved is moved by some other, and Plato, in stating that some things move themselves, are here not apart in their opinions but solely in their words.
No process to infinity in movers and moved. One must arrive at a first mover unmoved.
Chapter 1 cont. ἐπεὶ δὲ πᾶν τὸ κινούμενον ἀνάγκη κινεῖσθαι ὑπό τινος, ἐάν γέ τι κινῆται τὴν ἐν τόπῳ κίνησιν ὑπ' ἄλλου κινουμένου, καὶ πάλιν τὸ κινοῦν ὑπ' ἄλλου κινουμένου κινῆται κἀκεῖνο ὑφ' ἑτέρου καὶ ἀεὶ οὕτως, ἀνάγκη εἶναί τι τὸ πρῶτον κινοῦν, καὶ μὴ βαδίζειν εἰς ἄπειρον· μὴ γὰρ ἔστω, ἀλλὰ γενέσθω ἄπειρον. κινείσθω δὴ τὸ μὲν Α ὑπὸ τοῦ Β, τὸ δὲ Β ὑπὸ τοῦ Γ, τὸ δὲ Γ ὑπὸ τοῦ Δ, καὶ ἀεὶ τὸ ἐχόμενον ὑπὸ τοῦ ἐχομένου. ἐπεὶ οὖν ὑπόκειται τὸ κινοῦν κινούμενον κινεῖν, ἀνάγκη ἅμα γίγνεσθαι τὴν τοῦ κινουμένου καὶ τὴν τοῦ κινοῦντος κίνησιν (ἅμα γὰρ κινεῖ τὸ κινοῦν καὶ κινεῖται τὸ κινούμενον)· φανερὸν <�οὖν> ὅτι ἅμα ἔσται τοῦ Α καὶ τοῦ Β καὶ τοῦ Γ καὶ ἑκάστου τῶν κινούντων καὶ κινουμένων ἡ κίνησις. εἰλήφθω οὖν ἡ ἑκάστου κίνησις, καὶ ἔστω τοῦ μὲν Α ἐφ' ἧς Ε, τοῦ δὲ Β ἐφ' ἧς Ζ, τῶν <�δὲ> Γ Δ ἐφ' ὧν Η Θ. εἰ γὰρ ἀεὶ κινεῖται ἕκαστον ὑφ' ἑκάστου, ὅμως ἔσται λαβεῖν μίαν ἑκάστου κίνησιν τῷ ἀριθμῷ· πᾶσα γὰρ κίνησις ἔκ τινος εἴς τι, καὶ οὐκ ἄπειρος τοῖς ἐσχάτοις· λέγω δὴ ἀριθμῷ μίαν κίνησιν τὴν ἐκ τοῦ αὐτοῦ εἰς τὸ αὐτὸ τῷ ἀριθμῷ ἐν τῷ αὐτῷ χρόνῳ τῷ ἀριθμῷ γιγνομένην. ἔστι γὰρ κίνησις καὶ γένει καὶ εἴδει καὶ ἀριθμῷ ἡ αὐτή, (242b.) γένει μὲν ἡ τῆς αὐτῆς κατηγορίας, οἷον οὐσίας ἢ ποιότητος, εἴδει δὲ <�ἡ> ἐκ τοῦ αὐτοῦ τῷ εἴδει εἰς τὸ αὐτὸ τῷ εἴδει, οἷον ἐκ λευκοῦ εἰς μέλαν ἢ ἐξ ἀγαθοῦ εἰς κακὸν ἀδιάφορον τῷ εἴδει· ἀριθμῷ δὲ ἡ ἐξ ἑνὸς τῷ ἀριθμῷ <�εἰς ἓν τῷ ἀριθμῷ> ἐν τῷ αὐτῷ χρόνῳ, οἷον ἐκ τοῦδε τοῦ λευκοῦ εἰς τόδε τὸ μέλαν, ἢ ἐκ τοῦδε τοῦ τόπου εἰς τόνδε, ἐν τῷδε τῷ χρόνῳ· εἰ γὰρ ἐν ἄλλῳ, οὐκέτι ἔσται ἀριθμῷ μία κίνησις, ἀλλ' εἴδει. εἴρηται δὲ περὶ τούτων ἐν τοῖς πρότερον. εἰλήφθω δὲ καὶ ὁ χρόνος ἐν ᾧ κεκίνηται τὴν αὑτοῦ κίνησιν τὸ Α, καὶ ἔστω ἐφ' ᾧ Κ. πεπερασμένης δ' οὔσης τῆς τοῦ Α κινήσεως καὶ ὁ χρόνος ἔσται πεπερασμένος. ἐπεὶ δὴ ἄπειρα τὰ κινοῦντα καὶ τὰ κινούμενα, καὶ ἡ κίνησις ἡ ΕΖΗΘ ἡ ἐξ ἁπασῶν ἄπειρος ἔσται· ἐνδέχεται μὲν γὰρ ἴσην εἶναι τὴν τοῦ Α καὶ τοῦ Β καὶ τὴν τῶν ἄλλων, ἐνδέχεται δὲ μείζους τὰς τῶν ἄλλων, ὥστε εἴ τε ἴσαι εἴ τε μείζους, ἀμφοτέρως ἄπειρος ἡ ὅλη· λαμβάνομεν γὰρ τὸ ἐνδεχόμενον. ἐπεὶ δ' ἅμα κινεῖται καὶ τὸ Α καὶ τῶν ἄλλων ἕκαστον, ἡ ὅλη κίνησις ἐν τῷ αὐτῷ χρόνῳ ἔσται καὶ ἡ τοῦ Α· ἡ δὲ τοῦ Α ἐν πεπερασμένῳ· ὥστε εἴη ἂν ἄπειρος ἐν πεπερασμένῳ, τοῦτο δ' ἀδύνατον. Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, and so on continually: then the series cannot go on to infinity, but there must be some first movent. For let us suppose that this is not so and take the series to be infinite. Let A then be moved by B, B by G, G by D, and so on, each member of the series being moved by that which comes next to it. Then since ex hypothesi the movent while causing motion is also itself in motion, and the motion of the moved and the motion of the movent must proceed simultaneously (for the movent is causing motion and the moved is being moved simultaneously) it is evident that the respective motions of A, B, G, and each of the other moved movents are simultaneous. Let us take the motion of each separately and let E be the motion of A, Z of B, and H and O respectively the motions of G and D: for though they are all moved severally one by another, yet we may still take the motion of each as numerically one, since every motion is from something to something and is not infinite in respect of its extreme points. By a motion that is numerically one I mean a motion that proceeds from something numerically one and the same to something numerically one and the same in a period of time numerically one and the same: for a motion may be the same generically, specifically, or numerically: it is generically the same if it belongs to the same category, e.g. substance or quality: it is specifically the same if it proceeds from something specifically the same to something specifically the same, e.g. from white to black or from good to bad, which is not of a kind specifically distinct: it is numerically the same if it proceeds from something numerically one to something numerically one in the same period of time, e.g. from a particular white to a particular black, or from a particular place to a particular place, in a particular period of time: for if the period of time were not one and the same, the motion would no longer be numerically one though it would still be specifically one. We have dealt with this question above. Now let us further take the time in which A has completed its motion, and let it be represented by K. Then since the motion of A is finite the time will also be finite. But since the movents and the things moved are infinite, the motion EZHO, i.e. the motion that is composed of all the individual motions, must be infinite. For the motions of A, B, and the others may be equal, or the motions of the others may be greater: but assuming what is conceivable, we find that whether they are equal or some are greater, in both cases the whole motion is infinite. And since the motion of A and that of each of the others are simultaneous, the whole motion must occupy the same time as the motion of A: but the time occupied by the motion of A is finite: consequently the motion will be infinite in a finite time, which is impossible. οὕτω μὲν οὖν δόξειεν ἂν δεδεῖχθαι τὸ ἐξ ἀρχῆς, οὐ μὴν ἀποδείκνυται διὰ τὸ μηδὲν δείκνυσθαι ἀδύνατον· ἐνδέχεται γὰρ ἐν πεπερασμένῳ χρόνῳ ἄπειρον εἶναι κίνησιν, μὴ ἑνὸς ἀλλὰ πολλῶν. ὅπερ συμβαίνει καὶ ἐπὶ τούτων· ἕκαστον γὰρ κινεῖται τὴν ἑαυτοῦ κίνησιν, ἅμα δὲ πολλὰ κινεῖσθαι οὐκ ἀδύνατον. It might be thought that what we set out to prove has thus been shown, but our argument so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition: for in a finite time there may be an infinite motion, though not of one thing, but of many: and in the case that we are considering this is so: for each thing accomplishes its own motion, and there is no impossibility in many things being in motion simultaneously. ἀλλ' εἰ τὸ κινοῦν πρώτως κατὰ τόπον καὶ σωματικὴν κίνησιν ἀνάγκη ἢ ἅπτεσθαι ἢ συνεχὲς εἶναι τῷ κινουμένῳ, καθάπερ ὁρῶμεν ἐπὶ πάντων, ἀνάγκη τὰ κινούμενα καὶ τὰ κινοῦντα συνεχῆ εἶναι ἢ ἅπτεσθαι ἀλλήλων, ὥστ' εἶναί τι ἐξ ἁπάντων ἕν. τοῦτο δὲ εἴτε πεπερασμένον εἴτε ἄπειρον, οὐδὲν διαφέρει πρὸς τὰ νῦν· πάντως γὰρ ἡ κίνησις ἔσται ἄπειρος ἀπείρων ὄντων, εἴπερ ἐνδέχεται καὶ ἴσας εἶναι καὶ μείζους ἀλλήλων· ὃ γὰρ ἐνδέχεται, ληψόμεθα ὡς ὑπάρχον. εἰ οὖν τὸ μὲν ἐκ τῶν Α Β Γ Δ <�ἢ πεπερασμένον ἢ> ἄπειρόν τί ἐστιν, κινεῖται δὲ τὴν ΕΖΗΘ κίνησιν ἐν τῷ χρόνῳ τῷ Κ, οὗτος δὲ πεπέρανται, συμβαίνει ἐν πεπερασμένῳ χρόνῳ ἄπειρον διιέναι ἢ τὸ πεπερασμένον ἢ τὸ ἄπειρον. ἀμφοτέρως δὲ ἀδύνατον· ὥστε ἀνάγκη ἵστασθαι καὶ εἶναί τι πρῶτον κινοῦν καὶ κινούμενον. οὐδὲν γὰρ διαφέρει τὸ συμβαίνειν ἐξ ὑποθέσεως τὸ ἀδύνατον· (243a.) ἡ γὰρ ὑπόθεσις εἴληπται ἐνδεχομένη, τοῦ δ' ἐνδεχομένου τεθέντος οὐδὲν προσήκει γίγνεσθαι διὰ τοῦτο ἀδύνατον. But if (as we see to be universally the case) that which primarily is moved locally and corporeally must be either in contact with or continuous with that which moves it, the things moved and the movents must be continuous or in contact with one another, so that together they all form a single unity: whether this unity is finite or infinite makes no difference to our present argument; for in any case since the things in motion are infinite in number the whole motion will be infinite, if, as is theoretically possible, each motion is either equal to or greater than that which follows it in the series: for we shall take as actual that which is theoretically possible. If, then, A, B, G, D form an infinite magnitude that passes through the motion EZHO in the finite time K, this involves the conclusion that an infinite motion is passed through in a finite time: and whether the magnitude in question is finite or infinite this is in either case impossible. Therefore the series must come to an end, and there must be a first movent and a first moved: for the fact that this impossibility results only from the assumption of a particular case is immaterial, since the case assumed is theoretically possible, and the assumption of a theoretically possible case ought not to give rise to any impossible result.
Postquam ostendit philosophus quod omne quod movetur, movetur ab alio, hic accedit ad principale propositum ostendendum, scilicet quod sit primus motus et primus motor. Et circa hoc duo facit: primo proponit quod intendit; secundo probat propositum, ibi: si enim non est, sed in infinitum procedet et cetera. 891. After showing that whatever is moved is moved by some other, the Philosopher now turns to the proof of his main proposition, namely, that there exists a first motion and a first mover. About this he does two things: First he proposes what he intends; Secondly, he proves his proposition, at 892. Dicit ergo primo, quod cum ostensum sit universaliter, quod omne quod movetur ab aliquo alio movetur, necesse est hoc etiam verum esse in motu locali, scilicet ut omne quod movetur in loco, ab altero moveatur. Applicat autem specialiter ad motum localem quod supra universaliter demonstratum est, quia motus localis est primus motuum, ut in octavo ostendetur; et ideo secundum hunc motum procedit hic ad demonstrandum primum motorem. He says therefore first (678) that since it has been proved for all cases that whatever is moved is moved by some other, it must be true even in regard to local motion that whatever is being moved with respect to place is being moved by something else. Now he applies to local motion in particular the very proposition which he proved universally true, because local motion is the first of the motions, as will be proved in Book VIII. Therefore, it is according to this motion that he now proceeds to demonstrate a first mover. Accipiatur igitur aliquid quod movetur secundum locum; hoc movetur ab altero; aut ergo illud alterum movetur, aut non. Si non movetur, habetur propositum, scilicet quod aliquid sit movens immobile; quod est proprietas primi moventis. Si autem et ipsum movens movetur, oportet quod moveatur ab altero movente; et hoc iterum movens, si et ipsum movetur, movetur ab altero. Sed hoc non potest procedere in infinitum, sed oportet in aliquo stare. Erit ergo aliquid primum movens, quod erit prima causa motus: ita scilicet quod ipsum non movetur, sed movet alia. Therefore, let us take something that is being moved in regard to place. This thing is being moved by something else. Now that something else is in turn being moved by something else or it is riot. If it, is not, we have the proposition clinched; namely, that there exists a mover that is immovable, which is a property of the first mover. But if that something else is also being moved by something other, this other is being moved by still another which is itself being moved by yet another mover. This, however, cannot go on ad infinitum, but a halt must be made at some mover. Therefore, there will be a first mover which will be the first cause of the motion, and of such a nature that it is itself not being moved but moves the others. Deinde cum dicit: si enim non etc., probat quod supposuerat. Et circa hoc tria facit: primo inducit probationem; secundo ostendit probationem esse insufficientem, ibi: sic igitur videtur etc.; tertio supplet quoddam per quod ratio fortificatur, ibi: sed si id quod movetur et cetera. 892. Then at (679) he proves a statement not yet proved. About this he does three things: First he gives the proof; Secondly, he shows that the proof he gives is insufficient, at 893; Thirdly, he supplies what was lacking in the insufficient proof, at 894. Dicit ergo primo, quod si hoc non concedatur, quod sit aliqua prima causa motus, cum omne quod movetur ab alio moveatur, sequitur quod procedatur in infinitum in moventibus et motis. Et hoc ostendit esse impossibile. He says therefore first (680) that if it is not granted that there is a first cause of the motion, then, since whatever is being moved is moved by some other, it follows that an infinite series of movers and moved is involved. And he shows that such a situation is impossible. Sit enim a quoddam quod movetur secundum locum, et moveatur ab ipso b; b vero a c, c vero a d; et sic procedatur in infinitum ascendendo. Manifestum est autem, quod cum aliquid movet ex eo quod movetur, simul movetur movens et ipsum mobile; sicut si manus suo motu movet baculum, simul movetur manus et baculus. Sic ergo simul movetur b quando movetur a; et eadem ratione quando movetur b simul movetur c, et cum movetur c simul movetur d. Sic ergo simul et in eodem tempore est motus ipsius a et omnium aliorum; et poterit seorsum accipi motus uniuscuiusque horum infinitorum. Et quamvis unumquodque horum mobilium moveatur ab unoquoque moventium, non ita quod unum ab omnibus, sed singula a singulis; nihilominus tamen, licet sint infinita moventia et mobilia, tamen uniuscuiusque mobilium motus est unus numero. Et licet omnes motus sint infiniti numero, non tamen sunt infiniti in ultimis, idest per privationem ultimorum, sed uniuscuiusque motus est finitus, habens determinata ultima. Let A, then, be something that is being moved in respect of place and let it be moved by B; let B be moved by C, and C by D, and so on ad infinitum in ascending order. Now it is evident that, when something moves by virtue of the fact that it is itself being moved by another, then both the mover and the mobile are being moved simultaneously, just as, when the hand by its motion moves a stick, the hand and the stick are moved at one and the same time. Therefore, B is being moved simultaneously with A, and C with B, and D with C. Therefore, the motion of A and that of all the others exist together and at the same time. And we could have considered one by one each of these infinite motions. Likewise, although each one of these mobiles is being moved by some mover—not in the sense that one is being moved by all, but one by another—nevertheless, even though there be an infinitude of movers and mobiles, yet the motion of each of the mobiles is numerically one motion. And although all the motions are infinite in number, they are not infinite in a privative sense, i.e., as though lacking a boundary, but the motion of each mobile is finite and has its own definite boundaries. Et quod uniuscuiusque infinitorum mobilium motus sit unus numero et finitus, probat quia, cum omne quod movetur moveatur inter duos terminos, ex quodam scilicet in quiddam, necesse est quod secundum diversum modum identitatis terminorum, etiam ipse motus sit diversimode unus, scilicet aut numero aut specie aut genere. That the motion of each one of the infinite mobiles is numerically one and finite, he proves by the fact that since whatever is moved is moved between two termini, i.e., from something to something, then necessarily according to the diverse ways in which the termini are identical, the motion itself will be one in diverse ways, i.e., numerically, or specifically, or generically. Numero quidem est idem motus, qui est ex eodem termino a quo in idem numero sicut in terminum ad quem; ita tamen quod sit etiam in eodem numero tempore; et cum hoc oportet quod sit eiusdem mobilis numero. Et ad exponendum quod dixerat, subiungit quod motus numero unus est ex eodem in idem, sicut ex hoc albo, quod significat unum numero, in hoc nigrum, quod etiam nominat aliquid idem numero, et secundum hoc tempus determinatum, quod etiam est unum numero: quia si esset motus secundum aliud tempus, licet aequale, non esset numero unus, sed specie tantum. Motions are numerically the same when they are from the same terminus a quo into the same numerical terminus ad quem, provided that it takes place in the same numerical time and that the numerically same mobile is involved. To explain what he means, he adds that a motion that is numerically one is “from the same into the same”, for example, from this white, i.e., from the same numerical white, into this black, i.e., the same numerical black, and in this same numerical time— because if all the conditions but time were numerically the same, the motion would be not numerically, but specifically one. Sed motus est unus genere, qui est in eodem praedicamento, vel substantiae vel cuiuscumque alterius generis; sicut omnis generatio substantiae est eadem genere, et omnis alteratio similiter. But a motion is generically one, when it is in the same predicament, i.e., of substance or some other genus; for example, all generations of substance are generically the same, and all alterations likewise. Sed motus est specie unus, qui est ex eodem secundum speciem in idem secundum speciem; sicut omnis denigratio, quae est ex albo in nigrum, est eadem specie, et omnis depravatio, quae est ex bono in malum. Et haec etiam in quinto dicta sunt. But a motion is specifically one, when it is from the same specific terminus to the same specific terminus; for example, every case of blackening, which is from white to black, is specifically the same, and every case of becoming depraved, i.e., from good to bad, is specifically the same. All this was explained in Book V. His igitur duobus suppositis, scilicet quod simul movetur et movens et motum, et quod potest accipi motus uniuscuiusque mobilium tanquam finitus et unus; accipiatur motus huius mobilis quod est a, et sit e; et motus ipsius b sit z, et motus cd et omnium consequentium sit it. Tempus autem in quo movetur a, sit k. Sed quia motus ipsius a est determinatus, idest finitus, etiam tempus in quo est iste motus, scilicet k, est determinatum et non infinitum: quia sicut in sexto ostensum est, finitum et infinitum simul invenitur in tempore et motu. Ex dictis autem patet, quod in eodem tempore in quo movetur a, movetur et b, et omnia alia: ergo motus omnium, qui est ezit, est in tempore finito. Sed iste motus est infinitus, cum sit infinitorum. Ergo sequetur quod motus infinitus sit in tempore finito; quod est impossibile. Hoc autem ideo sequitur, quia in quo tempore movetur a, moventur omnia alia, quae sunt infinita numero. Keeping in mind, therefore, these two facts, namely, that the mover and the moved are being moved together, and that the motion of each of the mobiles can be taken as one and finite, let us take the motion of mobile A and call it motion E, and the motion of B and call it Z, and let the motion of C, D and of all the others following be called IT. Also let the time in which A is being moved be K. Now, since the motion of A is finite, then the time K of that motion is definite and not infinite, because we showed in Book VI that the finite in time corresponds to a finite in motion and an infinite in time corresponds to an infinite in motion. From what we have said, however, it is clear that in the very same time that A is being moved, B is being moved, and so for all the others; hence the motion of all, i.e., the motion EZIT, occurs in finite time. But this motion is infinite, since it is the motion of an infinite number. Therefore it will follow that an infinite motion occurs in finite time, which is impossible. Now why does our conclusion follow? Because in the very same time that A is being moved all the others are being moved and they are infinite in number. Nec differt quantum ad propositum pertinet, utrum motus omnium mobilium sit aequalis velocitatis, aut inferiora mobilia tardius moveantur et in maiori tempore; quia omnino sequetur quod motus infinitus sit in tempore finito, quia unumquodque mobilium necesse est quod habeat velocitatem et tarditatem finitam. Hoc autem est impossibile, scilicet motum infinitum esse in tempore finito. Ergo et primum est impossibile, scilicet quod procedatur in mobilibus et moventibus in infinitum. It makes no difference, so far as our proposition is concerned, whether the motion of all the mobiles had equal velocity or not, or whether the lower mobiles move more slowly and in a greater time, because in any case it will follow that an infinite motion occurs in finite time—since each of the mobiles must have a finite rapidity and a finite slowness. However, it is impossible for an infinite motion to occur in finite time. Therefore, it is also impossible that we go to infinity in the series of mobiles and movers. Deinde cum dicit: sic igitur etc., ostendit quod praecedens ratio non efficaciter concludit. Et dicit quod praedicto modo videtur demonstrari principale propositum, scilicet quod non in infinitum procedatur in moventibus et motis; non tamen efficaciter demonstratur, quia nullum inconveniens accidit ex praemissis. Contingens est enim et possibile, quod in tempore finito sit motus infinitus; ita tamen quod non sit unus et idem, sed alius et alius; inquantum scilicet infinita sunt quae moventur. Nihil enim prohibet infinita in tempore finito moveri simul. Et hoc concludebat ratio praedicta. Erant enim mobilia infinita diversa, et sic motus eorum erant diversi: quia ad unitatem motus non solum requiritur unitas temporis et termini, sed etiam unitas mobilis, ut in quinto dictum est. 893. Then at (680) he shows that the foregoing argument is not conclusive. And he says that in the above way we seemed to have demonstrated the main proposition, namely, that one does not go to infinity in the series of movers and mobiles. Yet it is not an efficacious proof, because no impossibility flows from these premises. For it is possible that there be an infinite motion in finite time, so long as the motion is not one and the same but other and other, insofar, namely, as an infinite number of things are being moved. For there is nothing to prevent an infinite number of things from being moved at once in finite time. And it was this that our argument concluded. For the infinite mobiles were diverse and so their motions were diverse, because for a motion to be one it is required not only that the time be one and that the termini be identical but also that the mobile be one, as was proved in Book V. Deinde cum dicit: sed si id quod movetur etc., ostendit quomodo praedicta ratio efficaciam habere possit: et primo quomodo habeat efficaciam ex suppositione facta; secundo quomodo habeat efficaciam simpliciter, ibi: nihil autem differat et cetera. 894. Then at (681) he shows how to make the argument efficacious. First, how it can be made efficacious by making another assumption; Secondly, how it is efficacious all by itself, at 895. Dicit ergo primo, quod id quod localiter et corporaliter movetur primo et immediate ab aliquo mobili movente, necesse est quod tangatur ab eo, sicut baculus tangitur a manu; vel quod continuetur ei, sicut continuatur una pars aeris alteri, et sicut pars continuatur animali. Et hoc videtur contingere in omnibus, quod movens semper coniungitur mobili altero istorum modorum. He says therefore first that what is locally and corporeally being moved first and immediately by a mobile mover must be touched by it, as a stick is touched by the hand, or must be continuous with it, as one part of the air is continuous with the next part, or as one part of an animal is continuous with another. And this seems to occur in all, i.e., that the mover is always in contact with the mobile in one of these ways. Accipiatur ergo alter istorum modorum, scilicet quod ex omnibus infinitis mobilibus et moventibus efficiatur unum, scilicet ipsum totum universum, per continuationem quandam. Hoc ergo, quia contingens est, supponatur: et istud totum, quod est quaedam magnitudo et continuum, vocetur abcd, et motus eius vocetur ezit. Et quia posset aliquis dicere quod ezit erat motus finitorum mobilium, et ita non potest esse motus totius infiniti; subiungit quod nihil differt quantum ad propositum pertinet, utrum accipiatur finita magnitudo quae movetur, aut infinita. Sicut enim simul quando movebatur a, in tempore scilicet finito, quod est k, movetur quodlibet finitorum mobilium, quae sunt numero infinita; ita etiam simul in eodem tempore movetur tota magnitudo infinita. Sequitur ergo impossibile, quodcumque horum detur, sive quod sit magnitudo finita constans ex magnitudinibus numero infinitis, sive quod sit magnitudo infinita, et motus eius in tempore finito; cum sit ostensum supra quod mobile infinitum non potest moveri tempore finito. Ergo impossibile est hoc ex quo sequebatur, scilicet quod procedatur in infinitum in moventibus et motis. Manifestum est ergo quod hoc quod unum moveatur ab altero, non procedit in infinitum: sed stabit alicubi, et erit aliquod primum mobile, quod scilicet moveatur ab altero immobili. Let us therefore take one of these ways, namely, that from all the infinite mobiles and movers there is formed one thing—namely, the whole universe—through some kind of continuity. Since this is something contingent, let us take it for granted and let that whole unit—which is a continuous magnitude—be called ABCD and its motion EZIT. And because someone could say that EZIT was the motion of finite mobiles and so not the motion of an infinite whole, he adds that, so far as our proposition is concerned, it makes no difference whether the magnitude is finite or infinite. For just as when A was being moved in a finite time K, each of the finite mobiles which are infinite in number were being moved at the same time, so also in the same time the entire infinite magnitude will be moved all at once. Therefore, an impossibility follows whichever one is taken, i.e., either a finite magnitude composed of magnitudes infinite in number, or an infinite magnitude whose motion occurs in finite time; for it has been proved above that an infinite mobile cannot be moved in finite time. Therefore the premise from which this impossibility followed is itself impossible, i.e., that we go to infinity in the series of movers and things moved. It is clear, therefore, that the process of one thing being moved by another does not go on ad infinitum, but a halt must be made and there will exist a first mobile which is being moved by a mover that is immovable. Et quia praedicta probatio procedit supposito quodam, scilicet quod omnia infinita moventia et mota continuentur ad invicem et constituant unam magnitudinem, et sic posset alicui videri quod non simpliciter concludatur; ideo subiungit quod non differt hanc demonstrationem processisse quodam supposito; quia ex contingenti supposito, etiam si sit falsum, non potest sequi aliquod impossibile. Cum ergo praedicta ratio ducat ad impossibile, illud impossibile non sequitur ex isto contingenti supposito, sed ex alio, quod oportet esse impossibile, cum ex eo impossibile sequatur. Et sic patet quod in demonstrationibus ad impossibile ducentibus, nihil refert utrum accipiatur falsum contingens adiunctum impossibili, vel verum. Ostenditur enim impossibile esse illud, ex quo, cum adiunctione contingentis falsi, sequitur impossibile, sicut si ex eo impossibile sequeretur, adiuncto quodam vero: quia sicut ex vero non potest sequi impossibile, ita nec ex contingenti. 895. Since our proof depended on an assumption, namely, that all the infinite movers and moved form a continuum and constitute one magnitude, it might seem to someone that the conclusion is not absolute, Consequently, he adds that it makes no difference to the validity of this conclusion that it should have proceeded from this assumption. For an impossibility cannot follow from an assumption that is contingent, even if the assumption be false. Therefore, since the proof led to an impossibility, that impossibility did not follow from our contingent premis but from some other cause which must be impossible, since an impossibility followed from it. So it is clear that in demonstrations that lead to an impossibility it makes no difference whether a false contingent assumption or something true be joined to what is impossible. For that is shown to be impossible which, by the addition of some false contingent statement, gives rise to an impossibility, just as if something impossible should follow from it by the addition of a true proposition. For just as an impossibility cannot follow from a true premis, so neither can it from a contingent one. Sed potest aliquis dicere, quod non est contingens omnia mobilia continuari; sed impossibile est continuari elementa ad invicem, et cum caelestibus corporibus. 896. But someone could say that for all mobiles to form one continuum is not contingent but impossible, for the elements cannot form a continuum with one another and with the heavenly bodies. Sed dicendum est quod alio modo accipitur contingens et impossibile, cum demonstratur aliquid de genere, et cum demonstratur aliquid de specie. Quia cum agitur de specie, oportet accipi ut impossibile esse illud, cui repugnat vel genus vel differentia speciei, ex quibus ratio speciei constituitur. Cum vero agitur de genere, accipitur ut contingens omne illud cui non repugnat ratio generis, licet ei repugnet differentia constituens speciem: sicut si loquerer de animali, possem accipere ut contingens, quod omne animal esset alatum; sed si descenderem ad considerationem hominis, impossibile esset hoc animal esse alatum. Quia igitur Aristoteles hic loquitur de mobilibus et moventibus in communi, nondum applicando ad determinata mobilia; esse autem contiguum vel continuum indifferenter se habet ad rationem moventis et mobilis; ideo accepit ut contingens, quod omnia mobilia sint continua ad invicem: quod tamen est impossibile, si mobilia considerentur secundum suas naturas determinatas. But it must be answered that “contingent” and “impossible” are taken in one sense when something is demonstrated about a genus and in another sense when something is demonstrated about a species. When a discussion is about the species, whatever is repugnant either to the genus or the specific difference, which forms the nature of the species, must be regarded as impossible. But when the discussion is about the genus, we can take as contingent anything to which the genus is not repugnant, even though the difference which constitutes a species of that genus is repugnant to it. For example, if I am speaking of animal, I can suppose as a contingent proposition that all animals are winged; but if I go a step further and consider man, it is impossible for this animal to have wings. Now since Aristotle is here speaking about mobiles and movers in a general way without making applications to particular mobiles, and to be in contact or to be continuous is a matter of indifference if you consider the general nature of mover and mobile, therefore he takes it as contingent that all mobiles mutually form a continuum, even though this is impossible if you consider the mobiles in their specific natures.
In local motion mover and moved must be together
Note that the Latin in chapters 2 & 3 is confused and does not match the Greek well.
