Authors/Thomas Aquinas/physics/L6/lect8

Lecture 8 Before every “being moved” is a “having been moved,” and conversely

Latin	English
	Lecture 8 Before every “being moved” is a “having been moved,” and conversely
lib. 6 l. 8 n. 1 Postquam philosophus ostendit qualiter sit accipere primum in mutatione et qualiter non, hic ostendit ordinem eorum quae in motu inveniuntur ad invicem: et primo praemittit quoddam necessarium ad propositum ostendendum; secundo ostendit propositum, ibi: ostenso autem hoc et cetera.	826. After explaining how a first is to be taken in motion and how not, the Philosopher now explains the order of precedence among the things present in motion. First he premises facts needed for explaining the proposition; Secondly, he explains the proposition, at 828.
lib. 6 l. 8 n. 2 Dicit ergo primo, quod omne quod mutatur, mutatur in tempore, ut supra ostensum est: sed in tempore aliquo dicitur aliquid mutari dupliciter; uno modo primo et per se, alio modo secundum alterum, idest ratione partis, sicut dicitur aliquid mutari in anno, quia mutatur in die. Hac ergo distinctione praemissa, proponit quod intendit probare: scilicet, si aliquid mutatur primo in aliquo tempore, necesse est quod mutetur in qualibet parte illius temporis. Et hoc probat dupliciter. Primo quidem ex definitione eius quod dicitur primum: hoc enim dicitur primo alicui convenire, quod convenit ei secundum quamlibet suam partem, ut in principio quinti dictum est. Secundo probat idem per rationem. Sit enim tempus in quo primo aliquid movetur xr: et quia omne tempus est divisibile, dividatur secundum k. Necesse est ergo dicere quod in parte temporis quae est xk, aut moveatur aut non moveatur; et similiter de parte quae est kr. Si ergo detur quod in neutra harum partium movetur, sequitur quod neque in toto xr moveatur, sed quiescat in eo: quia impossibile est quod aliquid moveatur in tempore, in cuius nulla parte movetur. Si autem detur quod in una parte temporis moveatur et non in alia, sequetur quod non primo moveatur in xr tempore: quia oporteret quod secundum utramque partem moveretur, et non secundum alteram tantum. Necesse est ergo dicere quod moveatur in qualibet parte temporis quod est xr. Et hoc est quod demonstrare volumus; scilicet quod in quo primo tempore aliquid movetur, in qualibet parte eius movetur.	827. He says therefore first (633 236 b19) that whatever is being changed is being changed in time, as we have explained. But something is being changed in a time in two ways: in one way, first and per se; in another way, by reason of something else, i.e., by reason of a part, as when something is said to be changed in a year, because it is being changed in a day. With this distinction in mind, he states what he intends to prove: namely, that if something is being first moved in a time, it is necessarily being moved in some part of that time. This he proves in two ways: First, from the definition of “first”, for here something is said to be in a thing “first”, if it belongs to it by reason of each and every part, as was said in the beginning of Book V. Secondly, he proves the same thing with an argument: Let XR be the time in which something is being first moved and, since time is divisible, let XR be divided at K. Then of necessity in the part XK of the time, the object is either being moved or not, and likewise for the part KR. Now if it be said that it is being moved in neither of those parts, it follows that it is not being moved in the whole time but is at rest throughout that time, for it is impossible for a thing to be in motion in a time without being in motion in some part of it. But if it be supposed that it is being moved in just one part of the time, it will follow that it is not being first moved in the time called XR; because that would require motion in respect to both parts and not in respect to just one. Therefore, of necessity, it must be in motion in each part of the time XR. And that is what we want to demonstrate: namely, that if something is being first moved in a time, it is being moved in every part of it.
lib. 6 l. 8 n. 3 Deinde cum dicit: ostenso autem hoc etc., procedit ad principale propositum ostendendum. Et circa hoc duo facit: primo inducit demonstrationes ad propositum ostendendum; secundo concludit veritatem determinatam, ibi: quare necesse est et cetera. Circa primum duo facit: primo ostendit quod ante omne moveri praecedit mutatum esse; secundo quod e converso ante quodlibet mutatum esse praecedit moveri, ibi: non solum autem quod mutatur et cetera.	828. Then at (634 236 b32) he sets about proving the main proposition. And about this he does two things: First he introduces the proofs of the proposition; Secondly, he concludes to the truth, at 838. About the first he does two things: First he shows that before each state of being moved there was a state of completed motion; Secondly, that, conversely, before each state of completed motion there was a state of being moved, at 832.
