Authors/Thomas Aquinas/physics/L4/lect14

Lecture 14 There is no void within bodies

Latin	English
	Lecture 14 There is no void within bodies
lib. 4 l. 14 n. 1 Postquam philosophus ostendit non esse vacuum separatum, hic ostendit non esse vacuum corporibus inditum. Et circa hoc tria facit: primo ponit rationem ponentium sic vacuum; secundo improbat eorum positionem, ibi: si igitur rarum dicunt etc.; tertio solvit rationem ipsorum, ibi: quoniam autem vacuum et cetera.	544. Having shown that there is no separated void, the Philosopher here shows that there is no void inherent in bodies. As to this he does three things: First he gives the reason proposed by those who posit such a void; Secondly, he disproves their position, at no. 546; Thirdly, he dissolves their argument, at no. 551.
lib. 4 l. 14 n. 2 Dicit ergo primo quod quidam philosophi fuerunt, qui opinati sunt quod vacuum sit in corporibus, accipientes rationem ex raro et denso. Videbatur enim eis quod rarefactio et condensatio fieret propter vacuum intrinsecum corporibus. Si vero non esset sic rarum et densum, dicebant quod non erat possibile ut partes alicuius corporis coirent, idest subintrarent ad invicem, et quod aliquod corpus calcaretur, idest comprimeretur per condensationem. Si autem hoc non sit, ducebant ad inconveniens, et ex parte motus localis, et ex parte motus generationis et corruptionis, sive alterationis. Ex parte quidem motus localis, quia oportebit dicere vel quod omnino motus non sit, vel quod uno moto moveatur totum universum, sicut dixit Xuthus philosophus. Et hoc ideo, quia si aliquod corpus movetur localiter, cum accedit ad locum plenum alio corpore, oportet quod illud corpus inde expellatur, et tendat in alium locum, et iterum corpus ibi inventum in alium: et nisi fiat condensatio corporum, oportebit quod omnia corpora moveantur. Ex parte vero generationis sive alterationis sequitur hoc inconveniens, quod semper fiat aequalis mutatio ex aere in aquam, et ex aqua in aerem: ut puta, si ex aqua unius cyathi generatus est aer, oportet quod ex tanto aere quantus est aer generatus, alibi generetur aqua. Et hoc ideo, quia maior quantitas est aeris quam aquae ex qua generatur. Occupat igitur aer generatus maiorem locum quam aqua ex qua generatur. Et sic oportet quod vel totum corpus universi occuparet maiorem locum; vel quod alibi tantumdem de aere convertatur in aquam: vel oportet dicere quod sit aliquid vacuum intra corpora, ad hoc quod fiat condensatio corporum; quia non opinabantur quod aliter contingeret condensari et rarefieri corpora, nisi vacuo in eis existente.	545. He says therefore first [378 216 b22] that there have been some philosophers who believed that there is a void in bodies, basing their argument on the existence of rarity and density. For they believed that rarefaction and condensation took place on account of a void inhering in bodies. If rarity and density did not exist, they say, the parts of bodies could not “go in,” i.e., enter each other, and “harden,” i.e., be compressed by condensation. But if this does not take place, they deduced certain difficulties both in respect to local motion, and in respect to the motions of generation and corruption, or alteration. In respect to local motion, because it would be necessary to admit either that motion does not exist at all, or that the whole universe is moved with one motion, as says Xuthus, a philosopher. This would be because if a body were moved locally, when it approached a place full of another body, this body would have to be expelled, and tend toward another place and the body found there would have to go to yet another place, so that, unless there were condensation of bodies, all bodies would have to be in motion. In regard to generation or alteration, this difficulty arises that there would also be an equal change of air into water and of water into air: for example, if air be generated from one cupful of water, it would be necessary that from a same amount of air as was generated, an amount of water be generated somewhere else. The reason is that there is now a greater amount [i.e. volume] of air than there previously was of water from which it was generated. The generated air therefore occupies a greater place than the water from which it was generated. Consequently, either the whole body of the universe would have to occupy a greater place, or else as much air in some other place would have to be converted into water, or else finally, it must be admitted that there is a void within bodies to allow them to be condensed, because these philosophers supposed that bodies could not become condensed and rarefied unless there was a void existing in them.