Τὸ δὲ πρῶτον κινοῦν, μὴ ὡς τὸ οὗ ἕνεκεν, ἀλλ' ὅθεν ἡ ἀρχὴ τῆς κινήσεως, ἅμα τῷ κινουμένῳ ἐστί (λέγω δὲ τὸ ἅμα, ὅτι οὐδέν ἐστιν αὐτῶν μεταξύ)· τοῦτο γὰρ κοινὸν ἐπὶ παντὸς κινουμένου καὶ κινοῦντός ἐστιν. That which is the first movement of a thing—in the sense that it supplies not 'that for the sake of which' but the source of the motion—is always together with that which is moved by it by 'together' I mean that there is nothing intermediate between them). This is universally true wherever one thing is moved by another. ἐπεὶ δὲ τρεῖς αἱ κινήσεις, ἥ τε κατὰ τόπον καὶ ἡ κατὰ τὸ ποιὸν καὶ ἡ κατὰ τὸ ποσόν, ἀνάγκη καὶ τὰ κινοῦντα τρία εἶναι, τό τε φέρον καὶ τὸ ἀλλοιοῦν καὶ τὸ αὖξον ἢ φθῖνον. πρῶτον οὖν εἴπωμεν περὶ τῆς φορᾶς· And since there are three kinds of motion, local, qualitative, and quantitative, there must also be three kinds of movent, that which causes locomotion, that which causes alteration, and that which causes increase or decrease. Let us begin with locomotion, for this is the primary motion. πρώτη γὰρ αὕτη τῶν κινήσεων. ἅπαν δὴ τὸ φερόμενον ἢ ὑφ' ἑαυτοῦ κινεῖται ἢ ὑπ' ἄλλου. ὅσα μὲν οὖν αὐτὰ ὑφ' αὑτῶν κινεῖται, φανερὸν ἐν τούτοις ὅτι ἅμα τὸ κινούμενον καὶ τὸ κινοῦν ἐστιν· ἐνυπάρχει γὰρ αὐτοῖς τὸ πρῶτον κινοῦν, ὥστ' οὐδέν ἐστιν ἀναμεταξύ· Everything that is in locomotion is moved either by itself or by something else. In the case of things that are moved by themselves it is evident that the moved and the movent are together: for they contain within themselves their first movent, so that there is nothing in between. ὅσα δ' ὑπ' ἄλλου κινεῖται, τετραχῶς ἀνάγκη γίγνεσθαι· τέτταρα γὰρ εἴδη τῆς ὑπ' ἄλλου φορᾶς, ἕλξις, ὦσις, ὄχησις, δίνησις. ἅπασαι γὰρ αἱ κατὰ τόπον κινήσεις ἀνάγονται εἰς ταύτας· The motion of things that are moved by something else must proceed in one of four ways: for there are four kinds of locomotion caused by something other than that which is in motion, viz. pulling, pushing, carrying, and twirling. All forms of locomotion are reducible to these. ἡ μὲν γὰρ ἔπωσις ὦσίς τίς ἐστιν, ὅταν τὸ ἀφ' αὑτοῦ κινοῦν ἐπακολουθοῦν ὠθῇ, ἡ δ' ἄπωσις, ὅταν μὴ ἐπακολουθῇ κινῆσαν, ἡ δὲ ῥῖψις, Thus pushing on is a form of pushing in which that which is causing motion away from itself follows up that which it pushes and continues to push it: pushing off occurs when the movent does not follow up the thing that it has moved: ὅταν (243b.) σφοδροτέραν ποιήσῃ τὴν ἀφ' αὑτοῦ κίνησιν τῆς κατὰ φύσιν φορᾶς, καὶ μέχρι τοσούτου φέρηται ἕως ἂν κρατῇ ἡ κίνησις. πάλιν ἡ δίωσις καὶ σύνωσις ἄπωσις καὶ ἕλξις εἰσίν· ἡ μὲν γὰρ δίωσις ἄπωσις (ἢ γὰρ ἀφ' αὑτοῦ ἢ ἀπ' ἄλλου ἐστὶν ἡ ἄπωσις), ἡ δὲ σύνωσις ἕλξις (καὶ γὰρ πρὸς αὑτὸ καὶ πρὸς ἄλλο ἡ ἕλξις). ὥστε καὶ ὅσα τούτων εἴδη, οἷον σπάθησις καὶ κέρκισις· ἡ μὲν γὰρ σύνωσις, ἡ δὲ δίωσις. (cf. 1824) throwing when the movent causes a motion away from itself more violent than the natural locomotion of the thing moved, which continues its course so long as it is controlled by the motion imparted to it. Again, pushing apart and pushing together are forms respectively of pushing off and pulling: pushing apart is pushing off, which may be a motion either away from the pusher or away from something else, while pushing together is pulling, which may be a motion towards something else as well as the puller. We may similarly classify all the varieties of these last two, e.g. packing and combing: the former is a form of pushing together, the latter a form of pushing apart. ὁμοίως δὲ καὶ αἱ ἄλλαι συγκρίσεις καὶ διακρίσεις—ἅπασαι γὰρ ἔσονται διώσεις ἢ συνώσεις—πλὴν ὅσαι ἐν γενέσει καὶ φθορᾷ εἰσιν. ἅμα δὲ φανερὸν ὅτι οὐδ' ἔστιν ἄλλο τι γένος κινήσεως ἡ σύγκρισις καὶ διάκρισις· ἅπασαι γὰρ διανέμονται εἴς τινας τῶν εἰρημένων. ἔτι δ' ἡ μὲν εἰσπνοὴ ἕλξις, ἡ δ' ἐκπνοὴ ὦσις. ὁμοίως δὲ καὶ ἡ πτύσις, καὶ ὅσαι ἄλλαι διὰ τοῦ σώματος ἢ ἐκκριτικαὶ ἢ ληπτικαὶ κινήσεις· αἱ μὲν γὰρ ἕλξεις εἰσίν, αἱ δ' ἀπώσεις. δεῖ δὲ καὶ τὰς ἄλλας τὰς κατὰ τόπον ἀνάγειν· ἅπασαι γὰρ πίπτουσιν εἰς τέσσαρας ταύτας. τούτων δὲ πάλιν ἡ ὄχησις καὶ ἡ δίνησις εἰς ἕλξιν καὶ ὦσιν. ἡ μὲν γὰρ ὄχησις κατὰ τούτων τινὰ τῶν τριῶν τρόπων ἐστίν (τὸ μὲν γὰρ ὀχούμενον κινεῖται κατὰ συμβεβηκός, ὅτι ἐν κινουμένῳ ἐστὶν ἢ ἐπὶ κινουμένου τινός, τὸ δ' ὀχοῦν ὀχεῖ ἢ ἑλκόμενον ἢ (244a.) ὠθούμενον ἢ δινούμενον, ὥστε κοινή ἐστιν ἁπασῶν τῶν τριῶν ἡ ὄχησις)· The same is true of the other processes of combination and separation (they will all be found to be forms of pushing apart or of pushing together), except such as are involved in the processes of becoming and perishing. (At same time it is evident that there is no other kind of motion but combination and separation: for they may all be apportioned to one or other of those already mentioned.) Again, inhaling is a form of pulling, exhaling a form of pushing: and the same is true of spitting and of all other motions that proceed through the body, whether secretive or assimilative, the assimilative being forms of pulling, the secretive of pushing off. All other kinds of locomotion must be similarly reduced, for they all fall under one or other of our four heads. And again, of these four, carrying and twirling are to pulling and pushing. For carrying always follows one of the other three methods, for that which is carried is in motion accidentally, because it is in or upon something that is in motion, and that which carries it is in doing so being either pulled or pushed or twirled; thus carrying belongs to all the other three kinds of motion in common. ἡ δὲ δίνησις σύγκειται ἐξ ἕλξεώς τε καὶ ὤσεως· ἀνάγκη γὰρ τὸ δινοῦν τὸ μὲν ἕλκειν τὸ δ' ὠθεῖν· τὸ μὲν γὰρ ἀφ' αὑτοῦ τὸ δὲ πρὸς αὑτὸ ἄγει. And twirling is a compound of pulling and pushing, for that which is twirling a thing must be pulling one part of the thing and pushing another part, since it impels one part away from itself and another part towards itself. ὥστ' εἰ τὸ ὠθοῦν καὶ τὸ ἕλκον ἅμα τῷ ὠθουμένῳ καὶ τῷ ἑλκομένῳ, φανερὸν ὅτι τοῦ κατὰ τόπον κινουμένου καὶ κινοῦντος οὐδέν ἐστι μεταξύ. If, therefore, it can be shown that that which is pushing and that which is pushing and pulling are adjacent respectively to that which is being pushed and that which is being pulled, it will be evident that in all locomotion there is nothing intermediate between moved and movent. ἀλλὰ μὴν τοῦτο δῆλον καὶ ἐκ τῶν ὁρισμῶν· ὦσις μὲν γάρ ἐστιν ἡ ἀφ' αὑτοῦ ἢ ἀπ' ἄλλου πρὸς ἄλλο κίνησις, ἕλξις δὲ ἡ ἀπ' ἄλλου πρὸς αὑτὸ ἢ πρὸς ἄλλο, ὅταν θάττων ἡ κίνησις ᾖ [τοῦ ἕλκοντος] τῆς χωριζούσης ἀπ' ἀλλήλων τὰ συνεχῆ· οὕτω γὰρ συνεφέλκεται θάτερον. (τάχα δὲ δόξειεν ἂν εἶναί τις ἕλξις καὶ ἄλλως· τὸ γὰρ ξύλον ἕλκει τὸ πῦρ οὐχ οὕτως. τὸ δ' οὐθὲν διαφέρει κινουμένου τοῦ ἕλκοντος ἢ μένοντος ἕλκειν· ὁτὲ μὲν γὰρ ἕλκει οὗ ἔστιν, ὁτὲ δὲ οὗ ἦν.) But the former fact is clear even from the definitions of pushing and pulling, for pushing is motion to something else from oneself or from something else, and pulling is motion from something else to oneself or to something else, when the motion of that which is pulling is quicker than the motion that would separate from one another the two things that are continuous: for it is this that causes one thing to be pulled on along with the other. (It might indeed be thought that there is a form of pulling that arises in another way: that wood, e.g. pulls fire in a manner different from that described above. But it makes no difference whether that which pulls is in motion or is stationary when it is pulling: in the latter case it pulls to the place where it is, while in the former it pulls to the place where it was.) ἀδύνατον δὲ ἢ ἀφ' αὑτοῦ πρὸς ἄλλο ἢ ἀπ' ἄλλου πρὸς αὑτὸ κινεῖν (244b.) μὴ ἁπτόμενον, ὥστε φανερὸν ὅτι τοῦ κατὰ τόπον κινουμένου καὶ κινοῦντος οὐδέν ἐστι μεταξύ. Now it is impossible to move anything either from oneself to something else or something else to oneself without being in contact with it: it is evident, therefore, that in all locomotion there is nothing intermediate between moved and movent.
Quia philosophus in demonstratione praecedenti supposuerat quod movens est contiguum vel continuum mobili, hoc intendit nunc probare. Et primo ostendit propositum; secundo probat quoddam, quod in hac probatione supponit, ibi: quoniam autem quae alterantur et cetera. 897. In the previous demonstration the Philosopher had assumed that a mover is continuous, or at least contiguous, with the mobile. This he now intends to prove. First he proves his proposition; Secondly, he proves something he had assumed in his proof, (L. 4) Circa primum duo facit: primo proponit intentum; secundo probat propositum, ibi: quoniam autem tres sunt motus et cetera. About the first he does two things: First he states his intention; Secondly, he proves his proposition, at 898. Dicit ergo primo, quod movens et motum sunt simul. Sed aliquid dicitur movere dupliciter. Uno modo sicut finis movet agentem; et tale movens aliquando distans est ab agente quem movet: alio modo sicut movet id quod est principium motus; et de tali movente hic intelligit. Et propter hoc addidit: non sicut cuius causa, sed unde est principium motus. He says therefore first (682) that mover and moved are together. But something is said to be “moved” in two senses. In one sense as the end moves the agent, and such a mover is sometimes distant from the agent it moves; in another sense as that moves which is the actual beginner of the motion. It is of this latter that Aristotle speaks, and that is why he adds “not as that for the sake of which, but as that from which the source of motion is.” Item movens sicut principium motus, quoddam est immediatum, et quoddam remotum. Intelligit autem hic de immediate movente, et ideo dixit primum movens; ut per primum significetur immediatum mobili, non autem id quod est primum in ordine moventium. Again, a mover as principle of motion can be immediate or remote. Aristotle speaks of what causes motion immediately and calls it the “first mover” which refers not to what is first in the series of movers but to a mover that is immediate to the mobile. Et quia in quinto dixerat ea esse simul quae sunt in eodem loco, posset aliquis credere ex hoc quod dicit quod movens et motum simul sunt, quod quando unum corpus movetur ab altero, quod oporteat ambo esse in eodem loco: et ideo ad hoc excludendum subiungit, quod simul dicit hic, non quidem esse in eodem loco, sed quia nihil est medium inter movens et motum; secundum quod contacta vel continua sunt simul, quia termini eorum sunt simul, vel quia sunt unum. And because in Book V he had said that things in the same place are together, one might, conclude from that and from the statement that mover and moved are together, that when one body is moved by another they must both be in the same place. Therefore, to prevent this misunderstanding, he adds that “together” is not taken here in the sense of being in the same place, but in the sense that nothing is intermediate between the mover and the moved. It is in this sense that things in contact, or things that are continuous are together, because their extremities are together or are one and the same. Et quia in praecedenti demonstratione processerat solum de motu locali, posset aliquis credere quod hoc haberet veritatem solum in huiusmodi motu: et ideo ad hoc removendum subiungit, quod hoc dictum est communiter, quod movens et motum sunt simul, et non specialiter de motu locali; quia hoc est commune in omni specie motus, quod movens et motum sunt simul, modo exposito. And because in the previous demonstration he proceeded solely along the line of local motion, this does not mean that his proposition is true only in cases of local motion. Therefore, to exclude this possible misunderstanding, he adds that the statement “mover and moved are together” must be taken in a sense common to all motions, for it is found in every kind of motion that mover and moved are together, in the sense explained. Deinde cum dicit: quoniam autem tres etc., probat propositum. Et circa hoc duo facit: primo enumerat species motus; secundo in singulis probat propositum, ibi: omne igitur quod fertur et cetera. 898. Then at (683) he proves his proposition. About this he does two things: First he enumerates the species of motion; Secondly, he proves his proposition for each kind, at 899. Dicit ergo primo quod tres sunt motus: unus secundum locum, qui dicitur loci mutatio: alius secundum qualitatem, qui dicitur alteratio: alius secundum quantitatem, qui dicitur augmentum et decrementum. Non facit autem mentionem de generatione et corruptione, quia non sunt motus, ut in quinto probatum est. Sed cum sint termini motus, scilicet alterationis, ut habitum est in sexto, per hoc quod probatur propositum in alteratione, sequitur etiam idem de generatione et corruptione. He says therefore first (683) that there are three kinds of motion: one is in respect to place and is called “local motion”; one is in respect of quantity and is called “growth and decrease; the third is in respect of quality and is called “alteration.” He makes no mention of generation and ceasing to-be, because they are not motions, as was explained in Book V. However, since generation and ceasing-to-be are the termini of a motion, i.e., of alteration, as was proved in Book VI, then if he proves his proposition in regard to alteration, it will also be proved in regard to generation and ceasing-to-be. Sicut igitur tres sunt species motus, ita tres sunt species mobilium, et etiam moventium; et in omnibus est verum quod dictum est, scilicet quod movens et motum sint simul, ut ostendetur in singulis. Sed primo hoc est ostendendum in motu locali, qui est primus motuum, ut in octavo probabitur. Now just as there are three kinds of motion, so there are three kinds of mobile and also three kinds of mover. And in all it is true that the mover and the moved are together, as will be shown for each case. But first it must be proved for local motion: which is the first of motions, as will be shown in Book VIII. Deinde cum dicit: omne igitur quod fertur etc., ostendit propositum in singulis trium praedictorum motuum: et primo in motu locali; secundo in motu alterationis, ibi: at vero neque alterati etc.; tertio in motu augmenti et decrementi, ibi: et quod augetur et augens et cetera. 899. Then at (684) he proves his proposition for each kind of motion: First in local motion; Secondly, in the motion of alteration, in L. 4; Thirdly, in the motion of growth and decrease, also in L. 4. Circa primum duo facit: primo ostendit propositum in quibus magis est manifestum; secundo in quibus magis latet, ibi: quod autem ab alio movetur et cetera. About the first he does two things: First he shows the proposition in cases that are evident; Secondly, in less evident cases, at 900. Dicit ergo primo, quod necesse est dicere quod omne quod movetur secundum locum, aut movetur a seipso aut ab altero. Quod autem dicit a seipso aliquid moveri, potest intelligi dupliciter. Uno modo ratione partium, sicut ostendet in octavo quod moventium seipsa, una pars movet et alia movetur: alio modo primo et per se, ut scilicet aliquid secundum se totum moveat se totum, sicut supra probavit quod hoc modo nihil movet seipsum. Si autem concedatur utroque modo aliquid moveri a seipso, manifestum est quod movens erit in ipso quod movetur, vel sicut idem est in seipso, vel sicut pars est in toto, ut anima in animali. Et sic sequetur quod simul sit movens et quod movetur, ita quod nihil erit ipsorum medium. He says therefore first (684) that we must say that whatever is being moved in respect of place is moved either by itself or by something else. To say that something is “moved by itself” can be taken in two senses: first, by reason of the parts, as when we shall prove in Book VIII that in things that move themselves one part moves and another part is moved; secondly, first and per se, i.e., so that the whole moves itself according to itself and as a whole, as when he proved earlier that in this way nothing moves itself. But if it be granted that something is moved by itself in both ways, it is clear that the mover will be in what is being moved, either in the way that a same thing is in itself, or as a part is in a whole, as a soul is in an animal. Thus it will follow that the mover and the moved are together in such a way that nothing exists between them. Deinde cum dicit: quod autem ab alio movetur etc., ostendit idem in iis quae moventur secundum locum ab alio, de quibus minus est manifestum. Et circa hoc tria facit: primo distinguit modos quibus aliquid contingit ab altero moveri; secundo reducit eos ad duos, ibi: manifestum igitur est etc.; tertio in illis duobus probat propositum, ibi: hoc autem manifestum et cetera. 900. Then at (685) he proves the same, in regard to things that are moved according to place by something else, in those cases where it is less evident. About this he does three things: First he distinguishes the ways in which something happens to be moved by something else; Secondly, he reduces these ways to two ways, at 906 bis; Thirdly, he proves his proposition for these two ways, at 907. Circa primum duo facit. Primo dividit modos quibus aliquid movetur ab altero; et dicit quod sunt quatuor, scilicet pulsio, tractio, vectio et vertigo. Omnes enim motus qui sunt ab alio, reducuntur in istos. About the first he does two things: First he divides the ways in which something is moved by something else into four: pushing, pulling, carrying and twirling. For all motions that are caused by something distinct from the moved are reduced to these four. Secundo ibi: pulsionis igitur etc., manifestat praemissos quatuor modos. Et primo manifestat pulsionem, quae est cum movens facit aliquod mobile a se distare movendo. Dividit autem pulsionem in duo, scilicet in impulsionem et expulsionem. Dicitur autem impulsio, quando movens sic pellit aliquod mobile, quod non deficit ipsi deferendo ipsum, sed simul cum eo tendit quo ducit: expulsio autem est, quando movens sic movet mobile, quod tamen deficit ei deserendo ipsum, nec comitatur ipsum usque ad finem motus. 901. Secondly, he explains these four ways. First he explains pushing as that which occurs when the mover makes a mobile be distant from him by moving it. Pushing is of two kinds: pushing on and pushing off. Pushing on occurs when the mover pushes a mobile but does not desert it but rather accompanies it to the place it is going. Pushing off (expulsion) occurs when the mover moves a mobile in such a way that it deserts and does not accompany it to the very end of the motion. Secundo ibi: vectio autem etc., manifestat de vectione; et dicit quod vectio fundatur in tribus aliis motibus, scilicet pulsione, tractione et vertigine, sicut quod est per accidens fundatur in eo quod est per se. Illud enim quod vehitur, non movetur per se, sed per accidens, inquantum scilicet aliquid alterum movetur, in quo ipsum est, sicut cum aliquis vehitur a navi in qua est; vel super quod est, sicut cum aliquis vehitur equo. Illud autem quod vehit, movetur per se, eo quod non est procedere in iis quae moventur per accidens in infinitum. Et sic oportet quod primum vehens moveatur aliquo motu per se, vel pulsu vel tractu vel vertigine. Ex quo manifestum est quod vectio in tribus aliis motibus continetur. 902. Then at (687) he explains carrying as a motion based on three other motions; namely, pushing, pulling and twirling, in the same way that what is per accidens is based on what is per se. For that which is carried is not moved per se but per accidens, inasmuch as something in which it exists is being moved; as, for example, when someone is carried by a ship on which he is, or carried by a horse upon which he is. That which carries is moved per se, since one does not proceed ad infinitum in things that are moved per accidens. And thus the first vehicle is moved per se on account of some motion which is either a push or a pull or a twirls. From this it is clear that carrying is contained in the other three motions. Tertio ibi: tractio autem etc., manifestat tertium modum, scilicet tractum. Et sciendum est quod tractio a pulsione differt, quia in pulsione movens se habet ad mobile ut terminus a quo est motus eius, in tractu vero se habet ut terminus ad quem. Illud ergo trahere dicitur, quod movet alterum ad seipsum. Movere autem aliquid secundum locum ad seipsum contingit tripliciter. Uno modo sicut finis movet; unde et finis dicitur trahere, secundum illud poetae: trahit sua quemque voluptas: et hoc modo potest dici quod locus trahit id quod naturaliter movetur ad locum. 903. Then at (688) he explains the third way, i.e., pulling. And note that pulling differs from pushing, because in the latter the mover is related to the mobile as terminus a quo of its motion, whereas in pulling he is related as the terminus ad quem. Therefore only what moves something to itself is said to “pull.” However, the act of moving something to oneself in respect of place occurs in three ways: first in the way that an end moves, i.e., in the sense in which the poets declare that the end is said to pull, when they say that one’s own desire pulls him. It is in this sense that a place may be said to pull what is naturally moved to a place. Alio modo potest dici aliquid trahere, quia movet illud ad seipsum alterando aliqualiter, ex qua alteratione contingit quod alteratum moveatur secundum locum: et hoc modo magnes dicitur trahere ferrum. Sicut enim generans movet gravia et levia, inquantum dat eis formam per quam moventur ad locum, ita et magnes dat aliquam qualitatem ferro, per quam movetur ad ipsum. Et quod hoc sit verum patet ex tribus. In a second way something is said to pull something else, when it moves it to itself by altering it somehow, so that as a result the altered object is moved in respect of place. It is in this way that a magnet is said to pull iron. For just as the generator of a thing moves heavy and light things inasmuch as it gives them the form through which they are moved to their place, so the magnet confers some quality on the iron by which it is moved toward itself. That this is true he makes clear by three facts: Primo quidem quia magnes non trahit ferrum ex quacumque distantia, sed ex propinquo: si autem ferrum moveretur ad magnetem solum sicut ad finem, sicut grave ad suum locum, ex qualibet distantia tenderet ad ipsum. First, because a magnet does not draw iron from just any distance but within a certain limit of nearness. But if the iron were moved to the magnet only as to an end in the way that a heavy body is moved to its place, it should do so no matter how great the distance they are separated by. Secundo quia si magnes aliis perungatur, ferrum attrahere non potest; quasi aliis vim alterativam ipsius impedientibus, aut etiam in contrarium alterantibus. Secondly, because if the magnet be covered with oil, it cannot draw the iron, because the oil impedes the altering quality or modifies it. Tertio quia ad hoc quod magnes attrahat ferrum, oportet prius ferrum liniri cum magnete, maxime si magnes sit parvus; quasi ex magnete aliquam virtutem ferrum accipiat ut ad eum moveatur. Sic igitur magnes attrahit ferrum non solum sicut finis, sed etiam sicut movens et alterans. Thirdly, because in order that a magnet attract iron, the iron must first be rubbed by the magnet, especially if the magnet is weak. It is as though the iron receives from the magnet some power by which it is moved toward it. Thus a magnet pulls the iron not only as an end but as a moving cause and as an altering cause. Tertio modo dicitur aliquid attrahere, quia movet ad seipsum motu locali tantum. Et sic definitur hic tractio, prout unum corpus trahit alterum, ita quod trahens simul moveatur cum eo quod trahitur. In a third way something is said to pull something else, because it moves it to itself in respect of local motion only. And it is in this sense that Aristotle here defines “pulling,” i.e., in the sense that one body pulls another in such a way that the puller accompanies what it pulls. Hoc est ergo quod dicit, quod tractio est cum motus trahentis ad seipsum vel ad alterum, sit velocior, non separatus ab eo quod trahitur. Dicit autem: ad ipsum vel ad alterum, quia movens voluntarium potest uti altero ut seipso: unde potest ab alio pellere sicut a seipso, et ad aliud trahere sicut ad seipsum. Sed hoc in motu naturali non contingit; immo semper pulsio naturalis est a pellente, et tractio naturalis ad trahentem. 904. This, therefore, is what he says, namely, that pulling occurs “when the motion of what pulls something toward itself or toward something else is swifter but not separated from what is pulled.” And he says “toward itself or toward something else,” because a voluntary mover can use something else just as itself; hence such a mover can both push something from something else as from itself, and pull something toward something else as toward itself. However, this does not happen in natural motions, where a natural push is always away from the pusher and a natural pull is toward the puller. Addit autem: cum velocior sit motus; quia contingit quandoque quod id quod trahitur, etiam per se movetur illuc quo trahitur; sed a trahente velociori motu compellitur moveri: et quia trahens movet suo motu, oportet quod motus trahentis sit velocior quam motus naturalis eius quod trahitur. He said, “when the motion is swifter,” because sometimes what is pulled is being moved toward its objective by its own motion, but is compelled by the puller to move with a swifter motion. And since the puller acts by its own motion, the motion of the puller must be swifter than the natural motion of what is being pulled. Adiungit autem: non separatus ab eo quod trahitur, ad differentiam pulsionis. Nam in pulsione pellens quandoque separatur ab eo quod pellit, quandoque vero non; sed trahens nunquam separatur ab eo quod trahitur; quinimmo simul movetur trahens cum eo quod trahitur. The reason for saying, “not separated from what is being pulled,” is to distinguish it from a push. For in some pushes the pusher separates itself from the object pushed and in some not, whereas the puller is never separated from what is pulled; indeed, both the puller and the pulled are moved at once. Exponit autem quod dixerat, ad ipsum vel ad alterum, quia contingit esse tractionem ad ipsum trahentem et ad alterum in motibus voluntariis, ut dictum est. Finally he said, “to itself or to something else” because a pull can be toward the puller or toward something else, as was explained for voluntary motions. Et quia sunt quidam motus in quibus non ita manifeste salvatur ratio tractionis, consequenter ostendit eos etiam reduci ad hos modos tractionis quos posuerat, scilicet ad seipsum et ad alterum. Et hoc est quod dicit, quod omnes alii tractus, qui non nominantur tractus, reducuntur in hos duos modos tractionis; quia sunt idem specie cum eis quantum ad hoc quod motus accipiunt speciem a terminis; quia et illi tractus sunt ad seipsum vel ad alterum, sicut patet in inspiratione et expiratione. Inspiratio enim est attractio aeris, expiratio vero est aeris expulsio; et similiter spuitio est expulsio sputi. Et similiter dicendum est de omnibus aliis motibus, per quoscumque aliqua corpora extra mittuntur vel intra recipiuntur; quia emissio reducitur ad pulsionem, receptio autem ad tractionem. 905. Since there are motions in which the presence of a pull is not clearly evident, he shows that even those are reduced to the types mentioned, i.e., that they are directed toward the puller or toward something else. And this is what he says, namely, that all other types of pulling which are not called “pull” are reduced to these two types, because they are specifically the same as one or the other of these two, insofar as a motion derives its species from its terminus—for the motions he has in mind are either toward the puller or toward something else, as is evident in inhaling and exhaling. For “inhaling” is pulling air in, and “exhaling” is pushing it out; likewise, spitting is the pushing out of spittle. The same is to be said of all those other motions by which bodies are expelled or drawn inwards, because emitting is reduced to pushing out and receiving to pulling. Et similiter spathesis est pulsio, et kerkisis est attractio. Spathe enim in Graeco dicitur ensis vel spatha: unde spathesis idem est quod spathatio, idest percussio per ensem, quae fit pellendo. Et ideo alia littera quae dicit speculatio, videtur esse vitio scriptoris corrupta; quia pro spathatione posuit speculationem. Kerkisis autem est attractio. Est autem kerkis in Graeco quoddam instrumentum quo utuntur textores, quod ad se trahunt texendo, quod Latine dicitur radius: unde alia littera habet radiatio. In like manner, spathesis is a type of pushing and kerkisis is a type of pulling. The former comes from the Greek word for sword; hence spathesis is to cut with a sword, which is done by pushing. Kerkisis, however, is from the Greek word “ kerkis ”—which refers to a weaver’s tool which he pulls toward himself as he weaves, called in Latin “radius” (hence another text has “radiatio”). Horum enim duorum, et quorumcumque motuum emissivorum et receptivorum, aliud est congregatio, quod pertinet ad attractionem, quia congregans movet aliquid ad alterum: aliud est disgregatio, quae pertinet ad pulsionem, quia pulsio est motus alicuius ab alio. Sic ergo patet quod omnis motus localis est aggregatio vel disgregatio; quia omnis motus localis est ab aliquo vel ad aliquid. Et per consequens patet quod omnis motus localis est pulsio vel tractio. These two motions, and indeed all cases of emitting or receiving are either a gathering, which pertains to drawing toward, the gatherer being one who moves something to something else, or a scattering, a scatterer being one who pushes, for a push is a motion of one thing from another. In this way it is clear that all local motion is either a gathering or a scattering, because every local motion is either from something or toward something. Consequently, all local motion is either a pushing or a pulling. Deinde cum dicit: vertigo autem etc., manifestat quid sit vertigo; et dicit quod vertigo est quidam motus compositus ex tractu et pulsu. Cum enim aliquid vertitur, ex una parte pellitur et ex alia trahitur. 906. Then at (689) he explains twirling as a motion composed of a pull and a push, for when something is twirled, it is on the one hand pushed, and on the other being pulled. Deinde cum dicit: manifestum igitur etc., ostendit quod omnes quatuor motus praedicti ad pulsum et tractum reducuntur, et quod idem est iudicium de omnibus et de istis duobus. Quia enim vectio consistit in tribus aliis, et vertigo componitur ex pulsu et tractu, relinquitur quod omnis motus localis qui est ab alio, reducitur ad pulsum et tractum. Unde manifestum est quod si in pulsu et tractu movens et motum sint simul, idest ita quod pellens sit simul cum eo quod pellitur, et trahens cum eo quod trahitur; consequens erit universaliter verum esse, quod nullum sit medium inter movens secundum locum et motum. 906 bis. Then at (690) he shows that the four general ways are reduced to pushing or pulling, and that whatever can be said of all four is contained in these two. For, since carrying consists of the other three, and twirling is composed of a push and a pull, what remains is that every local motion caused by a mover is reduced either to a push or a pull. Hence it is evident that if the mover and moved are together in the motions of pulling and of pushing, so that the pusher is together with what is being pushed, and the puller with what is being pulled, then it is universally true that there is nothing between the mover, in respect of place, and what is moved. Deinde cum dicit: hoc autem manifestum etc., probat propositum in his duobus motibus. Et primo ponit duas rationes ad propositum ostendendum; secundo excludit obiectionem, ibi: proiectio autem et cetera. 907. Then at (691) he proves his proposition for these two motions; First he presents two arguments that prove the proposition; Secondly, he answers an objection, at 908. Prima autem ratio sumitur ex definitione utriusque motus: quia pulsio est motus ab ipso movente vel ab aliquo alio in aliquid aliud; et sic oportet quod saltem in principio motus pellens sit simul cum eo quod pellitur, dum pellens id quod pellitur removet a se vel ab alio. Sed tractus est motus ad ipsum vel ad alterum, ut dictum est; et quod non separatur trahens ab eo quod trahitur. Ex quo manifestum est in his duobus motibus, quod movens et motum sint simul. The first argument is based on the definition of the two motions: for a “push” is a motion from the mover or from something else into something else; consequently, at the beginning of the motion the pusher must be together with what is being pushed, at least when the pusher removes from himself or from something else the object that is being pushed. A “pull,” however, is a motion toward the puller or toward something else, as we have said; a motion, I say, in which the puller is not separated from what is being pulled. Hence it is clear that in these two motions the mover and the moved are together. Secunda ratio sumitur ex congregatione et disgregatione. Dictum est enim quod pulsio est disgregatio, et tractio est congregatio. Et hoc est quod dicit: adhuc autem synosis, idest congregatio, et diosis, idest divisio. Non autem posset aliquid congregare vel disgregare, nisi adesset his quae congregantur et disgregantur. Et sic patet quod in pulsione et tractu movens et motum sunt simul. The second argument is based on gathering and scattering. For it was said above that pushing is scattering and pulling is gathering. Now, no one gathers (synosis) or scatters (diosis) without being present to the things he is gathering or scattering. Therefore, it is clear that in pulling and in pushing the mover and the moved are together. Deinde cum dicit: proiectio autem etc., excludit quandam obiectionem, quae accidere potest circa pulsionem. De tractione enim dictum est quod motus trahentis non separetur ab eo quod trahitur: sed in pulsione dictum est quod aliquando deficit pellens ab eo quod pellitur. Et talis pulsio vocatur expulsio, cuius species est proiectio, quae est quando aliquid pellitur cum quadam violentia in remotum; et sic in proiectione videtur quod movens et motum non sint simul. 908. Then at (692) he answers an objection that could be lodged against the push. For it was said of pulling that the motion of the puller is not separated from what is being pulled. But in pushing it was said that the pusher is in certain cases removed from the object pushed. Such a case of pushing is called “projection,” which occurs when something is pushed with some force into the distance. Hence it seems that in this case the mover and the moved are not together. Et ideo ad hoc excludendum dicit, quod proiectio est, quando motus eius quod fertur, sit velocior quam motus naturalis, et hoc propter aliquam fortem impulsionem factam. Cum enim aliquid proiicitur ex forti impulsione, movetur aer velociori motu quam sit motus eius naturalis; et ad motum aeris defertur corpus proiectum. Et quamdiu durat aer impulsus, tamdiu proiectum movetur: et hoc est quod dicit, quod facta tali impulsione, tamdiu accidit aliquid ferri proiectum, quamdiu in aere sit fortior motus quam eius motus naturalis. To answer this he says that projecting occurs when the motion of what is thrown becomes faster than its natural motion on account of a strong impulse. For when something is projected by a strong push, the air is moved with a motion swifter than its natural motion, and with air’s motion the projected body is carried along. And so long as the air stays pushed, so long does the projectile remain in motion. This is what Aristotle says, namely, that when such a push is made, so long as there remains in the air a motion stronger than its natural motion, so long does the projectile remain in motion. Sic ergo remota hac dubitatione, concludit quod movens et motum sint simul, et quod inter ea nihil est medium. Thus, with this objection answered, he concludes that the mover and the moved are together, and that nothing intervenes between the two.