lib. 6 l. 8 n. 4 Primum ostendit tribus rationibus: quarum prima talis est. Detur quod in xr primo tempore aliquod mobile motum sit per kl magnitudinem: manifestum est quod si accipiatur aliud mobile aeque velox, quod simul inceptum est moveri cum ipso, in medietate temporis motum erit per medium magnitudinis. Cum ergo sit aeque velox illud mobile quod ponitur moveri per totam magnitudinem, sequitur quod etiam ipsum in eodem tempore, scilicet in medietate temporis xr, motum est iam per eandem magnitudinem, quae scilicet est pars totius magnitudinis kl. Sequetur ergo quod illud quod movetur, prius est mutatum. Ut autem illud quod hic dicitur manifestius intelligatur, considerandum est quod sicut punctus nominat terminum lineae, ita mutatum esse nominat terminum motus. Quamcumque autem lineam vel partem lineae accipias, semper est dicere quod ante consummationem lineae totius, sit accipere aliquod punctum, secundum quod linea dividatur. Et similiter ante quemlibet motum, et ante quamcumque partem motus, est accipere aliquod mutatum esse: quia dum mobile est in moveri ad aliquem terminum, iam pertransivit aliquod signum, respectu cuius iam dicitur mutatum esse. Sed sicut punctum infra lineam est in potentia ante lineae divisionem, in actu autem quando iam linea est divisa, cum punctum sit ipsa lineae divisio; similiter hoc quod dico mutatum esse infra motum, est in potentia quando motus non ibi terminatur: sed si ibi terminetur, erit in actu. Et quia quod est in actu est notius eo quod est in potentia, ideo Aristoteles probavit quod illud quod continue movetur, iam mutatum est aliquid, per aliud mobile aeque velox, cuius motus iam terminatus est: sicut si quis probaret quod in aliqua linea esset punctum in potentia, per hoc quod alia linea eiusdem rationis esset divisa in actu.	829. He proves the first with three arguments, of which the first is: Let KL be the magnitude through which a mobile has been moved in the first time XR. It is clear that an equally fast mobile, which began its motion with the first one, will have covered half the magnitude in half the time. Since the first mobile (which we have said covers the entire magnitude) is as fast as the second, it follows that even it has in half the time already been moved through, half the magnitude KL. It will follow, therefore, that what is being moved has been previously moved. To get a better understanding of what we mean, it must be considered that just as “point” is a name for the terminus of a line, so “completed motion” is a name for the terminus of a motion. Now, no matter what line or what part of a line you take, it is always true that before the consummation of the whole line, you can take a point according to which the line can be divided. Likewise, before any motion or part of a motion, you can take a “state of completed motion”; because while the mobile is being moved to its terminus, it has already passed a certain stage in respect to which the mobile is said to have been already changed. But just as a point within a line is in potency before the line is actually divided (for a point is the very division of a line), so also the thing called “completed motion” (within a motion) is in potency as long as the motion does not stop there; but if it does stop there, it will be actual. And since what is in act is better known than what is in potency, therefore Aristotle proves his proposition (that what is being continually moved has already been moved) by referring to an equally fast mobile whose motion has already been completed. This is like proving that in a certain line there is a point in potency by showing that a like line has been actually divided.
