Authors/Thomas Aquinas/physics/L6/lect10

Lecture 10 Things pertaining to the division of “coming to a stand” and “rest”

Latin	English
	Lecture 10 Things pertaining to the division of “coming to a stand” and “rest”
lib. 6 l. 10 n. 1 Postquam philosophus determinavit de iis quae pertinent ad divisionem motus, hic determinat de iis quae pertinent ad divisionem quietis. Et quia statio est generatio quietis, ut in quinto dictum est, primo determinat ea quae pertinent ad stationem; secundo ea quae pertinent ad quietem, ibi: neque igitur quiescens et cetera. Circa primum tria facit: primo ostendit quod omne quod stat, movetur; secundo quod omne quod stat, stat in tempore, ibi: hoc autem demonstrato etc.; tertio ostendit quomodo primum dicatur in statione, ibi: in quo autem tempore et cetera.	851. After finishing the things that pertain to the division of motion, the Philosopher now determines about things that pertain to the division of rest. And because coming to rest is generation of rest, as we have said in Book V. First he determines the things that pertain to coming to rest; Secondly, the things that pertain to rest, at 856. About the first he does three things: First he shows that whatever is coming to rest is being moved! Secondly, whatever is coming to rest does so in time, at 853; Thirdly, how a first is spoken of in coming to rest, at 854.
lib. 6 l. 10 n. 2 Primum ostendit sic. Omne quod natum est moveri, eo tempore quando natum est moveri, et secundum illud et eo modo prout natum est, oportet quod moveatur vel quiescat: sed illud quod stat, idest tendit ad quietem, nondum quiescit; quia contingeret quod aliquid simul quiescens, idest in quietem tendens, quiesceret, idest in quiete esset: ergo omne quod stat, idest in quietem tendit, movetur quando stat.	852. He shows the first at (653 238 b23): Everything apt to be moved must be either in motion or at rest at the time when it is apt to be moved and in the place in which it is apt to be moved and in the way in which it is apt to be moved. But what is coming to rest is not yet at rest—otherwise, it would happen that a thing would be at the same time tending to rest and actually resting. Therefore, whatever is coining to rest is in motion, when it is coming to rest.
lib. 6 l. 10 n. 3 Deinde cum dicit: hoc autem demonstrato etc., probat quod omne quod stat, stat in tempore, duabus rationibus: quarum prima talis est. Omne quod movetur, movetur in tempore, ut supra probatum est: sed omne quod stat movetur, ut nunc probatum est: ergo omne quod stat, stat in tempore. Secunda ratio est, quia velocitas et tarditas determinantur secundum tempus: sed contingit aliquid velocius et tardius stare, idest in quietem tendere: ergo omne quod stat, stat in tempore.	853. Then at (654 238 b26) he proves by two arguments that whatever is coming to rest is doing so in time. For whatever is being moved is being moved in time, as has been proved. But whatever is coming to rest is being moved, as we have just proved. Therefore, whatever is coming to rest is coming to rest in time. The second argument is that swiftness and slowness are determined according to time. But it can happen that something comes to rest either more swiftly or more slowly. Therefore, whatever is coming to rest does so in time.