It is shown in alteration, and growth and decrease, that mover and moved are together
Chapter 2 cont. ἀλλὰ μὴν οὐδὲ τοῦ ἀλλοιουμένου καὶ τοῦ ἀλλοιοῦντος. τοῦτο δὲ δῆλον ἐξ ἐπαγωγῆς· ἐν ἅπασι γὰρ συμβαίνει ἅμα εἶναι τὸ ἔσχατον ἀλλοιοῦν καὶ τὸ πρῶτον ἀλλοιούμενον· Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be proved by induction: for in every case we find that the respective extremities of that which causes and that which undergoes alteration are adjacent. <�ὑπόκειται γὰρ ἡμῖν τὸ τὰ ἀλλοιούμενα κατὰ τὰς παθητικὰς καλουμένας ποιότητας πάσχοντα ἀλλοιοῦσθαι>. ἅπαν γὰρ σῶμα σώματος διαφέρει τοῖς αἰσθητοῖς ἢ πλείοσιν ἢ ἐλάττοσιν ἢ τῷ μᾶλλον καὶ ἧττον τοῖς αὐτοῖς· ἀλλὰ μὴν καὶ ἀλλοιοῦται τὸ ἀλλοιούμενον ὑπὸ τῶν εἰρημένων. ταῦτα γάρ ἐστι πάθη τῆς ὑποκειμένης ποιότητος· ἢ γὰρ θερμαινόμενον ἢ γλυκαινόμενον ἢ πυκνούμενον ἢ ξηραινόμενον ἢ λευκαινόμενον ἀλλοιοῦσθαί φαμεν, ὁμοίως τό τε ἄψυχον καὶ τὸ ἔμψυχον λέγοντες, καὶ πάλιν τῶν ἐμψύχων τά τε μὴ αἰσθητικὰ τῶν μερῶν καὶ αὐτὰς τὰς αἰσθήσεις. ἀλλοιοῦνται γάρ πως καὶ αἱ αἰσθήσεις· ἡ γὰρ αἴσθησις ἡ κατ' ἐνέργειαν κίνησίς ἐστι διὰ τοῦ σώματος, πασχούσης τι τῆς αἰσθήσεως. καθ' ὅσα μὲν οὖν τὸ ἄψυχον ἀλλοιοῦται, καὶ τὸ ἔμψυχον, καθ' ὅσα δὲ τὸ ἔμψυχον, οὐ κατὰ ταῦτα πάντα τὸ ἄψυχον (οὐ γὰρ ἀλλοιοῦται κατὰ τὰς αἰσθήσεις)· καὶ τὸ μὲν λανθάνει, τὸ δ' οὐ (245a.) λανθάνει πάσχον. οὐδὲν δὲ κωλύει καὶ τὸ ἔμψυχον λανθάνειν, ὅταν μὴ κατὰ τὰς αἰσθήσεις γίγνηται ἡ ἀλλοίωσις. εἴπερ οὖν ἀλλοιοῦται τὸ ἀλλοιούμενον ὑπὸ τῶν αἰσθητῶν, ἐν ἅπασί γε τούτοις φανερὸν ὅτι ἅμα ἐστὶ τὸ ἔσχατον ἀλλοιοῦν καὶ τὸ πρῶτον ἀλλοιούμενον· For our assumption is that things that are undergoing alteration are altered in virtue of their being affected in respect of their so-called affective qualities, since that which is of a certain quality is altered in so far as it is sensible, and the characteristics in which bodies differ from one another are sensible characteristics: for every body differs from another in possessing a greater or lesser number of sensible characteristics or in possessing the same sensible characteristics in a greater or lesser degree. But the alteration of that which undergoes alteration is also caused by the above-mentioned characteristics, which are affections of some particular underlying quality. Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white: and we make these assertions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts that have no power of sense-perception and of the senses themselves. For in a way even the senses undergo alteration, since the active sense is a motion through the body in the course of which the sense is affected in a certain way. We see, then, that the animate is capable of every kind of alteration of which the inanimate is capable: but the inanimate is not capable of every kind of alteration of which the animate is capable, since it is not capable of alteration in respect of the senses: moreover the inanimate is unconscious of being affected by alteration, whereas the animate is conscious of it, though there is nothing to prevent the animate also being unconscious of it when the process of the alteration does not concern the senses. Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration it is evident that the respective extremities of that which causes and that which undergoes alteration are adjacent. τῷ μὲν γὰρ συνεχὴς ὁ ἀήρ, τῷ δ' ἀέρι τὸ σῶμα. πάλιν δὲ τὸ μὲν χρῶμα τῷ φωτί, τὸ δὲ φῶς τῇ ὄψει. τὸν αὐτὸν δὲ τρόπον καὶ ἡ ἀκοὴ καὶ ἡ ὄσφρησις· πρῶτον γὰρ κινοῦν πρὸς τὸ κινούμενον ὁ ἀήρ. καὶ ἐπὶ τῆς γεύσεως ὁμοίως· ἅμα γὰρ τῇ γεύσει ὁ χυμός. ὡσαύτως δὲ καὶ ἐπὶ τῶν ἀψύχων καὶ ἀναισθήτων. ὥστ' οὐδὲν ἔσται μεταξὺ τοῦ ἀλλοιουμένου καὶ τοῦ ἀλλοιοῦντος. Thus the air is continuous with that which causes the alteration, and the body that undergoes alteration is continuous with the air. Again, the colour is continuous with the light and the light with the sight. And the same is true of hearing and smelling: for the primary movent in respect to the moved is the air. Similarly, in the case of tasting, the flavour is adjacent to the sense of taste. And it is just the same in the case of things that are inanimate and incapable of sense-perception. Thus there can be nothing intermediate between that which undergoes and that which causes alteration. οὐδὲ μὴν τοῦ αὐξανομένου τε καὶ αὔξοντος· αὐξάνει γὰρ τὸ πρῶτον αὖξον προσγιγνόμενον, ὥστε ἓν γίγνεσθαι τὸ ὅλον. καὶ πάλιν φθίνει τὸ φθῖνον ἀπογιγνομένου τινὸς τῶν τοῦ φθίνοντος. ἀνάγκη οὖν συνεχὲς εἶναι καὶ τὸ αὖξον καὶ τὸ φθῖνον, τῶν δὲ συνεχῶν οὐδὲν μεταξύ. Nor, again, can there be anything intermediate between that which suffers and that which causes increase: for the part of the latter that starts the increase does so by becoming attached in such a way to the former that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of the thing becoming detached. So that which causes increase and that which causes decrease must be continuous with that which suffers increase and that which suffers decrease respectively: and if two things are continuous with one another there can be nothing intermediate between them. Chapter 3 φανερὸν οὖν ὅτι τοῦ κινουμένου καὶ (245b.) τοῦ κινοῦντος πρώτου καὶ ἐσχάτου πρὸς τὸ κινούμενον οὐδέν ἐστιν ἀνὰ μέσον. It is evident, therefore, that between the extremities of the moved and the movent that are respectively first and last in reference to the moved there is nothing intermediate.
Postquam ostendit in motu locali, quod movens et motum sunt simul, ostendit idem in alteratione; quod scilicet nihil est medium alterantis et alterati. Et hoc probat primo per inductionem. In omnibus enim quae alterantur, manifestum est quod simul sunt ultimum alterans et primum alteratum. Videtur autem hoc habere instantiam in quibusdam alterationibus: sicut cum sol calefacit aerem sine hoc quod calefaciat orbes medios planetarum; et piscis quidam in reti detentus, stupefacit manus trahentis rete, absque hoc quod stupefaciat rete. 909. After showing that the mover and moved are together in local motion, he shows the same for alteration, i.e., that there is nothing between the thing altered and the cause of the alteration. This he proves first by induction at (693). For in all things that are altered, it is clear that the last thing altering, and the first thing altered, are together. However this seems to suggest a difficulty in certain alterations, e.g. when the sun heats the air without heating the intermediate orbs of the planets, or when a certain kind of fish held in a net shocks the hand of the one holding the net without shocking the net. Sed dicendum est quod passiva recipiunt actionem activorum secundum proprium modum; et ideo media quae sunt inter primum alterans et ultimum alteratum, aliquid patiuntur a primo alterante, sed forte non eodem modo sicut ultimum alteratum. Aliquid igitur patitur rete a pisce stupefaciente, sed non stupefactionem, quia eius non est capax: et orbes medii planetarum aliquid recipiunt a sole, scilicet lumen, non autem calorem. To this it must be said that things which are passive undergo the action of things that are active in their own special way, and therefore the intermediate between the first cause of an alteration and the last thing altered undergo something from the first cause, but perhaps not in the same way as the last thing affected. For the net undergoes something from the fish that causes the shock, but not a shock, because it is not capable of being shocked. And the intermediate orbs of the planets receive something from the sun, namely, its light, but not its heat. Secundo ibi: quale enim alteratur etc., probat idem per rationem: quae talis est. Omnis alteratio est similis alterationi quae fit secundum sensum: sed in alteratione quae est secundum sensum, alterans et alteratum sunt simul: ergo et in qualibet alteratione. 910. Secondly, at (694) he proves the same thing by an argument, which is this: Every alteration is similar to an alteration which affects a sense. But in an alteration which affects a sense the cause of the alteration and the thing altered are together. Therefore, the same is true in every alteration. Primum sic probat. Omnis alteratio fit secundum qualitatem sensibilem, quae est tertia species qualitatis. Secundum illa enim alterantur corpora, quibus primo corpora ab invicem differunt; quae sunt sensibiles qualitates: ut gravitas et levitas, durities et mollities, quae percipiuntur tactu; sonus et non sonus, qui percipiuntur auditu (sed tamen si sonus in actu accipiatur, est qualitas in aere, consequens aliquem motum localem; unde non videtur secundum huiusmodi qualitatem esse primo et per se alteratio: si vero sonus in aptitudine accipiatur, sic per aliquam alterationem fit aliquid sonabile vel non sonabile); albedo et nigredo, quae pertinent ad visum; dulcedo et amaritudo, quae pertinent ad gustum; humiditas et siccitas, densitas et raritas, quae pertinent ad tactum. Et eadem ratio est de his contrariis, et de mediis horum. Et similiter etiam sunt alia quae sub sensu cadunt, sicut calor et frigus, et lenitas et asperitas, quae etiam tactu comprehenduntur. To prove the major premis, he says that every alteration takes place according to a sensible quality, which is the third species of quality. For bodies are apt to be altered in respect of those qualities by which bodies are primarily distinguished one from the other, i.e. in sensible qualities, such as heaviness, lightness, hardness and softness, which are perceived by touch, sound and non-sound, which are perceived by hearing. (However, if sound is considered in act, it is a quality of the air, resulting from a local motion; consequently, it does not seem that there can be a primary and per se alteration according to a quality of this sort. But if sound is taken in an aptitudinal sense, then it is through some alteration that something becomes soundable or non-soundable.) There are also blackness and whiteness, which pertain to sight; sweetness and bitterness, which pertain to taste; dryness and wetness, density and rarity, which pertain to touch. The same goes for the contraries of these and for the intermediates. Likewise, there are others which are perceptible by sense, such as cold and heat, smoothness and roughness, which are apprehended by touch. Huiusmodi enim sunt quaedam passiones sub genere qualitatis contentae: et dicuntur passiones, quia passionem ingerunt sensibus, vel quia ab aliquibus passionibus causantur, ut in praedicamentis dicitur. Dicuntur autem passiones sensibilium corporum, quia sensibilia corpora secundum huiusmodi differunt; inquantum scilicet unum est calidum et aliud frigidum, unum grave et aliud leve, et sic de aliis; aut inquantum aliquod unum de praemissis inest duobus secundum magis et minus. Ignis enim differt ab aqua secundum differentiam calidi et frigidi; ab aere vero secundum magis et minus calidum. Et etiam secundum hoc attenditur sensibilium corporum differentia, inquantum patiuntur aliquod horum, licet non insit eis naturaliter; sicut dicimus differre calefacta ab infrigidatis, et ea quae fiunt dulcia ab his quae fiunt amara, per aliquam passionem, et non ex natura. All these are passions contained within the genus of quality. And they are called “passions” because they produce a passion in the sense (i.e., the senses come to be in the state of being acted upon) or because they are caused by certain passions, as is explained in the Predicaments. But they are called “passions of sensible bodies” because it is in respect of these that sensible bodies differ, inasmuch as one is hot and another cold, one is heavy and another light, and so on, or inasmuch as someone of them is present in two things, more so in one thing and less so in another. Fire, for example, differs from water by reason of the difference of hot and cold, and from air according to more and. less hot. Again, the difference of sensible bodies is based on the ability of some of them to receive one or the other of these qualities, although it not be in them naturally; for example, we say that heated objects differ from cooled objects and sweetened things from things made bitter, not because they are so by nature, but because they have been acted upon by these qualities. Alterari autem secundum huiusmodi qualitates, est omnium corporum sensibilium, tam animatorum quam inanimatorum. Et quia in corporibus animatis quaedam partes sunt animatae, idest sensitivae, ut oculus et manus, quaedam autem inanimatae, idest non sensitivae, ut capilli et ossa; utraeque partes secundum huiusmodi qualitates alterantur, quia sensus sentiendo patiuntur: actiones enim sensuum, ut auditio et visio, sunt quidam motus per corpus cum aliqua sensus passione. Non enim sensus habent aliquam actionem, nisi per organum corporeum: corpori autem convenit moveri et alterari. Unde passio et alteratio magis proprie dicitur in sensu quam in intellectu, cuius operatio non est per aliquod organum corporeum. The capacity to be altered in respect of qualities of these kinds is common to all sensible bodies both living and non-living. And some parts of living bodies are animate, i.e., capable of sensing, as the eye and the hand, and some parts inanimate, i.e., incapable of sensing, as the hair and bones, yet in either case all these parts are altered by qualities of this sort, because even the senses in sensing are acted upon. For the acts of the senses, such as hearing and seeing, are motions through the body and involve the sense being acted upon. For the senses have no action independent of a bodily organ, which is a body that is apt to be moved and altered. Hence passion and alteration are more properly spoken of in regard to the senses than to the intellect, whose operation does not take place through a bodily organ. Sic igitur patet quod secundum quascumque qualitates, et secundum quoscumque motus, alterantur corpora inanimata, secundum eosdem motus et easdem qualitates alterantur corpora animata. Sed non convertitur; quia in corporibus animatis invenitur alteratio secundum sensum, quae non invenitur in corporibus inanimatis. Non enim corpora inanimata cognoscunt suam alterationem, sed latet ea; quod non accideret, si secundum sensum alterarentur. Thus it is evident that according to whatever qualities and according to whatever ways inanimate bodies are altered, animate bodies are altered according to the same qualities and in the same ways. But not vice versa: for an alteration is found in animate bodies that is not found in inanimate bodies, i.e., the one according to sense. For inanimate bodies do not perceive the alterations they undergo—something that would not be, if they were altered in respect of sense. Et ne aliquis hoc reputaret impossibile, quod aliquid alteraretur secundum sensibilem qualitatem absque sensu alterationis, subiungit quod non solum hoc est verum in rebus inanimatis, sed hoc contingit etiam in rebus animatis. Nihil enim prohibet quod etiam animata corpora lateat cum alterantur; sicut cum aliqua alteratio accidit in ipsis absque alteratione sensus, sicut cum alterantur secundum partes non sensitivas. Lest anyone believe that it is impossible for something to be altered with respect to a sensible quality without a sensation of the alteration, he adds that this is true not only in inanimate things but also in the animate. For there is nothing to prevent living bodies from not perceiving that they are being affected by a quality, as when something happens in them without the sense being affected; for example, when they are altered in regard to non-sensitive parts. Ex hoc igitur patet, quod si passiones sensus sunt tales, quod nihil est medium inter agens et patiens; et omnis alteratio est per huiusmodi passiones quibus alterantur sensus, sequitur quod alterans inferens passiones et alteratum patiens sint simul, et nullum sit ipsorum medium. From this, therefore, it is evident that if the passions of the senses are such that there is nothing intermediate between the agent and the patient, and if it is true that every alteration takes place through passions by which senses are apt to be altered, it follows that the cause of an alteration (when it is producing a passion) and the object acted upon are together, and there is nothing intermediate between them. Deinde cum dicit: huic autem etc., probat secundum, quod in alteratione sensus alterans et alteratum sint simul, quia huic, scilicet sensui, puta visui, aer continuus est, idest absque medio coniunctus, aeri vero corpus visibile; et superficies quidem visibilis corporis, quae est subiectum coloris, terminatur ad lumen, idest ad aerem illuminatum, qui terminatur ad visum. Et sic patet quod aer alteratus, et alterans ipsum, sunt simul, et similiter visus alteratus cum aere alterante. Et similiter est in auditu et in odoratu, si comparentur ad id quod primum movet, scilicet ad sensibile corpus; quia hi sensus sunt per medium extrinsecum. Gustus autem et sapor sunt simul; non enim coniunguntur per aliquod medium extrinsecum: et simile est de tactu. Et eodem modo se habet in rebus inanimatis et insensibilibus, scilicet quod alterans et alteratum sunt simul. 911. Then at (695) he proves a second point, namely, that in alterations of the senses, the altering cause and the sense affected are together, because the air is continuous with the sense, for example, of sight, i.e., they are in immediate contacts just as the visible body is in contact with the air. Indeed, the visible body’s surface, which is the subject of color, is terminated at the light, i.e., at air which is illumined, which is terminated at the sense. And so it is evident that the altered air and what alters it are together, as are the altered sight and the air which alters sight. The same is true in hearing and in smelling, if you relate them to the first mover, namely, the sensible body, for these two senses are affected by an extrinsic medium. Taste, however, and its object are together, for they are not joined by means of an extrinsic medium, and the same goes for touch. Consequently, it remains that inanimate and insensible things are related in the same way, i.e., the cause of alteration and the thing altered are together. Deinde cum dicit: et quod augetur etc., probat idem in motu augmenti et decrementi. Et primo in motu augmenti. Oportet enim quod augetur et auget esse simul, quia augmentum est quaedam appositio: per appositionem enim alicuius quanti aliquid augetur. Et similiter est in decremento; quia causa decrementi est quaedam subtractio alicuius quanti. 912. Then at (696) he proves the same thing for the motion of growth and decrease. First of all in the motion of growth. For the cause of increase and the very thing that is increased must be together, because growing is a kind of “adding to,” a quantity being increased by adding to it another quantity. The same is true of decrease, because the cause of decrease is the taking away of some quantity. Et potest intelligi haec probatio dupliciter. Uno modo secundum quod ipsum quantum appositum vel subtractum, est proximum movens illis motibus: nam et Aristoteles dicit in secundo de anima, quod caro auget prout est quanta. Et sic manifeste simul cum movente motum est: non enim potest aliquid apponi vel subtrahi alicui, si non sit simul cum eo. Now this proof can be understood in two ways. In one way, that the very quantity added or taken away is the immediate mover in these motions, for Aristotle says in On the Soul II that flesh increases because it is quantified. Thus it is clear that the mover and the moved are together, for nothing can be added or taken away from something unless it be together with it. Procedit etiam haec ratio de principali agente. Appositio enim omnis congregatio quaedam est, subtractio autem disgregatio quaedam. Supra autem ostensum est, quod in motu congregationis et disgregationis movens et motum sunt simul: unde relinquitur, quod etiam in motu augmenti et decrementi. In another way, this argument can be understood in terms of the principal agent. For adding is a type of gathering and subtracting a type of scattering. But it was proved above that in the motions of gathering and scattering, the mover and the moved are together. Hence, what remains is that even in the motion of growth and decrease, they are together. Et sic ulterius concludit universaliter, quod inter ultimum movens et primum motum nihil est medium. In this way, then, he concludes universally that between the last mover and the first moved there is nothing in between.
Alteration is not found in the fourth species of quality (form and figure), nor in the first (habit and disposition)
Chapter 3 cont. 3 Ὅτι δὲ τὸ ἀλλοιούμενον ἅπαν ἀλλοιοῦται ὑπὸ τῶν αἰσθητῶν, καὶ ἐν μόνοις ὑπάρχει τούτοις ἀλλοίωσις ὅσα καθ' αὑτὰ λέγεται πάσχειν ὑπὸ τῶν αἰσθητῶν, ἐκ τῶνδε θεωρητέον. Everything, we say, that undergoes alteration is altered by sensible causes, and there is alteration only in things that are said to be essentially affected by sensible things. The truth of this is to be seen from the following considerations. τῶν γὰρ ἄλλων μάλιστ' ἄν τις ὑπολάβοι ἔν τε τοῖς σχήμασι καὶ ταῖς μορφαῖς καὶ ἐν ταῖς ἕξεσι καὶ ταῖς τούτων λήψεσι καὶ ἀποβολαῖς ἀλλοίωσιν ὑπάρχειν· ἐν οὐδετέροις δ' ἔστιν. Of all other things it would be most natural to suppose that there is alteration in figures and shapes, and in acquired states and in the processes of acquiring and losing these: but as a matter of fact in neither of these two classes of things is there alteration. τὸ μὲν γὰρ σχηματιζόμενον καὶ ῥυθμιζόμενον ὅταν ἐπιτελεσθῇ, οὐ λέγομεν ἐκεῖνο ἐξ οὗ ἐστιν, οἷον τὸν ἀνδριάντα χαλκὸν ἢ τὴν πυραμίδα κηρὸν ἢ τὴν κλίνην ξύλον, ἀλλὰ παρωνυμιάζοντες τὸ μὲν χαλκοῦν, τὸ δὲ κήρινον, τὸ δὲ ξύλινον. τὸ δὲ πεπονθὸς καὶ ἠλλοιωμένον προσαγορεύομεν· ὑγρὸν γὰρ καὶ θερμὸν καὶ σκληρὸν τὸν χαλκὸν λέγομεν καὶ τὸν κηρόν In the first place, when a particular formation of a thing is completed, we do not call it by the name of its material: e.g. we do not call the statue 'bronze' or the pyramid 'wax' or the bed 'wood', but we use a derived expression and call them 'of bronze', 'waxen', and 'wooden' respectively. But when a thing has been affected and altered in any way we still call it by the original name: thus we speak of the bronze or the wax being dry or fluid or hard or hot. (καὶ οὐ μόνον οὕτως, ἀλλὰ καὶ τὸ ὑγρὸν καὶ τὸ θερμὸν χαλκὸν λέγομεν), ὁμωνύμως τῷ πάθει προσαγορεύοντες τὴν (246a.) ὕλην. ὥστ' εἰ κατὰ μὲν τὸ σχῆμα καὶ τὴν μορφὴν οὐ λέγεται τὸ γεγονὸς ἐν ᾧ ἐστι τὸ σχῆμα, κατὰ δὲ τὰ πάθη καὶ τὰς ἀλλοιώσεις λέγεται, φανερὸν ὅτι οὐκ ἂν εἶεν αἱ γενέσεις ἀλλοιώσεις. And not only so: we also speak of the particular fluid or hot substance as being bronze, giving the material the same name as that which we use to describe the affection. Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a thing's affections or alterations we still call it by the name of its material, it is evident that becomings of the former kind cannot be alterations. ἔτι δὲ καὶ εἰπεῖν οὕτως ἄτοπον ἂν δόξειεν, ἠλλοιῶσθαι τὸν ἄνθρωπον ἢ τὴν οἰκίαν ἢ ἄλλο ὁτιοῦν τῶν γεγενημένων· ἀλλὰ γίγνεσθαι μὲν ἴσως ἕκαστον ἀναγκαῖον ἀλλοιουμένου τινός, οἷον τῆς ὕλης πυκνουμένης ἢ μανουμένης ἢ θερμαινομένης ἢ ψυχομένης, οὐ μέντοι τὰ γιγνόμενά γε ἀλλοιοῦται, οὐδ' ἡ γένεσις αὐτῶν ἀλλοίωσίς ἐστιν. Moreover it would seem absurd even to speak in this way, to speak, that is to say, of a man or house or anything else that has come into existence as having been altered. Though it may be true that every such becoming is necessarily the result of something's being altered, the result, e.g. of the material's being condensed or rarefied or heated or cooled, nevertheless it is not the things that are coming into existence that are altered, and their becoming is not an alteration. ἀλλὰ μὴν οὐδ' αἱ ἕξεις οὔθ' αἱ τοῦ σώματος οὔθ' αἱ τῆς ψυχῆς ἀλλοιώσεις. αἱ μὲν γὰρ ἀρεταὶ αἱ δὲ κακίαι τῶν ἕξεων· οὐκ ἔστι δὲ οὔτε ἡ ἀρετὴ οὔτε ἡ κακία ἀλλοίωσις, ἀλλ' ἡ μὲν ἀρετὴ τελείωσίς τις (ὅταν γὰρ λάβῃ τὴν αὑτοῦ ἀρετήν, τότε λέγεται τέλειον ἕκαστον—τότε γὰρ ἔστι μάλιστα [τὸ] κατὰ φύσιν—ὥσπερ κύκλος τέλειος, ὅταν μάλιστα γένηται κύκλος καὶ ὅταν βέλτιστος), ἡ δὲ κακία φθορὰ τούτου καὶ ἔκστασις· ὥσπερ οὖν οὐδὲ τὸ τῆς οἰκίας τελείωμα λέγομεν ἀλλοίωσιν (ἄτοπον γὰρ εἰ ὁ θριγκὸς καὶ ὁ κέραμος ἀλλοίωσις, ἢ εἰ θριγκουμένη καὶ κεραμουμένη ἀλλοιοῦται ἀλλὰ μὴ τελειοῦται ἡ οἰκία), τὸν αὐτὸν τρόπον καὶ ἐπὶ τῶν ἀρε(246b.) τῶν καὶ τῶν κακιῶν καὶ τῶν ἐχόντων ἢ λαμβανόντων· αἱ μὲν γὰρ τελειώσεις αἱ δὲ ἐκστάσεις εἰσίν, ὥστ' οὐκ ἀλλοιώσεις. Again, acquired states, whether of the body or of the soul, are not alterations. For some are excellences and others are defects, and neither excellence nor defect is an alteration: excellence is a perfection (for when anything acquires its proper excellence we call it perfect, since it is then if ever that we have a thing in its natural state: e.g. we have a perfect circle when we have one as good as possible), while defect is a perishing of or departure from this condition. So as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose that the coping or the tiling is an alteration or that in receiving its coping or its tiling a house is altered and not perfected), the same also holds good in the case of excellences and defects and of the persons or things that possess or acquire them: for excellences are perfections of a thing's nature and defects are departures from it: consequently they are not alterations.