lib. 4 l. 14 n. 3 Deinde cum dicit: si igitur rarum etc., destruit positionem praedictam. Et primo secundum unum intellectum; secundo secundum alium, ibi: si autem non est separabile et cetera. Dicit ergo primo quod illi qui dicunt vacuum esse in corporibus, dupliciter possunt hoc intelligere; uno modo quod in quolibet corpore sint multa quasi foramina vacua, quae sint separata secundum situm ab aliis partibus plenis, sicut est videre in spongia vel in pumice vel in aliquo alio huiusmodi: alio modo quod vacuum non sit separatum secundum situm ab aliis partibus corporis, utpote si dicamus quod dimensiones, quas dicebant esse vacuum, subintrent omnes partes corporis. Si autem primo modo dicant vacuum esse in corporibus, patet reprobatio huius ex praemissis. Per quam enim rationem ostenditur, quod non est aliquod vacuum separatum extra corpora, nec aliquis locus habens aliquod tale spatium proprium praeter dimensiones corporum; per eandem rationem probari potest, quod non est aliquod corpus hoc modo rarum, quod habeat intra se aliqua spatia vacua, distincta ab aliis partibus corporis.	546. Then [379 216 b30] he rejects this position: First according to one interpretation; Secondly, according to another interpretation, at no.547. He says therefore that those who posit a void within bodies can give this two interpretations: the first is that in each body there are, as it were, many empty openings, each existing separate in respect to situs from the other full parts, as can be seen in a sponge or in pumice or things of this sort. The second interpretation is that the void is not separate in respect to situs from the other parts of the body; as if we should say that the dimensions, which they said were the void would penetrate all the parts of the body. The refutation of their claim as to the first way of the void’s being in bodies is evident from what went before. For the very argument that shows there is not a separate void outside of bodies nor any place having such a space proper to itself over and above the dimensions of bodies. The same argument can be used to prove that there is no body so rarefied that it would have within itself any empty spaces distinct from the other parts of the body.
lib. 4 l. 14 n. 4 Deinde cum dicit: si autem non est separabile etc., improbat praedictam positionem quantum ad secundum intellectum, quatuor rationibus. Dicit ergo quod si vacuum non est sic in corporibus sicut separabile et distinctum ab aliis partibus, sed tamen inest aliquod vacuum in corporibus, minus quidem est impossibile, quia non sequuntur inconvenientia supra posita contra vacuum separatum; sed tamen ad hoc etiam sequuntur quaedam inconvenientia. Primo quidem quod vacuum non erit causa omnis motus localis, ut ipsi intendebant, sed solum motus qui est in sursum: quia vacuum secundum eos est causa raritatis, rarum autem invenitur esse leve, ut patet in igne, leve autem est quod movetur sursum; unde vacuum erit causa solum motus sursum.	547. He then [380 217 a1] disproves the aforesaid position as to the second interpretation and gives four reasons for rejecting it. He says, therefore, that if the void is not in bodies in such a way as to be separable and distinct from the other parts but is nevertheless present in bodies, the situation is less impossible, because the difficulties mentioned above against a separate void do not arise; yet against this also certain discrepancies do arise. First of all, the void will not be the cause of every local motion, as the maintained, but only of upward motion—for the void, according to them, is the cause of rarity, and the rare in turn is found to be light, as is evident in fire, and what is light travels upwards; consequently, the void will be the cause only of upward motion.
lib. 4 l. 14 n. 5 Secundam rationem ponit ibi: postea motus causa et cetera. Et dicit quod secundum istos qui ponunt vacuum in corporibus, vacuum est causa motus, non sicut in quo aliquid movetur, ut ponebant causam motus vacuum qui dicebant vacuum spatium separatum; sed eo modo ponunt vacuum causam motus, in quantum ipsum vacuum intrinsecum defert corpora; sicut si dicamus quod utres inflati, in eo quod feruntur ipsi sursum propter levitatem, deferunt sursum quidquid eis continuatur. Et sic vacuum inditum corporibus fert secum corpus in quo est. Sed hoc videtur esse impossibile: quia tunc oporteret quod vacuum movetur, et quod esset aliquis locus vacui; et eum vacuum et locus sint idem, sequetur quod vacui interioris erit vacuum exterius, in quod fertur; quod est impossibile.	548. He gives the second reason [381 217 a1] when he says that according to those who posit a void in bodies the void is the cause of motion, not as that in which something is moved (in the way that those who held for a separate empty space posited the void as a cause of motion), but as the cause of motion in such a way that the empty space within the bodies transports them: it is analogous to the case of inflated wine-skins, which, due to the fact that they are carried upward on account of their lightness, also carry upward whatever is attached to them. And in this way the void inherent in bodies carries with it the body in which it is. But this seems impossible: because then it would follow that the void would have to be subject to motion and that there would exist a certain place for the void. And since the void and place are the same, it will follow that of an interior void there will be an exterior void into which it is transported—which is impossible.
