Authors/Thomas Aquinas/physics/L8/lect16

Lecture 16 No change of place can be continuous and perpetual except the circular

Latin	English
	Lecture 16 No change of place can be continuous and perpetual except the circular
lib. 8 l. 16 n. 1 Postquam philosophus ostendit quod nulla mutatio potest esse continua et perpetua nisi localis, hic ostendit quod nulla loci mutatio potest esse continua et perpetua nisi circularis. Et circa hoc duo facit: primo ostendit propositum demonstrative; secundo logice, ibi: rationabiliter autem et cetera. Circa primum duo facit: primo ostendit propositum; secundo ex veritate demonstrata solvit quasdam dubitationes, ibi: unde et ad dubitationem et cetera. Circa primum tria facit: primo dicit quid principaliter intendat. Intendit enim ostendere quod possibile est esse quendam motum, qui unus existens, in infinitum continuetur; et quod talis motus est solus circularis. Et hoc primo ostendet.	1104. After showing that no change but local can be continuous and perpetual, the Philosopher now shows that no local change can be continuous and perpetual, unless it be a circular one. About this he does two things: First he proves his proposition by a demonstration; Secondly, dialectically, (L. 18). About the first he does two things: First he proves his proposition; Secondly, from the proven truth he solves some doubts, (L. 17). About the first he does three things: First he mentions what he chiefly intends. For he intends to prove that it is possible that there be a motion which, being one, might be continued ad infinitum, and that such a motion can be none but a circular one. This is the first thing he proves.
lib. 8 l. 16 n. 2 Secundo ibi: omne quidem enim movetur etc., ostendit quomodo procedendum sit. Quia enim omne quod localiter fertur, movetur vel circulariter, vel motu recto, vel motu composito ex utroque, sicut si aliquid moveretur per chordam et arcum; manifestum est quod si quis duorum simplicium motuum, scilicet vel circularis vel rectus, non potest esse in infinitum continuus, quod multo minus ille qui est compositus ex utroque. Unde oportet praetermittere motum compositum, et agere de simplicibus.	1105. Secondly, at (871 261 b28) he shows how to proceed. And he says that whatever is moved locally is moved with either a circular motion or a straight one or in a motion that combines these two, e.g., a motion through a chord and an arc. Hence it is clear that if either of the two simple motions, namely, the circular or the rectilinear, cannot be infinitely continuous, much less their combination. Therefore one must omit the latter and attend to the simple ones.
lib. 8 l. 16 n. 3 Tertio ibi: quod autem quod fertur etc., ostendit quod motus rectus qui est super magnitudinem rectam et finitam, non possit esse in infinitum continuus; et ita nullus motus rectus continuus potest esse in infinitum, nisi poneretur aliqua magnitudo infinita in actu; quod supra improbatum est in III physicorum. Ostendit autem hoc duplici ratione: quarum prima talis est. Si aliquis super rectam magnitudinem et finitam movetur in infinitum, oportet quod hoc fiat per reflexionem. Ostensum est enim in sexto, quod magnitudinem finitam pertransit aliquid tempore finito; cum ergo pervenitur ad terminum magnitudinis finitae, cessabit motus, nisi mobile revertatur per reflexionem ad principium magnitudinis unde cepit moveri. Sed illud quod reflectitur secundum motum rectum, movetur contrariis motibus. Quod sic probat. Contrarii motus sunt quorum termini sunt contrarii, ut in quinto habitum est. Sed contrarietates loci sunt sursum et deorsum, ante et retro, dextrum et sinistrum: omne autem quod reflectitur, secundum aliquam istarum contrarietatum necesse est quod reflectatur: omne ergo quod reflectitur, movetur contrariis motibus. Ostensum est autem supra in quinto, quis motus sit unus et continuus, ille scilicet qui est unius subiecti et in uno tempore et in eadem re non differenti secundum speciem. Haec enim tria considerantur in omni motu: primum est tempus; secundum est subiectum quod movetur, ut homo aut Deus, secundum eos qui corpora caelestia deos dicebant; tertium autem est in quo movetur, quod quidem in motu locali est locus, in alteratione passio, idest passibilis qualitas, in generatione et corruptione species, in augmento et diminutione magnitudo. Manifestum est autem quod contraria differunt secundum speciem: unde motus contrarii non possunt esse unus et continuus. Praedicta autem sex sunt loci differentiae; et sic oportet quod sint contraria, quia cuiuslibet generis differentiae sunt contrariae. Relinquitur ergo quod impossibile sit, id quod reflectitur moveri uno motu continuo.	1106. Thirdly, at (872 261 b31) he shows that a rectilinear motion upon a straight and finite magnitude cannot be infinitely continuous and that consequently no rectilinear motion can be infinitely continuous unless an actually infinite magnitude is assumed—and this was proved impossible in Physics III above. He proves his point with two arguments, of which the following is the first. If anything be moved ad infinitum upon a finite magnitude, it has to be done by reflexion. For it has been proved in Book VI that something will traverse a finite magnitude in finite time. When, therefore, the boundary of the finite magnitude is reached, the motion will cease, unless the mobile is returned by reflexion to the beginning of the magnitude whence the motion began. But what is reflected in a rectilinear motion is being moved with contrary motions. And this he now proves; Contrary motions are ones whose terminal points are contrary, as was proved in Book V. But the contrarieties of place are up and down, ahead and behind, right and left. Now, whatever is reflected must be reflected according to one or other of these contrarieties. Therefore, whatever is reflected is moved with contrary motions. But it was shown in Book V which motion is one and continuous: the one, namely, which is of one subject, in one time, and in the same category that does not differ specifically. For these three elements are considered in every motion: first, there is the time; secondly, the subject being moved, such as a man or a god, according to those who call the heavenly bodies “gods”; thirdly, there is that in which the motion occurs: in local motion it is a place; in alteration it is a passion, i.e., a passible quality; in generation and ceasing-to-be it is a form; in growth and decrease it is a magnitude. Now it is clear that contraries differ with respect to species; hence contrary motions cannot be one and continuous, But the six things listed above are differences of place and, consequently, they must be contrary, because the differences of any genus are contrary. It remains, therefore, that it is impossible for that which moves by a reflected motion to be moved by one continuous motion.