Quia in praecedenti ratione philosophus supposuerat quod omnis alteratio sit secundum sensibilia, hoc intendit hic probare. Et primo proponit quod intendit; secundo probat propositum, ibi: aliorum enim maxime et cetera. 913. Because the Philosopher had assumed in the preceding argument that every alteration takes place in respect of what is sensible, he now undertakes to prove this. First he proposes what he intends; Secondly, he proves the proposition, at 914. Dicit ergo primo, quod ex sequentibus considerandum est quod omnia quae alterantur, alterantur secundum qualitates sensibiles: et per consequens illis solum competit alterari, quae per se patiuntur ab huiusmodi qualitatibus. He says therefore first (697) that from what will follow it must be considered that all things that are altered, are altered according to sensible qualities, and that, consequently, to be altered belongs only to those things which are per se affected by such qualities. Deinde cum dicit: aliorum enim maxime etc., probat propositum arguendo a maiori. Quod quidem primo ponit; secundo quaedam quae supponit probat, ibi: ex quo quidem enim et cetera. 914. Then at (698) he proves his proposition a majori. First he posits the proposition; Secondly, he proves certain things he assumed, at 915- Dicit ergo primo, quod praeter qualitates sensibiles, maxime videtur esse alteratio in quarta specie qualitatis, quae est qualitas circa quantitatem, scilicet forma et figura: et in prima specie qualitatis, quae continet sub se habitus et dispositiones. Videtur enim quod alteratio quaedam sit, per hoc quod huiusmodi qualitates de novo removentur, aut de novo acquiruntur: non enim videtur hoc sine mutatione posse contingere; mutatio autem secundum qualitatem alteratio est, ut supra dictum est. He says therefore first (698) that in addition to the sensible qualities (the third species of quality), alteration seems to occur especially in respect to the fourth species of quality, a quality concerned with quantity, namely, form and figure, and to the first species, which contains habits and dispositions. For when such qualities are freshly removed or newly acquired, alteration seems to be involved—for these things seem unable to occur without some changes and a change in respect of quality is alteration, as was said above. Sed in praedictis qualitatibus primae et quartae speciei, non est alteratio primo et principaliter, sed secundario: quia huiusmodi qualitates consequuntur quasdam alterationes primarum qualitatum; sicut patet quod cum materia subiecta densatur aut rarescit, sequitur mutatio secundum figuram; et similiter cum calefiat aut infrigidetur, sequitur mutatio secundum sanitatem et aegritudinem, quae pertinent ad primam speciem qualitatis. Rarum autem et densum, calidum et frigidum sunt sensibiles qualitates: et sic patet quod non est alteratio in prima et quarta specie qualitatis primo et per se; sed remotio et acceptio huiusmodi qualitatum consequuntur ad aliquam alterationem, quae est secundum sensibiles qualitates. But in the above-mentioned qualities of the first and fourth species, there is no alteration primarily and principally but only in a secondary sense, for such qualities follow upon alterations of the primary qualities, as is clear from the fact that when the underlying matter becomes dense or rare, a consequent change of figure results, In like manner, when it becomes hot or cold, there follows a change in regard to health and sickness, which pertain to the first species of quality. Rare and dense, hot and cold are sensible qualities, and so it is clear that there is not alteration in the first and fourth species of quality primarily and per se; rather the receiving or removing of them are a consequence of some alteration affecting sensible qualities. Ex quo etiam patet quare non facit mentionem de secunda specie qualitatis, quae est potentia vel impotentia naturalis. Manifestum est enim quod potentia vel impotentia naturalis non accipitur aut removetur nisi transmutata natura, quod fit per alterationem; et ideo hoc quasi manifestum praetermisit. From this is also plain why he makes no mention of the second species of quality, i.e., natural potency and impotency. For it is clear that these latter are not received or lost without a change in the nature, which takes place through alteration. That is why he did not mention them. Deinde cum dicit: ex quo quidem etc., probat quod supposuerat. Et primo quod non sit alteratio in quarta specie qualitatis; secundo quod non sit in prima, ibi: neque enim in habitibus et cetera., quae dat esse specificum artificiato; formae enim artificiatorum sunt accidentia. 915. Then at (699) he proves what he had assumed: First, that alteration does not occur in the fourth species of quality; Secondly, that it does not occur in the first species, at 918. Circa primum ponit duas rationes: quarum prima sumitur ex modo loquendi. Ubi considerandum est quod forma et figura in hoc ab invicem differunt, quod figura importat terminationem quantitatis; est enim figura, quae termino vel terminis comprehenditur: forma vero dicitur In regard to the first he gives two reasons, the first of which (699) is based on the way people speak. Here it must be considered that form and figure mutually differ in this, that figure implies termination of quantity, for the figure is that which is confined by the terminus or termini; but form is something which gives artifacts a kind of species, for the forms of artifacts are accidents. Dicit ergo quod illud ex quo fit forma statuae, non dicimus formam; idest, materia statuae non praedicatur de statua in principali et recto; et similiter est in figura pyramidis vel lecti: sed in talibus materia praedicatur denominative; dicimus enim triangulum aeneum aut cereum aut ligneum, et simile est in aliis. Sed in his quae alterantur, et passionem praedicamus de subiecto, quia dicimus aes esse humidum aut forte aut calidum; et e converso, humidum vel calidum dicimus esse aes, aequaliter praedicantes materiam de passione, et e converso; et dicimus hominem esse album, et album esse hominem. Quia ergo in formis et figuris materia non aequaliter dicitur cum ipsa figura, ita quod alterum de altero dicatur in principali et recto, sed solum denominative materia praedicatur de figura et forma; in his autem quae alterantur, subiectum et passio aequaliter de invicem praedicantur; sequitur quod in formis et figuris non sit alteratio, sed solum in sensibilibus qualitatibus. He says therefore that that from which the form of a statue comes to be is not called a form, i.e., the matter of the statue is not predicated of the statue in principali et recto, and the same for the figure of a pyramid or of a couch; rather in all such cases the matter is predicated denominatively. For we say that a triangle is wooden or golden or waxen. But in things that are altered, we predicate of the subject the quality received by the alteration, for we say that brass is wet and strong and hot, and conversely we say that the wet thing or the hot thing is brass, i.e., we predicate the matter of the quality and the quality of the matter, In fine, we say that a man is a white thing and that some white thing is a man. Therefore, because in forms and figures the matter is not predicated conversely with the figure, so that either could be said of the other in principali et recto, but rather the matter is predicated of the figure only in a denominative way, whereas in things that are altered the subject and the quality are mutually predicated, it follows that in forms and figures there is not alteration but only in sensible qualities. Secundam rationem ponit ibi: amplius et aliter etc.; et sumitur a proprietate rei. Ridiculum enim est dicere quod homo vel domus vel quidquid aliud, alteretur ex hoc ipso quod accipit finem suae perfectionis: puta si domus perficitur per hoc quod tegitur, vel per hoc quod lateribus ornatur aut cooperitur, ridiculum est dicere quod domus alteretur, quando cooperitur aut lateratur. Est etiam manifestum quod alteratio non est eorum quae fiunt, inquantum fiunt; sed unumquodque perficitur et fit, inquantum accipit formam propriam et figuram. Non est ergo alteratio in acceptione figurae et formae. 916. He gives a second reason at (700) and it is based on a property of a thing. For it is foolish to say that a man or a house or anything else is altered just because it receives the end of its perfection. For example, if a house is made perfect when it gets a roof or when it is decorated or enclosed with walls, it is ridiculous to say that the house is being altered when it becomes roofed. It is also clear that alteration does not affect things that come to be, precisely as coming to be; rather a thing becomes perfect and comes to be inasmuch as it receives its own form and figure. Consequently, alteration is not involved in the receiving of figure and form. Ad evidentiam autem harum rationum considerandum est, quod inter omnes qualitates, figurae maxime consequuntur et demonstrant speciem rerum. Quod maxime in plantis et animalibus patet, in quibus nullo certiori iudicio diversitas specierum diiudicari potest, quam diversitate figurarum. Et hoc ideo, quia sicut quantitas propinquissime se habet ad substantiam inter alia accidentia, ita figura, quae est qualitas circa quantitatem, propinquissime se habet ad formam substantiae. Unde sicut posuerunt aliqui dimensiones esse substantiam rerum, ita posuerunt aliqui figuras esse substantiales formas. Et ex hoc contingit quod imago, quae est expressa rei repraesentatio, secundum figuram potissime attendatur, magis quam secundum colorem vel aliquid aliud. Et quia ars est imitatrix naturae, et artificiatum est quaedam rei naturalis imago, formae artificialium sunt figurae vel aliquid propinquum. Et ideo propter similitudinem huiusmodi formarum et figurarum ad formas substantiales, dicit philosophus quod secundum acceptionem formae et figurae non est alteratio, sed perfectio. Et exinde etiam est quod materia de huiusmodi non praedicatur nisi denominative, sicut etiam est in substantiis naturalibus: non enim dicimus hominem terram, sed terrenum. 917. In order to make these reasons clearer, we should consider that of all qualities in a thing, it is figure that both follows upon the species and indicates the species. This is particularly evident in animals and plants in which there is no more sure way to judge a diversity of species than by a diversity of figure. The reason for this is that just as quantity is the nearest of all the accidents to the substance, so the figure, which is a quality affecting quantity, is nearest to the substantial form. Hence, just as some philosophers supposed that dimensions were the substances of things, so they supposed that their figures were their substantial forms. It is for this reason that an image, which is an express representation of a thing, is based especially on the figure rather than on the color or something else. And since art imitates nature, and an artifact is an image of a natural thing, the forms of artificial things are the figure or something close to the figure. And therefore, on account of the similarity of forms and figures to substantial forms, the Philosopher says that the receiving of form and figure is not alteration but perfection. And that is also why the matter is not predicated of them except denominatively, similarly to the case of natural substances—for we do not say that a man is earth but of earth (terrenus). Deinde cum dicit: neque enim in habitibus etc., ostendit quod non est alteratio in prima specie qualitatis. Et primo quantum ad habitus et dispositiones corporis; secundo quantum ad habitus et dispositiones animae, ibi: neque itaque circa animae virtutes et cetera. 918. Then at (701) he shows that there is not alteration in the first species of quality. First in regard to habits and dispositions of the body; Secondly, in regard to habits and dispositions of the soul, (L. 6). Circa primum ponit talem rationem. Habitus qui sunt in prima specie qualitatis, etiam corporei, sunt quaedam virtutes et malitiae. Virtus enim universaliter cuiuslibet rei est quae bonum facit habentem, et opus eius bonum reddit: unde virtus corporis dicitur, secundum quam bene se habet et bene operatur, ut sanitas; e contrario autem est de malitia, ut de aegritudine. In regard to the first, he gives this argument: Habits which are in the first species of quality, even if they be bodily, are called virtues and vices. For in general the virtue of a thing is what makes it good and renders its work good; hence a virtue of the body is that according to which it is well kept in itself and acts well, e.g. health; or, on the other hand, it is a vice, as is sickness. Omnis autem virtus et malitia dicuntur ad aliquid. Et hoc manifestat per exempla. Sanitas enim, quae est quaedam virtus corporis, est quaedam commensuratio calidorum et frigidorum; et dico hanc commensurationem fieri, secundum debitam proportionem eorum quae sunt infra, idest humorum ex quibus componitur corpus, ad invicem et ad continens, idest ad totum corpus. Aliqua enim contemperatio humorum est sanitas in leone, quae non esset sanitas in homine, sed eius extinctio; quia eam humana natura ferre non posset. Now every virtue and vice is spoken of in reference to something else. And this he makes clear by examples. For health, which is a virtue of the body, is a definite harmony of the hot and the cold, and I say that this harmony is in respect to the due proportion of the things beneath, i.e., of the humors, of which the body is composed, both in relation to themselves and to what contains them, i.e., to the whole body. For a proportion of humors that would be health in a lion, would be not health, but destruction, for a man, for his nature would not stand it. Commentator autem exponit ad continens, idest ad aerem continentem. Sed primum melius est: quia sanitas animalis non attenditur per comparationem ad aerem; sed potius e converso dispositio aeris dicitur sana per comparationem ad animal. The Commentator refers the phrase “to what contains them” to the surrounding air. But the first explanation is better, because the health of an animal is not considered in relation to the air; rather the disposition of the air is called healthy in relation to the animal. Similiter pulchritudo et macies dicuntur ad aliquid (et sumitur macies pro dispositione, qua aliquis est expeditus ad motum et actionem). Huiusmodi enim sunt quaedam dispositiones eius quod est perfectum in sua natura per comparationem ad optimum, idest ad finem, qui est operatio. Sicut enim dictum est, ex hoc huiusmodi dispositiones virtutes dicuntur, quod bonum faciunt habentem, et opus eius bonum reddunt. Dicuntur ergo huiusmodi dispositiones per relationem ad debitum opus, quod est optimum rei. Likewise, beauty and agility are said in relation to something (“agility” is taken here for the disposition whereby one is disposed for motion and action). For such dispositions are in a thing that is perfect in its nature in comparison to the best, i.e., to the end, which is operation. For, as it was said, such dispositions are called virtues because they make their possessor good and his work good,. Therefore these dispositions are described in reference to their due work, which is the best of a thing. Nec oportet exponere optimum, aliquid extrinsecum, sicut quod est pulcherrimum aut sanissimum, ut Commentator exponit: accidit enim pulchritudini et sanitati relatio quae est ad extrinsecum optime dispositum; sed per se competit eis relatio quae est ad bonum opus. There is no use trying to explain “best” in terms of something extrinsic, as in the case of what is most beautiful or most healthy, as the Commentator does, for it is accidental to beauty and health that they be related to something extrinsic disposed in the best possible manner; rather what is per se is their relation to a good work. Et ne aliquis accipiat perfectum, quod iam adeptum est finem, dicit quod perfectum hic accipitur hoc quod est sanativum et dispositum secundum naturam. Non autem est hic intelligendum quod huiusmodi habitus et dispositiones hoc ipsum quod sunt, ad aliquid sint; quia sic non essent in genere qualitatis, sed relationis: sed quia eorum ratio ex aliqua relatione dependet. And lest anyone understand by “perfect” a thing that has already attained its end, he says that “perfect” is here taken in the sense of what is healthy and disposed according to nature. But it must not be supposed here that such habits and dispositions are of their very nature relations, for otherwise they would not be in the genus of quality. The point is that their definition depends on a relation Of some sort. Quia igitur huiusmodi habitus ad aliquid sunt; et in ad aliquid non est motus neque generatio neque alteratio, ut in quinto probatum est; manifestum est quod in huiusmodi habitibus non est alteratio primo et per se: sed eorum transmutatio consequitur aliquam priorem alterationem calidi et frigidi, aut alicuius huiusmodi; sicut etiam relationes esse incipiunt per consequentiam ad aliquos motus. Therefore, because habits of this kind imply a relation, and in relation there is neither motion nor generation nor alteration, as was proved in Book V, it is clear that in habits of this kind there is not alteration primarily and per se; rather a change follows upon a previous alteration of the hot and the cold or of something of this sort, just as relations begin to exist as a consequence of certain motions or changes.
No alteration in the first species of quality as to habits of the soul
Chapter 3 cont. ἔτι δὲ καί φαμεν ἁπάσας εἶναι τὰς ἀρετὰς ἐν τῷ πρός τι πὼς ἔχειν. τὰς μὲν γὰρ τοῦ σώματος, οἷον ὑγίειαν καὶ εὐεξίαν, ἐν κράσει καὶ συμμετρίᾳ θερμῶν καὶ ψυχρῶν τίθεμεν, ἢ αὐτῶν πρὸς αὑτὰ τῶν ἐντὸς ἢ πρὸς τὸ περιέχον· ὁμοίως δὲ καὶ τὸ κάλλος καὶ τὴν ἰσχὺν καὶ τὰς ἄλλας ἀρετὰς καὶ κακίας. ἑκάστη γάρ ἐστι τῷ πρός τι πὼς ἔχειν, καὶ περὶ τὰ οἰκεῖα πάθη εὖ ἢ κακῶς διατίθησι τὸ ἔχον· οἰκεῖα δ' ὑφ' ὧν γίγνεσθαι καὶ φθείρεσθαι πέφυκεν. ἐπεὶ οὖν τὰ πρός τι οὔτε αὐτά ἐστιν ἀλλοιώσεις, οὔτε ἔστιν αὐτῶν ἀλλοίωσις οὐδὲ γένεσις οὐδ' ὅλως μεταβολὴ οὐδεμία, φανερὸν ὅτι οὔθ' αἱ ἕξεις οὔθ' αἱ τῶν ἕξεων ἀποβολαὶ καὶ λήψεις ἀλλοιώσεις εἰσίν, ἀλλὰ γίγνεσθαι μὲν ἴσως αὐτὰς καὶ φθείρεσθαι ἀλλοιουμένων τινῶν ἀνάγκη, καθάπερ καὶ τὸ εἶδος καὶ τὴν μορφήν, οἷον θερμῶν καὶ ψυχρῶν ἢ ξηρῶν καὶ ὑγρῶν, ἢ ἐν οἷς τυγχάνουσιν οὖσαι πρώτοις. περὶ ταῦτα γὰρ ἑκάστη λέγεται κακία καὶ ἀρετή, ὑφ' ὧν ἀλλοιοῦσθαι πέφυκε τὸ ἔχον· ἡ μὲν γὰρ ἀρετὴ ποιεῖ ἢ ἀπαθὲς ἢ ὡδὶ παθητικόν, ἡ δὲ κακία παθητικὸν ἢ ἐναντίως ἀπαθές. Further, we say that all excellences depend upon particular relations. Thus bodily excellences such as health and a good state of body we regard as consisting in a blending of hot and cold elements within the body in due proportion, in relation either to one another or to the surrounding atmosphere: and in like manner we regard beauty, strength, and all the other bodily excellences and defects. Each of them exists in virtue of a particular relation and puts that which possesses it in a good or bad condition with regard to its proper affections, where by 'proper' affections I mean those influences that from the natural constitution of a thing tend to promote or destroy its existence. Since then, relatives are neither themselves alterations nor the subjects of alteration or of becoming or in fact of any change whatever, it is evident that neither states nor the processes of losing and acquiring states are alterations, though it may be true that their becoming or perishing is necessarily, like the becoming or perishing of a specific character or form, the result of the alteration of certain other things, e.g. hot and cold or dry and wet elements or the elements, whatever they may be, on which the states primarily depend. For each several bodily defect or excellence involves a relation with those things from which the possessor of the defect or excellence is naturally subject to alteration: thus excellence disposes its possessor to be unaffected by these influences or to be affected by those of them that ought to be admitted, while defect disposes its possessor to be affected by them or to be unaffected by those of them that ought to be admitted. ἐπὶ τῶν τῆς ψυχῆς ἕξεων· ἅπασαι γὰρ καὶ αὗται τῷ πρός τι πὼς ἔχειν, καὶ αἱ μὲν ἀρεταὶ τελειώσεις, αἱ δὲ κακίαι ἐκστάσεις. ἔτι δὲ ἡ μὲν ἀρετὴ εὖ διατίθησι πρὸς τὰ οἰκεῖα πάθη, ἡ δὲ κακία κακῶς. ὥστ' οὐδ' αὗται ἔσονται ἀλλοιώσεις· οὐδὲ δὴ αἱ ἀποβολαὶ καὶ αἱ λήψεις αὐτῶν. γίγνεσθαι δ' αὐτὰς ἀναγκαῖον ἀλλοιουμένου τοῦ αἰσθητικοῦ μέρους. ἀλλοιωθήσεται δ' ὑπὸ τῶν αἰσθητῶν· And the case is similar in regard to the states of the soul, all of which (like those of body) exist in virtue of particular relations, the excellences being perfections of nature and the defects departures from it: moreover, excellence puts its possessor in good condition, while defect puts its possessor in a bad condition, to meet his proper affections. Consequently these cannot any more than the bodily states be alterations, nor can the processes of losing and acquiring them be so, though their becoming is necessarily the result of an alteration of the sensitive part of the soul, and this is altered by sensible objects: ἅπασα γὰρ ἡ ἠθικὴ ἀρετὴ περὶ ἡδονὰς καὶ λύπας τὰς σωματικάς, αὗται δὲ ἢ ἐν τῷ πράττειν ἢ ἐν τῷ μεμνῆσθαι ἢ ἐν τῷ ἐλπίζειν. αἱ μὲν οὖν ἐν τῇ πράξει κατὰ τὴν αἴσθησίν εἰσιν, ὥσθ' ὑπ' αἰσθητοῦ τινὸς κινεῖσθαι, αἱ δ' ἐν τῇ μνήμῃ καὶ ἐν τῇ ἐλπίδι ἀπὸ ταύτης εἰσίν· ἢ γὰρ οἷα ἔπαθον μεμνημένοι ἥδονται, ἢ ἐλπίζοντες οἷα μέλλουσιν. ὥστ' ἀνάγκη πᾶσαν τὴν τοιαύτην ἡδονὴν ὑπὸ τῶν αἰσθητῶν γίγνεσθαι. ἐπεὶ δ' ἡδονῆς καὶ λύπης ἐγγιγνομένης καὶ ἡ κακία καὶ ἡ ἀρετὴ ἐγγίγνεται (περὶ ταύτας γάρ εἰσιν), αἱ δ' ἡδοναὶ καὶ αἱ λῦπαι ἀλλοιώσεις τοῦ αἰσθητικοῦ, φανερὸν ὅτι ἀλλοιουμένου τινὸς ἀνάγκη καὶ ταύτας ἀποβάλλειν καὶ λαμβάνειν. ὥσθ' ἡ μὲν γένεσις αὐτῶν μετ' ἀλλοιώσεως, αὐταὶ δ' οὐκ εἰσὶν ἀλλοιώσεις. for all moral excellence is concerned with bodily pleasures and pains, which again depend either upon acting or upon remembering or upon anticipating. Now those that depend upon action are determined by sense-perception, i.e. they are stimulated by something sensible: and those that depend upon memory or anticipation are likewise to be traced to sense-perception, for in these cases pleasure is felt either in remembering what one has experienced or in anticipating what one is going to experience. Thus all pleasure of this kind must be produced by sensible things: and since the presence in any one of moral defect or excellence involves the presence in him of pleasure or pain (with which moral excellence and defect are always concerned), and these pleasures and pains are alterations of the sensitive part, it is evident that the loss and acquisition of these states no less than the loss and acquisition of the states of the body must be the result of the alteration of something else. Consequently, though their becoming is accompanied by an alteration, they are not themselves alterations. (247b.) ἀλλὰ μὴν οὐδ' αἱ τοῦ νοητικοῦ μέρους ἕξεις ἀλλοιώσεις, οὐδ' ἔστιν αὐτῶν γένεσις. πολὺ γὰρ μάλιστα τὸ ἐπιστῆμον ἐν τῷ πρός τι πὼς ἔχειν λέγομεν. ἔτι δὲ καὶ φανερὸν ὅτι οὐκ ἔστιν αὐτῶν γένεσις· τὸ γὰρ κατὰ δύναμιν ἐπιστῆμον οὐδὲν αὐτὸ κινηθὲν ἀλλὰ τῷ ἄλλο ὑπάρξαι γίγνεται ἐπιστῆμον. Again, the states of the intellectual part of the soul are not alterations, nor is there any becoming of them. In the first place it is much more true of the possession of knowledge that it depends upon a particular relation. And further, it is evident that there is no becoming of these states. For that which is potentially possessed of knowledge becomes actually possessed of it not by being set in motion at all itself but by reason of the presence of something else: i.e. it is when it meets with the particular object that it knows in a manner the particular through its knowledge of the universal. ὅταν γὰρ γένηται τὸ κατὰ μέρος, ἐπίσταταί πως τὰ καθόλου τῷ ἐν μέρει. πάλιν δὲ τῆς χρήσεως καὶ τῆς ἐνεργείας οὐκ ἔστι γένεσις, εἰ μή τις καὶ τῆς ἀναβλέψεως καὶ τῆς ἁφῆς οἴεται γένεσιν εἶναι· τὸ γὰρ χρῆσθαι καὶ τὸ ἐνεργεῖν ὅμοιον τούτοις. (Again, there is no becoming of the actual use and activity of these states, unless it is thought that there is a becoming of vision and touching and that the activity in question is similar to these.) ἡ δ' ἐξ ἀρχῆς λῆψις τῆς ἐπιστήμης γένεσις οὐκ ἔστιν οὐδ' ἀλλοίωσις· τῷ γὰρ ἠρεμῆσαι καὶ στῆναι τὴν διάνοιαν ἐπίστασθαι καὶ φρονεῖν λεγόμεθα, εἰς δὲ τὸ ἠρεμεῖν οὐκ ἔστι γένεσις· ὅλως γὰρ οὐδεμιᾶς μεταβολῆς, καθάπερ εἴρηται πρότερον. ἔτι δ' ὥσπερ ὅταν ἐκ τοῦ μεθύειν ἢ καθεύδειν ἢ νοσεῖν εἰς τἀναντία μεταστῇ τις, οὔ φαμεν ἐπιστήμονα γεγονέναι πάλιν (καίτοι ἀδύνατος ἦν τῇ ἐπιστήμῃ χρῆσθαι πρότερον), οὕτως οὐδ' ὅταν ἐξ ἀρχῆς λαμβάνῃ τὴν ἕξιν· τῷ γὰρ καθίστασθαι τὴν ψυχὴν ἐκ τῆς φυσικῆς ταραχῆς φρόνιμόν τι γίγνεται καὶ ἐπιστῆμον. διὸ καὶ τὰ παιδία οὔτε μανθάνειν δύνανται οὔτε κατὰ τὰς αἰσθήσεις (248a.) ὁμοίως κρίνειν τοῖς πρεσβυτέροις· πολλὴ γὰρ ἡ ταραχὴ καὶ ἡ κίνησις. καθίσταται δὲ καὶ ἠρεμίζεται πρὸς ἔνια μὲν ὑπὸ τῆς φύσεως αὐτῆς, πρὸς ἔνια δ' ὑπ' ἄλλων, ἐν ἀμφοτέροις δὲ ἀλλοιουμένων τινῶν τῶν ἐν τῷ σώματι, καθάπερ ἐπὶ τῆς χρήσεως καὶ τῆς ἐνεργείας, ὅταν νήφων γένηται καὶ ἐγερθῇ. φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι τὸ ἀλλοιοῦσθαι καὶ ἡ ἀλλοίωσις ἔν τε τοῖς αἰσθητοῖς γίγνεται καὶ ἐν τῷ αἰσθητικῷ μορίῳ τῆς ψυχῆς, ἐν ἄλλῳ δ' οὐδενὶ πλὴν κατὰ συμβεβηκός. And the original acquisition of knowledge is not a becoming or an alteration: for the terms 'knowing' and 'understanding' imply that the intellect has reached a state of rest and come to a standstill, and there is no becoming that leads to a state of rest, since, as we have said above, change at all can have a becoming. Moreover, just as to say, when any one has passed from a state of intoxication or sleep or disease to the contrary state, that he has become possessed of knowledge again is incorrect in spite of the fact that he was previously incapable of using his knowledge, so, too, when any one originally acquires the state, it is incorrect to say that he becomes possessed of knowledge: for the possession of understanding and knowledge is produced by the soul's settling down out of the restlessness natural to it. Hence, too, in learning and in forming judgements on matters relating to their sense-perceptions children are inferior to adults owing to the great amount of restlessness and motion in their souls. Nature itself causes the soul to settle down and come to a state of rest for the performance of some of its functions, while for the performance of others other things do so: but in either case the result is brought about through the alteration of something in the body, as we see in the case of the use and activity of the intellect arising from a man's becoming sober or being awakened. It is evident, then, from the preceding argument that alteration and being altered occur in sensible things and in the sensitive part of the soul, and, except accidentally, in nothing else.
