Authors/Thomas Aquinas/physics/L4/lect12

Lecture 12 From the fastness and slowness of motion, a separated void is disproved

Latin	English
	Lecture 12 From the fastness and slowness of motion, a separated void is disproved
lib. 4 l. 12 n. 1 Hic ostendit vacuum non esse, ex parte velocitatis et tarditatis in motu. Et circa hoc duo facit: primo assignat causas propter quas velocitas et tarditas est in motu; secundo ex illis causis argumentatur ad propositum, ibi: hoc igitur per quod fertur et cetera. Dicit ergo primo quod unum et idem corpus grave, et quodcumque aliud, utpote lapis vel aliquid huiusmodi, propter duas causas velocius fertur; aut propter differentiam medii per quod fertur, ut per aerem vel terram vel aquam; aut propter differentiam ipsius mobilis, quia est vel gravius vel levius, caeteris paribus.	527. Here the Philosopher, arguing from the fast and slow in motion, shows that the void does not exist. About this he does two things: First he assigns the causes of fastness and slowness in motion; Secondly, he uses these reasons to argue to his point, at no. 529. He says therefore first that one and the same heavy body, and any other thing, for example, a stone or something of this sort, is in faster motion for two reasons: either on account of the medium in which it is being moved, e.g., air or earth or water; or on account of differences in the object, namely, that it is heavier or lighter, all other things being equal.
lib. 4 l. 12 n. 2 Deinde cum dicit: hoc igitur per quod fertur etc., ex praemissis causis argumentatur ad propositum. Et primo ex differentia medii; secundo ex differentia mobilis, ibi: secundum autem eorum et cetera. Circa primum duo facit: primo ponit rationem; secundo eam recapitulando recolligit, ibi: sed sicut in capitulo et cetera. Circa primum duo facit: primo ponit rationem; secundo ostendit conclusionem sequi ex praemissis, ibi: sit enim z vacuum et cetera.	528. Then [367 215 a29] he argues to his point from the aforesaid causes. First from the differences of the medium; Secondly, from the differences in the mobile object, at no. 539, As to the first he does two things: First he gives an argument; Secondly, he recapitulates, at no. 533. Concerning the first he does two things: First he gives his argument; Secondly, he shows that the conclusion follows from the premises, at no. 532.
lib. 4 l. 12 n. 3 Ponit ergo primo talem rationem. Proportio motus ad motum in velocitate est sicut proportio medii ad medium in subtilitate; sed spatii vacui ad spatium plenum nulla est proportio; ergo motus per vacuum non habet proportionem ad motum qui sit per plenum. Primo ergo manifestat primam propositionem huius rationis. Et dicit quod medium per quod aliquid fertur, est causa velocitatis et tarditatis, quia impedit corpus quod movetur. Et maxime quidem impedit quando medium fertur in contrarium, ut patet in navi, cuius motus impeditur a vento. Secundario autem impedit, si etiam quiescat: quia si simul moveretur cum mobili, non impediret, sed magis iuvaret, sicut fluvius qui defert navem inferius. Sed inter ea quae impediunt, magis impedit illud quod non facile dividitur; et tale est corpus magis grossum. Et hoc manifestat per exemplum. Sit enim corpus quod movetur a; spatium per quod movetur, sit b; et tempus in quo a movetur per b, sit c. Ponamus autem aliud spatium quod sit d, aequalis longitudinis cum b; sed tamen d sit plenum subtiliori corpore quam b, secundum aliquam analogiam, idest proportionem, corporis medii, quod impedit motum corporis; ut puta quod spatium b sit plenum aqua, spatium vero d sit plenum aere. Quanto ergo aer est subtilior aqua et minus spissus, tanto mobile quod est a, citius movebitur per spatium d, quam per spatium b. Quae est ergo proportio aeris ad aquam in subtilitate, eadem est proportio velocitatis ad velocitatem: et quanto est maior velocitas, tanto est minus tempus; quia velocior motus dicitur, qui est in minori tempore per aequale spatium, ut in sexto dicetur. Unde, si aer est in duplo subtilior quam aqua, sequetur quod tempus in quo a movetur per b, quod est plenum aqua, sit duplum tempore in quo pertransit d, quod est plenum aere: et ita tempus c, in quo pertransit spatium b, erit duplum tempore quod est e, in quo pertransit spatium d. Et sic poterimus universaliter accipere, quod in quacumque proportione medium, per quod aliquid fertur, est subtilius et minus impeditivum et facilius divisibile, in eadem proportione erit motus velocior.	