lib. 8 l. 16 n. 4 Et quia posset aliquis dubitare an id quod reflectitur contrariis motibus moveatur, propter hoc quod non apparet manifesta et determinata contrarietas in loco, sicut in aliis generibus in quibus est motus, ut supra in quinto dictum est: ideo addit quoddam signum ad hoc idem ostendendum, praeter rationem supra positam ex contrarietate terminorum. Et dicit quod signum huius est, quod motus qui est ab a in b, sit contrarius ei qui est a b in a, sicut contingit in motu reflexo: quia huiusmodi motus, si simul fiant, stant et repausant ad invicem, idest unus impedit alium et facit eum stare. Et non solum hoc contingit in reflexione motus recti, sed etiam in reflexione motus circularis. Signentur enim in aliquo circulo tria signa, scilicet abc: constat quod si incipiat moveri ab a in b, et postea moveatur ab a in c versus aliam partem, quod erit reflexio; et isti duo motus impediunt se, et unus sistit, idest facit stare, alium. Sed si continue moveatur aliquid ab a in b, et per b iterum in c, non erit reflexio. Ideo autem motus reflexi impediunt se invicem tam in recto quam in circulo, quia hoc est de natura contrariorum, quod se impediant et corrumpant. Motus autem qui sunt diversi et non contrarii, non se impediunt; sicut motus qui est sursum et qui est in latus, puta in dextrum vel sinistrum, non se impediunt, sed simul potest aliquid moveri et sursum et in dextrum.	1107. And because someone could doubt whether what is reflected is being moved with contrary motions, on the ground that there does not appear a manifest and determinate contrariety in place, such as does appear in the other genera in which motion occurs, as was said in Book V, he therefore, in order to show the same point, adds a certain sign over and above the argument above, which was based on the contrariety of termini. And he says that the sign of this is that a motion from A to B is contrary to one from B to A, as happens in a reflex motion, because such motions, if they take place simultaneously, “arrest and stop each other,” i.e., are such that one impedes the other and stops it. And this happens not only in reflex straight motion but in reflex circular motions. For let three points A, B and C be designated on a circle. It is evident that if something begins to be moved from A to B and later is moved from A to C, there was reflexion and those two motions block one another and one arrests the other, i.e., causes the other to stop. But if something is moved without interruption from A to B and again from B to C, there is no reflexion. But the reason why reflex motions impede one another, both in straight and in circular motions, is that it is the nature of contraries to impede and destroy one another. Motions, however, that are diverse but not contrary, do not impede one another, as, for example, an upward motion and a motion to the side, i.e., to the right or left, do not obstruct one another; rather something can at the same time be moved upwards and to the right.
