Authors/Thomas Aquinas/physics/L8/lect21

Lecture 21 Limitations of a finite mover

Latin	English
	Lecture 21 Limitations of a finite mover
lib. 8 l. 21 n. 1 Postquam philosophus ostendit qualis sit primus motus, hic ostendit quale sit primum movens. Et dividitur in partes duas: primo dicit de quo est intentio; secundo exequitur propositum, ibi: horum autem unum quidem et cetera. Dicit autem primo, quod cum dictum sit supra quod primum movens est immobile, nunc dicendum est quod primum movens est indivisibile et nullam habens magnitudinem, sicut omnino incorporeum. Sed antequam hoc ostendamus, oportet praedeterminare quaedam quae exiguntur ad huius probationem.	1141. After describing the condition of the first motion, the Philosopher here describes the condition of the first mover. And it is divided into two parts: First he mentions his intention; Secondly, he carries out his proposal, at 1142. He says First (901 266 a10), then, that since it was said above that the first mover is immobile, now we must assert that the first mover is indivisible and has no magnitude, as being wholly incorporeal. But before we show this, certain things necessary for this proof must be settled in advance.
lib. 8 l. 21 n. 2 Deinde cum dicit: horum autem unum quidem etc., exequitur propositum. Et primo praemittit quaedam quae sunt necessaria ad principalis propositi ostensionem; secundo ostendit principale propositum, ibi: determinatis autem his et cetera. Circa primum tria facit: primo ostendit quod ad motum infinitum requiritur potentia infinita; secundo quod potentia infinita non potest esse in magnitudine finita, ibi: quod autem omnino in finita magnitudine etc.; tertio quod primum motorem oportet esse unum, qui moveat motum continuum et sempiternum, ibi: de his autem quae feruntur et cetera. Dicit ergo primo, quod inter ea quae praedeterminanda sunt ante principale propositum, unum est quod impossibile est aliquod finitum secundum potentiam, movere per tempus infinitum. Quod sic ostendit. Tria sunt in quolibet motu: quorum unum est id quod movetur, aliud est ipsum movens, tertium autem est tempus in quo fit motus. Oportet autem quod aut omnia ista sint infinita, aut omnia sint finita, aut quod quaedam sint finita et quaedam infinita, vel duo tantum vel unum. Ponatur ergo primo quod a sit movens, et b sit mobile, et tempus infinitum sit c. Et ponatur quod aliqua pars ipsius a, quae est d, moveat aliquam partem b, quae est e. His ergo positionibus factis, concludi potest quod d movet e in tempore non aequali ipsi c, in quo a movebat b, sed in tempore minori. Probatum est enim in sexto quod totum mobile in maiori tempore pertransit aliquod signum, quam pars eius. Cum ergo tempus quod est c sit infinitum, relinquitur quod tempus in quo d movet e, non erit infinitum, sed finitum. Et sit illud tempus z; ut sicut a movet b in tempore c infinito, ita d moveat e in tempore z finito. Cum autem d sit pars ipsius a, si subtrahendo ab a addam ipsi d, totaliter ipsum a auferetur vel consumetur, cum sit finitum: omne enim finitum consumitur per subtractionem, si eadem quantitas semper sumatur, ut in tertio dictum est. Et similiter consumetur ipsum b, si continue subtrahatur aliquid ab ipso et apponatur ipsi e; quia b etiam ponebatur esse finitum. Sed quantumcumque auferam a tempore quod est c, etiam secundum eandem quantitatem auferendo, non consumetur totum c; quia ponitur esse infinitum. Ex hoc concludit quod totum a movet totum b in tempore aliquo finito, quod est pars ipsius c. Quod quidem sic sequitur ex praemissis, quia secundum proportionem qua additur ad mobile et ad motorem, additur etiam ad tempus motus. Cum ergo subtrahendo a toto mobili et motore, et addendo ad partes ipsorum, consumatur quandoque totum mobile et totum movens, ita quod totum quod erat in toto addetur parti; sequetur quod proportionaliter addendo ad tempus, resultabit tempus finitum, in quo totum movens movebit totum mobile. Et sic oportet quod si movens est finitum et mobile finitum, quod tempus sit finitum. Sic ergo non est possibile quod a finito movente moveatur aliquid motu infinito, scilicet secundum tempus infinitum. Et sic patet quod primo proponebatur, quod non contingit quod finitum movens moveat in tempore infinito.	1142. Then at (902 266 a12) he carries out his proposal: First he premises things required for proving the main proposition; Secondly, he proves the main proposition, at the end of L. 23. About the first he does three things: First he shows that an infinite motion supposes an infinite power; Secondly, that an infinite power cannot exist in a magnitude, at 1146; Thirdly, that the first mover must be one which causes a continuous and undying motion, (L. 22). He says therefore First (902 266 a12) that among the things to be established before the main proposition, one is that it is impossible for anything of finite power to cause motion for an infinite time. This he now proves. There are three things in every motion: one of which is what is moved, another is the mover, and the third is the time in which the motion occurs. But all three must be infinite, or all three finite, or some finite and some infinite, i.e., either two only or one. Suppose, therefore, that A is the mover, B the mobile, and C the infinite time. Then let D, a part of At move E, a part of B. Under these conditions, it could be concluded that D moves E in a time not equal to time C (in which A moved B) but in less time. For it has been proved in Book VI that the entire mobile requires more time to pass a certain point than it takes for a part of it. Therefore, since the time C is infinite, it follows that the time in which D moves E will not be infinite but finite. So let that time be Z, so that just as A moves B in the infinite time C, D moves E in the finite time Z. But since D is part of A, then if we add to D by subtracting from A, the A will eventually be entirely taken away or used up, since it is finite, and every finite is used up by subtraction, if the same quantity is continually taken away, as said in Book III. And likewise, B will be used up, if continual subtractions are made from it and added to E, because B is also finite. But no matter how much is taken from the time C—even if the same amount is continually taken away—all of C will not be used up, because it is infinite. From this he concludes that the entire A moves the entire B in a finite time, which is part of C. And this does indeed follow from the premises, because additions are made to the time of the motion in the same ratio as they are made to the mobile and to the mover, Since, therefore, by subtracting from the entire mobile and mover and by adding to their parts, the whole mobile the whole mover are at length used up, so that all that was in the whole is added to the part, it will follow that by proportional additions being made to the time, there will result a finite time in which the whole mover will move the whole mobile. Thus, if the mover is finite and the mobile also finite, the time too must be finite. According to this, therefore, it is not possible that by a finite mover anything be moved with an infinite motion, namely, according to an infinite time. And so what was first proposed is now plain, namely, that it does not happen that a finite mover should cause motion for an infinite time.