lib. 6 l. 10 n. 4 Deinde cum dicit: in quo autem tempore etc., ostendit qualiter dicatur primum in statione. Et circa hoc duo facit: primo ostendit qualiter dicatur aliquid stare in aliquo tempore primo, secundum quod primum opponitur ei quod dicitur secundum partem; secundo ostendit quod in statione non est accipere aliquam primam partem, ibi: sicut autem quod movetur et cetera. Dicit ergo primo quod si in aliquo tempore dicatur aliquid stare primo et per se, et non ratione partis, necesse est quod stetur in qualibet parte illius temporis. Dividetur enim tempus in duas partes; et si dicatur quod in neutra parte stet, sequetur quod non stet in toto, in quo tamen ponebatur stare; ergo stans non stat. Neque etiam potest dici quod in altera tantum parte stet: quia sic non primo staretur in toto tempore, sed solum ratione partis. Unde relinquitur quod stet in utroque. Sic enim dicitur primo stare in toto, quia stat in utraque parte, sicut dictum est supra de eo quod movetur.	854. Then at (655 238 b31) he shows how “first” is spoken of in coming to rest. About this he does two things: First he shows how something is said to be “first” coming to rest in a given time, where “first” is opposed to what is spoken of in reference to a part; Secondly, he shows that in coming to rest, it is not possible to discern a first part, at 855. He says therefore first (655 238 b31) that if at a certain time something is said to be coming to rest first and per se and not by reason of a part, then it must be coming to rest in each part of that time. For time can be divided into two parts, and if it is said that it is coming to rest in neither, it will follow that it is not coming to rest in the whole time, in which it was assumed to be coming to rest. Therefore, something coming to rest is not coming to rest. Nor can it be said that it is coming to rest in only one of the parts, because then it would not be coming to rest first, but only by reason of a part. Hence it will remain that it is coming to rest in both. For it is said to be coming to rest in the whole time only because it is coming to rest in each part, as was said above about things in motion.
lib. 6 l. 10 n. 5 Deinde cum dicit: sicut autem quod movetur etc., ostendit quod non est accipere aliquam primam partem in statione. Et dicit quod sicut non est accipere aliquam primam partem temporis, in qua aliquod mobile movetur, ita etiam est in statione; quia neque in ipso moveri, neque in ipso stare potest esse aliqua prima pars. Quod si non concedatur, sit prima pars temporis, in qua statur, ab: quae quidem non potest esse impartibilis, quia ostensum est supra quod motus non est in impartibili temporis, eo quod semper quod movetur, iam per aliquid motum est, ut supra ostensum est; demonstratum est etiam nunc, quod omne quod stat, movetur. Unde relinquitur quod ab sit divisibile. Ergo in qualibet parte eius statur: iam enim ostensum est quod quando in aliquo tempore dicitur stari primo et per se, et non ratione partis, in qualibet parte illius statur. Ergo cum sit pars prior toto, non erat ab primum in quo statur. Et quia omne illud in quo statur, est tempus, et non est aliquid indivisibile temporis; omne autem tempus est divisibile in infinitum: sequitur quod non erit accipere primum in quo stetur.	855. Then at (656 239 b36) he shows that there is no first part in coming to rest. And he says that just as it is not possible to find in time a first part in which a mobile is being moved, so also in regard to coming to rest, because in neither case can there be a first part. If this is denied, then let AB be the first part of time in which something is coming to rest. This part cannot be indivisible, because it has been shown above that motion does not occur in an indivisible of time (for it is always true that whatever is being moved has already been moved, as we have shown above) and, moreover, whatever is coming to rest is being moved, as we have just now proved. Hence AB must be divisible. Therefore, there is a coming to rest in each part of it, for we have just shown that when in a given time something is coming to rest first and per se and not by reason of a part, it is coming to rest in each part of that given time. Therefore, since the part is prior to the whole, AB was not, the first in which there was a coming to rest. And because that in which something is coming to rest is a time and all time is divisible ad infinitum, it follows that it is impossible to find a first in which something is coming to rest.