529. Therefore, he first gives this argument: The ratio of motion to motion in regard to speed is equal to the ration of medium to medium in respect of subtlety. But there is no ratio between empty space and full space. Therefore, motion in a void has no ratio to motion in the full. First of all he explains the first proposition of this argument. And he says that the medium through which a body is in motion is the cause of its fastness or slowness because it acts as an obstacle to the body in motion. The greatest obstacle occurs when the medium is in a contrary motion, as is evident in the case of a ship whose movement is impeded by the wind. The medium is an obstacle in a secondary way even if it is not in motion, because if it were in motion with the object it would not be an obstacle but a help, as the water which carries a ship downstream. But among obstacles a greater impediment is offered by things that are not easy to divide, such as the grosser bodies. He explains this by an example. Let the body in motion be A, and let the space through which it is being moved be B, and the time in which A is being moved through B be C. Let us posit another space, D, of the same length as B, but let D be full of a subtler body than the one in B, so that a certain analogy, i.e., ratio, exists between the bodies which impede the motion (for example, let B be full of water and D full of air). Now to the extent that air is subtler than water and less condensed, to that extent will the mobile A be more quickly moved through D than through B. Therefore the ratio of the velocities will equal the ratio of the subtlety of air to the subtlety of water. And the greater the velocity, the less the time: because that motion is faster which covers the same interval in less time, as will be shown in Book VI (L.3). Hence if air is twice as subtle as water, the time it takes A to be moved through B (full of’ water) will be twice the time for A to pass through D (full of air). Consequently, the time C in which it travels the distance B will be twice the time it takes E to pass through D. Therefore, we can take it as a general rule that in whatever ratio the medium (in which something is in motion) is subtler and less resistant and more easily divisible, in that ratio will the motion be faster.
lib. 4 l. 12 n. 4 Deinde cum dicit: vacuum autem nullam etc., manifestat secundam propositionem: et dicit quod vacuum non exceditur a pleno secundum aliquam proportionem. Et hoc probat per hoc, quod numerus non excedit nihil secundum aliquam proportionem, sed solum attenditur proportio aliqua numeri ad numerum, vel ad unitatem: sicut quatuor excedunt tria in uno, et adhuc in pluri excedunt duo, et adhuc in pluri unum. Unde dicitur maior proportio quatuor ad unum, quam ad duo vel tria. Sed quatuor non excedunt nihil secundum aliquam proportionem. Et hoc ideo quia necesse est quod omne excedens dividatur in id quod exceditur, et in excedentiam, idest in id in quo excedit: sicut quatuor dividitur in tria, et in unum in quo excedit tria. Si ergo quatuor excedunt nihil, sequetur quod quatuor dividantur in aliquot et nihil: quod est inconveniens. Unde etiam non potest dici, quod linea excedat punctum, nisi componeretur ex punctis, et divideretur in ea. Et similiter non potest dici quod vacuum habeat aliquam proportionem ad plenum: quia vacuum non cadit in compositionem pleni.	530. Then [368 215 b12] he explains the second proposition, and says that the void is not exceeded by the full according to some certain ratio. And he proves this by the fact that a number does not exceed nothing [zero] by any ratio, for ratios can exist only between one number and another, or between a number and unity; as four exceeds three by one, and exceeds two by more yet, and one by still more. Hence there is said to be a greater ratio existing between four and one, than between four and two, or four and three. But four does not exceed nothing according to any ratio. This is so because anything exceeding is necessarily divided into that which is exceeded and into the excess, i.e., that in which it exceeds; for example, four can be divided into three, and into one, which latter is the amount by which four exceeds 3. But if four exceeds nothing, it will follow that four can be divided into so much and nothing; which is unacceptable. For a same reason one could not say that a line exceeds a point unless it were composed of points and divided into points. In like manner, it cannot be said that the void has any ratio to the full; because the void is not a part of the full.