lib. 8 l. 21 n. 3 Movet autem Avicenna dubitationem circa hanc Aristotelis demonstrationem. Videtur enim non esse universalis: est enim aliquod finitum movens et mobile, a quo non potest aliquid subtrahi vel auferri, sicut est corpus caeleste; quod tamen in hac demonstratione non excipitur. Unde videtur quod vel demonstratio sit particularis, vel procedat ex falsa suppositione. Huic autem obiectioni respondet Averroes in commento, quod quamvis a caelo nihil posset subtrahi, haec tamen conditionalis est vera: si a caelo aliqua pars auferatur, pars illa movebit aut movebitur in minori tempore quam totum. Nihil enim prohibet conditionalem esse veram, cuius antecedens est impossibile; sicut patet in hac conditionali: si homo volat, habet alas. Quidquid autem tollit veritatem conditionalis verae, est falsum, licet antecedens conditionalis sit falsum. Veritas autem praedictae conditionalis non potest stare cum hoc quod finitum moveat tempore infinito, ut patet per deductionem Aristotelis. Sic igitur ex veritate praemissae conditionalis, concludit Aristoteles impossibile esse quod finitum moveat tempore infinito. Potest autem brevius dici, quod Aristoteles quando in demonstrationibus suis utitur ablatione vel subtractione, non semper per ablationem intelligenda est solutio continuitatis, quam impossibile est esse in corpore caelesti; sed ablatio intelligi potest secundum quamcumque designationem. Sicut in ligno continuo manente possum designare vel tactu vel cogitatione aliquod punctum, quasi dividens totum; et per hunc modum auferre aliquam partem a toto, et dicere quod minor albedo est in parte quam in toto. Et per hunc etiam modum potest dici quod minor virtus est ad movendum in parte corporis caelestis per designationem ablata, quam in toto.	1143. But Avicenna raises a difficulty about this demonstration of Aristotle. For it seems not to be universal, since there exists a finite mover and mobile from which nothing can be subtracted or taken away, such as a heavenly body, which nevertheless was not excluded from Aristotle’s proof. Hence it seems that the proof is either particular, or it proceeds from a false assumption. To this objection Averroes in his Commentary answers that although nothing can be subtracted from the heavenly body, yet the conditional is true, that if a part be taken away from the body, that part will move or be moved in less time than the whole body. For there is nothing to prevent a conditional from being true, even if its antecedent be impossible, as is patent from this conditional: If a man flies, he has wings. But whatever takes away the truth of a true conditional is false, even though the antecedent of the conditional be false. Now the truth of the above conditional cannot stand with the statement that the finite moves for an infinite time, as is evident through Aristotle’s deduction, Thus, therefore, from the truth of the foregoing conditional Aristotle concludes that it is impossible for a finite thing to cause motion for an infinite time. However, it may be said more briefly that when Aristotle in his demonstrations speaks of removing or subtracting, it does not always have to be understood in the sense of destroying a thing’s continuity, which is impossible in a heavenly body; rather, subtraction can be understood in the sense of designating. For example, I can without disturbing the continuity of a piece of wood designate by touch or thought a certain point as though dividing the whole, and in this way I can remove a part from the whole and say that there is less whiteness in that part than in the whole. In like manner, it can be said that there is less power to move in a part of a heavenly body— a part removed by designating it—than in the whole.
lib. 8 l. 21 n. 4 Alia autem dubitatio est difficilior. Non enim videtur esse contra rationem moventis finiti, quod moveat tempore infinito: quia si illud finitum sit incorruptibile vel impassibile secundum suam naturam, et non recedens a sua natura, semper eodem modo se habet ad movendum; quia idem eodem modo se habens, semper facit idem. Unde non est magis ratio quare non possit movere post, quam ante. Et hoc sensibiliter apparet: videmus enim quod sol potest in infinito tempore movere corpora inferiora. Ad huius autem dubitationis solutionem, investigandus est processus demonstrationis inductae. Certum enim debet esse, quod sic intelligenda est conclusio, quemadmodum sequitur ex praemissis. Considerandum est igitur quod tempus motus potest accipi dupliciter, praecipue in motu locali: uno modo secundum partes mobilis; alio modo secundum partes magnitudinis supra quam transit motus. Manifestum est enim quod prius una pars mobilis pertransit aliquod signum magnitudinis, quam totum mobile: similiter etiam totum mobile prius pertransit unam partem magnitudinis, quam totam. Apparet autem manifeste ex processu Aristotelis, quod hic loquitur de tempore motus, secundum quod tempus motus accipitur secundum partes mobilis; et non secundum quod accipitur secundum partes magnitudinis. Accipit enim in sua demonstratione, quod pars moventis moveat partem mobilis in minori tempore quam totum moveat totum: quod non esset verum si acciperemus tempus motus secundum partes magnitudinis quae motu pertransitur. Eadem enim est proportio partis motoris ad partes mobilis, quae est proportio totius motoris ad totum mobile. Unde aequali velocitate semper pars movebit partem, qua totum movet totum: et sic in aequali tempore pertransibit pars mobilis aliquam magnitudinem, mota a parte motoris, et totum mobile motum a toto motore. Vel forte in minori tempore movebitur totum quam pars: quia potentia unita maior est quam potentia divisa, et quanto maior est potentia moventis, velocior est motus, et tempus minus. Oportet ergo quod hoc intelligatur secundum quod accipitur tempus motus secundum partes mobilis: quia una pars mobilis in minori tempore pertransit aliquod signum, quam totum mobile. Et secundum hoc est impossibile quod tempore infinito moveatur, nisi sit mobile infinitum. Impossibile est autem quod mobile infinitum moveatur a motore finito: quia semper virtus motoris est maior quam virtus mobilis. Unde necesse est quod mobile infinitum moveatur a motore infinito. Et sic, sicut impossibile sequitur ex hoc quod ponitur quod motor finitus moveat mobile finitum, motu qui sit infinitus secundum partes mobilis; ita, remoto hoc inconvenienti, oportet ulterius hoc concludere, quod motus infinitus sit mobilis infiniti a motore infinito.	1144. But there is another and greater difficulty. For it does not seem to be against the prerogatives of a finite mover to cause motion for an infinite time, because if that finite thing is imperishable or impassible in its nature, and never loses its nature, it will maintain itself always in the same way with respect to causing motion, for a same thing, remaining in the same state, will always do the same. Hence, there would be no reason for its not being able to get later as it did before. This is evident to sense, for we observe that the sun can in an infinite time move lower bodies. To settle this difficulty, we must investigate the sequence of demonstration set forth by Aristotle. For it should be certain that the conclusion is to be interpreted in the sense in which it follows from the premises. We should consider, therefore, that the time of a motion may be taken in two senses, especially in local motion: in one sense, according to the parts of the mobile; in another sense, according to the parts of the magnitude along which the motion passes. For it is plain that one part of the mobile passes a designated point of the magnitude, before the whole does, and that the whole traverses part of the magnitude before it traverses all of it. Now, it is plainly clear from the procedure of Aristotle’s demonstration, that he is speaking of time of motion according to the parts of the mobile and not according to the parts of the magnitude. For in his demonstrations he assumes that part of the mover moves part of the mobile in less time than the whole moves the whole. But this could not be true, if we took time of motion according to the parts of the magnitude traversed by the motion; for the ratio of the part of the mover to the part of the mobile is the same as that of the whole mover to the whole mobile. Hence, a part will always move part with the same velocity as the whole moves the whole. Thus in an equal time part of the mobile moved by part of the mover will traverse some magnitude and the whole mobile moved by the whole mover will also. Or perhaps the whole will be moved in less time than the part, because a united force is greater than a divided force, and the greater the force of the mover, the swifter the motion and the less the time. Therefore, this must be understood in the sense that the time of motion is taken according to parts of the mobile, because one part of the mobile will pass a definite point in less time than the whole will. In this sense, it is impossible for anything but an infinite mobile to be moved for an infinite time. But an infinite mobile cannot be moved by a finite mover, since the power of the mover is always greater than the power of the mobile. Hence an infinite mobile must be moved by an infinite power. Consequently, just as an impossibility follows from the assumption that a finite mover moves a finite mobile with an infinite motion according to the parts of the mobile, so, this incompatibility once removed, one must further conclude that an infinite motion belongs to an infinite mobile from an infinite mover.