Postquam philosophus ostendit quod non est alteratio in prima specie qualitatis quantum ad dispositiones corporis, hic ostendit idem de habitibus animae. Et primo quantum ad partem appetitivam; secundo quantum ad partem intellectivam, ibi: at vero neque in intellectiva parte et cetera. 919. After showing that alteration does not occur in the first species of quality in respect of dispositions of the body, the Philosopher shows the same about the habits of the soul. First as to the appetitive part of the soul; Secondly, as to the intellectual part of the soul, at 923. Circa primum duo facit: primo ostendit quod non est alteratio primo et per se in transmutatione virtutis et malitiae; secundo quod transmutatio virtutis et malitiae consequitur ad quandam alterationem, ibi: fit quidem igitur et cetera. About the first he does two things: First he shows that there is no primary and per se alteration in changes that affect virtues and vices; Secondly, that changes involving virtue and vice are consequences of other alterations, at 921. Concludit ergo primo ex praemissis quod circa animae virtutes et malitias, quae pertinent ad partem appetitivam, non est primo et per se alteratio. Ideo autem hoc concludendo inducit, quia eisdem rationibus procedit ad probandum sequentia, quibus et priora. 920. He concludes therefore first (702) from the foregoing that with respect to virtues and vices which pertain to the appetitive part of the soul there is no primary and per se alteration. And he mentions this as a conclusion, because he will proceed to prove it with the same arguments as he proved the previous points. Ad hoc autem probandum assumit quandam propositionem, scilicet quod virtus sit perfectio quaedam. Quod quidem sic probat: quia unumquodque tunc est perfectum, quando pertingere potest ad propriam virtutem; sicut naturale corpus tunc perfectum est, quando potest aliud sibi simile facere, quod est virtus naturae. Quod etiam probat per hoc, quia tunc est aliquid maxime secundum naturam, quando naturae virtutem habet; virtus enim naturae est signum completionis naturae: cum autem aliquid habet complete suam naturam, tunc dicitur esse perfectum. Quod non solum in rebus naturalibus verum est, sed etiam in mathematicis, ut eorum forma accipiatur pro eorum natura: tunc enim maxime circulus est, idest perfectus circulus, quando maxime est secundum naturam, idest quando habet perfectionem suae formae. Sic ergo patet, quod cum ad perfectionem formae cuiuslibet rei consequatur virtus eius, quod tunc unumquodque perfectum est, quando habet suam virtutem. Et ita sequitur quod virtus sit perfectio quaedam. Accordingly, in order to prove this he makes the assumption that virtue is a kind of perfection. And this he proves in the following manner: A thing is perfect when it can attain to its own virtue (or power); for example, a natural body is perfect when it can make something like unto itself, and this is a virtue (or power) of the nature. He also proves this by the fact that a thing is most according to nature when it has the virtue of its nature (for virtue in a nature is a sign that the nature is complete), and when a thing has its nature completely, it is said to be perfect. And this is true not only in natural things, but also in mathematical, where their form is taken as the nature, for it is then that a figure is a perfect circle, namely, when it is most according to nature, i.e., when it has the perfection of that form. In this way, then, it is evident that since the virtue of a thing follows upon the perfection of its form, a thing is perfect when it possesses its virtue. Consequently, virtue is a kind of perfection. Ex hac autem propositione sic probata, Commentator sic argumentandum dicit. Omnis perfectio est simplex et indivisibilis: secundum autem nihil simplex et indivisibile est alteratio, neque aliquis motus, ut supra probatum est: ergo secundum virtutem non est alteratio. With the premise proved thus, the Commentator says that the full argument will be this: Every perfection is simple and indivisible; but no alteration or motion can affect what is simple and indivisible; therefore, in respect of virtue there can be no alteration, Sed iste processus non competit in eo quod subditur de malitia, quod scilicet est corruptio et remotio perfectionis. Etsi enim perfectio sit simplex et indivisibilis, recedere tamen a perfectione non est simplex et indivisibile, sed multipliciter contingens. Neque est etiam consuetudo Aristotelis, ut praetermittat illud ex quo principaliter conclusio dependet, nisi ex iuxta positis intelligi possit. But this reasoning will not apply to what Aristotle adds about vices, which are the removal and ceasing-to-be of a perfection. For although a perfection is simple and indivisible, yet the departure from perfection is not simple and indivisible, but occurs in many different ways. Again, it is not the custom of Aristotle to ignore a fact on which the conclusion chiefly depends, unless that fact is implied by something else he mentions. Et ideo melius dicendum est, quod arguendum est hic de virtute, sicut supra argumentatum est de forma et figura. Nihil enim dicitur alterari quando perficitur; et eadem ratione, neque quando corrumpitur. Si igitur virtus est perfectio quaedam, malitia vero corruptio, secundum virtutem et malitiam non est alteratio, sicut neque secundum formas et figuras. Therefore, it is better to say that the argument here must be like the one used above for form and figure. For nothing is said to be altered, when it is being made perfect, and for the same reason, when it is being corrupted. Hence, if virtue is a perfection and vice a corruption, there will be no alteration in respect of them any more than there is in respect of forms and figures. Deinde cum dicit: fit quidem igitur etc., ostendit quod transmutatio virtutis et malitiae consequitur aliquam alterationem. Et primo proponit quod intendit: et dicit quod acceptio virtutis et remotio malitiae, aut e contrario, fit cum aliquid alteratur, ad cuius alterationem consequitur acceptio et remotio virtutis et malitiae: sed tamen neutrum horum est alteratio primo et per se. 921. Then at (703) he shows that a change in virtue and vice is a result of some alteration. And first he proposes what he intends and says that the receiving of virtue and the removal of a vice, or vice versa, take place when something is altered in such a way that on the occasion of that alteration, there follows the receiving and loss of virtue and vice. Nevertheless, neither of these is a primary and per se alteration. Deinde cum dicit: quod autem alteretur etc., probat propositum: et dicit manifestum esse ex sequentibus, quod oporteat aliquid alterari ad hoc quod accipiatur et removeatur virtus vel malitia. Then at (704) he proves the proposition and says that it is clear from the following that something must be altered in order that it receive or lose a vice or a virtue. Et hoc videtur probare dupliciter. Primo quidem secundum duas opiniones hominum de virtute et malitia. Stoici enim dixerunt virtutes esse impassibilitates quasdam, nec posse esse virtutem in anima, nisi remotis omnibus passionibus animae, quae sunt timor, spes, et huiusmodi. Huiusmodi enim passiones dicebant esse quasdam animae perturbationes sive aegritudines: virtutem autem esse dicebant quandam quasi tranquillitatem animae et sanitatem. Unde e contrario malitiam dicebant esse omnem animae passibilitatem. This is seen to be proved in two ways. First, according to two opinions that men have about virtue and vice. For the Stoics declared that virtues are impassibilities and that no virtue can exist in the soul unless all the passions of the soul are first removed, i.e., fear, hope, and so on, For they said that such passions are disturbances and ailments of the soul, whereas virtue is a peaceful and healthy state of soul. Accordingly, they said that the very capacity to undergo emotion is an evil or vice of the soul. Opinio vero Peripateticorum ab Aristotele derivata, est quod virtus consistat in aliqua determinata moderatione passionum. Constituit enim virtus moralis medium in passionibus, ut dicitur in II Ethicorum. Et secundum hoc etiam malitia virtuti opposita non erit qualiscumque passibilitas, sed quaedam habilitas ad passiones contrarias virtuti, quae scilicet sunt secundum superabundantiam et defectum. However, the opinion of the Peripatetics, derived from Aristotle, is that virtue consists in a defined control of the passions. For a moral virtue establishes a mean in the passions, as is said in Ethics II. And according to this, even the vice opposed to a virtue is not any kind of passibility at all, but a certain inclination to the passions contrary to the virtue, which are reckoned in terms of excess and defect. Utrumlibet autem verum sit, oportet ad acceptionem virtutis, quod fiat aliqua transmutatio secundum passiones; scilicet vel quod passiones totaliter removeantur, vel quod modificentur. Passiones autem, cum sint in appetitu sensitivo, secundum eas contingit alteratio. Relinquitur ergo quod acceptio et remotio virtutis et malitiae sit secundum aliquam alterationem. Now, whichever may be true, the reception of virtue depends on some modification in the realm of the passions, i.e., either that the passions be entirely removed or that they be controlled. But the passions themselves, since they exist in the sense appetite, are subject to alteration. What remains, therefore, is that the receiving and loss of virtue and vice occur as a result of an alteration. Secundo ibi: et totam moralem etc., probat idem sic. Omnis virtus moralis consistit in aliqua delectatione et tristitia: non enim est iustus, qui non gaudet iustis operationibus et tristatur de contrariis, et simile est in aliis virtutibus moralibus. Et hoc ideo, quia omnis appetitivae virtutis, in qua est virtus moralis, operatio terminatur ad delectationem et tristitiam; cum delectatio consequatur ex adeptione eius in quod appetitus fertur, tristitia vero ex superventione eius quod appetitus refugit. Unde concupiscens vel sperans delectatur, quando consequitur quod concupiscit vel sperat; et similiter iratus quando punit; timens vero et odiens tristatur, quando supervenit malum quod refugit. Omnis autem tristitia et delectatio vel est secundum actum de re praesenti, vel per memoriam de re praeterita, vel per spem de futuro. Si ergo sit delectatio secundum actum, huius delectationis causa est sensus: non enim conveniens coniunctum delectationem faceret, si non sentiretur. Similiter autem si sit delectatio per memoriam vel per spem, hoc a sensu procedit, dum vel reminiscimur quales voluptates passi sumus secundum sensum in praeterito, vel dum speramus quales patiemur in futuro. Ex quo patet quod delectatio et tristitia secundum partem sensitivam est, in qua alteratio accidit, ut supra dictum est. Si ergo virtus moralis et malitia opposita in delectatione et tristitia est; secundum delectationem autem et tristitiam alterari contingit: sequitur quod acceptio et remotio virtutis et malitiae sit consequenter ad aliquam alterationem. 922. Then at (705) he proves the same thing in this way: Every moral virtue consists in some delight or sadness—for a person is not just unless he enjoys just works and becomes sad at their contrary; and the same is true of the other moral virtues. The reason for this is that the activity of every appetitive power, in which moral virtue exists, is terminated at delight or sadness, since delight follows upon the attainment of what the appetite seeks and sorrow upon the attainment of what the appetite dislikes. Hence, a person who desires or hopes is delighted when he attains what he desires or hopes. In like manner, the angry person is delighted, when he punishes. On the other hand, one who fears or hates something becomes sad when the evil he sought to escape occurs. But all sadness and delight are caused either by the actual presence of a thing or by the memory of a past thing or by hope of a future thing. Therefore, if delight concerns an actual present thing, the cause of this delight is a sense, for an agreeable thing does not delight unless it be sensed. Likewise, if the delight is based on memory or on hope, it proceeds from a sense, as when we remember sense pleasures we experienced in the past, or ones we hope to experience in the future. From which it is clear that delight and sadness are based on the soul’s sensitive part, in which alteration occurs, as was said above. If, therefore, delight and sadness are involved in moral virtue and moral vice and it is possible to undergo alteration in respect of delight and sadness, then it follows that the reception and loss of virtue and vice are consequent upon some alteration. Sed notandum, quod signanter dixit totam virtutem moralem in delectationibus et tristitiis esse, ad differentiam intellectualis virtutis, quae etiam suam delectationem habet: sed illa delectatio non est secundum sensum; unde nec contrarium habet, nec secundum eam alterari contingit, nisi metaphorice. It is significant that he said the whole of moral virtue consists in delights and sadnesses, in order to distinguish it from intellectual virtues, which also have their own delight. But that delight is not according to sense. Consequently, it has no contrary, nor can there be alteration in respect to it, except in a metaphorical sense. Deinde cum dicit: at vero neque etc., ostendit quod alteratio non est in parte animae intellectiva. Et primo probat hoc in generali; secundo in speciali, ibi: neque igitur actus et cetera. 923. Then at (706) he shows that alteration is not found in the intellectual part of the soul. First he proves this in general; Secondly, more in detail, at 924. Circa primum inducit talem rationem. Sciens maxime dicitur ad aliquid, scilicet ad scibile, cuius assimilatio in sciente, scientia est. Hoc autem sic probat. In nullo alio genere contingit quod aliquid de novo adveniat alicui absque eius mutatione, nisi in ad aliquid: fit enim aliquid aequale alicui, ipso non mutato, sed altero. Videmus autem quod nulla mutatione facta in potentia intellectiva, fit scientia, sed solum existente quodam in sensitiva parte: quia scilicet ex experientia particularium, quae pertinent ad sensitivam partem, accipimus scientiam universalis in intellectu, ut probatur in I Metaphys. et in II posteriorum. Cum igitur in ad aliquid non sit motus, ut supra probatum est, sequitur quod non sit alteratio in acceptione scientiae. In regard to the first (706) he gives this argument. Knowing is especially spoken of as in relation “to something else,” i.e., to the knowable, the likeness of which, existing in the knower, is science. This he now proves: It is only in “to something” (relation), and in no other genus, that something happens to a thing without its being changed; for something can become “equal” to something else without itself being changed, the other alone having been changed. Now we can see that even though no change occurs in the intellectual power, knowledge begins to exist in it—for merely on the occasion of something existing in the sensitive part science comes to be. In effect, from experiencing particular things, which pertain to the sensitive part, we receive knowledge of the universal in the intellect, as is proved in Metaphysics I and in Posterior Analytics II. Therefore, since there is no motion in “to something,” as was proved above, it follows that there is no alteration involved in receiving science. Deinde cum dicit: neque igitur actus etc., ostendit quod non sit in parte intellectiva alteratio, in speciali. Et primo quantum ad considerationem iam habentis scientiam, quae est scientiae usus; secundo quantum ad primam scientiae acceptionem, ibi: quae autem ex principio et cetera. 924. Then at (707) he shows in detail that there is no alteration in the intellectual part. First in the case of one who already has science and speculates upon it, which is to use science; Secondly, in the case of one who receives fresh science, at 925 Dicit ergo primo, quod ex quo in parte intellectiva non est alteratio, non potest dici quod ipse actus scientiae, qui est consideratio, sit generatio, nisi etiam aliquis dicat quod exterior inspectio oculi, et ipsum tangere, sint generationes quaedam. Sicut enim visio est actus visivae potentiae, et tangere est actus tactivae potentiae, ita et consideratio est actus potentiae intellectivae. Actus autem non dicit generationem alicuius principii, sed magis processum a principio activo. Unde ipsum intelligere non est generatio vel alteratio. Tamen nihil prohibet aliquem actum consequi generationem vel alterationem; sicut ad generationem ignis sequitur quod calefaciat. Et similiter ad immutationem sensus a sensibili sequitur ipsum videre vel tangere. He says therefore first that, although there is no alteration in the intellectual part of the soul, it cannot be said that the use of science, which is to consider, is a type of generation, any more than we can say that when the eye externally regards an object or when one touches, there is generation. For just as seeing is the act of the visual, and touching is the act of the tactual, potency, so to consider is an act of the intellectual potency. Now, act does not imply that a principle is being generated, but rather that there is a proceeding from some active principle. Consequently, to understand is neither generation nor alteration. However, there is nothing to prevent an act from following upon generation and alteration, as, subsequent to its generation, fire heats, In like manner, on the occasion of a sense being altered by the sensible, the act of seeing or touching occurs. Deinde cum dicit: quae autem ex principio etc., ostendit quod in acceptione scientiae non est generatio vel alteratio. 925. Then at (708) he shows that there is not generation and alteration when science is newly received. Quidquid enim advenit alicui per solam quietationem et residentiam aliquarum perturbationum vel motionum, non advenit per generationem et alterationem: sed scientia, quae est cognitio speculativa, et prudentia, quae est ratio practica, adveniunt animae per quietationem et residentiam corporalium motionum et sensibilium passionum: non ergo scientia et prudentia adveniunt animae per generationem vel alterationem. For whatever accrues to a thing solely through the subsiding of certain disturbances and motions does not accrue through generation and alteration. But science, which is speculative knowledge, and prudence, which is practical reason, accrue to the soul through the subsiding of bodily motions and sensible passions. Therefore, neither science nor prudence accrue to the soul through generation and alteration. Ad huius autem rationis manifestationem subiungit exempla. Ponatur quod aliquis habens scientiam dormiat vel inebrietur aut infirmetur, manifestum est quod non potest uti scientia et operari secundum eam: sed manifestum est quod quando perturbatio praedicta quiescit, et mens redit ad statum suum, tunc potest uti scientia, et secundum eam agere. Et tamen non dicimus quod cum dormiens excitatur, aut ebrius quiescit, aut animus infirmantis ad debitum ordinem per sanitatem reducitur, quod tunc factus sit sciens, quasi scientia de novo generata sit in ipso; quia inerat ei potentia habitualis ad congruitatem scientiae, idest ut reduceretur ad congruum statum quo uti scientia posset. To elucidate this argument he gives examples. For let us suppose that some person who possesses science is asleep or drunk or sick. It is clear that he cannot at such a time use his science and act according to it. But it is also clear that, when the disturbance subsides and the mind returns to its normal state, he can then use his science and act according to it, Yet, we do not say that when a sleeping person is awakened, or someone drunk becomes sober, or when the life of a sick person is restored to due order by health, that he then becomes a knower as though science were newly generated in him, for there already existed in him a habitual potency “to the congruousness of science,” i.e., to be restored to a congruous state in which he could use his science. Dicit autem quod tale aliquid contingit cum aliquis a principio acquirit scientiam. Videtur enim hoc fieri per hoc quod fit quaedam quietatio et residentia turbationis, idest inordinatarum motionum; quae pueris insunt, tum secundum corpus, quia natura tota est in mutatione propter augmentum; tum etiam secundum partem sensitivam, quia in eis passiones dominantur. Now, he says that something like that happens when a person newly acquires science. For this seems to take place on account of a certain quieting and subsiding of “turbulence,” i.e., of disordered motions, which are present in boys both in respect of their bodies, because their whole nature is undergoing change by reason of growing, and in respect of their sensitive part, because in them the passions rule. Unde hoc quod dicit quies, potest referri ad turbationem corporalis motus, quae quiescit natura veniente ad statum: quod autem dicit residentia, potest referri ad passiones partis sensitivae, quae non totaliter quiescunt, sed resident; ex hoc scilicet quod deprimuntur sub ratione, non autem usque ad perturbandam rationem ascendunt; sicut dicimus residentiam in liquoribus, quando id quod est faeculentum descendit inferius, et id quod est superius remanet purum. Hence when he says “quieting,” he seems to be referring to disturbances of the body, which are calmed when nature arrives to full estate; and when he rays “subsiding,” he seems to refer to the passions of the sensitive part, which are not completely at rest but subside by reason of their being controlled by reason to the extent that they do not disturb the reason. It is in this way that we say that certain liquids have subsided when the dregs descend to the bottom and what is pure remains at the top. Haec est igitur causa quare iuvenes non possunt addiscere, capiendo ea quae ab aliis dicuntur; neque per interiores sensus possunt iudicare de auditis aut de quibuscumque eorum cognitioni occurrentibus, ita bene sicut seniores vel presbyteri (quod idem est: nam presbyter in Graeco idem est quod senior in Latino). Et hoc ideo, quia multa perturbatio et multus motus est circa ipsos iuvenes, ut dictum est. Sed huiusmodi turbatio totaliter tollitur, vel etiam mitigatur, aliquando quidem a natura, sicut quando pervenitur ad statum senectutis, in quo huiusmodi motus quiescunt; aliquando autem ab aliquibus aliis causis, sicut ab exercitio et consuetudine: et tunc possunt bene addiscere et iudicare. Et inde est quod exercitium virtutum moralium, per quas huiusmodi passiones refraenantur, multum valet ad scientiam acquirendam. Why is it that youths cannot learn by taking in what is said by others, and why is it they cannot with their internal senses judge about what they hear or somehow comes to their knowledge, as well as older persons can? It is because the former are subject to many disturbances and many commotions, as we said. But disturbances of this sort can be entirely removed or at least mitigated, sometimes by nature, as when a person reaches old age, in which motions of this kind are put to rest, and sometimes by other causes such as by training and habit. It is then that they can learn and judge well. That is why the exercising of the moral virtues, through which passions of this kind are bridled, is of great value in acquiring science. Sive ergo per naturam, sive per exercitium virtutis turbatio passionum quiescat, attenditur in hoc quaedam alteratio, cum passiones huiusmodi sint secundum partem sensitivam; sicut etiam est aliqua alteratio corporalis, cum dormiens surgit et fit vigilans, procedens ad actum. Therefore, whether the passions are made to subside by the exercise of virtue or by nature, an alteration is involved, since these passions are located in the sensitive part, just as an alteration takes place in the body when a sleeping person arises, and becomes awake, and starts to act. Ex quo patet quod acceptio scientiae non est alteratio, sed sequitur alterationem. From this it is clear that newly to acquire science is not an alteration but is a consequence of an alteration. Ex hoc autem ulterius universaliter concludit, quod alteratio est in sensibus exterioribus, et in sensibilibus, et in tota parte animae sensitiva (quod dicit propter passiones interiores): sed in nulla alia parte animae est alteratio, nisi per accidens. From this, however, he further concludes universally that alteration can occur in the external senses, in sensible bodies, and in the entire sensitive part of the soul (which he says on account of the interior passions), but in no other part of the soul, except per accidens. Quod autem Aristoteles hic de acceptione scientiae dicit, videtur esse secundum Platonicam opinionem. Posuit enim Plato quod sicut formae separatae sunt causae generationis et existentiae rerum naturalium, per hoc quod materia corporalis participat aliqualiter huiusmodi formas separatas; ita etiam sunt causa scientiae in nobis, per hoc quod anima nostra eas aliqualiter participat; ita quod ipsa participatio formarum separatarum in anima nostra est scientia. Sic enim verum erit quod accipitur scientia a principio, non per generationem alicuius scientiae in anima, sed solum per quietationem corporalium et sensibilium passionum, quibus impediebatur anima scientia uti. Sic etiam verum erit quod nulla mutatione facta in intellectu, ad solam praesentiam sensibilium quorum experientiam accipimus, fit homo sciens, sicut de relativis accidit; quia sensibilia secundum hoc non sunt necessaria ad scientiam, nisi ut ab eis quodammodo anima excitetur. 926. What Aristotle says here about receiving science seems to agree with Plato’s opinion. For Plato taught that just as separated forms are the cause of the generation and existence of natural things, in the sense that corporeal matter participates these separated forms in some way, so also they are the cause of science in us, for our soul somehow participates of them, in such a way that it is the very participation of separated forms in our soul which is science. In this way, it will be true that science is newly acquired, not by its being generated in the soul, but merely by the subsiding of bodily and sensitive passions, which prevented the soul from using its science. And in this way it will also be true that even though no change occurs in the intellect, a man becomes a knower by the mere presence of the sensible things of which he has experience, as occurs in relative things. This means that sensible things are not required for knowledge except for the purpose of arousing the soul. Aristotelis autem opinio est, quod scientia fit in anima per hoc quod species intelligibiles, abstractae per intellectum agentem, recipiuntur in intellectu possibili, ut dicitur in III de anima. Unde et ibidem dicitur quod intelligere est quoddam pati; licet alia sit passibilitas sensus et intellectus. However, Aristotle’s opinion is that science comes to be in the soul through the intelligible species, abstracted by the agent intellect, being received in the possible intellect, as is said in On the Soul III. For which reason, he says in the same place that to understand is certain “undergoing” (passio), although the way the intellect “undergoes” differs from the way the senses do. Nec est inconveniens quod Aristoteles hac opinione Platonis utatur. Est enim suae consuetudinis quod antequam probet suam sententiam, utatur sententia aliorum; sicut in tertio usus est quod omne corpus sensibile habet gravitatem vel levitatem, secundum opinionem Platonis; cuius contrarium ipse ostendet in I de caelo. It is not unfitting that Aristotle should here make use of the opinion of Plato. For it is his custom to make use of the opinions of others before giving his own, just as in Book III he used Plato’s opinion that every sensible body has heaviness or lightness, the contrary of which he will prove in On the Heavens I. Salvantur tamen et hae rationes secundum opinionem Aristotelis. Ad cuius evidentiam considerandum est, quod susceptivum aliquod tripliciter potest se habere ad formam suscipiendam. 927. Nevertheless, these arguments based on the opinion of Aristotle are saved. To make this clear it must be considered that a receiver can be related in three ways to a form that is to be received. Quandoque enim est in ultima dispositione ad susceptionem formae, nullo impedimento existente nec in ipso nec in alio: et tunc statim ad praesentiam activi, susceptivum recipit formam absque aliqua alteratione, sicut patet in aere illuminato ad praesentiam solis. For sometimes the receiver is in the final disposition for the reception of the form and no impediments exist either in it or in anything else. Under these conditions, as soon as the active principle is present, the receiver accepts the form without any further alteration, as is evident when air is illumined, the sun being present, Aliquando autem susceptivum non est in ultima dispositione ad susceptionem formae: et tunc per se requiritur alteratio, secundum quam materia dispositionem acquirat ut sit propria huic formae, sicut cum de aere fit ignis. But sometimes the receiver is not in the final disposition required for receiving the form. In that case a per se alteration is required to put into the matter a disposition for this particular form, as, for example, when fire comes to be from air. Aliquando vero susceptivum est in ultima dispositione ad formam, sed adest aliquod impedimentum, sicut cum aer impeditur ad susceptionem luminis, vel per clausionem fenestrae, vel per nebulas: et tunc requiritur alteratio vel mutatio per accidens, quae removeat prohibens. Sometimes the receiver is in the final disposition for the form but an obstacle is present, as when air is prevented from receiving light either by closing a shutter, or by the presence of clouds. In these cases, an alteration or changed is required per accidens, i.e., the removal of the obstacle. Intellectus ergo possibilis secundum se consideratus, semper est in ultima dispositione ad recipiendam speciem intelligibilem. Si ergo non sit impedimentum, statim ad praesentiam obiectorum per experimentum acceptorum, advenit ei species intelligibilis, sicut speculo forma specularis ad praesentiam corporis; et secundum hoc procedit prima eius ratio, qua dixit scientiam esse ad aliquid. Si vero sit impedimentum, sicut in iuvenibus accidit, oportet huiusmodi impedimenta auferri ad hoc quod species intelligibilis in intellectu recipiatur; et sic per accidens necessaria est alteratio. Now the possible intellect, considered in itself, is always in the final disposition for receiving the intelligible species. Therefore, if there be no obstacle, then, whenever there are present objects received through experience, there will arise in the intellect an intelligible species, just as an image will appear in a mirror when a body is present. It was on this basis that Aristotle took his first argument, in which he said that science is “to something.” However, if there be an obstacles as happens in youths, then these obstacles must be removed in order to allow the intelligible species to be received in the intellect. In this case an alteration is necessary per accidens.
The comparing of motions; what is required
Chapter 4 Ἀπορήσειε δ' ἄν τις πότερόν ἐστι κίνησις πᾶσα πάσῃ συμβλητὴ ἢ οὔ. εἰ δή ἐστιν πᾶσα συμβλητή, καὶ ὁμοταχὲς τὸ ἐν ἴσῳ χρόνῳ ἴσον κινούμενον, ἔσται περιφερής τις ἴση εὐθείᾳ, καὶ μείζων δὴ καὶ ἐλάττων. ἔτι ἀλλοίωσις καὶ φορά τις ἴση, ὅταν ἐν ἴσῳ χρόνῳ τὸ μὲν ἀλλοιωθῇ τὸ δ' ἐνεχθῇ. ἔσται ἄρα ἴσον πάθος μήκει. ἀλλ' ἀδύνατον. A difficulty may be raised as to whether every motion is commensurable with every other or not. Now if they are all commensurable and if two things to have the same velocity must accomplish an equal motion in an equal time, then we may have a circumference equal to a straight line, or, of course, the one may be greater or less than the other. Further, if one thing alters and another accomplishes a locomotion in an equal time, we may have an alteration and a locomotion equal to one another: thus an affection will be equal to a length, which is impossible. ἀλλ' ἆρα ὅταν ἐν ἴσῳ ἴσον κινηθῇ, τότε ἰσοταχές, ἴσον δ' οὐκ ἔστιν πάθος μήκει, ὥστε οὐκ ἔστιν ἀλλοίωσις φορᾷ ἴση οὐδ' ἐλάττων, ὥστ' οὐ πᾶσα συμβλητή; But is it not only when an equal motion is accomplished by two things in an equal time that the velocities of the two are equal? Now an affection cannot be equal to a length. Therefore there cannot be an alteration equal to or less than a locomotion: and consequently it is not the case that every motion is commensurable with every other. ἐπὶ δὲ τοῦ κύκλου καὶ τῆς εὐθείας πῶς συμβήσεται; ἄτοπόν τε γὰρ εἰ μὴ ἔστιν κύκλῳ ὁμοίως τουτὶ κινεῖσθαι καὶ τουτὶ ἐπὶ τῆς εὐθείας, ἀλλ' εὐθὺς ἀνάγκη ἢ θᾶττον ἢ βραδύτερον, ὥσπερ ἂν εἰ κάταντες, τὸ δ' ἄναντες· But how will our conclusion work out in the case of the circle and the straight line? It would be absurd to suppose that the motion of one in a circle and of another in a straight line cannot be similar, but that the one must inevitably move more quickly or more slowly than the other, just as if the course of one were downhill and of the other uphill. οὐδὲ διαφέρει οὐδὲν τῷ λόγῳ, εἴ τίς φησιν ἀνάγκην εἶναι θᾶττον εὐθὺς ἢ βραδύτερον κινεῖσθαι· ἔσται γὰρ μείζων καὶ ἐλάττων ἡ περιφερὴς τῆς εὐθείας, ὥστε καὶ ἴση. εἰ γὰρ ἐν τῷ Α χρόνῳ (248b.) τὴν Β διελήλυθε τὸ δὲ τὴν Γ, μείζων ἂν εἴη ἡ Β τῆς Γ· οὕτω γὰρ τὸ θᾶττον ἐλέγετο. οὐκοῦν καὶ εἰ ἐν ἐλάττονι ἴσον, θᾶττον· ὥστ' ἔσται τι μέρος τοῦ Α ἐν ᾧ τὸ Β τοῦ κύκλου τὸ ἴσον δίεισι καὶ τὸ Γ ἐν ὅλῳ τῷ Α [τὴν Γ]. Moreover it does not as a matter of fact make any difference to the argument to say that the one motion must inevitably be quicker or slower than the other: for then the circumference can be greater or less than the straight line; and if so it is possible for the two to be equal. For if in the time A the quicker (B) passes over the distance B' and the slower (G) passes over the distance G', B' will be greater than G': for this is what we took 'quicker' to mean: and so quicker motion also implies that one thing traverses an equal distance in less time than another: consequently there will be a part of A in which B will pass over a part of the circle equal to G', while G will occupy the whole of A in passing over G'. ἀλλὰ μὴν εἰ ἔστιν συμβλητά, συμβαίνει τὸ ἄρτι ῥηθέν, ἴσην εὐθεῖαν εἶναι κύκλῳ. ἀλλ' οὐ συμβλητά· οὐδ' ἄρα αἱ κινήσεις, ἀλλ' ὅσα μὴ συνώνυμα, πάντ' ἀσύμβλητα. None the less, if the two motions are commensurable, we are confronted with the consequence stated above, viz. that there may be a straight line equal to a circle. But these are not commensurable: and so the corresponding motions are not commensurable either. οἷον διὰ τί οὐ συμβλητὸν πότερον ὀξύτερον τὸ γραφεῖον ἢ ὁ οἶνος ἢ ἡ νήτη; ὅτι ὁμώνυμα, οὐ συμβλητά· ἀλλ' ἡ νήτη τῇ παρανήτῃ συμβλητή, ὅτι τὸ αὐτὸ σημαίνει τὸ ὀξὺ ἐπ' ἀμφοῖν. ἆρ' οὖν οὐ ταὐτὸν τὸ ταχὺ ἐνταῦθα κἀκεῖ, πολὺ δ' ἔτι ἧττον ἐν ἀλλοιώσει καὶ φορᾷ; But may we say that things are always commensurable if the same terms are applied to them without equivocation? e.g. a pen, a wine, and the highest note in a scale are not commensurable: we cannot say whether any one of them is sharper than any other: and why is this? they are incommensurable because it is only equivocally that the same term 'sharp' is applied to them: whereas the highest note in a scale is commensurable with the leading-note, because the term 'sharp' has the same meaning as applied to both. Can it be, then, that the term 'quick' has not the same meaning as applied to straight motion and to circular motion respectively? If so, far less will it have the same meaning as applied to alteration and to locomotion. ἢ πρῶτον μὲν τοῦτο οὐκ ἀληθές, ὡς εἰ μὴ ὁμώνυμα συμβλητά; τὸ γὰρ πολὺ τὸ αὐτὸ σημαίνει ἐν ὕδατι καὶ ἀέρι, καὶ οὐ συμβλητά. εἰ δὲ μή, τό γε διπλάσιον ταὐτό (δύο γὰρ πρὸς ἕν), καὶ οὐ συμβλητά. Or shall we in the first place deny that things are always commensurable if the same terms are applied to them without equivocation? For the term 'much' has the same meaning whether applied to water or to air, yet water and air are not commensurable in respect of it: or, if this illustration is not considered satisfactory, 'double' at any rate would seem to have the same meaning as applied to each (denoting in each case the proportion of two to one), yet water and air are not commensurable in respect of it. ἢ καὶ ἐπὶ τούτων ὁ αὐτὸς λόγος; καὶ γὰρ τὸ πολὺ ὁμώνυμον. ἀλλ' ἐνίων καὶ οἱ λόγοι ὁμώνυμοι, οἷον εἰ λέγοι τις ὅτι τὸ πολὺ τὸ τοσοῦτον καὶ ἔτι, ἄλλο τὸ τοσοῦτον· καὶ τὸ ἴσον ὁμώνυμον, καὶ τὸ ἓν δέ, εἰ ἔτυχεν, εὐθὺς ὁμώνυμον. εἰ δὲ τοῦτο, But here again may we not take up the same position and say that the term 'much' is equivocal? In fact there are some terms of which even the definitions are equivocal; e.g. if 'much' were defined as 'so much and more','so much' would mean something different in different cases: 'equal' is similarly equivocal; and 'one' again is perhaps inevitably an equivocal term; and if 'one' is equivocal, so is 'two'. καὶ τὰ δύο, ἐπεὶ διὰ τί τὰ μὲν συμβλητὰ τὰ δ' οὔ, εἴπερ ἦν μία φύσις; Otherwise why is it that some things are commensurable while others are not, if the nature of the attribute in the two cases is really one and the same? ἢ ὅτι ἐν ἄλλῳ πρώτῳ δεκτικῷ; ὁ μὲν οὖν ἵππος καὶ ὁ κύων συμβλητά, πότερον λευκότερον (ἐν ᾧ γὰρ πρώτῳ, τὸ αὐτό, ἡ ἐπιφάνεια), καὶ κατὰ μέγεθος ὡσαύτως· ὕδωρ δὲ καὶ φωνὴ οὔ· ἐν ἄλλῳ γάρ. Can it be that the incommensurability of two things in respect of any attribute is due to a difference in that which is primarily capable of carrying the attribute? Thus horse and dog are so commensurable that we may say which is the whiter, since that which primarily contains the whiteness is the same in both, viz. the surface: and similarly they are commensurable in respect of size. But water and speech are not commensurable in respect of clearness, since that which primarily contains the attribute is different in the two cases. ἢ δῆλον ὅτι ἔσται οὕτω γε πάντα ἓν ποιεῖν, ἐν ἄλλῳ (249a.) δὲ ἕκαστον φάσκειν εἶναι, καὶ ἔσται ταὐτὸ <�τὸ> ἴσον καὶ γλυκὺ καὶ λευκόν, ἀλλ' ἄλλο ἐν ἄλλῳ; It would seem, however that we must reject this solution, since clearly we could thus make all equivocal attributes univocal and say merely that that contains each of them is different in different cases: thus 'equality', 'sweetness', and 'whiteness' will severally always be the same, though that which contains them is different in different cases. ἔτι δεκτικὸν οὐ τὸ τυχὸν <�τοῦ τυχόντος> ἐστίν, ἀλλ' ἓν ἑνὸς τὸ πρῶτον. Moreover, it is not any casual thing that is capable of carrying any attribute: each single attribute can be carried primarily only by one single thing. ἀλλ' ἆρα οὐ μόνον δεῖ τὰ συμβλητὰ μὴ ὁμώνυμα εἶναι ἀλλὰ καὶ μὴ ἔχειν διαφοράν, μήτε ὃ μήτε ἐν ᾧ; λέγω δὲ οἷον χρῶμα ἔχει διαί ρεσιν· τοιγαροῦν οὐ συμβλητὸν κατὰ τοῦτο (οἷον πότερον κεχρωμάτισται μᾶλλον, μὴ κατὰ τὶ χρῶμα, ἀλλ' ᾗ χρῶμα), ἀλλὰ κατὰ τὸ λευκόν. Must we then say that, if two things are to be commensurable in respect of any attribute, not only must the attribute in question be applicable to both without equivocation, but there must also be no specific differences either in the attribute itself or in that which contains the attribute—that these, I mean, must not be divisible in the way in which colour is divided into kinds? Thus in this respect one thing will not be commensurable with another, i.e. we cannot say that one is more coloured than the other where only colour in general and not any particular colour is meant; but they are commensurable in respect of whiteness.