lib. 4 l. 12 n. 5 Deinde cum dicit: ergo neque motum etc., ponit conclusionem, concludens quod non est possibile esse proportionem inter motum qui fit per vacuum, et motum qui fit per plenum; sed si aliquod corpus fertur per quodcumque subtilissimum in tanto spatio talique tempore, motus qui est per vacuum transcendet omnem proportionem datam.	531. Then [369 215 b20] he concludes that there can be no ratio between a motion in the void and a motion in the full: but that if any body is in motion in the subtlest of mediums over such and such a distance for such and such a time, the motion in the void will exceed any given ratio.
lib. 4 l. 12 n. 6 Deinde cum dicit: sit enim z vacuum etc., quia praedictam conclusionem ostensive ex principiis suppositis deduxerat, ne qua dubitatio oriatur de principiis praemissis, ut certior sit processus, probat eandem conclusionem deducendo ad impossibile. Si enim dicatur quod motus qui est per vacuum, habet aliquam proportionem velocitatis ad motum qui est per plenum, ponatur ergo quod spatium vacuum sit z, quod quidem sit aequale secundum magnitudinem, spatio b quod est plenum aqua, et spatio d quod est plenum aere. Si autem detur quod motus qui est per z, habeat aliquam proportionem secundum velocitatem ad motus qui sunt per b et d, oportet dicere quod motus qui est per z, quod est vacuum, sit in aliquo determinato tempore: quia velocitates distinguuntur secundum quantitates temporum, ut supra dictum est. Si ergo dicatur quod mobile quod est a, transeat per spatium vacuum quod est z, in aliquo tempore; sit illud tempus I, quod oportet esse minus quam tempus e, in quo pertransit spatium d, quod est plenum aere; et sic haec erit proportio motus per vacuum ad motum per plenum, quae est proportio temporis e ad tempus I. Sed necesse erit ponere quod in tanto tempore quantum est I, mobile quod est a, pertranseat quoddam spatium plenum subtiliori corpore ipsius d, idest ipso d. Et hoc quidem continget, si inveniatur aliquod corpus quod differat in subtilitate ab aere, quo ponebatur plenum spatium d, secundum illam proportionem quam habet tempus e ad tempus I; ut puta si dicatur illud corpus esse ignis, quo ponatur plenum spatium z, quod prius ponebatur vacuum: quia si corpus quo ponitur plenum spatium z, est tanto subtilius corpore quo ponitur plenum spatium d, quantum tempus e excedat tempus I, sequetur quod mobile quod est a, si feratur per z, quod est spatium plenum subtilissimo corpore, et per d, quod est spatium plenum aere, transibit per z e converso in maiori velocitate in tanto tempore, quantum est I. Si ergo nullum corpus sit in quo est z, sed ponatur hoc spatium vacuum, sicut et primo; adhuc debebit velocius moveri. Sed hoc est contra id quod fuit positum. Positum enim erat quod motus fieret per spatium z, quod est vacuum, in tempore I; et sic cum in tempore I transeat idem spatium, cum est plenum subtilissimo corpore, sequitur quod in eodem tempore transibit idem mobile unum et idem spatium, cum est vacuum et cum est plenum. Manifestum est ergo, quod si fuerit aliquod tempus, in quo mobile feratur per quodcumque spatium vacuum, sequetur hoc impossibile, quod in aequali tempore transibit plenum et vacuum: quia erit accipere aliquod corpus quod habebit proportionem ad aliud corpus, sicut habet proportionem tempus ad tempus.	532. Then [370 215 b22], because he had deduced the above conclusion in direct line from the assumed principles, he now, lest any doubt arise about those principles, and to make the process more certain, proves the same conclusion by deducing to the impossible. For if it be claimed that the speed of a motion taking place in the void has a ratio to the speed of a motion taking place in the full, then let the empty space be Z, which shall be equal in magnitude to the space B, full of water, and to the space D, full of air. Now if it is supposed that a motion through Z has a certain ratio in respect of speed to the motions through B and D, then it must be admitted that the motion through Z (the void) takes place in some definite portion of time, because velocities are distinguished according to the quantities of the times consumed, as was said above. If therefore we say the object A passes through the empty space Z in a definite time, let that time be I, which must be less than the time E required for A to pass through D, which is full of air. Then the ratio of the motion through the empty to the motion through the full will equal the ratio of time E to time I. But during time I, the mobile A will pass through a definite space that is full of a subtler body than exists in D, i.e., than D. And this will happen, if one can find a body which differs in subtlety from air (of which D is full) in the ratio that the time E has to the time I. For example, say the space Z, which had been originally empty space, is now full of fire. If the body of which Z is full is subtler than the body of which D is full, in the amount that the time E exceeds the time I, it will follow that the mobile A, if it is in motion through Z (which is the space now full of a most subtle body), and through D (which is the space full of air), it will pass through Z conversely at a greater speed in a time I. If therefore no body exists in Z but it is again considered to be empty space, as previously, it will have to move even faster. But this is against what was laid down, namely, that the motion through Z (empty space) required time I. Consequently, since in time I it passes over the same space when it is full of the most subtle of bodies, it follows that during the same time the same mobile passes through one and the same space, when that space is empty and when it is full. It is clear therefore that if it took a definite time for the mobile to pass through an empty space, the impossibility follows that in equal time it will pass through full and empty space, because there will be some body having the same ratio to some other body as one time has to another time.