lib. 8 l. 21 n. 5 Sed contra hoc potest aliquis obiicere, quod Aristoteles supra non probavit motum esse infinitum secundum partes mobilis, sicut motus corporis infiniti dicitur infinitus: quia totum universum corporeum finitum est, ut probatum est in tertio huius, et probabitur in I de caelo. Unde non videtur esse demonstratio Aristotelis sic verificata ad propositum concludendum, ut scilicet primus motor qui movet motum infinitum, sit infinitus. Sed dicendum quod id quod est prima causa motus infiniti, oportet quod sit per se causa infinitatis motus: quia semper causa quae est per se, est prior ea quae est per aliud, ut supra dictum est. Virtus autem causae per se determinatur ad effectum per se, et non ad effectum per accidens: sic enim supra in secundo docuit Aristoteles comparare causas effectibus. Cum autem contingat motum esse infinitum dupliciter, sicut dictum est, scilicet secundum partes mobilis, et secundum partes longitudinis supra quam transit motus; per se infinitum est in motu ex partibus mobilis, per accidens autem secundum partes longitudinis: quia quantitas motus quae attenditur secundum partes mobilis, competit ei secundum proprium subiectum, et ita inest ei per se, quantitas autem motus quae accipitur secundum partes longitudinis, accipitur secundum reiterationem motus ipsius mobilis, prout scilicet mobile totum, quod complevit motum suum super unam partem longitudinis, iterato pertransit aliam. Illud ergo quod est prima causa infinitatis motus, habet virtutem super infinitatem motus quae est per se, ut scilicet possit movere mobile infinitum si contingat: et ideo necesse est quod sit infinitum. Et quamvis primum mobile sit finitum, tamen habet quandam similitudinem cum infinito, ut dictum est in tertio. Ad hoc autem quod aliquid sit causa motus infiniti per reiterationem motus (quod est per accidens), non oportet quod habeat virtutem infinitam, sed sufficit si habet virtutem immobilem finitam: quia semper manente eadem virtute, poterit reiterare eundem effectum; sicut sol habet virtutem finitam, et tamen posset movere inferiora elementa tempore infinito, si motus esset sempiternus, secundum positionem Aristotelis. Non enim est prima causa infinitatis motus, sed quasi ab alio mota ad movendum tempore infinito, secundum positionem praedictam.	1145. But against this, someone could object that Aristotle did not prove above that motion is infinite according to the parts of the mobile in the way that the motion of an infinite body is said to be infinite, for the entire corporeal universe is finite, as was proved in Book III and will be proved in On the Heavens I. Hence the demonstration of Aristotle does not seem to be verified as concluding to his proposition, namely, that the first mover, which causes an infinite motion, is infinite. But it should be said that what is first cause of an infinite motion must be the per se cause of the infinity of the motion, because the cause which is per se is always prior to that which is so by virtue of something else, as has been said above. Now, the power of a per se cause is determined to a per se effect and not to a per accidens effect, for that is the way Aristotle taught causes are to be compared to their effects in Book II. But, because motion can be infinite in two ways, as has been said, namely, according to the parts of the mobile and according to the parts of the length along which the motion takes place, per se the infinite is in motion from the parts of the mobile, but per accidens according to the parts of the length—for the quantity of motion based on the parts of the mobile belongs to it by reason of its proper subject and so is present in it per se, whereas the quantity of motion based on the parts of the length is based on constant repetition of the mobile’s motion, in the sense that a whole mobile, having completed its entire motion upon one part of the length, now successively traverses another. The first cause, therefore, of the infinity of motion has power over the infinity of motion which is per se, in such a way, namely, as to enable it to move an infinite mobile, should there be such. Hence, it must be infinite. And even though the first mobile be finite, it has, nevertheless, a certain likeness to the infinite, as was said in Book III. But in order that something be the cause of a motion that is infinite through repetition (which is per accidens) infinite power is not required, but an immobile finite power is enough, because, so long as the power remains the same, it will be able to repeat the same effect, as the sun has a finite energy yet can move the lower elements in an infinite time, should motion be, as Aristotle posits, eternal. For it is not the first cause of the infinity of motion but is something as though moved by another to move in an infinite time, according to the position stated above.
lib. 8 l. 21 n. 6 Deinde cum dicit: quod autem omnino in finita etc., ostendit quod necesse est virtutem quae est in magnitudine, proportionari magnitudini in qua est. Et primo ostendit quod in magnitudine finita non potest esse potentia infinita, quod principalius intendit; secundo quod nec in magnitudine infinita potest esse potentia finita, ibi: nullum igitur finitum et cetera. Quod autem in magnitudine finita non contingat esse potentiam infinitam, probat, duas suppositiones praemittendo. Quarum prima est, quod maior potentia aequalem effectum perficit in minore tempore quam minor: sicut maior potentia calefactiva ad aequalem caliditatem perducit id in quo agit, in minori tempore; et simile est de potentia dulcorantis vel proiicientis, vel cuiuscumque moventis. Et ex hac suppositione concludit, quod cum potentia infinita sit maior quam potentia finita, necesse est quod si sit aliqua magnitudo finita habens potentiam infinitam, quod a tali agente sive unum patiens sive plura patiantur in eodem tempore maiorem mutationem, quam ab alio habente potentiam finitam: vel e converso quod aequalem mutationem patiens, ab eo patiatur in minori tempore. Utrumque enim potest intelligi in eo quod dicit et plus quam ab alio. Secunda suppositio est, quod cum omne quod movetur moveatur in tempore, ut in sexto probatum est, non potest esse quod patiens immutetur ab agente infinitae potentiae in non tempore. Immutatur ergo in tempore. Ex hoc sic procedit. Sit tempus in quo virtus infinita movet calefaciendo vel impellendo, a; tempus autem in quo aliqua virtus finita movet, sit ab, quod est maius quam a. Qualibet autem potentia finita potest accipi alia maior. Si ergo accipiamus aliam maiorem potentiam finitam quam primam, quae movebat in tempore ab, sequetur quod haec secunda potentia movebit in tempore minori; et iterum tertia potentia finita maior in tempore adhuc minori. Et sic semper accipiendo finitam potentiam, veniam aliquando ad hoc quod aliqua potentia finita moveat in tempore a: cum enim semper fiat additio ad potentiam finitam, excedetur omnis determinata proportio. Simul autem additur ad potentiam motivam et subtrahitur a tempore motus; quia maior potentia in minori tempore movere potest. Sic ergo sequetur quod finita potentia perficiat motum in aequali tempore cum potentia infinita, quae ponebatur movere in a. Hoc autem est impossibile: ergo nulla magnitudo finita habet potentiam infinitam.	1146. Then at (903 266 a23) he shows that the power in a magnitude must be proportional to the magnitude in which it exists. First he shows that in a finite magnitude there cannot be an infinite power—and this is what he chiefly intends; Secondly, that on the other hand, in an infinite magnitude there cannot be a finite power, at 1156. That an infinite power cannot exist in a finite magnitude he proves at (903 266 a23), but first he mentions two assumptions. The first is that a greater power produces an equal effect in less time than a lesser power, as a greater heating force raises a thing on which it acts to an equal temperature in less time, and the same is true of a sweetener, or a hurler, or any cause of motion. And from this assumption he concludes that since an infinite power is greater than a finite power, then, necessarily, if there is a finite magnitude possessing an infinite power, one or a number of things will in the same time undergo from such an agent a greater change than from another having finite power, or, conversely, that which undergoes an equal change will do so from it in less time. Either interpretation suits what Aristotle says here, namely, “...to a greater extent than by anything else.” The second assumption is that, since whatever is being moved is being moved in time, as was proved in Book VI, it cannot be that something undergoing is changed in no time by an agent of infinite power. Therefore, it is changed in time. From this he proceeds in the following manner: Let A be the time in which an infinite power causes change by heating or throwing, and let the time in which a finite power is causing change be AB, which is longer than A. Now, no matter what a finite power may be, a still greater may be taken. If, therefore, we take another finite power greater than the first and which caused change in time AB, it will act in a shorter time. Again, a third and greater power will cause the change in still less time, And thus by always taking a finite power I will at length come to a finite power that will produce the change in time A, for when an addition is continually made to a finite power, any predetermined ratio will be exceeded. But as the power is increased, the time is decreased, because a greater power can cause a change in less time. In this way, therefore, it will follow that a finite power will produce a change in a time equal to that used by the infinite power, which was assumed as acting in time A. But this is impossible. Therefore, no finite magnitude has an infinite power.