lib. 6 l. 8 n. 5 Secundam rationem ponit ibi: amplius autem et si in omni etc.: quae talis est. In toto tempore xr, vel in quocumque alio, dicitur aliquid mutatum esse, per hoc quod accipitur ultimum nunc ipsius temporis: non quod in nunc moveatur aliquid, sed quia in nunc terminatur motus. Unde hic non accipit mutatum esse pro eo quod est aliquando moveri, sed pro eo quod est terminari motum. Ideo autem necesse est terminari motum in ultimo nunc temporis mensurantis motum, quia ipsum nunc determinat tempus, idest est terminus ipsius, sicut punctum lineae; et oportet omne tempus esse medium inter duo nunc, sicut linea est inter duo puncta. Quia ergo moveri est in tempore, sequitur quod motum esse sit in nunc, quod est terminus temporis. Et si ita est de motu qui est in toto tempore, oportet etiam quod similiter dicatur de partibus motus, quae sunt in partibus temporis. Iam enim ostensum est quod si aliquid movetur primo in toto tempore, quod movetur in qualibet parte temporis. Quaelibet autem pars temporis accepta terminatur ad aliquod nunc. Oportet enim quod ultimum medietatis temporis sit divisio, idest ipsum nunc, quod dividit inter duas partes temporis. Quare sequitur quod illud quod movetur per totum, sit prius motum in medio, propter nunc quod determinat medium. Et eadem ratio est de qualibet alia parte temporis. Qualitercumque enim dividatur tempus, semper invenietur quaelibet pars temporis determinari a duobus nunc: et post primum nunc temporis mensurantis motum, quodcumque aliud nunc accipiatur, in eo iam motum est; quia illud nunc, quodcumque accipiatur, est terminus temporis mensurantis motum. Quia ergo omne tempus divisibile est in tempora; et omne tempus est medium inter duo nunc; et in omni nunc, quod est ultimum temporis mensurantis motum, aliquid motum est, sicut probatum est: sequitur quod omne quod mutatur sit infinities mutatum; quia mutatum esse est terminus motus, sicut punctum lineae et nunc temporis. Sicut ergo in qualibet linea est signare infinities punctum ante punctum, et in quolibet tempore infinities nunc ante nunc, propter hoc quod utrumque est divisibile in infinitum; ita in quolibet moveri est signare infinities mutatum esse, quia motus est in infinitum divisibilis, sicut linea et tempus, ut supra probatum est.	830. The second argument, which he gives at (635 237 a3), is this: In the whole time XR or in any other, something is said to have been changed by the very fact that a final “now” of the time is taken, not that something is being moved in that “now”, but that the motion is terminated then. Hence “having been moved” is taken here not for that which is at some time being moved but for the fact that the motion is ended. Now the reason why the motion must be terminated in the final “now” of the time that measures the motion is that that “now” terminates the time, just as a point terminates a line. And all time is midway between two “now’s”, just as a line is between two points. Therefore, since “being moved” occurs in time, it follows that “having been moved” occurs in the “now” which is the terminus of time. And if that is the case with a motion in a whole period of time, the same must be true of the parts of motion that occur in the parts of time. Now, we have already shown that if something is being first moved in the whole time, it is being moved in each part of the time. But whichever part of time you take, it is terminated at some “now”. For the terminus of half of the time is the “now” which divided the time into two parts. Therefore, it follows that what is being moved through the whole is previously moved at the middle of time, on account of the “now” which determines the middle. And the same reasoning applies to any part of time. For no matter how the time is divided, it will always be found that each part of the time is determined by two “now’s”, and after the first “now” of the time measuring the motion, no matter which other “now” is taken, the object has already been moved in that part of the time, for that “now”—whichever it is—is the terminus of the time measuring the motion. Now, because every period of time is divisible into times and each period exists between two “now’s”, and because in any “now” that happens to be the ending of a time measuring the motion, something has been moved, it follows that whatever is being changed has been changed an infinite number of times, because “having been changed” is the terminus of a motion, just as a point is of a line and a “now” is of a time. Therefore, just as it is possible in any line to pick out point ahead of point ad infinitum and in any period of time “now” before “now” (because both line and time are divisible ad infinitum), so in any “being moved” it is possible to pick out infinitely many “having been moved’s”, because motion, too, is divisible ad infinitum, just as the line and time, as was previously proved.
lib. 6 l. 8 n. 6 Tertiam rationem ponit ibi: amplius autem si id quod continue mutatur etc.: quae talis est. Omne quod mutatur, si non corrumpitur neque pausat a mutatione, idest neque desinit moveri, quasi continue mutatum, necesse est quod in quolibet nunc temporis in quo movetur, vel mutetur vel sit mutatum. Sed in nunc non mutatur, ut supra ostensum est: ergo necesse est quod in quolibet nunc temporis mensurantis motum continuum sit mutatum. Sed in quolibet tempore sunt infinita nunc, quia nunc est divisio temporis, et tempus est in infinitum divisibile: ergo omne quod mutatur est infinities mutatum. Et ita sequitur quod ante omne moveri sit mutatum esse, non quasi extra ipsum moveri existens, sed in ipso, ut terminans aliquam partem eius.	831. The third argument is in (636 237 a11): In the case of anything that is being changed (if it is not ceasing-to-be and does not cease to be moved, but is being continually changed), it is necessary that in each “now” of the time in which it is being moved, it is being changed or has been changed. But in the “now” nothing is being changed, as we have shown. Therefore, in each “now” of the time which measures continuous motion, the object has been changed, But in any portion of time there are an infinitude of “now’s”, because the “now” divides time, and time is infinitely divisible. Therefore, everything that is being changed has been changed an infinite number of times. And so it follows that before every state called “being moved” is a state called “having been moved”, which, however, does not exist outside the state of “being changed” but is in it and terminates a part of it.