Postquam philosophus ostendit quod in mobilibus et motoribus necesse est ponere aliquod primum; quia ea quae sunt unius ordinis videntur comparabilia esse, et hoc ipsum quod est prius et posterius comparationem importat, vult ex consequenti inquirere de motuum comparatione. Et circa hoc duo facit: primo enim ostendit qui motus sint comparabiles ad invicem; secundo qualiter motus ad invicem comparentur, ibi: quoniam autem movens movet et cetera. 928. After the Philosopher has shown that it is necessary to posit a first in mobiles and movers, now, because things which are of one order seem capable of being compared, and because to be “prior” and “subsequent” implies a comparison, he wishes to inquire about comparison of motions. Concerning this he does two things: First, he shows which motions can be mutually compared; Secondly, how motions are mutually compared, (L. 9). Circa primum tria facit: primo movet dubitationem; secundo obiicit ad partes dubitationis, ibi: si ergo cum in aequali etc.; tertio dubitationem solvit, ibi: sed quaecumque non aequivoca et cetera. About the first he does three things: First, he raises a question; Secondly, he objects against both parts of the question, at 929; Thirdly, he settles the question, at 933. Movet autem dubitationem primo quidem in communi, quaerens utrum omnis motus sit comparabilis cuilibet motui, vel non: deinde vero in speciali, dubitationem inferens primo quidem de motibus unius generis. Quia si omnis motus cuilibet motui sit comparabilis secundum velocitatem et tarditatem (dictum est autem in sexto quod aequaliter velox est, quod movetur in aequali tempore per aequale spatium), sequetur quod motus circularis sit aequalis recto et maior et minor in velocitate; et ulterius quod linea circularis sit aequalis lineae rectae in quantitate, aut maior et minor; ex quo aeque velox est quod per aequale movetur in aequali tempore. First he raises a general question (709) and asks whether just any motion at random may be compared to just any other motion or not. Then he raises a special question about motions in some one genus. Now if any motion at random may be compared to just any other motion with respect to swiftness and slowness (it having been said in Book VI that the equally swift is what is moved in equal time over an equal space), it will follow that a circular motion will be equal, or greater, or less, in swiftness than a rectilinear one, and further, that a curved line will be equal to a straight line in quantity, or larger or smaller, from the fact that the equally swift is that which traverses an equal distance in equal time. Deinde infert dubitationem de motibus diversorum generum. Si enim omnes motus comparabiles sunt in velocitate, sequetur quod si in aequali tempore hoc quidem alteretur, illud vero moveatur secundum locum, quod sit aequalis in velocitate alteratio loci mutationi. Et ulterius, per definitionem aeque velocis, sequetur quod passio, idest passibilis qualitas, secundum quam est alteratio, sit aequalis longitudini spatii, quae pertransitur per motum localem: quod est impossibile manifeste, quia non conveniunt in eadem ratione quantitatis. Then he raises a question about motions in diverse genera. For if all motions may be compared with respect to speed, it will follow that if in an equal time A is altered, and B is moved locally, then a local motion is equal in swiftness to an alteration. Further, by virtue of the definition of the equally swift, it will follow that a passion, i.e., passible quality, in respect of which there is alteration, is equal to the length of the distance traversed by the local motion. But this is plainly impossibles because they do not agree in the same notion of quantity. Deinde cum dicit: si ergo etc., obiicit ad propositam dubitationem: et primo quantum ad comparationem alterationis et loci mutationis; secundo quantum ad comparationem motus circularis et recti, ibi: in circulo autem et recto et cetera. 929. Then at (710) he raises objections against the question proposed: First, he objects against comparing alteration with local motion; Secondly, against comparing circular motion with rectilinear, at 930. Concludit ergo primo ex praemissa ratione ad impossibile ducente, contrarium posito; quasi dicat: dictum est quod inconveniens est passionem esse aequalem longitudini: sed tunc aliquid est aequaliter velox, cum in aequali tempore movetur per aequale: ergo, cum nulla passio sit aequalis longitudini, sequitur quod loci mutatio non est aequalis in velocitate alterationi, neque maior aut minor. Ex quo ulterius concludi poterit, quod non omnes motus sint comparabiles. First (710), therefore, from the foregoing argument which leads to an impossibility, he concludes to the contrary of what he posited, as though saying that, since it has been said that it is not feasible for a passion to be equal to a length, while whenever something is moved through an equal space in equal time, it is said to be equally swift, therefore, since no passion is equal to a length, it follows that a local motion is not equal in swiftness to an alteration, or greater or less. From this it may be further concluded that not all motions can be compared. Deinde cum dicit: in circulo autem etc., prosequitur quantum ad aliam partem dubitationis, scilicet de motu circulari et recto. Et primo obiicit ad hoc quod motus circularis sit aeque velox motui recto; secundo obiicit in contrarium, ibi: at vero si sunt comparabilia et cetera. 930. Then at (711) he considers the other part of the question, i.e., concerning circular and rectilinear motion. First he objects against a circular motion’s being as equally swift as a rectilinear motion; Secondly, he takes the contrary position, at 932. Circa primum duo facit: primo obiicit ad propositum; secundo excludit cavillosam responsionem, ibi: amplius nihil differt et cetera. About the first he does two things: First he objects against the proposition; Secondly, he dismisses a quibbling response, at 931. Obiicit autem primo sic. Motus circularis et rectus sunt differentiae motus localis, sicut et motus sursum et deorsum. Sed statim necesse est quod aliquid velocius aut tardius moveatur, si unum movetur sursum, aliud deorsum; vel etiam si idem quandoque movetur sursum, quandoque deorsum. Videtur ergo quod similiter oporteat dicere quod motus rectus sit velocior aut tardior circulari; sive idem sit quod movetur circulariter et recte, sive aliud et aliud. He objects first (711) in the following manner. Circular motion and rectilinear are differences of local motion, just as upward and downward are. But as soon as something is moved upwards and something else downwards, it is at once necessary that one be being moved faster or slower than the other—the same is true if the same thing is moved now upwards and later downwards. It seems therefore that in like manner we must say that a rectilinear motion is swifter or slower than a circular one, whether it be the same thing that is being moved in a straight line and in a circular one, or two different things. Est autem considerandum quod in hac ratione non facit mentionem de aeque veloci, sed de velociori et tardiori, quia haec ratio sumitur ex similitudine motus qui est sursum, cuius principium est levitas, et motus qui est deorsum, cuius principium est gravitas; quidam autem existimaverunt gravitatem et levitatem idem esse velocitati et tarditati (quod in quinto removit). It should be noted that in this argument he makes no mention of the equally swift but of the swifter and slower, because this argument is based on the likeness of an upward motion—whose principle is lightness—to a motion which is downward—whose principle is heaviness. Some, indeed, have held that heaviness and lightness are the same as swiftness and slowness—an opinion he rejected in Book V. Deinde cum dicit: amplius nihil differt etc., excludit quandam cavillosam obviationem. Posset enim aliquis propter rationem praemissam concedere quod motus circularis esset aut velocior aut tardior quam rectus, non autem aeque velox. 931. Then at (712) he rejects a quibble. For someone could concede on account of the foregoing reason that a circular motion is either swifter or slower than a rectilinear ones but not equally swift. Et hoc excludit, dicens quod nihil differt quantum ad praesentem rationem, si aliquis dicat quod necessarium est quod id quod movetur circulariter, moveatur velocius aut tardius quam id quod movetur recte; quia secundum hoc motus circularis erit maior vel minor in velocitate quam rectus; unde sequitur quod etiam esse possit aequalis. This he rejects, saying that it makes no difference, so far as the present discussion is concerned, once someone grants that it is necessary for what is being moved circularly to be moved more swiftly or more slowly than what is being moved in a straight line. For according to this the circular motion will be faster or slower than the rectilinear. Hence it follows that it could also be equal. Et quod hoc sequatur manifestat sic. Sit a tempus in quo aliquid velocius motum pertranseat ipsum b, qui est circulus: aliud autem tardius in eodem tempore pertranseat ipsum c, quod est recta linea. Quia ergo velocius in eodem tempore pertransit maius, sequetur quod b circulus sit aliquid maius quam c linea recta: sic enim supra in sexto definivimus velocius. Sed ibidem etiam diximus quod velocius in minori tempore pertransit aequale. Ergo erit accipere aliquam partem huius temporis quod est a, in qua corpus quod circulariter movetur, pertransibit aliquam partem huius circuli quod est b, et in eadem parte temporis pertransibit ipsum c; cum tamen corpus tardius in toto a tempore pertransiret totum c. Sequetur ergo quod illa pars circuli sit aequalis toti c, quia idem pertransit aequale in aequali tempore. Et sic linea circularis erit aequalis rectae, et motus circularis per consequens aeque velox recto. That this follows he now proves. Let A be the time in which the swifter traverses B, which is a circles and let something slower traverse the straight line C in the same time. Now, since the swifter traverses more in the same time, it will follow that circle B is larger than the straight line—that is the way the swifter was defined in Book VI. But we also said in that place that the swifter traverses an equal distance in less time. Therefore, we can take of time A a part during which the circularly moving body will traverse a part of this circle B and during which it will traverse C, while the slower body is traversing C in the entire time A. It will follow, therefore, that that part of the circle is equal to the entire C, because one and the same object traverses an equal distance in equal time. And in this way, a circular line will be equal to a straight line and a circular motion will, consequently, be as fast as a rectilinear. Deinde cum dicit: at vero si sunt comparabilia etc., obiicit in contrarium. Quia si motus circularis et rectus sunt comparabiles in velocitate, sequitur quod modo dictum est, scilicet quod linea recta sit aequalis circulo, propter hoc quod aeque velox est quod per aequale movetur. Sed linea circularis et linea recta non sunt comparabiles, ut possint dici aequales: ergo neque motus circularis et rectus possunt dici aeque veloces. 932. Then (713) he takes the contrary position. For if circular and rectilinear motions may be compared with respect to swiftness, it follows, as just said, that a straight line will be equal to a circular one, for the equally swift is what traverses an equal distance. But a circular line and a straight line cannot be compared, so as to be called equal. Therefore, neither can a circular motion be said to be as swift as a rectilinear. Deinde cum dicit: sed quaecumque non aequivoca etc., solvit propositam dubitationem. Et primo inquirit in communi quid cui sit comparabile; secundo adaptat ad propositum, ibi: sic et circa motum et cetera. 933. Then at (714) he settles the difficulty he raised. First he asks in general what may be compared to what; Secondly, he adapts this to his proposition, (L. 8). Circa primum tria facit: primo ponit unum quod requiritur ad comparationem; secundo secundum, ibi: aut quia sunt in alio etc.; tertio concludit tertium, ibi: sic ergo non solum oportet et cetera. About the first he does three things: First he states one thing that is required for comparison; Secondly, a second thing, at 937. Thirdly, he concludes a third requirement, (at 939) Circa primum tria facit: primo ponit quid requiratur ad comparationem; secundo obiicit in contrarium, ibi: aut primum quidem etc.; tertio solvit, ibi: aut et in his eadem ratio et cetera. About the first he does three things: First he mentions what is required for comparisons; Secondly, he takes the contrary position, at 935; Thirdly, he settles the matter, at 936. Dicit ergo primo, quod quaecumque non sunt aequivoca, videntur esse comparabilia; ita scilicet quod secundum ea quae non aequivoce praedicantur, possint ea de quibus praedicantur, ad invicem comparari. Sicut acutum aequivoce sumitur: uno enim modo dicitur in magnitudinibus, secundum quem modum angulus dicitur acutus, et stylus acutus; alio modo dicitur in saporibus, secundum quem modum vinum dicitur acutum; tertio modo dicitur in vocibus, secundum quem modum vox ultima, idest suprema, in melodiis, vel chorda in cythara dicitur acuta. 934. He says therefore first (714) that things seem to be capable of being compared so long as they are not equivocal, that is, in the line of things not predicated equivocally the subjects of predication may be compared. For example, “sharp” is an equivocal term: for in one sense it is applied to magnitudes, as when an angle is said to be “sharp” (acute) and when a pen-point is said to be “sharp”; in another sense it is applied to savors, as when wine is said to be “sharp” (dry); in a third sense it is applied to notes, as when the ultimate, i.e., highest, note in a melody, or a chord of a lyre is said to be “sharp.” Ideo ergo non potest fieri comparatio ut dicatur quid sit acutius, utrum stylus aut vinum aut vox ultima, quia acutum de eis aequivoce praedicatur: sed vox ultima potest comparari secundum acuitatem, ei quae est iuxta ipsam in ordine melodiae, propter hoc quod acutum non aequivoce, sed secundum eandem rationem praedicatur de utraque. Now, the reason why no answer can be made to the question, “Which of these is sharpest, the point, the wine or the voice?” is because “sharp” is predicated of them in an equivocal sense. But the highest note can be compared with respect to sharpness to another which is next to it in the scale, because in this case “sharp” is not taken equivocally, but is predicated of both in the same sense. Secundum hoc ergo poterit dici ad propositam quaestionem, quod ideo motus rectus et circularis non comparantur in velocitate, quia velox aequivoce dicitur hic et ibi. Et multo minus est eadem ratio velocis in alteratione et loci mutatione: unde etiam haec multo minus comparabilia sunt. Therefore, according to this, it could be replied to the proposed difficulty that the reason why a straight motion cannot be compared to a circular one is because the word “swift” is being used equivocally. And much less is the meaning of “swift” the same in respect to alteration and local motion. Consequently, these two are even less capable of being compared. Deinde cum dicit: aut primum quidem etc., obiicit contra id quod dictum est. Et dicit quod quantum ad primum aspectum hoc non videtur esse verum, quod si aliqua non sunt aequivoca, quod sint comparabilia. Inveniuntur enim aliqua non aequivoca, quae tamen non sunt comparabilia; sicut hoc ipsum quod est multum, secundum eandem rationem dicitur de aqua et de aere, et tamen non sunt comparabilia aer et aqua secundum multitudinem. 935. Then at (715) he objects against what was just said. And he says that at first sight it does not seem to be true that things may be compared so long as they are not equivocal. For there are some non-equivocal things which cannot be compared; for example, “much” is used in the same sense when applied to water and to air, yet water and air cannot be compared with respect to muchness. Si autem non velit aliquis hoc concedere quod multum idem significet propter eius communitatem, saltem concedet quod duplum, quod est species multiplicis, idem significat in aere et aqua: utrobique enim significat proportionem duorum ad unum. Et tamen non sunt comparabilia aer et aqua secundum duplum et dimidium, ut dicatur quod aqua est duplum aeris, aut e converso. Now if someone refuses to admit that “much” signifies the same thing on account of its general nature, he will at least grant that “double,” i.e., twice as much as, which is a species of muchness, signifies the same thing in regard to air and to water; for in both cases it signifies the ratio of 2 to 1. Nevertheless, air and water cannot be compared in terms of double and half, so as to be able to say that the amount of water is double that of the air or vice versa. Deinde cum dicit: aut et in his eadem ratio etc., solvit propositam obiectionem. Et circa hoc duo facit: primo ponit solutionem; secundo confirmat eam, quandam quaestionem movendo, ibi: quoniam propter quid et cetera. 936. Then at (716) he answers this objection. About this he does two things: First he gives the solution; Secondly, he confirms it by raising another question, at 937. Dicit ergo primo, quod potest dici quod in multo et duplo est eadem ratio quare non sunt comparabilia secundum quod dicuntur de aqua et aere, quae dicta est de acuto, secundum quod dicitur de stylo, vino et voce; quia etiam hoc ipsum quod est multum, aequivocum est. He says therefore first that it could be said that in “much” and “double” we discern the same reason for their inability to be compared, when they are applied to water and to air, as was discerned in “sharp” when it was applied to pen and wine and note; for “much” itself is equivocal. Et quia posset aliquis contra hoc obiicere ex hoc quod est eadem ratio multi secundum quod dicitur de utroque, ad hoc excludendum subiungit quod etiam rationes, idest definitiones, quorundam sunt aequivocae: sicut si dicat aliquis quod definitio multi est quod est tantum et adhuc amplius, hoc ipsum quod est tantundem et aequale, quod idem est, aequivocum est; quia aequale est quod habet unam quantitatem, non est autem eadem ratio unius quantitatis in omnibus. Ponitur autem hic ratio multi secundum quod multum importat comparationem, prout opponitur pauco; et non secundum quod accipitur absolute, prout opponitur uni. Now, because someone could object against this on the ground that the same notion of “much” is referred to when it is applied to both, then in order to reject this, he states that even the notions, i.e., definitions, of certain things are equivocal. For example, if someone should say that the definition of “much” is that it is “this amount and yet more,” “to be this amount” and “to be equal,” which is the same thing, is equivocal, for “to be equal” is to have one quantity, but the definition of “one quantity” is not the same in all things. (The notion of “much,” as used here, implies a comparison in the sense that it is the opposite of “a little,” i.e., it is not taken in its absolute sense of being the opposite of “one.”) Et quod dixerat de multo, dicit consequenter de duplo. Quamvis enim ratio dupli sit, quod est proportio duorum ad unum, tamen ista etiam ratio continet aequivocationem: quia forte potest dici quod ipsum unum est aequivocum; et si unum aequivoce dicitur, sequitur quod duo, quia duo nihil aliud est quam bis unum. And what he said of “much” he says consequently of “double.” For although the notion of “double” is that there is a ratio of 2 to 1, yet even that notion contains an equivocation, for it could be said that “one” is equivocal; and if “one” is equivocal, it follows that “two” is, because “two” is nothing more than “one” taken twice. Est autem considerandum, quod multa quidem secundum abstractam considerationem vel logici vel mathematici non sunt aequivoca, quae tamen secundum concretam rationem naturalis ad materiam applicantis, aequivoce quodammodo dicuntur, quia non secundum eandem rationem in qualibet materia recipiuntur: sicut quantitatem et unitatem, quae est principium numeri, non secundum eandem rationem contingit invenire in corporibus caelestibus et in igne et in aere et aqua. Now it should be observed that there are many things which, when considered in an abstract way in logic or mathematics, are not equivocal, but which are in a certain sense equivocal when they are taken in a concrete way, as the philosopher of nature takes them when he applies them to matter, for they are not taken according to the same aspect in all matter. For example, quantity, and unity (which is the principle of number) are not found according to the same aspect in the heavenly bodies, and in fire and air and water. Deinde cum dicit: quoniam propter quid etc., confirmat quod dictum est, movendo quandam quaestionem. Si enim dicatur quod sit una natura multi et dupli et aliorum huiusmodi, quae non sunt comparabilia, sicut eorum quae univoce praedicantur; remanet quaestio quare quaedam quae habent unam naturam, sunt comparabilia, quaedam vero non sunt comparabilia. Videtur enim quod de similibus debeat esse idem iudicium. 937. Then at (717) he confirms what has been said by raising a certain other question. For if it be held that there is one nature of “much” and of “double” and of other like things which cannot be compared, as there is also one nature of things that are predicated univocally, the question still remains, why it is that among things having one nature some can be compared and some not. For it seems that when things are similar, there should be a same judgment about them. Deinde cum dicit: aut quia sunt in alio etc., respondet ad quaestionem motam, ponendo secundum quod ad comparationem requiritur. Et circa hoc duo facit: primo ponit secundum quod requiritur ad comparationem; secundo ostendit quod nec istud sufficit, ibi: aut manifestum est et cetera. Then at (718) he answers this question by positing the second requirement for things to be compared. About this he does two things: First he mentions the second requirement; Secondly, he shows that even that one is not enough, at 938. Dicit ergo primo, quod ista potest esse ratio quare quaedam quorum est una natura, sunt comparabilia, quaedam vero non: quia si una natura recipiatur in diversis secundum unum primum subiectum, erunt illa ad invicem comparabilia; sicut equus et canis comparari possunt secundum albedinem, ut dicatur quod eorum sit albius, quia non solum est eadem natura albedinis in utroque, sed etiam est unum primum subiectum in quo recipitur albedo, scilicet superficies. Et similiter magnitudo est comparabilis in utroque, ut dicatur quod eorum sit maius; quia idem est subiectum magnitudinis in utroque, scilicet substantia corporis mixti. Sed aqua et vox non sunt comparabilia secundum magnitudinem, ut dicatur quod vox est maior quam aqua, aut e converso; quia licet magnitudo secundum se sit eadem, non tamen est idem receptivum: quia secundum quod dicitur de aqua, subiectum eius est substantia; secundum autem quod dicitur de voce, subiectum eius est sonus, qui est qualitas. He says therefore first (718) that the reason why some things possessing one nature can be compared, while other things having one nature cannot, could be that when some one nature is received according to one first subject in diverse things, they will be comparable, as horse and dog can be compared with respect to whiteness, one being able to be said “whiter” than the other, because not only is the same nature of whiteness in both, but there is one first subject in which whiteness is received, namely, the surface. In like manner, the magnitude of each may be compared, so that one can be called “larger” than the other, because there is one same subject of magnitude in each, namely, the substance of a mixed body. But water and a note cannot be compared with respect to magnitude so as to say that the note is “greater” than the water or vice versa, because although magnitude in itself is the same, the receiver of it is not the same. For when magnitude is said of water, its subject is a substance, but when it is said of a note, its subject is sound, which is a quality. Deinde cum dicit: aut manifestum est etc., ostendit quod nec hoc sufficit, duabus rationibus. Quarum prima est: si propter hoc solum aliqua essent comparabilia, quia est subiectum non differens, sequeretur quod omnia haberent unam naturam; quia de quibuscumque diversis posset dici, quod non differunt nisi quia sunt in alio et alio subiecto primo. Et secundum hoc sequeretur quod hoc ipsum quod est aequale, et quod est dulce, et quod est album, esset una et eadem natura; sed differret solum per hoc quod est in alio et alio receptivo. Et hoc videtur inconveniens, quod omnia habeant unam naturam. 938. Then at (719) he shows that this second requirement does not complete the list of requirements, for two reasons. The first of these is this: If things were comparable just because there is a non-differing subject, it would follow that all things have one nature, for it could be said of all things whatsoever that they do not differ except insofar as they exist in some one or other first subject. And according to this, it would follow that “to be equal” and “to be sweet” and “to be white” are one and the same nature, differing only by reason of being received in one or another receiver. And this is seen to be unacceptable, namely, that all things have one nature. Est autem considerandum, quod ponere diversitatem rerum propter diversitatem susceptivi tantum, est opinio Platonica, quae posuit unum ex parte formae, et dualitatem ex parte materiae; ut tota diversitatis ratio ex materiali principio proveniret. Unde et unum et ens posuit univoce dici, et unam significare naturam: sed secundum diversitatem susceptivorum, rerum species diversificari. But it should be noted that positing a diversity of things on the sole ground of diversity of subject is a Platonist opinion, which attributed unity to form and duality to matter, so that the entire reason of diversity came from the material principle. That was why he stated that “one” and “being” are predicated univocally, and that they signify one nature but that the species of things are diversified by reason of a diversity of receivers. Secunda ratio, quam ponit ibi: amplius susceptivum etc., est quod non quodlibet est susceptivum cuiuslibet; sed unum est primo susceptivum unius; et sic forma et susceptivum ad invicem dicuntur. Si ergo sunt plura prima susceptiva, necesse est quod sint plures naturae susceptae: aut si est una natura suscepta, necesse est quod sit unum primum susceptivum. The second reason which he gives, at (720), is that not just anything is capable of receiving just anything else at random, but one is primarily the receiver of one; consequently, the form and what receives it are in proportion. Therefore, if there are many first receivers, there must necessarily be many natures capable of being received; or if one nature has been received, then necessarily there is one first receiver. Deinde cum dicit: sic ergo non solum etc., concludit quod requiritur tertium ad hoc quod aliqua sint comparabilia. Et dicit quod oportet ea quae sunt comparabilia, non solum non esse aequivoca, quod erat primum; sed etiam non habere differentiam, neque ex parte subiecti primi in quo aliquid recipitur, quod erat secundum; neque ex parte eius quod recipitur, quod est forma vel natura; et hoc est tertium. 939. Then at (721) he concludes that there is a third requirement for things to be comparable. And he says that things which can be compared must be not only non-equivocal (which is the first requirement) but must also not possess any difference either on the side of the first subject in which something is received (which is the second requirement) or on the side of what is received, which is a form or a nature (and this is the third). Et exemplificat de hoc tertio. Quia color dividitur in diversas species coloris: unde non est comparabile secundum quod de eis praedicatur; licet non dicatur aequivoce, et licet etiam habeat unum primum subiectum, quod est superficies, quod est primum subiectum generis, non autem alicuius speciei coloris. Non enim possumus dicere quid sit magis coloratum, utrum album vel nigrum: haec enim comparatio non esset secundum aliquam determinatam speciem coloris, sed secundum ipsum colorem communem. Secundum vero album, quod non dividitur in diversas species, potest fieri comparatio omnium alborum, ut dicatur quid sit albius. And he gives examples of this third requirement. For “color” is divided into various species of color; hence it cannot be compared solely on the ground that it is predicated of these colors, even though it be not predicated equivocally, and even though it have one first subject, which is a surface, and which is a first subject of the genus “color”, but not of any species of color. For we cannot say which is more colored, white or black, because this comparison would not be in terms of some definite species of color, but in terms of color in general. But in terms of whiteness, which is not divided into various species, all white things may be compared, so that it can be said which one is whiter.