lib. 8 l. 21 n. 7 Dubitatur autem circa hanc rationem multipliciter. Primo namque videtur quod haec ratio nullo modo concludat. Quod enim per se convenit alicui, per nullam potentiam potest ab eo removeri, quantumcumque sit magna: non enim est ex defectu potentiae, vel infinitati potentiae repugnat, si dicatur fieri non posse quod homo non sit animal. Esse autem in tempore per se convenit motui: ponitur enim motus in definitione temporis, ut supra in quarto habitum est. Ergo si ponatur etiam potentia infinita movens, non sequitur quod motus sit in non tempore, ut Aristoteles hic concludit. Item si consideretur processus philosophi, ex hoc concludit quod motus sit in non tempore, quia potentia movens est infinita; sed potentia infinita movens potest etiam non esse in corpore; ergo eadem ratione sequitur quod talis potentia, si sit infinita, movebit in non tempore. Non ergo per hoc quod est impossibile moveri in non tempore, potest concludi quod nulla virtus infinita est in magnitudine, sed quod simpliciter nulla virtus movens sit infinita. Item, ad magnitudinem potentiae duo pertinere videntur, scilicet velocitas motus et diuturnitas ipsius; et secundum excessum potentiae videmus fieri excessum in utroque dictorum. Sed secundum excessum potentiae infinitae, supra ostendit quod motus perpetuus est ab aliqua potentia infinita, non autem quod aliqua potentia infinita non sit in magnitudine. Ergo similiter et hic, secundum excessum in velocitate non debet concludere quod nulla virtus infinita sit in magnitudine, sed quod virtus quae movet tempore infinito, propter sui infinitatem moveat etiam in non tempore. Item videtur conclusio esse falsa. Quanto enim est maior virtus alicuius corporis, tanto diutius potest conservari in esse: si ergo nullius corporis potentia esset infinita, nullum corpus posset in infinitum durare. Quod patet esse falsum tam secundum opinionem ipsius, quam secundum sententiam fidei Christianae, quae ponit substantiam mundi in infinitum duraturam. Posset etiam moveri obiectio de divisione et additione quibus utitur, quae non conveniunt rerum naturae; sed quia de hoc superius satis dictum est, praetermittatur ad praesens.	1147. Now, there are many doubts about this argument. First, it seems not to conclude in any way. For what belongs per se to a thing cannot be taken from it by any power however great, for it is not due to any lack of power, nor does it conflict with infinity of power, if it be said that it is impossible for man not to be an animal. But to exist in time belongs per se to motion, for motion is found in the definition of time, as was had above in Book IV. Therefore, if an infinite moving power is conceded to exist, it does not follow that motion exists in non-time as Aristotle here concludes. Likewise, if the sequence of the argument of the Philosopher is considered, it will be seen that his conclusion that motion exists in non-time is inferred from the fact that the moving power is infinite; but an infinite moving power can also not be in a body. Therefore, for the same reason, it follows that such a power, if it is infinite, will move in non-time. Hence, from the impossibility of being moved in non-time it cannot be inferred that no infinite power exists in a magnitude, but absolutely that no moving power at all is infinite. Again, two things seem to pertain to the magnitude of a power, namely, the swiftness of motion and its diuturnity; and any superabundance in the power causes a corresponding superabundance in each of these two things. But with respect to the superabundance of an infinite power, he showed above that a perpetual motion depends on an infinite power, but not that an infinite power does not exist in a magnitude. Therefore, here too, with respect to excess of swiftness, he ought not to conclude that no infinite power exists in a magnitude, but that the power which moves in an infinite time would, on account of its infinity, also move in non-time. Again, the conclusion seems to be false. For the greater the power of a body, the longer it can endure. If, therefore, the power of no body were infinite, no body could endure ad infinitum. Now this is plainly false, both according to his own opinion and according to the tenets of the Christian faith, which posits that the substance of the world will endure ad infinitum. It could also be objected that the division and addition which he uses have no correspondence in reality, but since this was sufficiently discussed previously, it can be passed over at the present time.
lib. 8 l. 21 n. 8 His ergo dubitationibus per ordinem respondentes, dicendum est ad primam, quod philosophus non intendit hic facere demonstrationem ostensivam, sed demonstrationem ad impossibile ducentem; in qua, quia ex aliquo dato aliquid sequitur quod est impossibile, concluditur primum datum impossibile esse. Non autem est verum quod primum datum simul cum conclusione esse sit possibile; sicut si daretur quod esset aliqua potentia quae posset removere genus a specie, sequeretur quod illa potentia posset facere quod homo non esset animal: sed quia hoc est impossibile, impossibile est et primum; non autem ex hoc potest concludi esse possibile, quod sit aliqua potentia quae faciat hominem non esse animal. Ita ex hoc quod est aliquam potentiam infinitam esse in magnitudine, ex necessitate sequitur motum esse in non tempore: sed quia hoc est impossibile, impossibile est infinitam potentiam esse in magnitudine; nec potest ex hoc concludi esse possibile quod potentia infinita moveat in non tempore.	1148. Answering, therefore, these doubts in order, it must be said with respect to the first one, that the Philosopher in this place does not intend an ostensive demonstration but one that leads to an impossibility, in which, since from something given an impossibility follows, that which was given is concluded to be impossible. For it is not true that the first supposition can possibly co-exist with the conclusion. Thus the supposition that there was some power which could remove the genus from a species, would allow us to conclude that that power could make man not be animal; but because this is impossible, the supposition too is impossible. From this, then, it cannot be concluded that it is possible for a power to exist that could make man not be animal. So, too, from the fact that an infinite power exists in a magnitude, it follows of necessity that motion exists in non-time; but since this is impossible, it is impossible for an infinite power to exist in a magnitude; nor can it be concluded from this that it is possible for an infinite power to move in non-time.