lib. 6 l. 8 n. 7 Deinde cum dicit: non solum autem quod mutatur etc., probat quod e converso ante omne mutatum esse, praecedat mutari. Et primo ex parte temporis; secundo ex parte rei secundum quam est motus, ibi: amplius autem in magnitudine et cetera. Circa primum tria facit: primo proponit propositum; secundo demonstrat quoddam necessarium ad probandum propositum, ibi: omne enim quod ex quodam etc.; tertio inducit probationem principalis propositi, ibi: quoniam igitur et cetera. Dicit ergo primo quod non solum omne quod mutatur necesse est mutatum esse iam, sed etiam omne quod mutatum est necesse est prius mutari: quia mutatum esse est terminus eius quod est moveri. Unde oportet quod ante mutatum esse praecedat moveri.	832. Then at (637 237 a17) he proves that on the other hand a state of “being changed” precedes each state of “having been changed”. First he proves it from the viewpoint of the time; Secondly, from the viewpoint of the sphere in which the motion occurs, at 836. About the first he does three things: First he states the proposition; Secondly, he proves certain things needed for proving the proposition, at 833. Thirdly, he gives the proof of the main proposition, at 835. He says therefore first that not only is it true that whatever is being changed had already been changed, but that every state of “having been changed” must be preceded by a state of “being changed”, because the former is the terminus of the latter. Therefore, every “having been changed” must be preceded by a “being changed”.
lib. 6 l. 8 n. 8 Deinde cum dicit: omne enim etc., ponit quoddam necessarium ad propositi probationem, scilicet quod omne quod mutatur ex quodam in quiddam, sit mutatum in tempore. Sed advertendum quod hic mutatum esse non est idem quod terminari motum: supra enim ostensum est quod illud temporis, in quo primo dicitur mutatum esse, est indivisibile. Sed accipitur hic mutatum esse, secundum quod significat quod aliquid prius movebatur; quasi dicat: omne quod movebatur, movebatur in tempore. Et hoc probat sic. Si hoc non est verum, sit aliquid mutatum ex a in b, idest ex uno termino in alterum, in ipso nunc. Hoc posito, sequitur quod quando est in ipso a, idest in termino a quo, in eodem nunc nondum est mutatum: quia iam supra ostensum est, quod illud quod mutatum est, quando mutatum est, non est in termino a quo, sed magis in termino ad quem; sequeretur ergo quod simul esset in a et in b. Oportet ergo dicere quod in alio nunc sit in a, et in alio nunc sit mutatum. Sed inter quaelibet duo nunc est tempus medium, quia duo nunc non possunt esse sibi coniuncta immediate, ut supra ostensum est. Relinquitur ergo quod omne quod mutatur, mutatur in tempore.	633. Then at (638 237 a19) he states something needed for his proof of the proposition, i.e., that whatever is being changed from something to something was changed in time. But note carefully that here the words, “was changed”, do not refer to the termination of motion, for it was explained above that the time in which a thing “was changed” is an indivisible. But here “was changed” signifies that something was previously being moved, as though he said: “Whatever was being moved was being moved in time”. This he now proves: If our proposition is not true, then let there be something that was changed from A to B, i.e., from one term to another, in a “now”. From this it follows that when it is in A, i.e., in the terminus a quo in the same “now” it was not yet changed, because it has already been proved that what was changed, when it was being changed is not in the terminus a quo but more in he terminus ad quem. Otherwise, it would follow that it was at once in A and in B. Therefore, it is necessary to say that in one “now” it is in A, and in another it was being changed. But between two “now’s” there is a time, because two “now’s” cannot be immediately connected, as we have shown. What remains, therefore, is that whatever is being changed is being changed in time.