lib. 4 l. 12 n. 7 Deinde cum dicit: sed sicut in capitulo est dicere etc., summatim colligit ea, in quibus virtus consistit praemissae rationis. Et dicit quod sicut contingit recapitulando dicere, manifesta est causa, quare praedictum inconveniens accidat: quia scilicet quilibet motus est proportionatus cuilibet motui secundum velocitatem: quia omnis motus est in tempore, et qualibet duo tempora, si sint finita, habent proportionem ad invicem. Sed vacui ad plenum non est proportio, ut probatum est. Unde si ponatur motus fieri per vacuum, necesse est quod sequatur inconveniens. Ultimo autem epilogans concludit, quod praedicta inconvenientia accidunt, si accipiantur diversae velocitates motuum secundum differentiam mediorum.	533. Then [371 216 a4] he summarized that in which the force of the previous reasoning consists. And he says that we can now say in recapitulation that the reason why the conflict mentioned in the above occurs is clear: it is because every motion has a ratio to every other motion in respect to speed. For every motion requires time, and any two periods of time, if they are finite, have a ratio one to the other. But there is no ratio between the empty and the full, as we proved. Hence the supposition that motion occurs in the void leads to the conflict mentioned. In a final summary [372 216 a11] he concludes that the above mentioned conflicts occur if the different species of motion are taken according to differences of the media.
lib. 4 l. 12 n. 8 Sed contra hanc rationem Aristotelis insurgunt plures difficultates. Quarum quidem prima est, quod non videtur sequi, si fiat motus per vacuum, quod non habeat proportionem in velocitate ad motum qui fit per plenum. Quilibet enim motus habet determinatam velocitatem ex proportione potentiae motoris ad mobile, etiam si nullum sit impedimentum. Et hoc patet per exemplum et per rationem. Per exemplum quidem in corporibus caelestibus, quorum motus a nullo impeditur; et tamen eorum est determinata velocitas, secundum determinatum tempus. Per rationem autem, quia ex hoc ipso quod in magnitudine, per quam transit motus, est accipere prius et posterius, contingit etiam accipere prius et posterius in motu; ex quo sequitur motum esse in determinato tempore. Sed verum est quod huic velocitati potest aliquid subtrahi ex aliquo impediente. Non igitur oportet quod proportio motus ad motum in velocitate, sit sicut proportio impedimenti ad impedimentum, ita quod si non sit aliquod impedimentum, quod motus fiat in non tempore: sed oportet quod secundum proportionem impedimenti ad impedimentum, sit proportio retardationis ad retardationem. Unde posito quod motus sit per vacuum, sequitur quod nulla retardatio accidat supra velocitatem naturalem; et non sequitur quod motus qui est per vacuum, non habeat proportionem ad motum qui fit per plenum.	534. But several difficulties arise against this reasoning of Aristotle. The first is that it does not seem to follow that if motion takes place in the void that it has no ratio to motion in the full. For every motion has its definite velocity from the ratio of the motive energy to the mobile, even if no obstacle exists. And this is evident both from an example and from reason. From an example, indeed, in the heavenly bodies, whose motion encounters no obstacle and yet they have a definite velocity depending on the amount of time. From reason also: for, since it is possible to point out a “before” and “after” in the magnitude through which the motion takes place, so also one can take a “before” and “after” in the motion from which it follows that motion is in a determined time. But it is true that this velocity can be diminished on account of an obstacle. Yet it is not necessary therefore to make the ratio of motion to motion in respect of velocity be as the ratio of obstacle to obstacle, so as to make the motion occur in no time, if there be no obstacle; rather, the ratio of one slowing up to another slowing up must correspond to the ratio of obstacle to obstacle. Hence on the assumption that motion takes place in the void, it follows that no slowing up happens to the natural speed, but it does not follow that a motion in the void will have no ratio to motion in the full.