lib. 4 l. 14 n. 6 Tertiam rationem ponit ibi: amplius quomodo et cetera. Et dicit quod si motus sursum causa est vacuum, deferens corpus sursum, cum nihil sit assignare quod deferat corpus deorsum, non erit assignare quare gravia deorsum ferantur.	549. The third reason [382 217 a5] is given when he says that if the cause of upward motion is the void carrying a body upward, then since there is nothing to carry the body down, there would be no explanation of why heavy bodies are carried downwards.
lib. 4 l. 14 n. 7 Quartam rationem ponit ibi: et manifestum est et cetera. Et dicit quod si rarum causat motum sursum propter vacuitatem, oportebit quod quanto aliquid est rarius et magis vacuum, tanto velocius feratur sursum: et si sit omnino vacuum, velocissime feretur. Sed hoc est impossibile, quia quod est omnino vacuum non potest moveri, eadem ratione qua supra ostensum est quod in spatio vacuo non potest esse motus; quia non esset comparare velocitates vacui et pleni, neque ex parte spatii neque ex parte mobilis, secundum aliquam determinatam proportionem, eo quod pleni ad vacuum nulla est proportio. Non ergo vacuum potest esse causa motus sursum.	550. Be then gives the fourth reason [833], and says that if the rare causes upward motion on account of emptiness, then the rarer and more empty a thing is, the faster it should be carried upward. And if it were completely empty, it should move with a maximum speed. But this is impossible, because what is completely empty cannot be moved, for the same reason by which it was shown above that motion is impossible in an empty space; for there is no way to compare the speeds of the empty and of the full (whether you consider the space or the mobile) according to some definite ratio, because there is no ratio between the full and the empty. Therefore the void cannot be the cause of upward motion.
lib. 4 l. 14 n. 8 Deinde cum dicit: quoniam autem vacuum etc., solvit praemissam rationem. Et primo repetit eam, magis ipsam explanans; secundo solvit eam, ibi: nos autem dicimus et cetera. Dicit ergo primo, quod quia non dicimus esse vacuum, neque in corporibus neque extra, oportet solvere quae ab aliis inducuntur, quia vere ingerunt dubitationem. Et primo ex parte motus localis: quia aut non erit omnino motus localis, nisi sit raritas et densitas, quam non intelligebant fieri nisi per vacuum; aut oportebit dicere quod ad motum cuiuslibet corporis etiam ipsum caelum in sursum feratur, vel aliqua pars eius, quod vocat turbationem caeli. Aut iterum ex parte generationis et corruptionis, oportebit quod semper aequalis aqua fiat ex aere, et alibi aer ex aqua: quia cum plus de aere generetur ex aqua, necesse est, nisi fiat condensatio, quam non credebant posse fieri sine vacuo, aut quod corpus quod habetur ultimum secundum communem opinionem, scilicet corpus caeleste, depellatur per exuberantiam inferiorum corporum; aut quod alibi in quocumque loco tantumdem de aere convertatur in aquam, ad hoc quod totum corpus universi inveniatur semper aequale. Sed quia ad hoc quod dixerat de motu locali, posset quodammodo obviari, iterum repetit ut excludat illud: et dicit quod aut sequitur quod nihil moveatur: quia secundum praedicta, tumultuatio caeli accidet quocumque transmutato. Sed hoc est verum, nisi intelligatur motus fieri circulariter; ut puta quod a moveatur ad locum b, et b ad locum c, et c ad locum d, et iterum d ad locum a. Sic enim non oportebit, posita circulari latione, quod uno moto, totum universum turbetur. Sed nos non videmus quod omnis loci mutatio naturalium corporum sit in circulum, sed multae sunt in rectum. Unde adhuc sequetur tumultuatio caeli, nisi ponatur condensatio et vacuum. Haec est igitur ratio propter quam aliqui ponebant esse vacuum.	551. Then [385 217 a6] be answers a previous argument: First he repeats it, explaining it more extensively; Secondly, he solves it, at no. 552. He says therefore first that because we do not admit a void either in bodies or outside of them, we must answer the arguments of our opponents, because they present a real difficulty. First of all on the side of local motion: either (1) local motion will not be if there is not rarity and density, which they believed could not be produced without the void; or (2) we will be forced to say that whenever a body is moved, the very heavens or some part of them are borne outward, which he calls the “bulging” of the