lib. 6 l. 8 n. 9 Videtur autem quod hic concluditur habere instantiam in generatione et corruptione, inter quorum terminos non est aliquod medium. Si enim inter nunc in quo est in termino a quo, et inter nunc in quo est in termino ad quem, sit tempus medium, sequetur quod aliquid sit medium inter esse et non esse; quia in illo medio tempore, id quod mutatur neque esset ens, neque non ens. Sed quia ratio quae hic ponitur demonstrativa est, oportet quod hic dicitur aliquo modo etiam in generatione et corruptione salvari: ita tamen quod aliquo modo etiam huiusmodi mutationes sint momentaneae, cum non possit esse aliquod medium inter extrema earum. Est igitur dicendum quod illud quod mutatur de non esse in esse, vel e converso, non est simul in non esse et esse: sed sicut in octavo dicetur, non est dare ultimum instans, in quo id quod generatur sit non ens; sed est dare primum instans in quo est ens, ita quod in toto tempore praecedenti illud instans, est non ens. Inter tempus autem et instans quod terminat motum, non est aliquod medium: et sic non oportet quod sit medium inter esse et non esse. Sed quia tempus quod praecedit instans in quo primo est quod generatur, mensurat aliquem motum, sequitur quod sicut illud instans in quo primo est quod generatur, est terminus praecedentis temporis mensurantis motum, ita incipere esse est terminus praecedentis motus. Si ergo generatio dicatur ipsa inceptio essendi, sic est terminus motus, et sic est in instanti: quia terminari motum, quod est mutatum esse, est in indivisibili temporis, ut supra ostensum est. Si autem generatio accipiatur ipsa inceptio essendi cum toto motu praecedente cuius est terminus, sic non est in instanti, sed in tempore: ita quod in toto tempore praecedenti est non ens illud quod generatur, et in ultimo instanti est ens. Et similiter dicendum est de corruptione.	334. But it seems that this conclusion has no application in generation and ceasing-to-be, between whose two termini there is nothing intermediate. For if between the “now” in which something is at the terminus a quo and the “now” in which it is at the terminus ad quem a period of time occurs, it will follow that there is something between being and non-being, because in that intermediate time the subject of change would be neither being nor non-being. Nevertheless, because the argument which Aristotle gives here is demonstrative, it must be said that it applies somehow even to generation and ceasing-to-be but in the sense that such changes are also instantaneous, since there can be no medium between the termini. So it must be said that whatever is being changed from non-being to being or vice versa is not in being and non-being at the same time. But, as will be said in Book VIII, there is no final instant in which what is generated is a non-being, but there is a first instant in which it is a being, so that in the entire time preceding that instant, it is non-being. However, between that “now” and the time preceding, there is nothing intermediate, so that between being and non-being there is no medium. Now, since the time which precedes the instant in which something is generated first, is the measure of some motion, it follows that just as that instant in which something is first generated is the terminus of the preceding time that measures the motion, so the first instant of the being of the thing generated is the terminus of a preceding change. If, therefore, generation is said to be the very beginning of being, it must be the terminus of a motion, and thus it takes place in an instant, because a motion’s being terminated—which is the same as having been changed—occurs in an indivisible of time, as we have shown. However, if generation is taken as the very beginning of being plus the entire preceding motion of which it is the terminus, then it occurs not in an instant but in time, so that what is being generated is a non-being during the entire preceding time and a being in the final instant. And the same applies to ceasing-to-be.
lib. 6 l. 8 n. 10 Deinde cum dicit: quoniam igitur in tempore etc., probat principale propositum tali ratione. Omne quod mutatum est, in tempore mutabatur, ut probatum est: omne autem tempus est divisibile: quod autem in aliquo tempore mutatur, in qualibet parte illius temporis mutatur: ergo oportet dicere, quod illud quod mutatum est in toto aliquo tempore, mutabatur prius in medietate temporis, et iterum in medietate medietatis: et sic semper procedetur, propter hoc quod tempus est in infinitum divisibile. Ergo sequitur quod omne quod mutatum est, prius mutabatur: et ita ante omne mutatum esse praecedit mutari.	835. Then at (639 237 a25) he proves the main proposition with the following reason: Whatever has been changed was being changed in time, as we have proved; but time is divisible and whatever is being changed in time is being changed in part of time. Therefore, it is necessary to say that what has been changed in some entire period of time was previously being changed during half of the time and again during half of that half and so on, because time is divisible infinitely. Therefore, it follows that what has been changed was previously being changed. Consequently, before every state of “having been changed” there is a previous state of “being changed”.