lib. 6 l. 10 n. 6 Deinde cum dicit: neque igitur quiescens etc., ostendit idem de quiete. Et circa hoc duo facit: primo ostendit quod non est accipere primum in quiete; secundo ponit quandam considerationem, per quam motus a quiete distinguitur, ibi: quoniam autem omne quod movetur et cetera. Et quia eadem ratio est quare non sit primum in motu, statione et quiete, ideo ex his quae supra dicta sunt de motu et statione, concludit idem in quiete. Et dicit quod non est accipere aliquod primum in quo quiescens quieverit. Et ad hoc probandum resumit quoddam quod supra probatum est, scilicet quod nihil quiescat in impartibili temporis; et resumit etiam duas rationes quibus hoc supra probatum est. Quarum prima est, quod motus non est in indivisibili temporis: in eodem autem est quiescere et moveri; quia non dicimus quiescere, nisi quando id quod aptum natum est moveri, non movetur tunc quando aptum natum est moveri et secundum id secundum quod natum est moveri, puta qualitatem aut locum, aut aliquid huiusmodi. Unde relinquitur quod nihil quiescat in impartibili temporis. Secunda ratio est, quia tunc dicimus aliquid quiescere, quando similiter se habet nunc sicut prius; ac si non diiudicemus quietem per aliquod unum tantum, sed per comparationem duorum ad invicem, ex eo scilicet quod similiter se habet in duobus. Sed in impartibili non est accipere nunc et prius, neque aliqua duo: ergo illud temporis in quo aliquid quiescit, non est impartibile. Isto autem probato, procedit ulterius ad principale propositum ostendendum. Si enim illud in quo aliquid quiescit est partibile, habens in se prius est posterius, sequitur quod sit tempus: haec est enim ratio temporis. Et si est tempus, oportet quod in qualibet partium eius quiescat. Et hoc demonstrabitur eodem modo, sicut et supra monstratum est in motu et statione: quia scilicet si non quiescit in qualibet parte, aut ergo in nulla, aut in una tantum. Si in nulla, ergo neque in toto: si in una tantum, ergo in illa primo et non in toto. Si vero in qualibet parte temporis quiescit, non erit aliquid accipere primum in quiete, sicut neque in motu. Et huius causa est, quia unumquodque quiescit et movetur in tempore; sed in tempore non est accipere aliquod primum, sicut neque in magnitudine, neque in aliquo continuo, propter hoc quod omne continuum divisibile est in infinitum, et sic semper est accipere partem minorem parte. Et inde est quod neque in motu, neque in statione, neque in quiete est aliquid primum.	856. Then at (657 239 a10) he shows the same thing is true for rest. About this he does two things: First he shows that there is no first in rest; Secondly, he gives a method to distinguish motion from rest, And because it is for the same reason that no first is found in notion and in coming-to-rest and in rest, therefore, he concludes the same thing for rest as he concluded for motion and coming-to rest. And he says that there is no first in which a thing at rest has been at rest. To prove this he repeats something previously proved, namely, that nothing is at rest in an indivisible of time. Likewise, he repeats the two reasons he used when he proved this. The first of which is that there is no motion in an indivisible of time. But to rest and to be in motion are in the same: because we do not say that something is resting, unless what is capable of being moved is not being moved when it is apt to be moved and in the sphere in which it is apt to be moved; for example, quality or place or something of this sort. Hence it remains that nothing is at rest in an indivisible of time. The second reason is that it is then that we say something is at rest when it maintains itself as it was previously: as if to say that we do not judge rest by reason of one factor only but by comparing two things to one another and seeing that there is a similar situation in both. But it is impossible to find in something indivisible a “now” and something previous, or any two things. Therefore, that element of time in which something is at rest is not indivisible. Having established this, he proceeds further to prove the main. proposition. For if that in which something is at rest is divisible into parts that possess a prior and a subsequent, it follows that it is a time; for this is the very nature of time. And if it is time, then it must be resting in each part of it. And this will be demonstrated in the same way that it was demonstrated in motion and in coming to rest; namely, that if it is not at rest in each part, it will be at rest in no part or in one only. If in no part, then not in the whole; if in one only, then in that part first and not in the whole first. But if it is at rest in each part of the time, it will not be possible to discover a first in rest any more than in motion. The reason for this is that things are at rest and in motion in time. But in time there is no first any more than in a magnitude or in any continuum, for every continuum is divisible ad infinitum and, consequently, it is always possible to find a part smaller than another. And that is why there is no first in motion or in coming-to-rest or in rest.