heavens. Secondly, from the viewpoint of generation and corruption a transformation of water into air will always have to be balanced by an equal transformation of air into water somewhere else; for since more air is generated from water it is required (unless condensation takes place which they thought impossible without a void) either (1) that the body which was held to be outermost according to common opinion, namely, the heavenly body, be pushed outward by the swelling of lower bodies; or (2) that somewhere else there must be an equal amount of air converted into water, so that the entire bulk of the universe remain always equal. But because one could in a certain way elude what he had said about local motion, he mentions this [evasion] again in order to exclude it. Thus he repeats, “Or it follows that nothing is moved.” Now according to the foregoing a disturbance of the heavens occurs whenever anything is transmuted. And this is true unless the motion is rotational: for example, let A be in motion to place B, and B to place C, and C to place D, and again D to place A. In this case, on the assumption of rotational motion, it will not be necessary, if one thing moves, that the whole universe be disturbed. But we do not see every local motion of natural bodies to be rotational, but many are in a straight line. Hence, there will be still disturbance of the heavens, unless condensation and the void be admitted. This then is the argument which prompted some to posit the void.
lib. 4 l. 14 n. 9 Deinde cum dicit: nos autem dicimus etc., solvit praemissam rationem. Tota autem vis praemissae rationis in hoc consistit, quod rarefactio et condensatio fiat per vacuum. Unde hic obviat Aristoteles ostendens quod contingit rarefieri et condensari sine vacuo. Et primo ostendit propositum; secundo inducit conclusionem principaliter intentam, ibi: ex dictis igitur manifestum est et cetera. Circa primum tria facit: primo manifestat propositum per rationem; secundo per exempla, ibi: sicut enim ex frigido fit calidum etc.; tertio per effectus rari et densi, ibi: est autem densum quidem et cetera. Circa primum duo facit: primo praemittit quaedam necessaria ad propositum; secundo probat propositum, ibi: est igitur et corporis et cetera.	552. Then 385] he answers this argument. Now the entire force of this argument consists in this, that rarefaction and condensation take place by means of the void. Accordingly, Aristotle meets this by showing that rarefaction and condensation can take place without a void. First, he reveals his proposition; Secondly, he introduces the conclusion be mainly intends, at no. 557. As to the first he does three things: First he explains his proposition by an argument; Secondly, by examples, at no. 555; Thirdly, by the effects of rarity and density, at no. 556. As to the first he does two things: First he premises certain things necessary for his proposition; Secondly, he proves his proposition, at no. 554.
lib. 4 l. 14 n. 10 Praemittit autem quatuor, quae accipit ex subiectis, id est ex his quae supponuntur in scientia naturali, et supra etiam manifestata sunt in primo huius libri. Quorum primum est, quod una est materia contrariorum, ut calidi et frigidi, vel cuiuscumque alterius naturalis contrarietatis: contraria enim nata sunt fieri circa idem. Secundum est, quod omne quod in actu est, necessario fit ex eo quod est in potentia. Tertium est, quod materia non est separabilis a contrariis, ita ut sit absque eis: sed tamen secundum rationem materia est aliud a contrariis. Quartum est, quod materia per hoc quod nunc est sub uno contrario et postea sub alio, non est alia et alia, sed eadem numero.	553. Now [385 217 a21] he lays down four preliminary statements which he takes from the “subjects,” i.e., the presuppositions of natural science, and which were already explained in Book I. The first of these is that the matter of contraries is one; for example, of the hot and the cold, or of any other natural contrariety—for contraries are apt to affect the same thing. The second is that whatever is in act had to come into being from what was in potency. The third is that matter is not separable from contraries so as to exist without them—but yet, according to motion, the matter is distinct from the contraries. The fourth is that matter is not, by virtue of being, now under one contrary, now under another, other and other, but numerically one.