lib. 6 l. 8 n. 11 Deinde cum dicit: amplius autem in magnitudine etc., ostendit idem, ratione accepta ex parte eius secundum quod mutatur. Et primo quantum ad motus qui sunt in quantitate; secundo quantum ad alias mutationes, ibi: eadem enim demonstratio est et cetera. Dicit ergo primo, quod hoc quod dictum est ex parte temporis, communiter ad omnem mutationem, manifestius potest accipi ex parte magnitudinis: quia magnitudo manifestior est quam tempus, et magnitudo continua est sicut et tempus, et in ea aliquid mutatur, scilicet illud quod movetur secundum locum, vel quod movetur secundum augmentum et decrementum. Sit ergo aliquid mutatum ex c in d. Non autem potest dici quod totum quod est cd sit indivisibile; quia oportet quod cd sit pars alicuius magnitudinis, sicut motus qui est ex c in d est pars totius motus: similiter enim dividitur magnitudo et motus, ut supra ostensum est. Si autem aliquod indivisibile sit pars magnitudinis, sequitur quod duo impartibilia erunt immediate coniuncta; quod est impossibile, ut supra ostensum est. Non ergo potest dici quod totum cd sit indivisibile. Ergo necesse est quod illud quod est inter c et d, sit quaedam magnitudo, et per consequens quod in infinitum dividi possit. Sed semper prius mutatur in parte magnitudinis, quam sit mutatum per totam magnitudinem. Ergo necesse est omne quod mutatum est, prius mutari; sicut necesse est quod ante quamlibet magnitudinem totam, sit pars eius.	836. Then at (640 237 a28) he proves the same point with an argument based on the sphere of motion. First as to motions in quantity; Secondly, as to other changes, at 837. He says therefore first (640 237 a28) that what was said, from the viewpoint of time, to be common to every change, becomes clearer from the viewpoint of magnitude, for magnitude is better known than time, and magnitude is continuous, as a line, and in it something is changed, namely, that which is according to place, or according to increase and decrease. Therefore, consider something changed from C to D. Now, it cannot be said that the whole of CD is indivisible, because CD has to be part of a magnitude, just as the motion from C to D is part of a whole motion, for there is a correspondence between division of magnitude and division of motion, as we have shown. But if an indivisible is a part of a magnitude, it follows that two indivisibles are immediate neighbors—which is impossible, as we have shown. Therefore, the whole CD cannot be an indivisible, Consequently, that which is between C and D is a magnitude and can be infinitely divided. And something is always first changed in part of a magnitude before it has been changed throughout the entire magnitude. Therefore, anything that has been changed was previously being changed, just as before any whole magnitude there are its parts.
lib. 6 l. 8 n. 12 Deinde cum dicit: eadem enim demonstratio etc., ostendit quod idem necesse est esse in illis mutationibus, quae non sunt secundum aliqua continua; sicut de alteratione, quae est inter contrarias qualitates, et de generatione et corruptione, quae sunt inter contradictorie opposita. Licet enim in his non possit hoc demonstrari ex parte rei secundum quam est motus, accipietur tamen tempus in quo sunt huiusmodi mutationes, et eodem modo procedetur. Sic igitur in tribus mutationibus, scilicet alteratione et corruptione et generatione, habet locum sola prima ratio: in aliis autem tribus, scilicet augmento et decremento et loci mutatione, habet locum utraque.	837. Then at (641 237 a35) he shows that the same point is true in those changes which do not take place in terms of a continuum; for example, alteration, which is between contrary qualities, and generation and ceasing-to-be, which are between contradictories. And although in those changes the demonstration is not derived from things in which the motion is, yet it is possible to take the time in which the changes occur, and then the demonstration will proceed the same way. Thus in the three changes, which are alteration, generation and ceasing-to-be, only the first argument holds, while in the other three, namely, growth, decrease and local motion, both arguments hold.
lib. 6 l. 8 n. 13 Deinde cum dicit: quare necesse etc., concludit principale propositum: et primo in communi; secundo specialiter quantum ad generationem et corruptionem, ibi: manifestum igitur et cetera. Concludit ergo primo ex praemissis, quod necesse est omne mutatum prius mutari, et omne quod mutatur prius esse mutatum. Et sic verum est dicere quod hoc ipso quod est mutari, prius est mutatum esse: et iterum, hoc ipso quod est mutatum esse, est prius mutari. Et ita manifestum fit quod nullo modo comprehenditur aliquid primum. Et huius causa est, quia in motu non coniungitur impartibile impartibili, ita quod totus motus componatur ex impartibilibus: quia si hoc esset, esset accipere aliquod primum. Hoc autem non est verum: quia motus est divisibilis in infinitum, sicut etiam et lineae, quae in infinitum diminuuntur per divisionem, et in infinitum augmentantur per additionem oppositam diminutioni; dum scilicet quod subtrahitur ab uno, alteri additur, ut in tertio est ostensum. Manifestum est enim in linea, quod ante quamlibet partem lineae est accipere punctum in medio illius partis; et ante illud punctum medium est accipere aliquam partem lineae; et sic in infinitum. Non tamen linea est infinita; quia ante primum punctum lineae non est aliqua pars lineae. Et similiter considerandum est in motu: quia cum quaelibet pars motus sit divisibilis, ante quamlibet partem motus est accipere indivisibile aliquid in medio illius partis, quod est mutatum esse; et ante illud indivisibile est accipere partem motus; et sic in infinitum. Non tamen sequitur quod motus sit infinitus: quia ante primum indivisibile motus, non est aliqua pars motus. Illud tamen primum indivisibile non dicitur mutatum esse, sicut nec primum punctum lineae dicitur divisio.	