lib. 6 l. 10 n. 7 Deinde cum dicit: quoniam autem omne quod movetur etc., ponit quandam considerationem, per quam distinguitur id quod movetur ab eo quod quiescit. Et primo ponit eam; secundo probat, ibi: quiescere enim est et cetera. Circa primum praemittit duas suppositiones: quarum una est, quod omne quod movetur, movetur in tempore; secunda est, quod omne quod mutatur, mutatur ex uno termino in alium. Et ex his duobus intendit concludere tertium, scilicet quod si accipiatur aliquod mobile quod primo et per se moveatur, et non solum ratione suae partis, impossibile est quod sit secundum aliquid unum et idem illius rei in qua est motus, puta in uno et eodem loco vel in una et eadem dispositione albedinis, in aliquo tempore, ita quod accipiamus in tempore esse secundum se, et non ratione alicuius quod in tempore sit. Ideo autem oportet quod accipiatur mobile quod primum movetur, quia nihil prohibet aliquid moveri secundum partem, et tamen ipsum manet per totum tempus in uno et eodem loco, sicut cum homo sedens movet pedem. Ideo autem dicit ex parte temporis, in quo tempore movetur secundum se, et non quo in illius aliquo: quia aliquid, dum movetur, potest dici quod est in aliquo uno et eodem loco in tali die; sed hoc dicitur quia fuit in illo loco non in toto die, sed in aliquo nunc illius diei.	857. Then at (658 239 a23) he gives a way through which what is in motion is distinguished from what is at rest. First he mentions it; Secondly, he proves it, at 858. In regard to the first he premises two suppositions, the first of which is that whatever is being moved is being moved in time. The second is that whatever is being changed is being changed from one terminus to another. From these two facts he intends to conclude a third; namely, that if you take a mobile, which is being moved first and per se and not by reason of its part only, it cannot remain one and the same with respect to that in which the motion is—for example, it cannot remain in one and the same place, or retain one and the same degree of whiteness—during a given period of time, provided that you take it as being in time according to itself and not according to something which is in time. The reason why you must take a mobile which is being moved first and per se is that there is nothing to prevent a thing from being moved according to a part even though it remains in one and the same place throughout the entire time, as when a man sitting down moves his foot. And the reason why he speaks of a time throughout which something is being moved per se and not by reason of some element of time is that while a thing is being moved it can be said that on such and such a day it is in one and the same place; but this would be said, because it was in that place not throughout the day but in some “now” of that day.
lib. 6 l. 10 n. 8 Deinde cum dicit: quiescere enim est etc., probat propositum. Et dicit quod si id quod mutatur, sit per totum aliquod tempus in aliquo uno et eodem, puta in uno loco, sequitur quod quiescat; propter hoc quod in quodam tempore est in uno et eodem loco et ipsum et quaelibet pars eius, et iam supra dictum est quod hoc est quiescere, cum verum sit dicere de aliquo quod ipsum et partes eius sunt in uno et eodem in diversis nunc. Si ergo haec est definitio eius quod est quiescere, et non contingit aliquid simul quiescere et moveri; sequitur quod non contingat id quod movetur esse totum secundum aliquid, idest in aliquo, puta in uno et eodem loco, secundum primum tempus, idest secundum aliquod totum tempus, et non tantum secundum aliquid eius. Et quare hoc sequatur ostendit. Quia omne tempus est divisibile in diversas partes, quarum una est prior altera: unde si per totum tempus sit in aliquo uno, verum erit dicere quod in alia et in alia parte temporis ipsum mobile et partes eius sint in uno et eodem, puta loco; quod est quiescere. Quia si dicatur quod non est in diversis partibus temporis in uno et eodem, sed solum in uno et eodem est per unum nunc, non sequitur quod sit tempus in quo est secundum aliquid, idest in aliquo uno et eodem, sed quod sit in uno et eodem secundum terminum temporis, idest secundum nunc. Licet autem ex hoc quod est aliquid esse in tempore in uno et eodem, sequatur quod quiescat, hoc tamen non sequitur de nunc, si sit ibi in uno solo nunc. Quia omne quod movetur, in quolibet nunc temporis in quo movetur, semper est manens, idest existens, secundum aliquid rei in qua est motus, puta secundum locum aut qualitatem aut quantitatem: non tamen quiescit, quia iam ostensum est quod neque quiescere neque moveri contingit in ipso nunc. Sed verum est dicere quod in ipso nunc aliquid non movetur, et quod in ipso nunc est alicubi, vel secundum aliquid, etiam illud quod movetur. Sed non contingit illud quod movetur, esse quiescens in tempore secundum aliquid: accideret enim quod aliquid, dum fertur, quiesceret; quod est impossibile. Relinquitur ergo quod omne quod movetur, quamdiu movetur, nunquam est in uno et eodem per duo nunc, sed per unum solum.	