Which motions may be compared
Chapter 4 cont. οὕτω καὶ περὶ κίνησιν ὁμοταχὲς τῷ ἐν ἴσῳ χρόνῳ κινεῖσθαι ἴσον τοσονδί· Similarly in the case of motion: two things are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion. εἰ δὴ τοῦ μήκους ἐν τῳδὶ τὸ μὲν ἠλλοιώθη τὸ δ' ἠνέχθη, ἴση ἄρα αὕτη ἡ ἀλλοίωσις καὶ ὁμοταχὴς τῇ φορᾷ; ἀλλ' ἄτοπον. αἴτιον δ' ὅτι ἡ κίνησις ἔχει εἴδη, Suppose, then, that in a certain time an alteration is undergone by one half of a body's length and a locomotion is accomplished the other half: can be say that in this case the alteration is equal to the locomotion and of the same velocity? That would be absurd, and the reason is that there are different species of motion. ὥστ' εἰ τὰ ἐν ἴσῳ χρόνῳ ἐνεχθέντα ἴσον μῆκος ἰσοταχῆ ἔσται, ἴση ἡ εὐθεῖα καὶ ἡ περιφερής. And if in consequence of this we must say that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference. πότερον οὖν αἴτιον, ὅτι ἡ φορὰ γένος ἢ ὅτι ἡ γραμμὴ γένος; ὁ μὲν γὰρ χρόνος ὁ αὐτός, ἂν δὲ τῷ εἴδει ᾖ ἄλλα, καὶ ἐκεῖνα εἴδει διαφέρει. καὶ γὰρ ἡ φορὰ εἴδη ἔχει, ἂν ἐκεῖνο ἔχῃ εἴδη ἐφ' οὗ κινεῖται What, then, is the reason of this? Is it that locomotion is a genus or that line is a genus? (We may leave the time out of account, since that is one and the same.) If the lines are specifically different, the locomotions also differ specifically from one another: for locomotion is specifically differentiated according to the specific differentiation of that over which it takes place. (It is also similarly differentiated, it would seem, accordingly as the instrument of the locomotion is different: (ὁτὲ δὲ ἐὰν ᾧ, οἷον εἰ πόδες, βάδισις, εἰ δὲ πτέρυγες, πτῆσις. ἢ οὔ, ἀλλὰ τοῖς σχήμασιν ἡ φορὰ ἄλλη;). thus if feet are the instrument, it is walking, if wings it is flying; but perhaps we should rather say that this is not so, and that in this case the differences in the locomotion are merely differences of posture in that which is in motion.) ὥστε τὰ ἐν ἴσῳ ταὐτὸ μέγεθος κινούμενα ἰσοταχῆ, τὸ αὐτὸ δὲ καὶ ἀδιάφορον εἴδει καὶ κινήσει ἀδιάφορον· ὥστε τοῦτο σκεπτέον, τίς διαφορὰ κινήσεως. We may say, therefore, that things are of equal velocity in an equal time they traverse the same magnitude: and when I call it 'the same' I mean that it contains no specific difference and therefore no difference in the motion that takes place over it. So we have now to consider how motion is differentiated: καὶ σημαίνει ὁ λόγος οὗτος ὅτι τὸ γένος οὐχ ἕν τι, ἀλλὰ παρὰ τοῦτο λανθάνει πολλά, εἰσίν τε τῶν ὁμωνυμιῶν αἱ μὲν πολὺ ἀπέχουσαι, αἱ δὲ ἔχουσαί τινα ὁμοιότητα, αἱ δ' ἐγγὺς ἢ γένει ἢ ἀναλογίᾳ, διὸ οὐ δοκοῦσιν ὁμωνυμίαι εἶναι οὖσαι. and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that in the case of equivocal terms sometimes the different senses in which they are used are far removed from one another, while sometimes there is a certain likeness between them, and sometimes again they are nearly related either generically or analogically, with the result that they seem not to be equivocal though they really are. πότε οὖν ἕτερον τὸ εἶδος, ἐὰν ταὐτὸ ἐν ἄλλῳ, ἢ ἂν ἄλλο ἐν ἄλλῳ; καὶ τίς ὅρος; ἢ τῷ κρινοῦμεν ὅτι ταὐτὸν τὸ λευκὸν καὶ τὸ γλυκὺ ἢ ἄλλο—ὅτι ἐν ἄλλῳ φαίνεται ἕτερον, ἢ ὅτι ὅλως οὐ ταὐτό; When, then, is there a difference of species? Is an attribute specifically different if the subject is different while the attribute is the same, or must the attribute itself be different as well? And how are we to define the limits of a species? What will enable us to decide that particular instances of whiteness or sweetness are the same or different? Is it enough that it appears different in one subject from what appears in another? Or must there be no sameness at all? περὶ δὲ δὴ ἀλλοιώσεως, πῶς ἔσται ἰσοταχὴς ἑτέρᾳ ἑτέρα; εἰ δή ἐστι τὸ ὑγιάζεσθαι ἀλλοιοῦσθαι, ἔστι τὸν μὲν ταχὺ τὸν δὲ βραδέως ἰαθῆναι, καὶ ἅμα τινάς, ὥστ' (249b.) ἔσται ἀλλοίωσις ἰσοταχής· ἐν ἴσῳ γὰρ χρόνῳ ἠλλοιώθη. And further, where alteration is in question, how is one alteration to be of equal velocity with another? One person may be cured quickly and another slowly, and cures may also be simultaneous: so that, recovery of health being an alteration, we have here alterations of equal velocity, since each alteration occupies an equal time. ἀλλὰ τί ἠλλοιώθη; τὸ γὰρ ἴσον οὐκ ἔστιν ἐνταῦθα λεγόμενον, ἀλλ' ὡς ἐν τῷ ποσῷ ἰσότης, ἐνταῦθα ὁμοιότης. But what alteration? We cannot here speak of an 'equal' alteration: what corresponds in the category of quality to equality in the category of quantity is 'likeness'. ἀλλ' ἔστω ἰσοταχὲς τὸ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ μεταβάλλον. However, let us say that there is equal velocity where the same change is accomplished in an equal time. πότερον οὖν ἐν ᾧ τὸ πάθος ἢ τὸ πάθος δεῖ συμβάλλειν; Are we, then, to find the commensurability in the subject of the affection or in the affection itself? ἐνταῦθα μὲν δὴ ὅτι ὑγίεια ἡ αὐτή, ἔστιν λαβεῖν ὅτι οὔτε μᾶλλον οὔτε ἧττον ἀλλ' ὁμοίως ὑπάρχει. ἐὰν δὲ τὸ πάθος ἄλλο ᾖ, οἷον ἀλλοιοῦται τὸ λευκαινόμενον καὶ τὸ ὑγιαζόμενον, τούτοις οὐδὲν τὸ αὐτὸ οὐδ' ἴσον οὐδ' ὅμοιον, ᾗ ἤδη ταῦτα εἴδη ποιεῖ ἀλλοιώσεως, καὶ οὐκ ἔστι μία ὥσπερ οὐδ' αἱ φοραί. ὥστε ληπτέον πόσα εἴδη ἀλλοιώσεως καὶ πόσα φορᾶς. εἰ μὲν οὖν τὰ κινούμενα εἴδει διαφέρει, ὧν εἰσὶν αἱ κινήσεις καθ' αὑτὰ καὶ μὴ κατὰ συμβεβηκός, καὶ αἱ κινήσεις εἴδει διοίσουσιν· εἰ δὲ γένει, γένει, εἰ δ' ἀριθμῷ, ἀριθμῷ. In the case that we have just been considering it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that both are alike. If on the other hand the affection is different in the two cases, e.g. when the alterations take the form of becoming white and becoming healthy respectively, here there is no sameness or equality or likeness inasmuch as the difference in the affections at once makes the alterations specifically different, and there is no unity of alteration any more than there would be unity of locomotion under like conditions. So we must find out how many species there are of alteration and of locomotion respectively. Now if the things that are in motion—that is to say, the things to which the motions belong essentially and not accidentally—differ specifically, then their respective motions will also differ specifically: if on the other hand they differ generically or numerically, the motions also will differ generically or numerically as the case may be. ἀλλὰ δὴ πότερον εἰς τὸ πάθος δεῖ βλέψαι, ἐὰν ᾖ τὸ αὐτὸ ἢ ὅμοιον, εἰ ἰσοταχεῖς αἱ ἀλλοιώσεις, ἢ εἰς τὸ ἀλλοιούμενον, οἷον εἰ τοῦ μὲν τοσονδὶ λελεύκανται τοῦ δὲ τοσονδί; ἢ εἰς ἄμφω, καὶ ἡ αὐτὴ μὲν ἢ ἄλλη τῷ πάθει, εἰ τὸ αὐτὸ <�ἢ μὴ τὸ> αὐτό, ἴση δ' ἢ ἄνισος, εἰ ἐκεῖνο <�ἴσον ἢ> ἄνισον; But there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the affections, or in the things altered, to see e.g. whether a certain quantity of each has become white. Or ought we not rather to look for it in both? That is to say, the alterations are the same or different according as the affections are the same or different, while they are equal or unequal according as the things altered are equal or unequal. καὶ ἐπὶ γενέσεως δὲ καὶ φθορᾶς τὸ αὐτὸ σκεπτέον. πῶς ἰσοταχὴς ἡ γένεσις; εἰ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ καὶ ἄτομον, οἷον ἄνθρωπος ἀλλὰ μὴ ζῷον· θάττων δ', εἰ ἐν ἴσῳ ἕτερον (οὐ γὰρ ἔχομέν τινα δύο ἐν οἷς ἡ ἑτερότης ὡς ἡ ἀνομοιότης), And now we must consider the same question in the case of becoming and perishing: how is one becoming of equal velocity with another? They are of equal velocity if in an equal time there are produced two things that are the same and specifically inseparable, e.g. two men (not merely generically inseparable as e.g. two animals). Similarly one is quicker than the other if in an equal time the product is different in the two cases. I state it thus because we have no pair of terms that will convey this 'difference' in the way in which unlikeness is conveyed. ἤ, εἰ ἔστιν ἀριθμὸς ἡ οὐσία, πλείων καὶ ἐλάττων ἀριθμὸς ὁμοειδής· ἀλλ' ἀνώνυμον τὸ κοινόν, καὶ τὸ ἑκάτερον [ποιόν· τὸ μὲν ποιόν,] ὥσπερ τὸ πλεῖον πάθος ἢ τὸ ὑπερέχον μᾶλλον, τὸ δὲ ποσὸν μεῖζον. If we adopt the theory that it is number that constitutes being, we may indeed speak of a 'greater number' and a 'lesser number' within the same species, but there is no common term that will include both relations, nor are there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of an affection by 'more', of a quantity by 'greater.'
Postquam philosophus ostendit in communi, quid requiratur ad hoc quod aliqua sint comparabilia, applicat inventam veritatem ad comparationem motuum, de qua hic intendit. Et primo in communi; secundo comparando motus diversorum generum, ibi: si autem aliud etc.; tertio comparando motus unius generis ad invicem, ibi: quare si quae in aequali et cetera. 940. After pointing out in general what is required in order that things be able to be compared, the Philosopher now applies the truth found to the comparison of motions. First in general; Secondly, by comparing motions that belong to diverse genera, at 941; Thirdly, by comparing one motion to another in the same genus, at 942. Dicit ergo primo, quod sicut in aliis requiritur ad hoc quod sint comparabilia, quod non sint aequivoca, et quod sit idem primum susceptivum, et quod sit eadem species; sic et circa motum aeque velox dicitur illud quod movetur in aequali tempore, per tantum et aequale alterius longitudinis, in hac, idest secundum mutationem eiusdem speciei. He says therefore first (722) that just as in other matters the requirements for comparability are that the things compared be not equivocal, and that there be an identical first receiver, and that they be of the same species, so also in regard to motion, “equally swift” is said of things that are moved in equal time, through such-and-such an equal length, with respect to a change of the same kind. Deinde cum dicit: si autem aliud etc., agit de comparatione motuum diversorum generum. Et dicit secundum praemissa, quod si unum mobile alteretur, aliud vero ducatur, idest secundum locum moveatur, numquid potest dici quod alteratio sit aeque velox loci mutationi? Sed hoc dicere esset inconveniens. Cuius causa est, quia motus habet diversas species, et iam dictum est quod ea quae non sunt unius speciei, non sunt comparabilia. Quia ergo loci mutatio non est eiusdem speciei cum alteratione, non sunt comparabiles velocitates alterationis et loci mutationis. 941. Then at (723) he discusses the comparison of motions in diverse genera. And he asks, in keeping with what went before, “If one mobile be altered and another moved locally, can the alteration be said to be ‘as swift as’ the local motion?” To say “yes” would be unacceptable. The reason is that the two motions are of different species—and it has already been said that things not of the same species cannot be compared. Therefore, since local motion is not of the same species as alteration, the swiftness of the two cannot be compared. Deinde cum dicit: quare si quae in aequali tempore etc., agit de comparatione motuum unius generis in uno genere. Et primo quantum ad loci mutationem; secundo quantum ad alterationem, ibi: de alteratione autem quomodo etc.; tertio quantum ad generationem et corruptionem, ibi: et in generatione autem et cetera. 942. Then at (724) he discusses the comparison of motions in some one species within some one genus. First as to change of place; Secondly, as to alteration, at 949; Thirdly, as to generation and ceasing-to-be, at 954. De augmento autem et diminutione mentionem non facit, quia eadem ratio est in his et in loci mutatione, cum sint et ipsi secundum aliquam magnitudinem. (He makes no mention of growth and decrease, because they share with local motion the common characteristic of being according to some magnitude,) Circa primum tria facit: primo ostendit quid requiritur ad hoc quod duo motus locales sint ad invicem comparabiles; secundo excludit quoddam quod videbatur ad hoc requiri, ibi: aliquando autem in quo etc.; tertio concludit principale intentum, ibi: quare quae in aequali tempore et cetera. In regard to the first he does three things: First he shows what is required in order that two local motions be able to be mutually compared; Secondly, he shows that one factor which seems to be required is not, at 945; Thirdly, he concludes to what he chiefly intended, at 946. Circa primum duo facit: primo concludit inconveniens quod sequeretur si omnes loci mutationes essent comparabiles; secundo assignat causam quare non sint comparabiles, ibi: utrum ergo causa et cetera. About the first he does two things: First he concludes to the impossibility that would follow if all local motions could be compared; Secondly, he tells why not all can be compared at 944. Dicit ergo primo, quod si aeque velocia sunt quae moventur localiter per aequalem magnitudinem in aequali tempore, et omnes loci mutationes contingit esse aeque veloces, sequetur quod sit aequalis rectus et circularis. Quod potest intelligi dupliciter: uno modo de motu recto et circulari; alio modo de linea recta et circulari; et hoc melius est, hoc enim sequitur ex eo quod praemisit. Si enim omnis motus rectus et circularis sunt aeque veloces; sunt autem aeque veloces motus, quando aequales magnitudines pertranseunt in aequali tempore; sequitur quod magnitudo recta et circularis sint aequales. Quod relinquitur pro inconvenienti. 943. He says therefore first (724) that if the equally swift are things moved locally through an equal magnitude in equal time, and if all local motions should be equally swift, it would follow that what is straight is equal to what is circular. Now, this statement may be understood in two senses: first, in respect to a rectilinear motion and a circular one, secondly, in respect to a straight line and a circular one. The latter is the better sense, because it follows from the foregoing. For if all rectilinear and circular motions are equally swift-and they are so when they traverse an equal magnitude in equal time—it follows that a straight line is equal to a circular one, a situation that must be rejected as impossible. Deinde cum dicit: utrum ergo causa etc., inquirit de causa incomparabilitatis motus recti et circularis. Quia enim concluserat quod si sunt aeque veloces, sequitur etiam magnitudines esse aequales, quod inconveniens videtur; posset aliquis dubitare utrum causa huius incomparabilitatis sit ex parte motus, vel ex parte magnitudinum. Et hoc est quod quaerit: utrum causa quare motus rectus non sit aeque velox motui circulari, sit quia loci mutatio est genus continens sub se diversas species (dictum est autem supra quod ea quae sunt diversa secundum speciem, non comparantur); aut causa eius est, quia linea est genus continens sub se rectum et circulare, sicut diversas species. Ex parte autem temporis non potest esse causa huius incomparabilitatis, quia omne tempus est atomus, idest indivisibile, secundum speciem. 944. Then at (725) he investigates the reason why rectilinear motions cannot be compared with circular ones. For since he had concluded that if they are equal, then the magnitudes are equal—which is seen to be impossible—someone might wonder whether the reason for this inability to be compared is due to the motion or to the magnitude. And this is his question: “Is the reason why a straight motion is not as equally swift as a circular one due to the fact that change of place is a genus containing diverse species under it (for it was said above that things of diverse species are not comparable), or is it because line is a genus containing under it straight and circular as species?” Of course, time cannot be the reason, for all time is “atomic,” i.e., indivisible, as to species. Huic ergo quaestioni respondet quod utrumque simul coniungitur; quia ex utraque parte invenitur differentia speciei: ita tamen quod diversitas speciei in loci mutatione causatur ex diversitate speciei in magnitudine super quam est motus. Et hoc est quod dicit, quod si illud super quod movetur, habet species, sequitur quod loci mutatio species habeat. To this question, therefore, he responds that both reasons hold, because in both cases is found a difference of species, but in such a way, nevertheless, that the diversity of species it local motion is due to the diversity of species of the magnitudes in connection with which the motion takes place. And this is what he says, namely, that if that upon which the motion occurs has species, it follows that the local motion will have species. Deinde cum dicit: aliquando autem in quo etc., excludit quoddam quod posset videri esse requirendum ad identitatem speciei et comparabilitatem in motibus localibus. Et dicit quod aliquando loci mutationes diversificantur secundum illud in quo, idest per quod sicut per instrumentum est loci mutatio; sicut si pedes sint quibus aliquid movetur, dicitur ambulatio; si autem sint alae, dicitur volatio. Sed hoc non facit diversitatem speciei in motibus localibus, sed figuris loci mutatio alia: idest, ista diversitas mutationum non est secundum speciem, sed solum secundum quandam figuram motus, ut Commentator exponit. 945. Then at (726) he rejects a factor that might seem to be required for identity of species and comparability in local motions. And he says that sometimes changes of place are diversified by reason of “that in which,” i.e., by reason of that through which, as through an instrument, a local motion takes place; for example, if the feet are the instruments of local motion, it is walking, but if wings are, it is called flying. Yet this does not make for diversity of species in local motions but for a diversity of figure, as the Commentator says. Sed melius potest dici, quod hic intendit dicere quod loci mutatio specie non diversificatur per instrumenta motus, sed per figuras magnitudinis super quam transit motus: sic enim rectum et circulare differunt. Et ratio huius est, quia motus non recipiunt speciem a mobilibus, sed potius a rebus secundum quas mobilia moventur; instrumenta autem se tenent ex parte mobilium, figurae autem ex parte rei in qua est motus. However, it could possibly better be said that Aristotle here intends to say that changes of place are not diversified by reason of the instruments of motion but by reason of the figure of the magnitude traversed. For it is in this way that “straight” and “circular” differ. The reason is that motions are not diversified on account of the mobiles but on account of the things in respect to which the mobiles are moved. Now instruments lean more to the mobile, whereas figures are on the part of that in which the motion occurs. Deinde cum dicit: quare quae in aequali tempore etc., concludit propositum. Et circa hoc tria facit: primo concludit principale propositum; secundo elicit quoddam consideratione dignum ex conclusione praemissa, ibi: et significat ratio haec etc.; tertio inquirit de diversitate speciei, ibi: quando igitur altera est species et cetera. 946, Then at (727) he concludes his proposition. Concerning this he does three things: First he concludes to the main proposition; Secondly, he draws from the conclusion a fact to be considered, at 947; Thirdly, he investigates the problem of diversity of species, at 948. Concludit ergo primo, quod ex quo motus non sunt comparabiles nisi sint unius speciei; et motus locales non sint unius speciei nisi sit eadem magnitudo secundum speciem: sequitur quod illa sint aeque velocia, quae moventur in aequali tempore secundum magnitudinem eandem: sed ita tamen, quod idem accipiatur quod est indifferens specie. Sic enim et motui conveniet quod sit indifferens specie. Et ideo hoc praecipue considerandum est in comparatione motuum, quae sit differentia motus: quia si est differentia genere vel specie, non sunt comparabiles; si autem est differentia secundum accidens, comparabiles sunt. He concludes therefore first (727) that since motions are not comparable unless they are of the same species, and local motions are not of one species unless they traverse the same specific magnitude, it follows that those are equally swift which traverse the same magnitude in equal time, where “same” refers to what is not different in species. For it is in this way that motions, too, do not differ in species, And therefore the main thing to be considered in the question of the comparison of motions is their differences. For if they differ either in genus or in species, they cannot be compared. But if they differ in accidentals, they can be. Deinde cum dicit: et significat ratio haec etc., elicit ex praemissis quoddam consideratione dignum, scilicet quod genus non est aliquid unum simpliciter, species autem est aliquid unum simpliciter. Et hoc significatur ex ratione praecedenti, qua ostensum est quod ea quae sunt unius generis, non sunt comparabilia; quae vero sunt unius speciei, comparabilia sunt; cum tamen supra dictum sit, quod eadem natura comparabilium est: ex quo videtur quod genus non sit una natura, sed species sit una natura. 947. Then at (728) he draws from the foregoing a fact worthy of consideration, namely, that a genus is not something absolutely one, whereas a species is. This is made known first of all from the preceding argument in which it was shown that things not of one genus are not comparable, whereas things of one species are; and secondly, from the preceding lecture, in which it was stated that the nature of comparable things is one. From this it can be gathered that a genus is not one nature, while a species is. Et huius ratio est, quia species sumitur a forma ultima, quae simpliciter una est in rerum natura: genus autem non sumitur a forma aliqua quae sit una in rerum natura, sed secundum rationem tantum; non est enim aliqua forma ex qua homo sit animal, praeter illam ex qua homo est homo. Omnes igitur homines, qui sunt unius speciei, conveniunt in forma quae constituit speciem, quia quilibet habet animam rationalem: sed non est in homine, equo aut asino aliqua anima communis, quae constituat animal, praeter illam animam quae constituit hominem vel equum aut asinum (quod si esset, tunc genus esset unum et comparabile, sicut et species); sed in sola consideratione accipitur forma generis, per abstractionem intellectus a differentiis. The reason for this is that the species is taken from the ultimate form, which is absolutely one in the universe of things, but the genus is not taken from a form that is one in the universe of things but from one that is so in conception only. For the form on account of which man is animal is not distinct from the one on account of which man is man. Therefore, all men who are of one species agree in the form which constitutes their species, because each has a rational soul. But there is not in man, horse, and ass, some common soul which makes them animal, over and above the soul that makes one a man, or a horse, or an ass. (If there were, then the genus would be one and comparable, just as the species.) But it is only in our mental consideration that a generic form is extracted, namely, it is brought about by the intellect’s abstracting from the differences. Sic igitur species est unum quid a forma una in rerum natura existente: genus autem non est unum; quia secundum diversas formas in rerum natura existentes, diversae species generis praedicationem suscipiunt. Et sic genus est unum logice, sed non physice. Consequently a species is one quiddity deriving from a unity of form existing in the universe of things. The genus, however, is not one, because according to the diverse forms existing in the universe of things, diverse species are capable of receiving a same genus as a predicate. Consequently, a genus is one thing logically but not physically. Quia ergo genus quodammodo est unum, et non simpliciter, iuxta genera latent multa: idest, per similitudinem et propinquitatem ad unitatem generis, multorum aequivocatio latet. Now, because a genus, although not purely one, is still in some sense one, the equivocation of many things is often masked on account of their likeness and their closeness to a unity of genus. Sunt autem quaedam aequivocationum multum distantes, in quibus sola communitas nominum attenditur; sicut si canis dicatur caeleste sidus, et animal latrabile. Quaedam vero sunt quae habent quandam similitudinem; sicut si hoc nomen homo dicatur de vero homine et de homine picto, inquantum habet similitudinem quandam veri hominis. Now certain equivocal things are very unlike and possess in common only a name, as when a heavenly body, and the animal which barks, are called “dogs.” Other things, however, have a certain likeness, as when the word “man” is applied to a real man, and to one that is in a painting, on account of the latter’s likeness to a real man. Quaedam vero aequivocationes sunt proximae: aut propter convenientiam in genere (sicut si corpus dicatur de corpore caelesti et de corpore corruptibili, aequivoce dicitur, naturaliter loquendo, quia eorum non est materia una. Conveniunt tamen in genere logico: et propter hanc generis convenientiam videntur omnino non aequivoca esse): aut etiam sunt propinquae secundum aliquam similitudinem; sicut ille qui docet in scholis dicitur magister, et similiter ille qui praeest domui dicitur magister domus, aequivoce, et tamen propinqua aequivocatione propter similitudinem; uterque enim est rector, hic quidem scholarum, ille vero domus. Unde propter hanc propinquitatem vel generis vel similitudinis, non videntur esse aequivocationes, cum tamen sint. Still other equivocations are very close. This may be on account of agreement in genus. For example, when “body” is said of a heavenly body and of a corruptible body, it is equivocation, because naturally speaking the matter is not one. They agree, however, in logical genus, for which reason they appear not to be equivocal. Or it may be on account of some likeness. For example, one who teaches in the schools is called “master.” and so is the head of a house, equivocally; this is by a close equivocation, however, on account of the likeness, for each is a ruler, one in the schools, the other in the house, Hence, on account of their close resemblance in genus or likeness things do not appear to be equivocal which nevertheless are. Deinde cum dicit: quando igitur altera etc., quia dixerat quod considerandum est quae sit differentia motus, utrum scilicet motus differant specie; hic inquirit quomodo differentia speciei accipi possit, tam in motibus quam in aliis. Et quia essentiam speciei significat definitio, quaerit duas quaestiones: unam de specie, et aliam de definitione. 948. Then at (749) because he had said that we must consider the question of the differences of motion, i.e., whether motions differ specifically, he now inquires how specific differences may be taken in motions and in other things as well. And because the definition designates the essence of the species, he poses two questions: one about the species, and one about the definition. Quaerit ergo primo de specie, quando sit iudicanda altera species: utrum ex hoc solo quod eadem natura sit in alio et alio susceptibili, sicut Platonici posuerunt. Sed hoc secundum praemissa non potest esse verum. Dictum est enim quod genus non est simpliciter unum: et ideo differentia speciei non attenditur per hoc quod aliquid idem sit in alio et alio, nisi secundum Platonicos, qui posuerunt genus esse simpliciter unum. Et propter hoc, quasi quaestionem solvens, subiungit: aut si aliud in alio; quasi dicat: non propter hoc est alia species, quia est idem in alio; sed quia est alia natura in alio susceptibili. He first of all asks about species: “When is something to be reckoned of a different species from another? Is it only because the same nature is found in different receivers, as Plato held?” According to the foregoing this cannot be the case. For it has been said that a genus is not absolutely one; therefore a difference of species is not reckoned on the basis that some same thing is in one and another, except for the Platonists who posited that a genus is absolutely one. On this account, as though answering the question, Aristotle adds that a species is different, not because the same thing is in a different subject, but because a different nature is in a different subject. Secundam quaestionem movet de definitione: et est quaestio quid sit terminus, idest, quae sit definitio declarans speciem. Et quia ea quae sunt idem definitione, sunt idem simpliciter, ideo quasi solvens subiungit, quod illud est propria definitio rei, quo possumus discernere utrum sit idem aut aliud, puta album vel dulce. Et hoc quod dico aliud, potest duobus modis accipi, sicut et prius: uno scilicet modo ut album dicatur aliud a dulci, quia in albo invenitur alia natura subiecta quam in dulci; alio modo, quia non solum secundum naturam subiectam differunt, sed omnino non sunt idem. Quae quidem duo sunt eadem cum his quae supra posuit: si idem in alio, aut si aliud in alio. Manifestum est enim quod eadem est ratio identitatis et diversitatis, et in specie et in definitione. The second question is about definition, and it is this: “What is a term, i.e., what is the definition which declares a species?” And because things that have the same definition are absolutely the same, he then, as if answering the question, adds that the proper definition of a thing is that by which we can discern whether some thing is the same or other, e.g. white or sweet. And “other” may be taken in two ways as before: in one way, as meaning that the white is said to be something other than the sweet, because in the white thing is found a subject nature other than the one in the sweet; in another way, as meaning that they differ not only in subject nature but that they are wholly not the same. These two are the same as the two he mentioned above, when he said: “If the same thing is found in things that are other, or if differing things are found in differing things.” For it is clear that there is a same reason of identity and diversity in species and in definition. Deinde cum dicit: de alteratione autem etc., agit de comparatione alterationum. Et circa hoc duo facit: primo ostendit quod una alteratio est aeque velox alteri; secundo inquirit secundum quid aequalitas velocitatis attendatur in alteratione, ibi: sed quid alteratum est et cetera. 949. Then at (730) he discusses the comparison of alterations, About this he does two things: First he shows that one alteration is as equally fast as another; Secondly, he investigates from what aspect equality of quickness in alteration is considered, at 950. Quaerit ergo primo de alteratione, quomodo sit una alteratio aequaliter velox alteri alterationi. Et quod duae alterationes sint aeque veloces, probat. Sanari enim est alterari: contingit autem unum cito sanari, et alium tarde; et contingit etiam quosdam simul sanari: ergo una alteratio est aeque velox alteri; illud enim dicitur aeque velociter moveri, quod in aequali tempore movetur. He asks therefore first about alteration, how one alteration is as equally fast as another. And that two alterations are equally fast, he proves. For being healed is to be altered. But one can be healed swiftly and another slowly, and likewise some come to be healed at the same time. Therefore, one alteration is as equally swift as another, for what is moved in an equal time is said to be moved with equal speed. Deinde cum dicit: sed quid alteratum etc., quia in motu locali, ad hoc quod sit aequalis velocitas, requiritur non solum aequalitas temporis, sed etiam aequalitas magnitudinis quae pertransitur; supposito quod in alteratione aequalitas temporis requiratur ad aequalem velocitatem, inquirit quid aliud requiratur. Et hoc est quod dicit: sed quid alteratum est? Idest, quid est illud, ad quod cum pervenerit alteratio in aequali tempore, possit dici aeque velox? 950. Then at (731), because equality of speed in local motion requires not only equality of time but also of magnitude traversed, and assuming that in alteration equality of time is required for equality of speed, he asks what else is required. And this is what he says: “What is it that must be reached in equal time in order that an alteration be called equally swift?” Et ratio dubitationis est, quia in qualitate, circa quam est alteratio, non invenitur aequale: ut possimus dicere quod quando pervenit ad aequalem quantitatem in aequali tempore, sit aeque velox alteratio; sicut dicebatur in motu locali, et etiam dici potest in augmento et diminutione. Sed sicut in quantitate invenitur aequalitas, ita et in qualitate invenitur similitudo. And the reason for this question is that in quality, with which alteration is concerned, equal is not found, so as to enable us to say that when an equal quantity is reached in equal time there is an equally fast alteration, as indeed happens in local motion, as well as in growth and decrease. But as equality is found in quantity, likeness is found in quality. Huic ergo quaestioni respondet cum subdit: sed sit idem et cetera. Et primo ponit responsionem ad quaestionem: et dicit quod alteratio debet dici aeque velox, si in aequali tempore mutatum sit idem, idest illud quod est alteratum. To this question he responds at (732). And first he answers the question, and says that alterations should be called equally swift if in an equal time it is the same thing which has been changed, i.e., altered. Secundo ibi: utrum ergo etc., movet quaestionem circa positam solutionem: et est quaestio quam primo movet, talis. Cum enim dictum sit quod aeque velox alteratio est, si sit idem quod alteratum est in aequali tempore; in eo autem quod est alteratum duo est considerare, scilicet passionem secundum quam fit alteratio, et subiectum in quo est passio: est ergo quaestio utrum huiusmodi comparationem oporteat accipere secundum identitatem passionis, an secundum identitatem subiecti in quo est passio. 951. Secondly, he raises a question about this answer. Since it has been said that there is an equally swift alteration, if it is the same thing that has been altered in an equal time, and since in that which has been altered there are two things to consider, namely, the quality with respect to which alteration occurred, and secondly, the subject in which the quality exists, the question arises: “Should a comparison of this sort be regarded from the viewpoint of the identity of the quality or of the identity of the subject in which the quality exists?” Secundo ibi: hic igitur etc., solvit quaestionem quantum ad unam partem: et dicit quod in alteratione ex parte passionis duplex identitas attendi debet, ad hoc quod sit aeque velox alteratio. Primo quidem quod sit eadem qualitas secundum speciem: puta ut accipiatur eadem sanitas, ut oculi aut alicuius huiusmodi. Secundo ut eadem qualitas accepta similiter insit, neque magis neque minus. Sed si passio, idest passibilis qualitas, est altera secundum speciem, puta si unum alteratum fiat album et aliud sanetur; in his duabus passionibus nihil est idem, neque aequale, neque simile. Unde secundum diversitatem harum passionum fiunt diversae species alterationis, et non est una alteratio: sicut etiam supra dictum est, quod motus rectus et circularis non sunt una loci mutatio. Et ideo ad comparandum tam loci mutationes quam alterationes, considerandum est quot sint species alterationis vel loci mutationis, utrum scilicet eadem vel plures. Et hoc quidem potest considerari ex rebus in quibus est motus: quia si illa quae moventur, idest secundum quae est motus per se et non secundum accidens, differunt specie, et motus specie differunt; si vero differunt genere, et motus differunt genere; et si numero, et motus differunt numero, ut in quinto dictum est. 952. Then at (734) he answers one part of the question and says that with respect to the quality received in alteration, two types of identity must be considered in order that alterations be equally swift. First, that the same specific quality be involved, for example, the same health, of the eye or of something similar; secondly, that the quality which is taken be present in the same way, and neither more nor less. But if the qualities in question differ specifically, e.g., if one alteration involves becoming white, and another healthy, in these two cases nothing is the same; they are neither equal nor alike. Hence a diversity of these qualities causes a diversity in species of alteration, so that the alterations are not one, just as it was said above that a straight motion and a circular one are not one local motion. Consequently, whenever you wish to compare either local motions or alterations, you have to consider the species of alterations or of local motion to see whether they are the same or many. And this may be considered from the things in which motions occur, for if the things which are moved, i.e., in which motion occurs per se, and not per accidens, differ specifically, then the motions differ specifically; if they differ generically, so do the motions differ generically; if they differ numerically, then also the motions differ numerically, as was pointed out in Book V. Tertio ibi: sed utrum oporteat etc., determinata una parte quaestionis quam moverat, quaerit de alia. Et est quaestio utrum ad hoc quod iudicentur alterationes esse similes vel aeque veloces, oporteat respicere solum ad passionem, si sit eadem; aut etiam oporteat respicere ad subiectum quod alteratur; ita scilicet quod si huius corporis tanta pars sit albata in hoc tempore, et alterius corporis aequalis pars sit albata in eodem vel aequali tempore, dicatur alteratio aeque velox. 953. Thirdly, at (735), having determined one part of the question he raised, he now attacks the other. The question is this: “In order that alterations be adjudged similar or equally swift should regard be paid only to the quality to see if it is the same, or also to the subject which is altered; that is, if a certain portion of this body becomes white in a certain time and an equal part of another becomes white in the same or in equal time, should the alterations be judged equally swift?” Et solvit quod oportet ad utrumque respicere, scilicet ad passionem et subiectum: diversimode tamen. Quia iudicamus alterationem esse eandem vel aliam ex parte passionis, secundum quod est eadem vel alia: sed iudicamus alterationem aequalem vel inaequalem, secundum quod pars subiecti alterati est aequalis vel inaequalis: si enim huius corporis albetur magna pars, alterius autem parva, erit quidem alteratio eadem specie, sed non aequalis. And he answers that attention must be paid to both, i.e., to the quality involved and to the subject, but in different ways. For from the viewpoint of the quality we judge an alteration to be the same or different according to whether the quality is the same or not; but we judge an alteration to be equal or unequal, if the part of the subject altered is equal or unequal: for if a large part of this body becomes white and a small part of another becomes white, the alterations will be specifically the same, but they will not be equal. Deinde cum dicit: et in generatione etc., ostendit quomodo debeat fieri comparatio in generatione et corruptione. Et primo secundum opinionem propriam; secundo secundum opinionem Platonis, ibi: et si est numerus substantia et cetera. 954. Then at (736) he shows how comparison should be made with respect to generation and ceasing-to-be. First, according to his own opinion; Secondly, according to the opinion of Plato, at 955. Dicit ergo primo, quod in generatione et corruptione, ad hoc quod generatio dicatur aeque velox, considerandum est si in aequali tempore sit idem quod generatur et indivisibile secundum speciem: puta si in utraque generatione generetur homo in aequali tempore, est aeque velox generatio. Sed non est aeque velox generatio ex hoc solo quod in aequali tempore generatur animal; quia quaedam animalia propter sui perfectionem indigent maiori tempore ad generationem: sed velocior dicitur esse generatio, si in aequali tempore generetur alterum; puta si in tanto tempore, in quo ex una parte generatur canis, ex alia parte generetur equus, esset equi velocior generatio. He says therefore first (736) that in generation and ceasing-to-be, in order that a generation be called equally swift, we must consider whether in an equal time the same thing is generated and is something indivisible as to species; for example, if a man is begotten in equal time in both generations, they are equally swift. But generations are not equally swift just because an animal is generated in equal time, for some animals on account of their perfection require more time for being generated~ But generation is said to be swifter, if something else is generated in an equal time; for example, if in the time required for the generation of a dog, a horse should be generated, the generation of the horse would be swifter. Et quia in alteratione ex parte passionis dixerat duo consideranda, scilicet si est eadem sanitas, et iterum si similiter existit et neque magis neque minus; hic autem in generatione unum tantum dixit considerandum, scilicet si sit idem quod generatur; huius modo causam assignat dicens: non enim habemus aliqua duo in quibus alteritas, sicut dissimilitudo. Quasi dicat: ideo in generatione hoc solum considerandum utrum sit idem quod generatur, quia in generatione non habemus aliquid quod possit variari per duo, secundum quae attendatur aliqua alteritas; sicut in alteratione accidit dissimilitudo per hoc quod una et eadem qualitas variatur secundum magis et minus: substantia enim, cuius est generari, non recipit magis et minus. And because he had said that, in alteration, from the viewpoint of the quality involved, two things must be considered, namely, whether it is the same health and whether it exists in the same way and not more or less, while here he says that in generation only one thing has to be considered, namely, whether it is the same that is being generated, he now gives the reason for this difference, saying: “For we do not have two things in which there is an otherness called unlikeness.” It is as if he said: “The reason why in generation the only thing to be considered is whether it is the same that is being generated, is that in generation we do not have something that could vary with regard to two things, according to which a difference could be discerned, in the way that unlikeness occurs in alteration through the fact that one and the same quality can vary according to more and less. For a substance, which is the proper terminus of generation, is not capable of more and less.” Deinde cum dicit: et si est numerus etc., agit de comparatione generationis secundum opinionem Platonis, qui ponebat numerum esse substantiam rei, propter hoc quod unum quod est principium numeri, putabat esse idem cum uno quod convertitur cum ente, et rei substantiam significat. Ipsum autem quod est unum, est omnino unius naturae et speciei. Si ergo numerus, qui nihil est aliud quam aggregatio unitatum, sit substantia rerum secundum Platonicos, sequetur quod dicetur quidem maior et minor numerus secundum diversam speciem quantitatis; sed tamen quantum ad substantiam erit similis speciei. Et inde est quod Plato posuit speciem, unum: contraria vero, per quae diversificantur res, magnum et parvum, quae sunt ex parte materiae. Et sic sequetur quod sicut una et eadem sanitas habet duo, inquantum recipit magis et minus; sic etiam et substantia, quae est numerus, cum sit unius speciei ex parte unitatis, habebit aliqua duo, inquantum est maior et minor numerus. Sed in substantia non est commune nomen positum, quod significet utrumque, idest diversitatem quae accidit ex maioritate et minoritate numeri; sicut in passionibus, cum passio plus inest, aut qualitercumque est excellens, dicitur magis, ut puta magis album vel magis sanum; in quantitate autem, cum fuerit excellens, dicitur maius, ut maius corpus aut maior superficies. Sic autem non habemus nomen positum, quo communiter significetur excellentia substantiae, quae est ex maioritate numeri, secundum Platonicos. 955. Then at (737) he discusses the comparison of generations according to the opinion of Plato, who supposed that number is the substance of a thing. For he thought that the “one” which is the principle of number is the substance of a thing. Now what is “one” is entirely of one nature and species. Therefore, if number, which is nothing more than an aggregate of units, is, according to Plato, the substance of things, it follows that a number will be called larger or smaller according to the species of quantity, but yet as to substance it will be of like species. And hence it is that Plato declared that one is the species, but that the contraries through which things differ are “the large and the small,” which are considered from the side of the matter. Accordingly, it will follow that just as one and the same health has two aspects, inasmuch as it receives more and less, so also substance, which is number, since it is of the same species on account of unity, will have two aspects according as the number is larger or smaller. But in substance no general word exists to signify both, i.e., the diversity which arises from the largeness and smallness of number, whereas in qualities, when more of one is in a subject or when it is in any way outstanding, the quality is said to be “more”—for example, “more white” or “more healthy”, while in quantity, excellence is described as “greater,” as a “greater body” or a “greater surface.” But in this sense there is no common word to signify excellence in substance—which is due to the largeness of number, according to the Platonists.