lib. 8 l. 21 n. 9 Ad secundam autem dubitationem respondet Averroes in commento huius loci, dicens quod ratio Aristotelis hic procedit de potentia, ratione suae infinitatis. Finitum autem et infinitum convenit quantitati, ut supra in primo habitum est: unde potentiae quae non est in magnitudine, non proprie competit quod sit finita vel infinita. Sed haec responsio est et contra intentionem Aristotelis, et contra veritatem. Contra intentionem quidem Aristotelis est, quia Aristoteles in praecedenti demonstratione probavit quod potentia movens tempore infinito sit infinita: et ex hoc infra concludit quod potentia movens caelum non est potentia in magnitudine. Est etiam contra veritatem: quia cum omnis potentia activa sit secundum aliquam formam, eo modo convenit magnitudo potentiae, et per consequens finitum et infinitum, sicut convenit formae. Formae autem convenit magnitudo et per se, et per accidens: per se quidem, secundum perfectionem ipsius formae, sicut dicitur magna albedo etiam parvae nivis, secundum perfectionem propriae rationis; per accidens autem secundum quod aliqua forma habet extensionem in subiecto, sicut dicitur magna albedo propter magnitudinem superficiei. Haec autem secunda magnitudo non potest competere potentiae quae non est in magnitudine: sed prima magnitudo maxime ei competit, quia potentiae immateriales, quanto sunt minus contractae per applicationem ad materiam, tanto sunt perfectiores et universaliores. Velocitas autem motus non consequitur magnitudinem virtutis quae est per accidens, per extensionem ad magnitudinem subiecti, sed magis eam quae est per se, secundum propriam perfectionem: quia quanto aliquod ens actu est perfectius, tanto est vehementius activum. Unde non potest dici quod potentia quae non est in magnitudine, quia non est infinita infinitate magnitudinis quae est ex magnitudine subiecti, propter hoc non causet augmentum velocitatis in infinitum, quod est movere in non tempore. Unde et idem Commentator hanc dubitationem aliter solvit in XI Metaphys., ubi dicit quod corpus caeleste movetur a duplici motore, scilicet a motore coniuncto, qui est anima caeli, et a motore separato, qui non movetur neque per se neque per accidens. Et quia ille motor separatus est infinitae virtutis, motus caeli acquirit ab eo perpetuam durationem: quia vero motor coniunctus est finitae virtutis, ideo motus caeli acquirit ab eo velocitatem determinatam. Sed nec ista responsio sufficiens est. Cum enim utrumque videatur consequi potentiam infinitam, scilicet quod moveat tempore infinito, ut praecedens demonstratio conclusit, et quod moveat in non tempore, ut videtur concludere haec demonstratio: iterum restat dubitatio quare anima caeli, quae movet in virtute motoris separati infiniti, magis ab eo sortiatur ut possit movere tempore infinito, quam ut moveat velocitate infinita, idest in non tempore.	1149. To the second doubt Averroes responds in his Commentary at this place that the argument of Aristotle here proceeds from power under the aspect of its infinity. But “finite” and “infinite” belong to quantity, as was proved in Book I. Hence, finite and infinite do not properly belong to a power that is not in a magnitude. But this answer is contrary both to the intention of Aristotle, and to the truth. It is contrary to Aristotle’s intention, because in the preceding demonstration Aristotle proved that a power which causes motion for an infinite time is infinite, and from this he later concludes that the power moving the heavens is not a power existing in a magnitude. It is also against the truth: for since every active power is according to some form, magnitude, and consequently its finiteness and infinity, belong to a power in the way it belongs to form. But magnitude belongs to form both per se and per accidens: it belongs per se, according to the perfection of the form, as a whiteness is called “great” even in a small amount of snow, according to the perfection of its proper notion; it belongs per accidens, according to the extension that a form has in a subject, as a whiteness can be called “great” on account of the size of its surface. Now, this second magnitude cannot belong to a power not in a magnitude, but the first magnitude most truly does, because non-material powers, the less they are restricted through union with matter, the more perfect and more universal they are. But swiftness of motion does not follow upon a magnitude of power which is per accidens, by extension with the magnitude of the subject; rather, it follows one that is per se, according to its proper perfection, because the more perfect a thing is in act, the more vehemently is it active. Hence it cannot be said that a power which does not exist in a magnitude, because it is not infinite with the infinity of magnitude which depends on the magnitude of the subject, therefore cannot cause an increase of swiftness ad infinitum, i.e., move in non-time. Hence the same Commentator solves this same difficulty in another way in Metaphysics XI, where he says that a heavenly body is moved by a two-fold mover, i.e., by a conjoined mover, which is the soul of the heavens, and by a separated mover, which is not moved either per se or per accidens. And because that separated mover has infinite power, the movement of the heaven acquires from it a perpetual duration; but because the conjoined mover has finite power, the movement of the heaven acquires from it a determinate swiftness. But even this answer is not sufficient. For since both seem to follow upon an infinite power, namely, that it act for an infinite time, as the preceding demonstration concluded, and that it act in non-time, as this demonstration seems to conclude, the doubt still remains why the soul of the heaven which acts in virtue of an infinite separated mover obtains from it the ability to act for an infinite time rather than the ability to act with infinite swiftness, i.e., in non-time.
lib. 8 l. 21 n. 10 Ad hanc igitur dubitationem dicendum est, quod omnis potentia quae non est in magnitudine, movet per intellectum: sic enim philosophus probat caelum moveri a suo motore, in XI Metaphys. Nulla autem potentia quae est in magnitudine, movet quasi intelligens: probatum est enim in III de anima, quod intellectus non est virtus alicuius corporis. Haec autem est differentia inter agens per intellectum et agens materiale, quia actio agentis materialis proportionatur naturae agentis; tanta enim procedit calefactio quantus est calor: sed actio agentis per intellectum, non proportionatur naturae ipsius, sed formae apprehensae; non enim aedificator tantum aedificat quantum potest, sed quantum exigit ratio formae conceptae. Sic igitur si aliqua esset virtus infinita in magnitudine, sequeretur quod motus ab ipsa procedens esset secundum proportionem eius: et ita procedit demonstratio praesens. Si autem sit virtus infinita non in magnitudine, motus ab ipsa non procedit secundum proportionem virtutis, sed secundum rationem formae apprehensae, idest secundum quod convenit fini et naturae subiecti. Est etiam aliud attendendum, quod sicut probatum est in sexto huius, nihil movetur nisi magnitudinem habens: unde velocitas motus est effectus receptus a movente in aliquo habente magnitudinem. Manifestum est autem, quod nihil habens magnitudinem potest recipere effectum aequalem proportionaliter potentiae quae non est in magnitudine; quia omnis natura corporea comparatur ad naturam incorpoream sicut quoddam particulare ad absolutum et universale. Unde non potest concludi, si virtus infinita non sit in magnitudine, quod ex ea consequatur in aliquo corpore infinita velocitas, quae est effectus proportionatus tali potentiae, ut dictum est. Sed nihil prohibet in aliqua magnitudine recipi effectum virtutis quae est in magnitudine, quia causa proportionatur effectui. Unde si poneretur quod aliqua virtus infinita esset in magnitudine, sequeretur quod effectus correspondens esset in magnitudine, scilicet velocitas infinita. Et hoc est impossibile: ergo et primum.	1150. In answer to this doubt it must be said that every power not in a magnitude acts through intellect, for so the Philosopher proves in Metaphysics XI that the heaven is moved by its mover. But no power in a magnitude acts as though through intellect, for it was proved in On the Soul III that the intellect is not a power of any body. Now this is the difference between an agent that acts through intellect and a material agent: the action of the material agent is proportioned to the nature of the agent, for a heating process proceeds in proportion to the heat, but the action of an intellectual agent is not proportioned to its nature but to the form apprehended, for a builder does not build as much as he can, but as much as the notion of the conceived form requires. Consequently, if an infinite power existed in a magnitude, it would follow that the motion produced by it would be in proportion, to it, as the present demonstration shows. But if an infinite power is not in a magnitude, a motion does not proceed from that power in proportion to its power but according to the notion of the thing apprehended, i.e., according as it fits the end and nature of the subject. Another point that should be noted is that, as was proved in Book VII only things having magnitude are moved; wherefore, the swiftness of motion is an effect received from the mover into something having magnitude. But it is plain that nothing having magnitude can receive an effect equal proportionately to the power which is not in a magnitude, because every corporeal nature is related to the incorporeal as a certain particular to what is absolute and universal, Hence, it cannot be concluded, if an infinite power is not in a magnitude, that from it there results in a body an infinite swiftness, which is the effect proportionate to such a power, as has been said. But there is nothing to prevent a magnitude from receiving the effect of a power existing in a magnitude, because the cause is proportioned to the effect. Hence if it were supposed that an infinite power existed in a magnitude, it would follow that a corresponding effect would exist in a magnitude, namely, an infinite swiftness. But this is impossible; therefore, the first too is impossible.
lib. 8 l. 21 n. 11 Ex his autem patet solutio tertiae dubitationis. Nam moveri tempore infinito non repugnat rationi magnitudinis motae: convenit enim magnitudini circulari, ut supra ostensum est. Sed moveri velocitate infinita, idest in non tempore, contrariatur rationi magnitudinis, ut in sexto probatum est. Unde a primo movente infinitae virtutis, secundum Aristotelem, causatur motus diuturnitatis infinitae; non autem motus velocitatis infinitae.	1151. From this the resolution of the third doubt is clear. For to be moved for an infinite time is not repugnant to the notion of a moved magnitude, for it befits a circular magnitude, as was shown above. But to be moved with an infinite speed, i.e., in non-time, is contrary to the notion of a magnitude, as was proved in Book VI. Hence the first mover, possessing infinite power, is, according to Aristotle, the cause of a motion that lasts an infinite time, but not one that has infinite speed.