lib. 4 l. 12 n. 9 Huic autem obiectioni Averroes in commento suo resistere conatur. Et primo quidem conatur ostendere hanc obiectionem ex falsa imaginatione procedere. Dicit enim quod ponentes praedictam obiectionem imaginantur additionem in tarditate motus fieri, sicut fit additio in magnitudine lineae, quod pars addita sit alia a parte cui additur. Ita enim videtur praedicta obiectio procedere, ac si tardatio fiat per hoc, quod aliquis motus addatur alteri motui, ita quod subtracto illo motu addito per impedimentum retardans, remaneat quantitas motus naturalis. Sed hoc dicit non esse simile: quia cum retardatur motus, quaelibet pars motus fit tardior; non autem quaelibet pars lineae fit maior. Deinde ostendere nititur, quomodo ratio Aristotelis necessitatem habeat. Et dicit quod velocitas vel tarditas motus consurgit quidem ex proportione motoris ad mobile; sed oportet mobile esse aliquo modo resistens motori, sicut patiens quodammodo est contrarium agenti. Quae quidem resistentia potest esse ex tribus. Primo quidem ex ipso situ mobilis: ex hoc enim ipso quod movens intendit transferre mobile ad aliquod ubi, ipsum mobile in alio ubi existens repugnat intentioni motoris; secundo ex natura mobilis, sicut apparet in motibus violentis, ut cum grave proiicitur sursum; tertio ex parte medii. Omnia enim haec tria accipienda sunt simul ut unum resistens, ad hoc quod causetur una causa tarditatis in motu. Quando igitur mobile, seorsum consideratum secundum quod differt a movente, est aliquid ens actu, potest inveniri resistentia mobilis ad motorem, vel ex parte mobilis tantum, sicut accidit in corporibus caelestibus, vel ex parte mobilis et medii simul, sicut accidit in corporibus animatis quae sunt hic. Sed in gravibus et levibus, subtracto eo quod mobile habet a movente, scilicet forma, quae est principium motus, quam dat generans, quod est movens, non remanet nisi materia, ex cuius parte nulla resistentia potest considerari ad movens; unde relinquitur in talibus sola resistentia ex parte medii. Sic igitur in corporibus caelestibus est differentia velocitatis solum secundum proportionem motoris ad mobile; in corporibus vero animatis secundum proportionem motoris ad mobile et ad medium resistens simul. Et in talibus procederet obiectio praedicta, quod remota retardatione quae est ex parte medii impedientis, adhuc remanet determinata quantitas temporis in motu, secundum proportionem motoris ad mobile. Sed in gravibus et levibus non potest esse retardatio velocitatis, nisi secundum resistentiam medii; et in talibus procedit ratio Aristotelis.	535. Averroes attempts to counter this objection in his commentary. First he tries to show that this objection proceeds from false imagination. For he says that those who make the above objection imagine that an addition in slowness of motion occurs just like an addition in the magnitude of a line, where the added part is distinct from the part to which the addition is made. For the above objection seems to proceed as though slowing up takes place by adding one motion to another motion in such a way that if you were to subtract the motion that was added through the obstacle which slows, the quantity of natural motion would then be left. But this is not the case, because when a motion is slowed up, each part of the motion becomes slower, whereas each part of a line does not become larger. Then he attempts to show how Aristotle’s argument concludes with necessity. And he says that the speed or slowness of a motion does indeed arise from the proportion of the mover to the mobile; but the mobile must in some manner resist the mover, as the patient is in a certain way contrary to the agent. This resistance can arise from three sources: First, from the situs of the mobile; for from the very fact that the mover intends to transfer the mobile to some certain place, the mobile, existing in some other place, resists the intention of the mover. Secondly, from the nature of the mobile, as is evident in compulsory motions, as when a heavy object is thrown upwards. Thirdly, from the medium. All three are taken together as one resistance, to constitute one cause of slowing up in the motion. Therefore when the mobile, considered in isolation as different from the mover, is a being in act, the resistance of the mobile to the mover can be traced either to the mobile only, as happens in the heavenly bodies, or to the mobile and medium together, as happens in the case of animate bodies on this earth. But in heavy and light objects, if you take away what the mobile receives from the mover, viz., the form which is the principle of motion given by the generator, i.e., by the mover, nothing remains but the matter which can offer no resistance to the mover. Hence in light and heavy objects the only source of resistance is the medium. Consequently, in heavenly bodies differences in velocity arise only on account of the ratio between mover and mobile; in animate bodies from the proportion of the mover to the mobile and to the resisting medium—both together. And it is in these latter cases that the given objection would have effect, viz., that if you remove the slowing up caused by the impeding medium, there still remains a definite amount of time in the motion, according to the proportion of the mover to the mobile. But in heavy and light bodies, there can be no slowing up of speed, except what the resistance of the medium causes—and in such cases Aristotle’s argument applies.