858. Then at (659 239 a26) he proves the proposition. And he says that if what is being changed is throughout a definite period of time in one and the same state—for example, in one place—it follows that it is at rest, due to the fact that in that time there is present in one and the same place the entire mobile and each part of it; for we have already said that to be at rest means to be able to say of something that it and its parts are in one and the same state in different “now’s”, If, therefore, this is the definition of being at rest and if nothing can be at rest and in motion at the same time, it follows that the whole which is being moved cannot be totally in one state, e.g., in one and the same place, during the whole time and not only in something of it. Why this follows he now explains. Every period of time is divisible into diverse parts, of which one is prior to another. Hence if something is in one state throughout the entire period, it will be true to say that in one and in another part of the time the whole mobile and its parts are in one and the same state, e.g., place—and this is to be at rest. For if it is said to be in one and the same state not in different parts of time but throughout one “now”, it does not follow that there is a time in which it is in one and the same state, but that there is a “now” in which it is in one and the same state. For although from the fact that if something remains in one and the same state during a period of time, the conclusion can be drawn that it is at rest, that conclusion cannot be drawn if it remains in one and the same state in just one “now”. For whatever is being moved is always stable, i.e., existing, vis-a-vis something of that in which it is being moved in each “now” of the time in which it is being moved; for example, place or quality or quantity, Yet it is not for that reason at rest, because it has already been proved that neither rest nor motion can occur in a “now”. But it is true to say that in the very “now” something is not being moved and that in the “now” even what is being moved is somewhere or according to something. But what is being moved in time cannot be under any aspect at rest, for then it would happen that something is at rest while it is in motion—which is impossible. What remains, therefore, is that whatever is being moved is never, as long as it is being moved, in one and the same state for two “now’s” but for only one.
lib. 6 l. 10 n. 9 Et hoc patet in motu locali. Sit enim magnitudo ac, et dividatur in duo media in puncto b, et accipiatur aliquod corpus quod sit o, aequale utrique, scilicet ab et bc, et moveatur de ab in bc. Si autem accipiantur loca totaliter ab invicem distincta, non est hic accipere nisi duo loca: sed manifestum est quod mobile non simul sed successive deserit primum locum et subintrat secundum; unde secundum quod locus est divisibilis in infinitum, secundum hoc multiplicantur loca in infinitum. Quia si dividatur ab in duo media in puncto d, et bc in duo media in puncto e, manifestum est quod de erit alius locus ab utroque. Et similiter semper divisione facta, fiet alius locus. Et idem etiam manifestum est in alteratione: quia quod de albo transit in nigrum, per infinitos gradus albedinis et nigredinis et mediorum colorum pertransit. Non tamen sequitur quod cum sint infinita media, quod nullo modo possit perveniri ad ultimum; quia huiusmodi media loca non sunt infinita in actu, sed in potentia tantum; sicut et magnitudo non est divisa actu in infinitum, sed in potentia divisibilis.	859. And this point is clear in local motion. For let AC be a magnitude divided in half at B and let 0 be a body equal to each half, i.e., to AB and to BC, and let that body be moved from AB to BC. If no part of one of these two places can be a part of the other, there will be only two places for that body on AC. But it is evident that 0 does not relinquish its first place and enter the second all at once but successively. Hence, because place is divisible ad infinitum, the places also are multiplied ad infinitum. For if the half part AB is again halved at D and the other half part BC at E, it is evident that DE will be a place distinct from both AB and BC. By continuing such divisions other and other places will be found. The same point is clear in alteration. For what passes from white to black passes through an infinitude of shades of whiteness and blackness and intermediate colors. However, it does not follow that since there are an infinitude of intermediates, the ultimate cannot be reached, because these intermediate places are infinite not in act but only in potency, just as a magnitude is not actually divided infinitely but is potentially divisible.