lib. 8 l. 21 n. 12 Ad quartam vero dubitationem, solvit Alexander, ut Averroes dicit hic in commento, quod corpus caeleste acquirit aeternitatem a motore separato, quod est infinitae virtutis, sicut et perpetuitatem motus. Unde sicut non est ex infinitate caelestis corporis quod in perpetuum moveatur, ita non est ex infinitate corporis caelestis quod in perpetuum duret; sed utrumque est ex infinitate motoris separati. Hanc autem responsionem Averroes improbare nititur et hic in commento, et in XI Metaphys., dicens quod impossibile est quod aliquid acquirat perpetuitatem essendi ab alio; quia sequeretur quod id quod in se est corruptibile, fieret aeternum. Sed perpetuitatem motus potest aliquid acquirere ab altero: eo quod motus est actus mobilis a movente. Dicit ergo quod in corpore caelesti, quantum est de se, non est aliqua potentia ad non esse, quia eius substantiae non est aliquid contrarium: sed in ipso est aliqua potentia ad quietem, quia motui eius contrariatur quies. Et inde est quod non indiget acquirere perpetuitatem essendi ab alio: sed perpetuitatem motus ab alio acquirere indiget. Quod autem in corpore caelesti non sit aliqua potentia ad non esse, ex hoc contingere dicit, quod corpus caeleste dicit non esse compositum ex materia et forma quasi ex potentia et actu; sed dicit ipsum esse materiam actu existentem, et formam eius dicit animam ipsius; ita tamen quod non constituatur in esse per formam, sed solum in moveri. Et sic dicit in eo esse, non potentiam ad esse, sed solum ad ubi, sicut philosophus dicit in XI Metaphys.	1152. The fourth doubt is, according to Averroes in his Commentary, answered by Alexander’s saying that a heavenly body acquires eternity from a separated mover having infinite power, as well as perpetuity of motion. Hence, just as it is not from the infinity of a heavenly body that it is perpetually moved, so, too, it is not from the infinity of the heavenly body that it endures forever. Both are from the infinity of the separated mover. Now Averroes tries to refute this answer, both in his Commentary on this passage and in Metaphysics XI, and says that it is impossible for something to acquire perpetuity of existence from another, because it would follow that something in se perishable could be eternal. Yet something can acquire perpetuity of motion from another, for motion is an act existing in a mobile but caused by a mover. He says therefore that in a heavenly body considered in itself there is no potency to non-existence, because its substance has no contrary, but there is a potency to rest, because rest is contrary to its motion. And that is why it does not have to acquire perpetuity of existence from another, but must acquire perpetuity of motion from another. That a heavenly body has no potency to non-existence happens, he says, because a heavenly body is not composed of matter and form as though of potency and act. Rather, says he, such a body is matter existing in act, while its form is its soul, in such a way that it is not constituted in being through the form, but only in motion. Consequently, says he, there is present in it not a potency to existence, but solely a potency to “where” (place), as the Philosopher says in Metaphysics XI.
lib. 8 l. 21 n. 13 Sed haec solutio et veritati repugnat, et intentioni Aristotelis. Veritati quidem repugnat multipliciter: et primo quia dicit quod corpus caeleste non componitur ex materia et forma: hoc enim est omnino impossibile. Manifestum est enim corpus caeleste esse aliquid actu; alioquin non moveretur: quod enim est in potentia tantum, non est subiectum motus, ut in sexto habitum est. Oportet autem omne quod est actu, vel esse formam subsistentem, sicut substantiae separatae; vel habere formam in alio, quod quidem se habet ad formam sicut materia, et sicut potentia ad actum. Non autem potest dici quod corpus caeleste sit forma subsistens: quia sic esset intellectum in actu, non cadens sub sensu neque sub quantitate. Relinquitur ergo quod est compositum ex materia et forma, et ex potentia et actu; et sic est in ipso quodammodo potentia ad non esse. Sed dato quod corpus caeleste non sit compositum ex materia et forma, adhuc oportet in ipso ponere aliquo modo potentiam essendi. Necesse est enim quod omnis substantia simplex subsistens, vel ipsa sit suum esse, vel participet esse. Substantia autem simplex quae est ipsum esse subsistens, non potest esse nisi una, sicut nec albedo, si esset subsistens, posset esse nisi una. Omnis ergo substantia quae est post primam substantiam simplicem, participat esse. Omne autem participans componitur ex participante et participato, et participans est in potentia ad participatum. In omni ergo substantia quantumcumque simplici, post primam substantiam simplicem, est potentia essendi. Deceptus autem fuit per aequivocationem potentiae. Nam potentia quandoque dicitur quod se habet ad opposita. Et hoc excluditur a corpore caelesti, et a substantiis simplicibus separatis: quia non est in eis potentia ad non esse, secundum intentionem Aristotelis; eo quod substantiae simplices sunt formae tantum, formae autem per se convenit esse; materia autem corporis caelestis non est in potentia ad aliam formam. Sicut enim corpus caeleste comparatur ad suam figuram, cuius est subiectum, ut potentia ad actum, et tamen non potest non habere talem figuram: ita materia corporis caelestis comparatur ad talem formam ut potentia ad actum, et tamen non est in potentia ad privationem huius formae, vel ad non esse. Non enim omnis potentia est oppositorum: alioquin possibile non sequeretur ad necesse, sicut dicitur in II perihermeneias. Est etiam eius positio contra intentionem Aristotelis, qui in I de caelo in quadam demonstratione utitur quod corpus caeleste habeat potentiam vel virtutem ad hoc quod sit semper. Non potest ergo evadere inconveniens per hoc quod dicit quod in corpore caelesti non est potentia essendi: hoc enim est manifeste falsum, et contra intentionem Aristotelis.	1153. But this solution conforms neither to the truth nor to the intention of Aristotle. It is not in conformity with truth on a number of counts: First, because he says that a heavenly body is not composed of matter and form—which is utterly impossible. For it is plain that a heavenly body is something actual, otherwise it would not be in motion—something that is in potency only is not a subject of motion, as was proved in Book VI. But, whatever is actual is either a subsisting form, as are the separated substances, or has form in something else, which is related to the form as matter, and as potency to act. Now, it cannot be said that a heavenly body is a subsistent form, because then it would be understood in act and neither sensible nor existing under quantity. Therefore, it must be a composite of matter and form, and of potency and act. Consequently, there is in it in some sense a potency to non-existence. But even if a heavenly body were not a composite of matter and form, it would still be necessary to place in it, in some sense, a potency in respect of existence. For every simple self-subsisting substance is necessarily either its own existence or it shares in existence. But a simple substance which is self-subsistent existence itself cannot be but one, just as whiteness, if whiteness were a subsistent being, could be but one. Consequently, every substance after the first simple substance participates existence. But every participant is composed of the participant and what it participates, and the participant is in potency to what it participates. Therefore, in every substance, however simple, other than the first simple substance, there is a potency to existence. Now he was deceived by the equivocation in “potency.” For potency sometimes refers to what is open to opposites. In this sense, potency is excluded from a heavenly body and from separated simple substances, because, in Aristotle’s opinion, they have no potency to non-existence, for simple substances are forms only, and it belongs per se to a form that it exist, while the matter of a heavenly body is not in potency to another form. For just as a heavenly body is related to its figure, of which it is the subject, as potency to act, and yet cannot not have such a figure, so the matter of the heavenly body is related to its form as potency to act, and yet it is not in potency to being deprived of this form or to non-being. For not every potency is open to opposites; otherwise possibility would not follow upon necessity, as is said in Perihermeneias II. His position is also contrary to the intention of Aristotle, who in On the Heavens I, in a certain demonstration, uses the fact that a heavenly body has the potency or the virtue to exist always. Therefore, he cannot avoid the incompatibility by saying that in a heavenly body there is no potency to existing: for this is evidently false and contrary to the intention of Aristotle.