lib. 4 l. 14 n. 11 Deinde cum dicit: est igitur et corporis materia etc., ex praemissis ostendit propositum in hunc modum. Eadem numero est materia contrariorum: magnum autem et parvum sunt contraria circa quantitatem: ergo eadem numero est materia magni et parvi. Et hoc manifestum est in transmutatione substantiali. Cum enim generatur aer ex aqua, eadem materia quae prius erat sub aqua, facta est sub aere, non accipiendo aliquid quod prius non haberet, sed illud quod prius erat in potentia in materia, reductum est in actum. Et similiter est cum e converso ex aere generatur aqua. Sed hoc interest, quod cum ex aqua generatur aer, fit mutatio ex parvo in magnum; quia maior est quantitas aeris generati, quam aquae ex qua generatur; cum autem ex aere fit aqua, fit e converso transmutatio a magnitudine in parvitatem. Ergo et cum aer multus existens reducitur ad minorem quantitatem per condensationem, vel ex minori in maiorem per rarefactionem, eadem materia est quae fit utrumque in actu, scilicet magnum et parvum, prius existens ad haec in potentia. Non ergo condensatio fit per hoc quod aliquae aliae partes subintrando adveniant; vel rarefactio per hoc quod partes inhaerentes extrahantur, ut existimabant ponentes vacuum inter corpora; sed per hoc quod materia earundem partium accipit nunc maiorem, nunc minorem quantitatem: ut sic rarefieri nihil aliud sit, quam materiam recipere maiores dimensiones per reductionem de potentia in actum; condensari autem e converso. Sicut autem materia est in potentia ad determinatas formas, ita etiam est in potentia ad determinatam quantitatem. Unde rarefactio et condensatio non procedit in rebus naturalibus in infinitum.	554. Then [386 217 a26] from these preliminaries he proves his point in this way: The matter of contraries is one in number. But the large and the small are contraries in respect of quantity. Therefore the matter of the large and the small to numerically the same. And this is clear in substantial transmutation. For when air is generated from water, the same matter which previously was under the water, came to be under air, not receiving anything that it previously lacked, but rather that which was previously in potency in the matter was reduced to act. And the same is true in reverse, when from air water is generated. But there is this difference: when air is generated from water, there is a change from small to large; because the quantity of air generated is larger than the quantity of water from which it was generated. But when, from air, water is made, there is produced contrariwise a transmutation from largeness to smallness. Therefore when a large amount of air is reduced to a smaller amount by condensation, or from a small amount to a larger amount by rarefaction, it is the same matter which becomes both in act, namely, large and small, while being previously in potency to them. Therefore condensation does not take place by certain parts moving into others, or rarefaction by inhering parts being extracted, as those thought who posited a void within bodies. Rather it is because the matter of the same parts now has greater, now lesser, quantity: hence, to become rare is nothing other than for matter to receive greater dimensions by being reduced from potency to act; and the opposite for becoming dense. For just as matter is in potency to definite forms, so it is in potency to definite quantity. Hence rarefaction and condensation do not proceed ad infinitum in natural things.