838. Then at (642 237 b3) he concludes to the main proposition: First, in general; Secondly, with special application to generation and ceasing-to-be, at 839. He concludes therefore first (642 237 b3) from the foregoing that everything which has been changed was previously being changed, and that everything which is being changed has previously been changed. Consequently, it is true that a state of “having been changed” preceded a state of “being changed”, and vice versa. And so it is clear that a first something cannot be definitely pointed to. The reason for this is that in motion an indivisible is not joined to an indivisible so as to make a motion be composed of indivisibles, because, if that were the case, we could discover a first. But it is not true, for motion is infinitely divisible just as a line is, which can be infinitely decreased by division and increased by addition opposite to the decrease, in the sense that what is taken from one is being added to another, as was shown in Book III. For it is evident that in a line, before each part of a line, one can take a point in its midst, and before that midpoint is a part of the line, and so on ad infinitum. However, the line is not infinite, because no part of the line is in front of the first point of the line. Well, the same thing is true of motion. For since each part of motion is divisible, before each part of the motion there is in the midst of that part an indivisible, which is called “having been changed”, and before that indivisible there is a part of the motion, and so on ad infinitum. Yet it does not follow that the motion is infinite, cause in front of the first indivisible of motion there was no part of motion. But note that the first indivisible is not one called “having been changed”, any more than the first point of a line is a dividing point.
lib. 6 l. 8 n. 14 Deinde cum dicit: manifestum igitur etc., concludit idem specialiter in generatione et corruptione. Et hoc ideo, quia aliter se habet mutatum esse ad mutari in generatione et corruptione, et aliter in aliis. In aliis enim mutatum esse et mutari est secundum idem, sicut alteratum esse et alterari est secundum album. Nam alterari est mutari secundum albedinem, alteratum autem esse est mutatum esse secundum albedinem: et idem dicendum est in motu locali, et augmento et decremento. Sed in generatione secundum aliud est mutatum esse, et secundum aliud mutari. Nam mutatum esse est secundum formam: mutari vero non est secundum negationem formae, quae non suscipit magis et minus secundum se; sed mutari est secundum aliquid adiunctum negationi, quod suscipit magis et minus, quod est qualitas. Et ideo generatum esse est terminus eius quod est alterari, et similiter corruptum esse. Et quia motus denominatur a termino ad quem, ut in principio quinti dictum est, ipsum alterari, quia habet duos terminos, scilicet formam substantialem et qualitatem, dupliciter nominatur; quia potest dici et alterari, et fieri et corrumpi. Et hoc modo accipit hic fieri et corrumpi pro ipso alterari, secundum quod terminatur ad esse vel non esse. Unde dicit quod illud quod factum est, necesse est prius fieri, et illud quod fit, necesse est factum esse, quaecumque tamen sunt divisibilia et continua. Quod quidem ponitur, ut Commentator dicit, ad excludendum quaedam quae indivisibiliter fiunt absque motu continuo, sicut intelligere et sentire: quae etiam non dicuntur motus nisi aequivoce, ut in tertio de anima dicitur. Vel potest dici aliter, quod hoc philosophus addidit ut accipiatur generatio cum toto motu continuo praecedente.	839. ‘Then at (643 237 b9) he comes to the same conclusion with reference to generation and ceasing-to-be. And he makes a special point of these changes, because the relation of “having been changed” to “being changed” in generation and ceasing-to-be is not the same as it is in other changes. For in the others, the state of “having been changed” and the state of “being changed” occur in respect to the same thing; for example, to whiteness, in the case of alteration. For “to be being altered” is to be being changed in respect to whiteness, and “to have been altered” is to have been changed in regard to whiteness; and the same is true in local motion, in growth and in decrease. But in generation “having been changed” refers to one thing and “being changed” to another. For the former is based on the form, but the latter, though not based on negation of a form (which is not of itself susceptible of more and less) is based on something joined to such a negation, something, that is, which is susceptible of more and less, namely, a quality. Therefore, “to have been generated” is the terminus of “being altered” and the same is true of “having been corrupted”. And because motions get their name from the terminus ad quem, as we have said in the beginning of Book V, “to be altered” (since it has two termini, namely, substantial form and quality) has two names: for it can be called “to be altered”, and “to come to be and cease to be”. And this is the sense in which coming-to-be and ceasing-to-be are substituted for “being altered”, i.e., because the alteration terminates at being or non-being. And consequently, Aristotle says that what has been made was previously being made, and what is being made must necessarily have been made, provided that divisible and continuous things are involved. And Aristotle makes that addition (as the Commentator says) in order to exclude things that indivisibly come to be without continuous motion; for example, understanding and sensing, which are motions only in an analogous sense, as will be shown in Book III of On the Soul. But it could be that Aristotle made this addition in order to show that generation should include the entire continuous motion that precedes it.