Rules for the comparison of motions
Chapter 5 Ἐπεὶ δὲ τὸ κινοῦν κινεῖ τι ἀεὶ καὶ ἔν τινι καὶ μέχρι του (λέγω δὲ τὸ μὲν ἔν τινι, ὅτι ἐν χρόνῳ, τὸ δὲ μέχρι του, ὅτι ποσόν τι μῆκος· ἀεὶ γὰρ ἅμα κινεῖ καὶ κεκίνηκεν, ὥστε ποσόν τι ἔσται ὃ ἐκινήθη, καὶ ἐν ποσῷ), Now since wherever there is a movent, its motion always acts upon something, is always in something, and always extends to something (by 'is always in something' I mean that it occupies a time: and by 'extends to something' I mean that it involves the traversing of a certain amount of distance: for at any moment when a thing is causing motion, it also has caused motion, so that there must always be a certain amount of distance that has been traversed and a certain amount of time that has been occupied). εἰ δὴ τὸ μὲν Α τὸ κινοῦν, τὸ δὲ Β τὸ κινούμενον, ὅσον δὲ κεκίνηται (250a.) μῆκος τὸ Γ, ἐν ὅσῳ δέ, ὁ χρόνος, ἐφ' οὗ τὸ Δ, ἐν δὴ τῷ ἴσῳ χρόνῳ ἡ ἴση δύναμις ἡ ἐφ' οὗ τὸ Α τὸ ἥμισυ τοῦ Β διπλασίαν τῆς Γ κινήσει, τὴν δὲ τὸ Γ ἐν τῷ ἡμίσει τοῦ Δ· οὕτω γὰρ ἀνάλογον ἔσται. If then, force A has moved B a distance G in a time D, then in the same time the same force A will move 1/2B twice the distance G, and in 1/2D it will move 1/2B the whole distance for G: thus the rules of proportion will be observed. καὶ εἰ ἡ αὐτὴ δύναμις τὸ αὐτὸ ἐν τῳδὶ τῷ χρόνῳ τοσήνδε κινεῖ καὶ τὴν ἡμίσειαν ἐν τῷ ἡμίσει, καὶ ἡ ἡμίσεια ἰσχὺς τὸ ἥμισυ κινήσει ἐν τῷ ἴσῳ χρόνῳ τὸ ἴσον. οἷον τῆς Α δυνάμεως ἔστω ἡμίσεια ἡ τὸ Ε καὶ τοῦ Β τὸ Ζ ἥμισυ· ὁμοίως δὴ ἔχουσι καὶ ἀνάλογον ἡ ἰσχὺς πρὸς τὸ βάρος, ὥστε ἴσον ἐν ἴσῳ χρόνῳ κινήσουσιν. Again if a given force move a given weight a certain distance in a certain time and half the distance in half the time, half the motive power will move half the weight the same distance in the same time. Let E represent half the motive power A and Z half the weight B: then the ratio between the motive power and the weight in the one case is similar and proportionate to the ratio in the other, so that each force will cause the same distance to be traversed in the same time. καὶ εἰ τὸ Ε τὸ Ζ κινεῖ ἐν τῷ Δ τὴν Γ, οὐκ ἀνάγκη ἐν τῷ ἴσῳ χρόνῳ τὸ ἐφ' οὗ Ε τὸ διπλάσιον τοῦ Ζ κινεῖν τὴν ἡμίσειαν τῆς Γ· But if E move Z a distance G in a time D, it does not necessarily follow that E can move twice Z half the distance G in the same time. εἰ δὴ τὸ Α τὴν τὸ Β κινεῖ ἐν τῷ Δ ὅσην ἡ τὸ Γ, τὸ ἥμισυ τοῦ Α τὸ ἐφ' ᾧ Ε τὴν τὸ Β οὐ κινήσει ἐν τῷ χρόνῳ ἐφ' ᾧ τὸ Δ οὐδ' ἔν τινι τοῦ Δ τι τῆς Γ ἀνάλογον πρὸς τὴν ὅλην τὴν Γ ὡς τὸ Α πρὸς τὸ Ε· ὅλως γὰρ εἰ ἔτυχεν οὐ κινήσει οὐδέν· οὐ γὰρ εἰ ἡ ὅλη ἰσχὺς τοσήνδε ἐκίνησεν, ἡ ἡμίσεια οὐ κινήσει οὔτε ποσὴν οὔτ' ἐν ὁποσῳοῦν· εἷς γὰρ ἂν κινοίη τὸ πλοῖον, εἴπερ ἥ τε τῶν νεωλκῶν τέμνεται ἰσχὺς εἰς τὸν ἀριθμὸν καὶ τὸ μῆκος ὃ πάντες ἐκίνησαν. If, then, A move B a distance G in a time D, it does not follow that E, being half of A, will in the time D or in any fraction of it cause B to traverse a part of G the ratio between which and the whole of G is proportionate to that between A and E (whatever fraction of AE may be): in fact it might well be that it will cause no motion at all; for it does not follow that, if a given motive power causes a certain amount of motion, half that power will cause motion either of any particular amount or in any length of time: otherwise one man might move a ship, since both the motive power of the ship-haulers and the distance that they all cause the ship to traverse are divisible into as many parts as there are men. διὰ τοῦτο ὁ Ζήνωνος λόγος οὐκ ἀληθής, ὡς ψοφεῖ τῆς κέγχρου ὁτιοῦν μέρος· οὐδὲν γὰρ κωλύει μὴ κινεῖν τὸν ἀέρα ἐν μηδενὶ χρόνῳ τοῦτον ὃν ἐκίνησεν πεσὼν ὁ ὅλος μέδιμνος. οὐδὲ δὴ τοσοῦτον μόριον, ὅσον ἂν κινήσειεν τοῦ ὅλου εἰ εἴη καθ' αὑτὸ τοῦτο, οὐ κινεῖ. οὐδὲ γὰρ οὐδὲν ἔστιν ἀλλ' ἢ δυνάμει ἐν τῷ ὅλῳ. Hence Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially. εἰ δὲ τὰ <�κινοῦντα> δύο, καὶ ἑκάτερον τῶνδε ἑκάτερον κινεῖ τὸ τοσόνδε ἐν τοσῷδε, καὶ συντιθέμεναι αἱ δυνάμεις τὸ σύνθετον ἐκ τῶν βαρῶν τὸ ἴσον κινήσουσιν μῆκος καὶ ἐν ἴσῳ χρόνῳ· ἀνάλογον γάρ. If on the other hand we have two forces each of which separately moves one of two weights a given distance in a given time, then the forces in combination will move the combined weights an equal distance in an equal time: for in this case the rules of proportion apply. ἆρ' οὖν οὕτω καὶ ἐπ' ἀλλοιώσεως καὶ ἐπ' αὐξήσεως; τὶ μὲν γὰρ τὸ αὖξον, τὶ δὲ τὸ αὐξανόμενον, ἐν ποσῷ δὲ χρόνῳ καὶ ποσὸν τὸ μὲν αὔξει τὸ δὲ αὐξάνεται. καὶ τὸ ἀλλοιοῦν καὶ τὸ ἀλλοιούμενον ὡσαύτως—τὶ καὶ ποσὸν (250b.) κατὰ τὸ μᾶλλον καὶ ἧττον ἠλλοίωται, καὶ ἐν ποσῷ χρόνῳ, ἐν διπλασίῳ διπλάσιον, Then does this hold good of alteration and of increase also? Surely it does, for in any given case we have a definite thing that cause increase and a definite thing that suffers increase, and the one causes and the other suffers a certain amount of increase in a certain amount of time. Similarly we have a definite thing that causes alteration and a definite thing that undergoes alteration, and a certain amount, or rather degree, of alteration is completed in a certain amount of time: καὶ τὸ διπλάσιον ἐν διπλασίῳ· τὸ δ' ἥμισυ ἐν ἡμίσει χρόνῳ (ἢ ἐν ἡμίσει ἥμισυ), ἢ ἐν ἴσῳ διπλάσιον. thus in twice as much time twice as much alteration will be completed and conversely twice as much alteration will occupy twice as much time: and the alteration of half of its object will occupy half as much time and in half as much time half of the object will be altered: or again, in the same amount of time it will be altered twice as much. εἰ δὲ τὸ ἀλλοιοῦν ἢ αὖξον τὸ τοσόνδε ἐν τῷ τοσῷδε αὔξει ἢ ἀλλοιοῖ, οὐκ ἀνάγκη καὶ τὸ ἥμισυ ἐν ἡμίσει καὶ ἐν ἡμίσει ἥμισυ, ἀλλ' οὐδέν, εἰ ἔτυχεν, ἀλλοιώσει ἢ αὐξήσει, ὥσπερ καὶ ἐπὶ τοῦ βάρους. On the other hand if that which causes alteration or increase causes a certain amount of increase or alteration respectively in a certain amount of time, it does not necessarily follow that half the force will occupy twice the time in altering or increasing the object, or that in twice the time the alteration or increase will be completed by it: it may happen that there will be no alteration or increase at all, the case being the same as with the weight.
Postquam philosophus ostendit qui motus sint comparabiles ad invicem, hic docet quomodo comparentur. Et primo in motu locali; secundo in aliis motibus, ibi: sic igitur est in alteratione et cetera. 956. After showing which motions are mutually comparable, the Philosopher now teaches how they are compared: First in local motions; Secondly, in other motions, at 962. Circa primum duo facit: primo ponit ea secundum quae oportet comparari motus locales ad invicem; secundo accipit regulas comparationis secundum praedicta, ibi: si igitur a quod est movens et cetera. About the first he does two things: First he mentions the aspects according to which local motions ought to be mutually compared; Secondly, he sets forth the rules of comparison in the light of the foregoing, at 957. Dicit ergo primo, quod movens localiter semper movet aliquod mobile, et iterum in aliquo tempore, et usque ad aliquam quantitatem spatii. Quod ideo oportet esse, quia sicut in sexto probatum est, semper simul aliquid movet et movit. Probatum est enim ibi, quod omne quod movetur, iam est motum per aliquam partem spatii, et per aliquam partem temporis. Unde sequitur quod et illud quod movetur est aliquod quantum et divisibile, et etiam illud per quod movetur, et tempus in quo movetur. Movens autem non omne est quantum, ut in octavo probabitur: sed tamen manifestum est aliquod quantum esse movens; et de hoc movente hic proponit regulas comparationis. He says therefore first (738) that the mover in local motion always moves some mobile, in some definite time, and through some quantity of space. And this is required, because, as was proved in Book VI, something always moves and has moved, simultaneously. For it was proved there that whatever is being moved has already been moved through some part of a distance and through some part of time. Hence it follows that what is being moved is something quantitative and divisible, as are the distance and the time involved. However, not every mover is quantified, as will be proved in Book VIII; nevertheless, it is clear that some quantitative things are movers and it is in respect to those that he proposes the following rules of comparison, Deinde cum dicit: si igitur a etc., ponit regulas comparationis. Et primo secundum divisionem mobilis; secundo quando movens dividitur, ibi: et si eadem potentia et cetera. 957. Then at (739) he lays down the rules of comparison. First according to division of the mobile; Secondly, when the mover is divided, at 958. Dicit ergo primo: accipiatur aliquod movens quod sit a, et aliquod mobile quod sit b, et longitudo spatii pertransiti quae sit c; et tempus in quo a movet b per c sit d. Si ergo accipiatur aliqua alia potentia movens, aequalis potentiae ipsi a, sequetur quod illa potentia movebit medietatem mobilis quod est b, in eodem tempore per longitudinem quae sit dupla quam c; sed medietatem mobilis movebit per totam longitudinem c, in medietate temporis quod est d. He says therefore first (739): Let A be a mover, and B a mobile, and C the length of space traversed, and D the time in which A moves B through C. If therefore we take another moving power, equal to the power of A, it will follow that it will move half of the mobile B through a distance twice C in the same time; but in half the time D it will move half of mobile B through the entire length C, Ex his igitur verbis philosophi duae regulae generales accipi possunt. Quarum prima est, quod si aliqua potentia movet aliquod mobile per aliquod spatium in aliquo tempore, medietatem illius mobilis per duplum spatium movebit vel aequalis potentia in eodem tempore, vel eadem in alio aequali. From these statements of the Philosopher two general rules may be gathered. The first is that if some power moves a mobile through some certain distance in a given time, then it or an equal power will move half of that mobile through twice the distance in the same time or in an equal time. Alia regula est, quod medietatem mobilis movebit per idem spatium aequalis potentia in medietate temporis. Et horum ratio est, quia sic conservabitur eadem analogia, idest eadem proportio. Manifestum est enim quod velocitas motus est ex victoria potentiae moventis super mobile: quanto autem mobile fuerit minus, tanto potentia moventis magis excedit ipsum: unde velocius movebit. Velocitas autem motus diminuit tempus, et auget longitudinem spatii: quia velocius est quod in aequali tempore pertransit maiorem magnitudinem, et aequalem magnitudinem in minori tempore, ut in sexto probatum est. Ergo secundum proportionem qua subtrahitur a mobili, oportet subtrahi de tempore, vel addi ad longitudinem spatii, dummodo movens sit idem vel aequale. The other rule is that an equal power will move half the mobile over the same distance in half the time. The reason behind these rules is that the same proportion is being kept. For it is clear that the swiftness of a motion results from the victory of the mover’s power over the mobile, because the weaker the mobile the more the strength of the mover prevails over it and the more swiftly will it move the mobile. The swiftness of a motion cuts down on the time and increases the length traversed, for the swifter is what traverses a greater distance in an equal time or an equal distance in less time, as was proved in Book VI. Therefore, according to the same proportion by which the mobile is diminished, either the time is diminished or the length traversed is increased, provided, of course, that the mover is the same or an equal mover. Deinde cum dicit: et si eadem potentia etc., docet comparare motus ex parte moventis: et primo secundum divisionem moventis; secundo secundum oppositam congregationem, ibi: si vero duo et utrumque et cetera. 958. Then at (740) he teaches how motions are to be compared from the viewpoint of the mover, First according to a division of the mover; Secondly, and conversely, according to an assemblage of movers, at 9610 Circa primum tria facit: primo ponit comparationem veram; secundo removet comparationes falsas, ibi: et si e ipsum z etc.; tertio ex hoc solvit rationem Zenonis, ibi: propter hoc Zenonis ratio et cetera. About the first he does three things: First he sets forth a true comparison; Secondly, he rejects some false comparisons, at 959; Thirdly, from this he answers an argument of Zeno, at 960. Dicit ergo primo, quod si aliqua potentia idem mobile movet in eodem tempore per tantum spatium, ipsamet movet medietatem mobilis in medietate temporis per idem spatium; vel in eodem tempore movet medium mobilis per duplum spatium; sicut et de aequali potentia dictum est. Et ulterius, si dividatur potentia, media potentia movebit medietatem mobilis per idem spatium in aequali tempore. Sed hoc intelligendum est, quando potentia est talis quae per divisionem non corrumpitur. Loquitur enim secundum considerationem communem, nondum applicando ad aliquam specialem naturam, sicut et in omnibus quae praemisit. Et ponit exemplum. Si enim accipiatur medietas huius potentiae quae est a, et dicatur e; et accipiatur medietas mobilis quod est b, et dicatur z: sicut a movebat b per c in tempore d, ita e movebit z per idem spatium in aequali tempore; quia et hic etiam servatur eadem proportio virtutis motivae ad corpus ponderosum quod movetur. Unde sequitur quod in aequali tempore fiat motus per aequale spatium, sicut dictum est. He says therefore first (740) that if a power moves the same mobile through a certain distance in a given time, it moves half the mobile the same distance in half the time, or it moves half the mobile through twice the distance in the given original time, as was said of an equal power. Further, if the power be divided, half the power will move half the mobile through the same distance in the given time. However, this must be understood of a mover that is not destroyed by division, for he has been speaking in a general way without making application to the particular natures involved. And he gives an example: Let E be half of power A and let Z be half of mobile B, then just as A moved B through C in time D, so E will move Z through the same distance in the same amount of time, because the same proportion of motive power to body mass moved is preserved. Hence, it follows that in an equal time the motion will traverse an equal distance, as was said. Deinde cum dicit: et si e ipsum z etc., excludit duas falsas comparationes. Quarum prima est, quod addatur ad mobile, et non addatur ad potentiam moventem. Unde dicit quod si e, quod est medietas motivae potentiae, moveat z, quod est medietas mobilis, in tempore d secundum spatium c; non est necessarium quod ipsa potentia dimidiata, quae est e, moveat mobile quod sit in duplo maius quam z, in aequali tempore secundum medietatem spatii quod est c; quia poterit esse quod dimidia potentia duplum mobile nullo modo movere poterit. Sed si posset movere, teneret haec comparatio. 959. Then at (741) he rejects two false comparisons. The first consists in adding to the mobile without adding to the motive power. Hence he says that if E, which is half the motive power, moves Z9 which is half the mobile, a distance C in time D, it is not necessarily true that the halved power E will move a mobile twice Z through half the distance in the given time, for it could happen that the halved power cannot move the doubled mobile at all. But if it can move it, the comparison will hold. Secunda falsa comparatio est, quando dividitur movens, et non dividitur mobile. Et hanc excludit ibi: si vero a etc.: dicens quod si potentia movens quae est a, moveat mobile quod est b, in tempore d, per spatium quod est c; non oportet quod medietas moventis moveat totum mobile quod est b, in tempore d, neque etiam per quamcumque partem spatii c, cuius partis sit proportio ad totum spatium c sicut e converso erat quando comparabamus a ad z, idest totam potentiam motivam ad partem mobilis. Illa enim erat conveniens comparatio, sed hic non: quia potest contingere quod medietas moventis non movebit totum mobile per aliquod spatium. Si enim aliqua tota virtus movet totum mobile, non sequitur quod medietas illius virtutis moveat totum mobile, neque per quantumcumque spatium, neque in quocumque tempore: quia sequeretur quod solus unus homo posset movere navem per aliquod spatium, si potentia trahentium dividatur secundum numerum trahentium, et secundum longitudinem spatii per quod omnes simul trahunt navem. The second false comparison occurs when the mover is divided and the mobile is not divided. This he rejects at (742), saying that if the motive power A moves the mobile B through distance C in time D, it does not necessarily follow that half the motive power will move the entire mobile B in time D through a part of distance C such that this part of C is related to the entire distance C as A was related to Z in our other example. For when A was compared with Z, it was a suitable comparison, but in the present case it is not, for it can happen that half the motive power will not move the whole mobile any distance. For if some whole power moves some whole mobile, it does not follow that half of it will move the same mobile any distance, no matter how much time is allowed. Otherwise it would follow that a man by himself could move a whole ship a certain distance, if the combined power of the shiphaulers is divided by the number of haulers and the distance they haul it be so divided. Deinde cum dicit: propter hoc Zenonis ratio etc., secundum praemissa solvit rationem Zenonis, qui volebat probare quod quodlibet granum milii faciat aliquem sonum, proiectum in terra, quia totus modius milii, quando in terram effunditur, facit aliquem sonum. Sed Aristoteles dicit quod haec Zenonis ratio non est vera, scilicet quod quaelibet pars milii sonet, idest quodlibet granum milii sonum faciat cum cadit in terram: quia nihil prohibet dicere quod granum milii in nullo tempore movet aerem intantum ut faciat sonum, quem aerem movet ad sonum faciendum totius modius cadens. 960. Then at (743) he uses the foregoing to answer an argument of Zeno who wished to prove that each grain of millet falling to the earth makes a sound, because an entire bushel of it, when poured to the earth, makes a sound. But Aristotle says that this argument of Zeno is not true, i.e., that each grain of millet makes a sound when it falls to the earth. For there is no reason why any such part should in any length of time move the air to produce a sound, as does the whole bushel in falling. Et ex hoc possumus concludere quod non est necessarium, quod si aliqua quantacumque pars existens in toto, movet, quod separatim per se existens movere possit: quia pars in toto non est in actu, sed in potentia, maxime in continuis. Sic enim aliquid est ens, sicut et unum; unum autem est quod est in se indivisum et ab aliis divisum: pars autem prout est in toto, non est divisa in actu, sed in potentia tantum: unde non est actu ens neque una, sed in potentia tantum. Et propter hoc etiam non agit pars, sed totum. And from this we can conclude that it is not necessary, if a part existing in a whole causes a motion, that this part, now existing in isolation from the whole, can cause a motion. For in the whole the part is not actual but potential, especially in continua. For a thing is a being in the same way that it is one, and “one” is that which is undivided in itself and divided from others. But a part, precisely as existing in a whole, is not actually divided from it but only potentially; hence it is not actually one but only potentially. For this reason, it is not the part but the whole that acts. Deinde cum dicit: si vero duo, et utrumque etc., ponit comparationem secundum aggregationem moventium. Et dicit quod si sint duo, et utrumque eorum moveat; quorum utrumque per se moveat tantum mobile in tanto tempore per tantum spatium: quando coniunguntur istae duae potentiae moventium, movebunt illud quod est coniunctum ex ponderibus motis, per aequale spatium in aequali tempore: quia in hoc etiam servatur eadem analogia. 961. Then at (744) he sets forth a comparison based on an aggregate of movers and says that if there are two and each of them causes motion and if each by itself is moving its own mobile a certain distance in a given time, then when the two are united they will move the mobiles—which are now joined together—through an equal distance in the same time, because even in this case the same proportion is maintained. Deinde cum dicit: sic igitur est in alteratione etc., ponit easdem comparationis regulas in aliis motibus. Et circa hoc tria facit: primo ostendit divisibilitatem eorum secundum quae attenduntur comparationes motuum; secundo ponit comparationes veras, ibi: in duplo duplum etc.; tertio removet comparationes falsas, ibi: si autem alterans et cetera. 962. Then at (745) he sets forth the same rules of comparison for other motions. About this he does three things: First he shows that the things according to which the comparison of motions must be judged are divisible; Secondly, he sets forth the true comparison, at 963; Thirdly, he rejects some false comparisons, at 964. Dicit ergo primo quantum ad augmentum, quod sunt tria, scilicet augens, et id quod augetur, et tempus: et haec tria habent aliquam quantitatem. Est etiam quarto accipere quantitatem, secundum quam augens auget, et auctum augetur. Et haec etiam quatuor est accipere in alteratione: scilicet alterans, et quod alteratur, et quantitas passionis secundum quam fit alteratio, quae inest secundum magis et minus, et iterum quantitas temporis in quo fit alteratio; sicut et haec quatuor in motu locali inveniebantur. He says therefore first (745), in respect to growth, that there are three things involved, namely, the cause of increase, the thing increased, and the time; and these three have a certain quantity. Also there is a fourth thing to be considered, namely, the quantity of increase produced by the cause and received by the growing thing. And these four things must be considered also in alteration, namely, the cause of alteration, the thing altered, the amount or degree of alteration (which is present according to more and less), and the amount of time. These four, of course, are the same as are involved in local motion. Deinde cum dicit: in duplo duplum etc., ponit comparationes veras. Et dicit quod si aliqua potentia secundum hos motus moveat tantum in tanto tempore, in duplo tempore movebit duplum: et si moveat duplum, hic erit in duplo tempore. Et similiter movebit eadem potentia medium in medio tempore: aut si moveat in medio tempore, erit dimidium quod est motum. Aut si sit dupla potentia, in aequali tempore movebit duplum. 963. Then at (746) he sets forth the true comparison and says that if a power moves something to a certain amount in a given time according to these motions, then it will move to twice the amount in twice the time; and if it moves to twice the amount, it will be in twice the time. Likewise, the same power will move to half the amount in half the time, or if it moves in half the time, then the motion will be to half the amount, Or if there is twice the power, it will move something to twice the amount in an equal time. Deinde cum dicit: si autem alterans etc., excludit falsam comparationem. Et dicit quod si aliqua potentia moveat motu alterationis et augmenti tantum in tanto tempore, non necesse est quod medietas potentiae moveat medietatem in eodem tempore, aut in medio tempore tantundem: sed forte continget quod nihil augmentabit vel alterabit, sicut et in gravi, idest sicut dictum est quod dimidiata potentia non potest movere totum pondus, neque per totum spatium, neque per aliquam eius partem. 964. Then at (747) he dismisses a false comparison and says that if what causes alteration or increase causes a certain amount of increase or alteration respectively in a certain amount of time, it does not necessarily follow that half the force will alter or increase half the object or some given amount in half the time; for it may happen that there will be no alteration or increase at all, the case being the same as with the locally mobile that has weight. Est enim intelligendum, quod hoc quod dicit: in medio medium, aut in aequali duplum, ly duplum et medium (quod in accusativo ponitur) non accipitur pro dimidio vel duplo ipsius mobilis, sed pro dimidio et duplo ex parte rei in qua est motus, scilicet qualitatis aut quantitatis, quae ita se habent in istis duobus motibus, sicut longitudo spatii in motu locali: alioquin non similiter esset in istis motibus et in motu locali. In motu enim locali, dictum est quod si tanta potentia movet tantum mobile, medietas movebit medietatem mobilis: hic autem dicitur quod medietas forte nihil movebit. Sed intelligendum est de toto mobili integro: quia virtus motiva dimidiata non movebit ipsum, neque per tantam quantitatem aut qualitatem, neque per eius medium. It should be observed that when Aristotle says “half will be moved in half or double will be moved in an equal,” “double” and “half” (in the accusative case) refer, not to the mobile but to the sphere of motion, i.e., the quality or the quantity, which are related to alteration and growth as length of distance is related to local motion. For in local motion it was said that if a certain power moves a certain mobile, half will move half the mobile, but here it is said that half might not move anything. But it must be understood that we are speaking of an integral mobile whole, which will not be moved by a halved motive power to any amount of quantity or degree of quality, much less to half.