lib. 4 l. 14 n. 12 Deinde cum dicit: sicut enim ex frigido fit calidum etc., manifestat idem per exempla. Et quia rarefactio et condensatio pertinet ad motum alterationis, ponit exemplum de aliis alterationibus. Et dicit quod sicut eadem materia mutatur ex frigido in calidum et ex calido in frigidum, propter hoc quod utrumque istorum erat in potentia in materia; sic etiam et aliquid fit ex calido magis calidum, non propter hoc quod aliqua pars materiae fiat calida quae prius non erat calida, cum esset minus calidum; sed quia tota materia reducitur in actum magis vel minus calidi. Aliud etiam exemplum ponit de qualitate circa quantitatem. Et dicit quod si circumferentia et convexitas maioris circuli restringatur ad minorem circulum, manifestum est quod fit magis curvum: non tamen ista ratione, quod ambitus, id est circularitas, facta sit in aliqua parte quae primo non fuisset curvata sed recta; sed per hoc quod idem ipsum quod prius erat minus curvatum, magis curvatur. Non enim in huiusmodi alterationibus fit aliquid magis vel minus deficiendo, id est per subtractionem, neque etiam per additionem; sed per unius et eiusdem transmutationem de perfecto ad imperfectum, aut e converso. Et hoc patet per hoc quod in eo quod est simpliciter et uniformiter aliquale, non est invenire aliquam partem quae sit sine tali qualitate; sicut non est accipere in scintilla ignis aliquam partem in qua non sit caliditas et albedo, id est claritas. Sic igitur et prior calor advenit posteriori, non per hoc quod aliqua pars quae non erat calida, sit facta calida; sed per hoc quod illud quod erat minus calidum, fit magis calidum. Unde et magnitudo et parvitas sensibilis corporis non extenditur vel ampliatur in rarefactione et condensatione per hoc, quod materia aliquid superadditum accipiat; sed quia materia, quae prius erat in potentia ad magnum et parvum, transmutatur de uno in alterum. Et ideo rarum et densum non fit per additionem partium subintrantium, vel per subtractionem earundem; sed per hoc quod una est materia rari et densi.	555. Then [387 217 a31] he makes the same thing clear from examples. And because rarefaction and condensation pertain to the motion of alteration, [i.e., change in quality] he gives an example of other alterations. And he says that just as the same matter is changed from cold to hot and from hot to cold, because both were in the matter potentially, so also something passes from hot to hotter, not because some part of the matter previously not hot becomes hot which was not so when It was less hot, but because the entire matter is reduced into the act of being more or less hot. He gives another example of a quality in the matter of quantity. And he says that if the circumference and convexity of a larger circle are brought in to that of a smaller circle, they become more curved. This happens not because an “ambit,” or curvature, begins to exist in some part that previously was not curved but straight, but because the same that was previously less curved, becomes more curved. For in alterations of this sort things do not become more and less by “defect,” i.e., by subtraction, or addition but by the transmutation of one and the same thing from perfect to imperfect, or from imperfect to perfect. This is evident in the case of what is absolutely and uniformly “such and such”: it is impossible to find in it any part lacking that quality, just as it is impossible in a flame to find any part lacking heat and “whiteness,” i.e., clarity. So also prior heat comes to a later heat, not because a part previously not hot became hot, but because what was less hot became hotter. So too the largeness and smallness of a sensible body is not extended or increased in rarefaction and condensation by the matter receiving some addition, but by the matter which was previously in potency to large and small being transmuted from one to the other. Therefore the rare and the dense are not produced by the addition of penetrating parts or by their removal, but by there being one matter of the rare and of the dense.
lib. 4 l. 14 n. 13 Deinde cum dicit: est autem densum etc., manifestat propositum per effectus rari et densi. Ex differentia enim raritatis et densitatis consequitur differentia aliarum qualitatum, scilicet gravis et levis, duri et mollis. Et sic patet quod rarum et densum diversificant qualitates et non quantitates. Dicit ergo quod ad raritatem sequitur levitas, et ad densitatem sequitur gravitas. Et hoc rationabiliter: quia rarum est ex hoc, quod materia recipit maiores dimensiones; densum autem ex hoc, quod materia recipit minores dimensiones: et sic si accipiantur diversa corpora aequalis quantitatis, unum rarum et aliud densum, densum habet plus de materia. Dictum est autem supra in tractatu de loco, quod corpus contentum comparatur ad continens sicut materia ad formam: et sic grave, quod tendit versus medium contentum, rationabiliter est magis densum, habens plus de materia. Sicut ergo circumferentia circuli maioris reducta ad minorem circulum, non recipit concavitatem in aliqua sui parte, in qua non erat prius, sed quod prius erat concavum, reducitur ad maiorem concavitatem; et