lib. 8 l. 21 n. 14 Videamus ergo utrum convenienter impugnet solutionem Alexandri, qui dicit quod corpus caeleste acquirit aeternitatem ab alio. Esset siquidem conveniens eius improbatio, si Alexander posuisset quod corpus caeleste de se haberet potentiam ad esse et non esse, et acquireret ab alio esse semper. Et hoc dico supposita intentione ipsius, ut non excludamus omnipotentiam Dei, per quam corruptibile hoc potest induere incorruptionem: quod nunc discutere ad propositum non pertinet. Sed tamen Averroes, etiam sua intentione supposita, non potest concludere contra Alexandrum, qui non posuit quod corpus caeleste acquirat aeternitatem ab alio, quasi de se habens potentiam ad esse et non esse, sed quasi non habens a se esse. Omne enim quod non est suum esse, participat esse a causa prima, quae est suum esse. Unde et ipsemet confitetur in libro de substantia orbis, quod Deus est causa caeli non solum quantum ad motum eius, sed etiam quantum ad substantiam ipsius: quod non est nisi quia ab eo habet esse. Non autem habet ab eo esse nisi perpetuum: habet ergo perpetuitatem ab alio. Et in hoc etiam consonant dicta Aristotelis, qui dicit in V Metaphys., et supra in principio huius octavi, quod quaedam sunt necessaria quae habent causam suae necessitatis. Hoc ergo supposito, plana est solutio secundum intentionem Alexandri, quod sicut corpus caeleste habet moveri ab alio, ita et esse. Unde sicut motus perpetuus demonstrat infinitam virtutem motoris, non autem ipsius mobilis; ita et perpetua eius duratio demonstrat infinitam virtutem causae a qua habet esse.	1154. Therefore, let us see whether he adequately refuted the solution of Alexander who says that a heavenly body acquires its perpetuity from something else. His refutation would indeed be good, if Alexander had posited that a heavenly body had of itself a potency to existence and non-existence, and that it acquired from something else its perpetual existence. This I say while keeping in mind his intention, and not excluding the omnipotence of God, by which “this corruptible can put on incorruptibility”—to discuss which now does not pertain to the present question. Still Averroes, even supposing his intention, cannot conclude against Alexander, who did not posit that the heavenly body acquires its perpetuity from something else, as though it had a potency to existence and non-existence, but as though not having its existence from itself. For whatever is not its own existence participates existence from the first cause that is its own existence. Hence, he himself professes in his book, On the Substance of the Orb, that God is the cause of the heavens not only with respect to its motion, but with respect to its substance as well, which would not be true unless it has its existence from something else. But the only existence it has from another is a perpetual one; consequently, its perpetuity is from another. And this is in agreement with the teachings of Aristotle who, in Metaphysics V and in the beginning of this Book VIII of the Physics, says that there a some necessary things that have a cause of their necessity. In the light of this, the solution according to the intention of Alexander is plain, namely, that just as a heavenly body derives its motion elsewhere, so too its existence. Hence, just as a perpetual motion demonstrates the infinite power of the mover but not of the mobile, so too its perpetual duration demonstrates the infinite power of the cause from which it derives its existence.
lib. 8 l. 21 n. 15 Non tamen omnino eodem modo se habet potentia corporis caelestis ad esse et ad moveri perpetuo. Non quidem secundum differentiam quam ipse assignat, quod in corpore caelesti sit quantum ad moveri potentia ad opposita, quae sunt quies et motus: sed ad opposita quae sunt diversa ubi. Sed differunt quantum ad aliud. Nam motus secundum se cadit in tempore: esse vero non cadit secundum se in tempore, sed solum secundum quod subiacet motui. Si ergo sit aliquod esse quod non subiacet motui, illud esse nullo modo cadit sub tempore. Potentia ergo quae est ad moveri in tempore infinito, respicit infinitatem temporis directe et per se. Sed potentia quae est ad esse tempore infinito, si quidem illud esse sit transmutabile, respicit quantitatem temporis: et ideo maior virtus vel potentia requiritur ad hoc quod aliquid duret in esse transmutabili maiori tempore. Sed potentia quae est respectu esse intransmutabilis, nullo modo respicit quantitatem temporis. Unde magnitudo vel infinitas temporis nihil facit ad magnitudinem vel infinitatem potentiae respectu talis esse. Dato ergo per impossibile quod corpus caeleste non haberet esse ab alio, adhuc non posset ex perpetuitate ipsius concludi, quod in eo esset virtus infinita.	1155. But the potency of a heavenly body to existence is not exactly the same as its potency to perpetual motion. However, the difference is not the one he assigns, namely, that in a heavenly body there is with respect to motion a potency to opposites, these being rest and motion; rather it is to opposites which are different “where’s” (places). But they differ in respect of something else. For motion according to itself falls under time, whereas existence according to itself does not fall under time, but only according as it is subject to motion, Therefore, if there is an existence not subject to motion, it in no wise falls under time. Hence, the potency to be moved for an infinite time regards the infinity of time directly and per se. But a potency to exist for an infinite time, if that existence is transmutable, regards a quantity of time and, therefore, a greater power is required for something to endure in transmutable existence for a longer time, But a potency in respect to intransmutable existence has no relationship to a quantity of time. Hence the magnitude or infinity of time has nothing to do with the magnitude or infinity of the power in respect to such existence. Therefore, granting the impossible assumption that a heavenly body did not derive its existence elsewhere, its perpetuity would not be grounds for concluding that an infinite power exists in it.
lib. 8 l. 21 n. 16 Deinde cum dicit: nullum itaque finitum etc., probat quod in magnitudine infinita non potest esse potentia finita. Et hoc duabus rationibus: circa quarum primam tria facit. Primo ponit conclusionem intentam, dicens quod sicut in magnitudine finita non potest esse potentia infinita, ita nec in aliquo quanto infinito potest esse potentia finita secundum totum (nam pars infiniti si accipiatur finita, habebit potentiam finitam). Hoc autem inducit non quasi necessarium ad principale propositum ostendendum, sed quasi cohaerens et affine conclusioni prius demonstratae.	1156. Then at (904 266 b5) he proves that in an infinite magnitude there cannot exist a finite power, And this he does with two arguments, with respect to the first of which he does three things: First he mentions the conclusion intended, namely, that just as there cannot be an infinite power in a finite magnitude, so neither can there be a finite power in an infinite quantity taken as a whole (for if a finite part of the infinite be taken, it will have a finite power). He mentions this conclusion not as though it were needed for proving his principal conclusion but as cohering with, and akin to, the conclusion previously demonstrated.
lib. 8 l. 21 n. 17 Secundo ibi: et tamen contingit etc., ponit quoddam per quod alicui videri posset quod in magnitudine infinita sit potentia finita: videmus enim quod aliqua minor magnitudo habet maiorem virtutem quam maior magnitudo, sicut parvus ignis habet maiorem virtutem activam quam multus aer. Sed per hoc non potest haberi quod quantum infinitum habeat potentiam finitam: quia si accipiatur aliqua adhuc magis excedens magnitudo, habebit maiorem virtutem; sicut si aer maior secundum aliquam quantitatem habet minus de virtute quam parvus ignis, si multum augeatur aeris quantitas, habebit maiorem virtutem quam parvus ignis.	1157. Secondly, at (905 266 b7) he mentions something that could lead someone to suppose that there is a finite power in an infinite magnitude. For we see some lesser magnitude that has greater energy than a larger magnitude, as a small amount of fire has more active power than a large amount of air. But that does not permit us to conclude that an infinite quantity has a finite power, because if a still greater magnitude is taken, it will have greater power; for example, even though a greater quantity of air has less power than a small fire, yet if the quantity of air be much increased, it will have more power than the small fire.