lib. 4 l. 12 n. 10 Sed haec omnino videntur esse frivola. Primo quidem, quia licet quantitas tarditatis non sit secundum modum quantitatis continuae, ut addatur motus motui, sed secundum modum quantitatis intensivae, sicut cum aliquid est altero albius; tamen quantitas temporis ex qua Aristoteles argumentatur, est secundum modum quantitatis continuae, et fit tempus maius per additionem temporis ad tempus; unde subtracto tempore quod additur ex impediente, remanet tempus naturalis velocitatis. Deinde quia in gravibus et levibus remota forma, quam dat generans, remanet per intellectum corpus quantum; quod ex hoc ipso quod quantum est, in opposito situ existens, habet resistentiam ad motorem; non enim potest intelligi alia resistentia in corporibus caelestibus ad suos motores. Unde nec etiam in gravibus et levibus sequetur ratio Aristotelis, secundum quod ipse dicit. Et ideo melius et brevius dicendum est, quod ratio Aristotelis inducta, est ratio ad contradicendum positioni, et non ratio demonstrativa simpliciter. Ponentes autem vacuum, hac de causa ipsum ponebant, ut non impediretur motus: et sic secundum eos causa motus erat ex parte medii, quod non impedit motum. Et ideo contra eos Aristoteles argumentatur, ac si tota causa velocitatis et tarditatis esset ex parte medii; sicut etiam et supra evidenter hoc ostendit dicens, quod si natura est causa motus simplicium corporum, non oportet ponere vacuum ut causam motus eorum: per quod dat intelligere quod totam causam motus ponebant ex parte medii, et non ex natura mobilis.	536. But all this seems quite frivolous. First, because, although the quantity of slowing up is not parallel to the mode of continuous quantity, so that motion is added to motion, but parallel to the mode of intensive quantity, as when something is whiter than something else, yet the quantity of time from which Aristotle argues is parallel to the manner of continuous quantity—and time becomes greater by the addition of time to time. Hence if you subtract the time which was added on account of the obstacle, the time of the natural velocity remains. Then, because if you remove the form which the generator gives to light and heavy bodies there still remains in the understanding “quantified body,” which from the very fact that it is a quantified body existing in an opposite situs offers resistance to the mover. For we cannot suppose in heavenly bodies any other resistance to their movers. Hence, as he [Averroes] presents the case, even in the case of heavy and light bodies the reasoning of Aristotle would not follow. Therefore it is better and briefer to say that the argument brought forward by Aristotle is an argument aimed at contradicting his opponent’s position and not a demonstrative argument in the absolute sense. For those who posited a void did so in order that motion be not prevented. Thus, according to them, the cause of motion was on the part of a medium which did not impede motion. And therefore Aristotle argued against them as though the total cause of fastness and slowness derived from the medium, as he clearly shows above when he says that if nature is the cause of the motion of simple bodies, it is not necessary to posit the void as the cause of their motion. In this way he gives us to understand that they supposed the total cause of the motion to depend on the medium and not on the nature of the mobile.