sicut quaecumque pars ignis quam quis receperit, est calida: ita et totum corpus fit rarum et densum conductione, id est contractione, et distensione unius et eiusdem materiae, secundum quod movetur ad maiorem vel minorem dimensionem. Et hoc patet per ea quae sequuntur ex raro et denso, quae sunt qualitates. Nam ad densum sequitur grave et durum. Et de gravi quidem ratio assignata est; de duro autem ratio manifesta est: quia durum dicitur quod magis resistit pulsui vel divisioni; quod autem habet plus de materia, minus est divisibile, quia minus obedit agenti, propter hoc quod est magis remotum ab actu. E converso autem, ad rarum sequitur leve et molle. Sed grave et durum in aliquibus dissonant, sicut in ferro et plumbo: nam plumbum est gravius, sed ferrum est durius. Et huius ratio est, quia plumbum habet plus de terrestri: sed id quod est aquae in eo, est imperfectius congelatum et digestum.	556. Then [388 217 b11] he manifests his proposition by the effects of the rare and of the dense. For from a difference in rarity and density there follows a difference in other qualities; namely, in heaviness and lightness, hardness and softness. Consequently, rarity and density diversify qualities and not quantities. He says therefore, that lightness follows rarity, and heaviness density. And with good reason: for rarity arises from matter receiving greater dimensions, density from matter receiving lesser dimensions. Consequently, if you take diverse bodies of equal quantity, one being rare and the other dense, then the dense has more matter. Now it was said above in the treatise on place that the contained body is related to the container, as is matter to form; consequently, a heavy body which tends toward the middle [i.e., center]contained is with good reason more dense because it has more matter. Just as, therefore, the circumference of a larger circle, when it is restricted to a smaller circle does not receive concavity in a part not previously concave, but rather a part previously concave was reduced to a greater concavity, and just as any part of fire that anyone may take will be hot, so also it is the whole body that becomes rare or dense by the “conduction,” i.e., contraction, or expansion of one and the same matter, accordingly as it is moved to greater or smaller dimensions. This is clear from what follows from rarity and density, namely, qualities. For the heavy and the hard follow from density. Why heaviness follows density has already been explained. Why hardness follows is easy to explain: that is hard which is better able to resist both pressure and cleavage; but what has more matter is less divisible, because it is less obedient to something acting upon it, on account of its being more remote from actuality. Contrariwise, lightness and softness follow upon rarity. But the heavy and the hard fail to coincide in some things: for lead is heavier, but iron is harder. The reason for this is that lead has more of the element “earth” in it, but what there is of “water” in it is less perfectly congealed and distributed.
lib. 4 l. 14 n. 14 Deinde cum dicit: ex dictis igitur manifestum est etc., concludit principale propositum. Et dicit manifestum esse ex dictis, quod non est vacuum aliquod spatium separatum; neque simpliciter est extra corpus existens; neque existens in raro secundum aliqua foramina vacua; neque etiam existens est in potentia in corpore raro, secundum illos qui non ponebant vacuum quod est in corporibus separatum a pleno. Et sic nullo modo est vacuum, nisi aliquis penitus velit vocare vacuum materiam, quae quodammodo est causa gravitatis et levitatis, et sic est causa motus secundum locum. Densum enim et rarum sunt causa motus secundum contrarietatem gravis et levis; sed secundum contrarietatem duri et mollis, sunt causa passibile et impassibile: nam molle est id quod facile patitur divisionem, durum autem e contra, ut dictum est. Sed hoc non pertinet ad loci mutationem, sed magis ad alterationem. Et sic concludit determinatum esse de vacuo, quomodo sit, et quomodo non sit.	557. Then [389 217 b20] he concludes his chief proposition. And he says it is clear from the foregoing that there is no separate empty space: it is not anything existing absolutely outside a body; or in a rarefied thing after the manner of empty holes; or in potency in a rarefied body, according to those who did not posit a void that exists in bodies as something separated from the fullness of the body. Consequently, in no way is there a void, unless someone simply wants to call matter the void, since it is somehow the cause of heaviness and lightness, and consequently the cause of motion in respect of place. For density and rarity are causes of motion according to the contrariety of heavy and light; but in regard to the contrariety of hard and soft, passible and non-passible are the causes: for the soft is that which easily suffers division and the hard contrariwise, as was said. However, this does not pertain to local motion but rather to [the motion called] “alteration.” And so he concludes that it has been determined in what way the void exists and in what way it does not.