lib. 8 l. 21 n. 18 Tertio ibi: sit igitur in quo est ab etc., ponit demonstrationem intentam: quae talis est. Sit quantum infinitum ab; et sit bc magnitudo finita alterius generis, quae habet quandam potentiam finitam; et sit quoddam mobile d, quod moveatur a magnitudine bc, in tempore quod est ez. Et quia bc est magnitudo finita, poterit accipi maior magnitudo: accipiatur ergo maior secundum duplam proportionem. Quanto autem est maior potentia moventis, tanto in minori tempore movet, ut habitum est in septimo: ergo duplum ipsius bc movebit idem mobile, scilicet d, in medio tempore, quod sit zt, ita quod intelligatur tempus ez dividi per medium in puncto t. Semper autem sic addendo ad bc, minuetur tempus motus: sed quantumcumque addatur ad bc, nunquam potest transire ab, quod improportionaliter excedit bc, sicut infinitum finitum. Et cum ab habeat potentiam finitam, movet in tempore finito d: et sic semper diminuendo de tempore quo movebat bc, perveniemus ad aliquod tempus minus quam sit tempus in quo movebat ab, quia omne finitum transcenditur per divisionem. Sequetur ergo quod minor potentia moveat in minori tempore; quod est impossibile. Relinquitur ergo quod in magnitudine infinita erat potentia infinita, quia scilicet potentia magnitudinis infinitae excedit omnem potentiam finitam. Et hoc probatum est per subtractionem temporis: quia omnis potentiae finitae necesse est ponere quoddam determinatum tempus in quo movet. Quod ex hoc apparet: quia si tanta potentia movet in tanto tempore, maior movebit in minori tempore, sed tamen determinato, idest finito, secundum conversam proportionem; ut scilicet quantum additur ad potentiam, tantum diminuatur de tempore. Et sic quantumcumque addas ad potentiam finitam, dummodo remaneat potentia finita, semper habebit tempus finitum: quia erit accipere aliquod tempus quod erit tanto minus tempore prius dato, quanto potentia superexcrescens ex additione, est maior potentia prius data. Sed potentia infinita excellit in movendo omne determinatum tempus, sicut in omnibus aliis infinitis contingit: quia omne infinitum, sicut multitudo et magnitudo, excedit omne determinatum sui generis. Et sic manifestum est quod potentia infinita excedit omnem potentiam finitam, ex quo excessus potentiae super potentiam est sicut minoratio temporis a tempore, ut dictum est. Unde patet quod conclusio praedicta, scilicet quod magnitudinis infinitae sit potentia infinita, ex necessitate sequitur ex praemissis.	1158. Thirdly, at (906 266 b8) he presents his intended demonstration: Let AB be an infinite quantity, and BC a finite magnitude of another kind, having a finite power; let D be a mobile that is being moved by the magnitude BC in time EZ. But because BC is a finite magnitude, it is possible to take a larger magnitude; let us therefore take one which is in double proportion. Now, the greater the power of a moving cause, the more it moves in less time, as was proved in Book VII. Therefore, the double of BC will move the same mobile, namely, D in one-half the time, namely, ZT, so that the time EZ is bisected by the point T. By continually adding to BC, the time of the motion will be decreased, yet no matter how much is added to BC, it can never traverse AB, which exceeds BC beyond any proportion, as the infinite exceeds the finite. And since AB has finite power, it moves D in a finite time. Consequently, by continually lessening the time BC consumes in moving, we shall reach a time less than the time consumed by AB in its action of moving, because every finite is surpassed by dividing. It will follow, therefore, that the lesser power will move in less time, and this is impossible. What remains, therefore, is that there was an infinite power in the infinite magnitude, for the power of the infinite magnitude exceeded every finite power. This has been proved by subtracting time, because every finite power must have some determinate time in which it causes motion. This is clear from the following consideration: If so much power acts in so much time, a greater power will move in a time smaller but yet definite, i.e., finite, according to an inverse proportion, such that, by as much as is added to the power, by so much is the time decreased. Consequently, no matter how much is added to a finite power, so long as the power remains finite, so will the time always remain finite, for a time will be reached that will be as much less than a previously given time as the power growing by addition is greater than a power previously given. But an infinite power in causing motion surpasses every determinate time, just as happens in all other cases involving the infinite—for every infinite, such as that of number and magnitude, exceeds everything determinate in its genus. Thus it is plain that an infinite power exceeds every finite power, because the excess of power over power corresponds to the decrease of time from time, as has been said. Hence, it is evident that the above-stated conclusion, namely, that the power of an infinite magnitude is infinite, follows of necessity from the premises.
lib. 8 l. 21 n. 19 Deinde cum dicit: est autem hoc demonstrare etc., ponit ad idem aliam demonstrationem, quae non differt a prima nisi in hoc, quod prima concludebat accipiendo potentiam finitam existentem in magnitudine finita alterius generis, haec autem secunda demonstratio procedit accipiendo quandam aliam potentiam finitam, existentem in alia magnitudine finita eiusdem generis, cuius est magnitudo infinita: puta si sit aer magnitudinis infinitae, habens potentiam finitam, accipiemus quandam potentiam finitam existentem in aliqua magnitudine finita alterius aeris. Hac positione facta, manifestum est quod potentia finita magnitudinis finitae aliquoties multiplicata, mensurabit potentiam finitam, quae est in magnitudine infinita; quia omne finitum mensuratur ab aliquo finito minori aliquoties sumpto, vel etiam exceditur. Cum ergo in magnitudine eiusdem generis oporteat quod maior magnitudo habeat maiorem potentiam, sicut maior aer habet maiorem potentiam quam minor; necesse erit quod illa magnitudo finita quae habebit eandem proportionem ad magnitudinem finitam prius acceptam, quam habet potentia finita infinitae magnitudinis ad potentiam magnitudinis finitae prius acceptae, habeat aequalem potentiam potentiae magnitudinis infinitae. Sicut si potentia finita magnitudinis infinitae erit centupla potentiae finitae cuiusdam magnitudinis finitae datae, oportebit quod magnitudo quae est centupla illius magnitudinis finitae, habeat aequalem potentiam magnitudini infinitae; ex quo proportionaliter in re eiusdem generis augetur magnitudo et potentia. Hoc autem est impossibile quod conclusum est; quia oporteret quod vel magnitudo finita esset aequalis infinitae, vel quod minor magnitudo eiusdem generis habeat aequalem potentiam maiori. Est ergo impossibile et primum ex quo sequitur, scilicet quod magnitudo infinita habeat potentiam finitam. Sic ergo epilogando concludit duas conclusiones demonstrativas, scilicet quod in magnitudine finita non possit esse potentia infinita, et quod in magnitudine infinita non possit esse potentia finita.	1159. Then at (907 266 b20) he cites for the same another proof, which differs from the first merely in this, that the first proceeds on the assumption of a finite power existing in a finite magnitude of another kind; but this second proof proceeds on the assumption of a certain other finite power, in another finite magnitude of the same genus as the infinite magnitude. For example, if air is the infinite magnitude having a finite power, we will assume a finite power existing in some finite magnitude of another specimen of air. On these grounds, it is clear that the finite power of the finite magnitude will, if sufficiently multiplied, measure the finite power in the infinite magnitude, because a finite thing is measured or even exceeded by a smaller finite thing taken a certain number of times. Since, therefore, in a magnitude of the same kind, the greater must have more power, as a greater amount of air has more power than a smaller amount, it will be necessary that that finite magnitude which will have the same proportion to the finite magnitude previously taken, as the finite power of the infinite magnitude has to the power of the finite magnitude previously taken, have a power equal to the power of the infinite magnitude. For example, if the finite power of an infinite magnitude were to be 100 times the finite power of a given finite magnitude, then the magnitude 100 times the size of that finite magnitude has a power equal to the power of the infinite magnitude, for in a thing of the same genus the magnitude and the power increase in proportion. However, the conclusion we have reached is impossible, because either the finite magnitude would have to be equal to an infinite ones or a smaller magnitude of the same genus would have a power equal to a larger magnitude of the same genus. Therefore, the assumption from which this conclusion followed is also impossible, namely, that an infinite magnitude may have a finite power. In summary, therefore, he concludes to two demonstrated conclusions, namely, that in a finite magnitude there cannot be infinite power, and that in an infinite magnitude there cannot be finite power.