lib. 4 l. 12 n. 11 Secunda autem dubitatio contra rationem praedictam est, quia si medium quod est plenum, impedit, ut ipse dicit, sequitur quod non sit in hoc medio inferiori aliquis motus purus non impeditus, quod videtur inconveniens. Et ad hoc Commentator praedictus respondet, quod hoc impedimentum quod est ex medio, requirit motus naturalis gravium et levium, ut possit esse resistentia mobilis ad motorem, saltem ex parte medii. Sed melius dicendum est quod omnis motus naturalis incipit a loco non naturali, et tendit in locum naturalem. Unde quandiu ad locum naturalem perveniat, non est inconveniens si aliquid non naturale ei coniungatur. Paulatim enim recedit ab eo quod est contra naturam, et tendit in id quod est secundum naturam: et propter hoc motus naturalis in fine intenditur.	537. The second difficulty against [Aristotle’s] argument is that if the medium which is full impedes, as he says it does, then it follows that there will not be any pure unimpeded motion in this lower medium—and this seems unfitting. To this the Commentator replies that the impediment that arises from the medium is required by the natural motion of heavy and light bodies, so that there can be resistance of the mobile to the mover, at least on the side of the medium. But it is better to say that every natural motion begins from a place that is not natural and tends to a natural place. Hence until it reaches its natural place it is not unfitting if something unnatural be attached to it. For it gradually departs from what is against its nature and tends to what is in keeping with its nature. And for this reason a natural motion accelerates as it nears its end.
lib. 4 l. 12 n. 12 Tertia obiectio est, quia cum in corporibus naturalibus sit determinatus terminus raritatis, non videtur quod semper sit accipere corpus rarius et rarius secundum quamlibet proportionem temporis ad tempus. Sed dicendum est, quod hoc quod sit determinata raritas in rebus naturalibus, non est ex natura corporis mobilis inquantum est mobile, sed ex natura determinatarum formarum, quae requirunt determinatas raritates vel densitates. In hoc autem libro agitur de corpore mobili in communi: et ideo frequenter utitur Aristoteles in hoc libro in suis rationibus, quibusdam, quae sunt falsa, si considerentur naturae determinatae corporum; possibilia autem, si consideretur natura corporis in communi. Vel potest dici, quod hic etiam procedit secundum opinionem antiquorum philosophorum, qui ponebant rarum et densum prima principia formalia; secundum quos raritas et densitas in infinitum augeri poterant, cum non sequerentur alias priores formas, secundum quarum exigentiam determinarentur.	538. The third objection is that since in natural bodies there is a fixed limit of rarity, it does not seem that one can keep supposing a rarer and rarer body according to any given proportion of time to time. In reply it should be said that a fixed rarity in natural things is not due to the nature of the mobile body insofar as it is mobile, but to the nature of specific forms that require specific rareness and density. But in this book we are dealing with mobile body in general, and therefore Aristotle frequently uses in his arguments things which are false if the specific natures of bodies are considered, but possible if the nature of body in general is considered. Or it can be replied that he is here also proceeding according to the opinion of the earlier philosophers who posited the rare and the dense as the first formal principles. According to them, rarity and density could be increased ad infinitum since these did not depend on other previous forms according to whose exigencies they would be determined.