lib. 6 l. 8 n. 15 Sed id quod fit, prius factum esse, diversimode invenitur in diversis. Quaedam enim sunt simplicia, quae habent simplicem generationem, sicut aer aut ignis: et in istis non generatur pars ante partem, sed simul generatur et alteratur totum et partes. Et in talibus id quod factum est, ipsummet prius fiebat; et quod fit, ipsummet prius factum est, propter continuitatem alterationis praecedentis. Quaedam vero sunt composita ex dissimilibus partibus, quorum pars generatur post partem, sicut in animali prius generatur cor, et in domo fundamentum: et in istis quod fit, prius factum est, non ipsummet, sed aliquid eius. Et hoc est quod subdit, quod non semper id quod fit, prius ipsummet factum est, sed aliquando aliquid eius factum est, sicut fundamentum domus. Sed quia oportet devenire ad aliquam partem quae tota simul fit, oportet quod in aliqua parte id quod fit, factum sit secundum aliquem terminum acceptum in alteratione praecedenti: sicut dum generatur animal iam factum est cor, et dum generatur cor iam factum est aliquid; non quidem aliqua pars cordis, sed aliqua alteratio facta est, ordinata ad generationem cordis. Et sicut dictum est de generatione, ita intelligendum est de corruptione. Statim enim ei quod fit et corrumpitur, inest quoddam infinitum, cum sit continuum; quia ipsum fieri et ipsum corrumpi continuum est. Et ideo non est fieri, nisi aliquid factum sit prius: neque est aliquid factum esse, nisi fiat prius. Et similiter dicendum est de corrumpi et de corruptum esse. Semper enim corruptum esse est prius ipso corrumpi, et corrumpi est prius hoc quod est corruptum esse. Unde manifestum est quod omne quod factum est, necesse est prius fieri; et omne quod fit, necesse est prius factum esse aliquo modo. Et hoc ideo, quia omnis magnitudo et omne tempus sunt in infinitum divisibilia. Et ideo in quocumque tempore fit aliquid, hoc non erit sicut in primo, quia erit accipere partem priorem. Et hoc quod dictum est de generatione et corruptione, intelligendum est etiam de illuminatione, quae est terminus motus localis corporis illuminantis, sicut generatio et corruptio est terminus alterationis.	840. But the statement “what is being made has been previously made” applies in different ways to different things. For some things, such as air and water, are simple and have simple generation—in these cases, part is not generated after part, but the whole and the parts are altered and generated at once. And it is in such that what has been made was previously being made and what is being made has been previously made, on account of the preceding alteration being continuous. But other things are composites of unlike parts. In these cases, part is generated after part, as in an animal the heart is first generated, and in a house the foundation. In such things what is being made was not itself previously made, but a part was. And this is what he adds, namely, that it is not always so that what is being made has been itself previously made but something pertaining to it has been made, as the foundation of a house. But since we must come to a part that is entirely being made at once, then in some part, that which is being made has been made in relation to a terminus taken in the preceding alteration; for example, in the generation of an animal, the heart has already been made and while the heart is being generated, something has already been made—not indeed that there has been made some part of the heart, but some alteration ordained to the generation of the heart. And what has been said of generation is to be understood with regard to ceasing-to-be. For immediately there is in something that is produced in being and is corrupted, something infinite, since it is continuous. For the very coming-to-be and the ceasing-to-be are continuous. Therefore, there is no “being produced in being”, unless something has been previously made, and nothing has been made unless it was previously being produced in being. And the same is true of ceasing-to-be and having ceased-to-be. For a “having-ceased-to-be” is always prior to a “ceasing-to-be” and a “ceasing-to-be” prior to a “having ceased-to-be”. From this it is evident that whatever has been made was previously being made, and that all that is being made has in some way previously been made. And the reason is that every magnitude and every period of time are infinitely divisible. Consequently, in whatever period of time something comes to be, it is not coming to be in that time as in a first time, because it always possible to find a period previous. And what we have said of generation and ceasing-to-be is true also of illumination, which is the termination of the local motion of the illuminating body, just as generation and ceasing-to-be is the terminus of an alteration.