lib. 4 l. 12 n. 13 Deinde cum dicit: secundum autem eorum etc., ostendit non esse vacuum separatum, ex velocitate et tarditate motus, secundum quod omnino causa sumitur ex parte mobilis. Et dicit quod haec quae dicentur consequuntur, si consideretur differentia velocitatis et tarditatis, secundum quod mobilia quae feruntur se invicem excellunt; quia videmus quod per aequale spatium finitum, citius feruntur ea quae habent maiorem inclinationem aut secundum gravitatem aut secundum levitatem; sive sint maiora in quantitate, aequaliter gravia vel levia existentia, sive sint aequalia in quantitate, et sint magis gravia vel levia. Et hoc dico si similiter se habeant secundum figuras: nam corpus latum tardius movetur, si deficiat in gravitate vel magnitudine, quam corpus acutae figurae. Et secundum proportionem quam habent magnitudines motae ad invicem vel in gravitate vel in magnitudine, est proportio velocitatis. Unde et oportebit ita esse etiam si sit motus per vacuum, scilicet quod corpus gravius seu levius aut magis acutum velocius feratur per medium vacuum. Sed hoc non potest esse: quia non est assignare aliquam causam propter quam unum corpus alio velocius feratur. Si enim motus fiat per spatium plenum aliquo corpore, potest assignari causa maioris vel minoris velocitatis, secundum aliquam praedictarum causarum: hoc enim est, quia illud quod movetur maius existens, ex sua fortitudine velocius dividit medium; vel propter aptitudinem figurae, quia acutum est penetrabilius, aut propter inclinationem maiorem, quam habet vel ex gravitate vel ex levitate, vel etiam propter violentiam prohibentis. Vacuum autem dividi non potest citius vel tardius: unde sequetur quod omnia aequali velocitate movebuntur per vacuum. Sed hoc manifeste apparet impossibile. Patet igitur ex ipsa velocitate motus, quod vacuum non est. Attendendum est autem quod in processu huius rationis est similis difficultas sicut et in prima. Videtur enim supponere, quod differentia velocitatis in motibus non sit nisi propter differentiam divisionis medii: cum tamen in corporibus caelestibus sint diversae velocitates, in quibus non est aliquod plenum medium resistens, quod dividi oporteat per motum corporis caelestis. Sed solvenda est haec dubitatio sicut et prius.	539. Then [373 216 a12] he shows there is no separated void, arguing from the speed and slowness of motion, insofar as the cause is taken entirely from the viewpoint of the mobile. And he says that what he is about to say will follow logically, if we attend to the difference of speed and slowness insofar as bodies in motion exceed one another. For we see that over a given equal space, greater speed is shown by bodies having a greater inclination due either to heaviness or lightness, whether they are greater in quantity but equally heavy or light, or whether they are equal in quantity but unequal in heaviness or lightness. And I say this if they are similar in shape. For a wide body is moved more slowly if it be deficient in heaviness or size than a body with a pointed shape. And the ratio of the velocity corresponds to the ratio which the moving magnitudes have to one another in respect to their weight or in respect to their magnitude. And this will have to be true also if the motion occurs in the void, namely, that a heavier body or a lighter body or a more pointed body will be moved faster through an empty medium. But this cannot be, since it is impossible to explain why one body would be moved faster than another. For if the motion takes place within a space filled with some body, an explanation for the greater or lesser speed can be given—it will be due to any of the aforesaid causes. The explanation is that a greater body will on account of its strength divide the medium more quickly, either an account of its shape, because what is sharp has greater penetrating power; or on account of a greater inclination traceable either to the heaviness or lightness of the body; or even to the force imparted by that which projects it. But the void cannot be cleaved faster or slower. Hence it will be moved through a void with equal speed. But this clearly appears as impossible. And so from a consideration of the velocity of motion, it is evident that the void does not exist. It should be observed that in this reasoning process there exists the same difficulty as in the first one. For he seems to suppose that difference in velocity in motions is due only to the different ways in which the medium can be cleaved, whereas the fact is that there are differences of velocity among the heavenly bodies in which there is no full medium resisting which has to be cleaved by the motion of the heavenly body. But this difficulty should be solved as the above one was.
lib. 4 l. 12 n. 14 Ultimo, autem epilogando concludit manifestum esse ex dictis, quod si ponatur vacuum esse, accidit contrarium eius quod supponebant probantes esse vacuum. Illi enim procedebant, ac si motus esse non possit, si vacuum non sit. Sed ostensum est contrarium: scilicet, si vacuum sit, quod motus non est. Sic igitur praemissi philosophi opinantur vacuum esse quoddam discretum et separatum secundum se, scilicet quoddam spatium habens dimensiones separatas: et huiusmodi vacuum opinantur necesse esse, si sit motus secundum locum. Ponere autem sic vacuum separatum, idem est quod dicere locum esse quoddam spatium distinctum a corporibus; quod est impossibile, ut supra ostensum est in tractatu de loco.	540. Finally [374 216 a21] he summarizes, and concludes that from the foregoing it is clear that in regard to the philosophers who posit a void, the contrary of what they supposed as a reason for proving it occurs. For they proceeded on the assumption that motion could not take place unless there was a void. But the contrary has been proved; namely, that if there be a void, there is no motion. Thus, therefore, those philosophers believe that the void is some distinct and separate thing—a space having separate dimensions—and they believed it was such a space that had to exist if local motion were to be possible. However, to posit such a separated void is the same as saying that place is a kind of space distinct from bodies—which is impossible, as was shown in the treatise on place.