lib. 8 l. 16 n. 5 Deinde cum dicit: maxime autem manifestum etc., ponit secundam rationem ad ostendendum quod motus reflexus non potest esse in infinitum continuus: quae quidem ratio accipitur ex quiete, quam necesse est intervenire. Dicit ergo quod maxime ex hoc manifestum est quod impossibile est motum rectum esse continuum in infinitum, quia necesse est id quod reflectitur quiescere inter duos motus. Et hoc verum est non solum si moveatur per lineam rectam, sed etiam si feratur secundum circulum. Et ne aliquis intelligat ferri secundum circulum, idem esse quod ferri circulariter, ad hoc excludendum subdit, quod non est idem ferri circulo, idest circulariter secundum proprietatem circuli, et ferri circulum, idest pertransire suo motu circulum. Contingit enim aliquando quod secundum quandam continuationem sit motus eius quod movetur, dum scilicet pertransit partem post partem secundum ordinem partium circuli; et hoc est ferri circulariter. Quandoque autem contingit quod pertransit circulum, quando redierit ad principium unde incepit moveri, non pertransire ultra secundum ordinem partium circuli, sed redire retro; et hoc est reflecti. Sive ergo fiat reflexio in linea recta, sive in linea circulari, necesse est quod interveniat quies media.	1108. Then at (873 262 a12) he gives a second argument to show that reflex motions cannot be continuous ad infinitum, and it is an argument based on the pause that must intervene. He says, therefore, that it is above all the fact that what is reflected must rest between two motions which makes it clear that it is impossible for a rectilinear motion to be infinitely continuous. And this is true not only if something is moved through a straight line but also if it is carried along according to a circle. And lest anyone suppose that being carried along “according to a circle” is the same as being carried along “circularly,” to exclude this he adds that it is not the same to be carried along circularly according to the characteristics of a circle and to be carried along a circle, i.e., to traverse a circle. For sometimes it occurs that the motion of what is moved is according to a certain continuity, as, namely, it traverses part after part according to the order of parts of the circle, and this is “to be carried along circularly.” But sometimes it occurs that what traverses a circle has not, when it returns to the point whence the motion began, travelled in an onward direction according to the order of the parts of the circle, but has returned backwards—and this is “to be reflected.” Whether, therefore, the reflexion occurs in a straight line or a circular line, a pause must intervene.
lib. 8 l. 16 n. 6 Et huius rei fides accipi potest non solum ex sensu, quia sensibiliter hoc apparet, sed etiam ex ratione. Cuius quidem rationis principium hoc sumendum est, quod cum tria sint in magnitudine quae pertransitur, scilicet principium, medium et finis, medium utrumque est respectu utriusque; quia respectu finis est principium, et respectu principii est finis; et sic cum sit unum subiecto, est duo ratione. Iterum aliud principium est sumendum, quod aliud est quod est in potentia et quod est in actu. His ergo visis, considerandum est ex dictis, quod quodlibet signum, idest quodlibet punctum signatum, infra terminos lineae supra quam aliquid movetur, medium est in potentia; sed non est medium in actu, nisi fiat divisio secundum motum, ita scilicet quod in illo puncto id quod movetur stet, et iterum ab illo puncto incipiat moveri: quia sic medium illud fiet actu principium et finis; principium quidem posterioris, inquantum inde incipit rursus moveri, finis autem primi, inquantum scilicet ibi terminatus est primus motus per quietem. Sit enim una linea in cuius principio sit a, in medio b, in fine c. Moveatur ergo ab a in b, et ibi stet; et iterum incipiat moveri a b, et feratur usque in c. Sic enim manifestum erit quod b est actu finis prioris motus, et principium posterioris. Sed si aliquid feratur continue ab a in c sine interpositione alicuius quietis, non est possibile dicere mobile factum esse, idest advenire, neque abesse, idest abscedere, neque in hoc signo quod est a, neque in hoc signo quod est b; sed solum hoc potest dici, quod in a vel in b sit in quodam nunc (non autem in aliquo tempore, nisi forte secundum hoc quod aliquid dicitur esse alicubi in tempore, quia est ibi in nunc temporis. Et ita quod movetur continue ab a in c in aliquo tempore, erit in b in nunc, quod est divisio quaedam illius temporis: et sic dicetur esse in b in illo toto tempore, eo modo loquendi quo dicitur aliquid moveri in die, quia movetur in parte illius diei). Et quia hoc videbatur dubium, quod id quod fertur non adsit et absit cuicumque signo in magnitudine signato, quae motu pertransitur continuo, ostendit hoc consequenter: dicens quod si aliquis concedat quod mobile adsit et absit alicui signo in magnitudine signato, sequitur quod ibi quiescat. Impossibile est enim quod in eodem instanti adsit et absit mobile ab hoc signo quod est b: quia adesse alicubi et abesse sunt contraria, quae non possunt esse in eodem instanti. Oportet ergo quod in alio et alio nunc temporis mobile adsit et absit alicui signo magnitudinis. Inter quaelibet autem duo nunc est tempus medium: ergo sequetur quod mobile quod est a, quiescit in b. Omne enim quod est alicubi per aliquod tempus, est in eodem prius et posterius. Et similiter est dicendum in omnibus aliis signis vel punctis, quia de omnibus eadem ratio est. Unde manifestum est quod illud quod continue fertur per magnitudinem aliquam, in nullo intermedio signo magnitudinis adest et abest, idest accedit et recedit. Cum enim dicitur quod mobile adsit alicui signo, vel fiat in eo, vel accedat ad ipsum, per omnia huiusmodi significatur quod illud signum sit terminus motus. Cum autem dicitur quod absit vel abscedat, significatur quod sit principium motus. Non est autem actu medium signum magnitudinis nec principium nec finis motus, quia nec terminatur nec incipit ibi motus; sed in potentia tantum (posset enim ibi motus incipere vel terminari). Unde nec adest nec abest mobile a signo medio, sed simpliciter dicitur esse ibi in nunc. Esse enim mobile in aliquo signo magnitudinis, comparatur ad totum motum sicut nunc ad tempus.	1109. Belief in this can be based not only on sense, for it is sensibly evident, but also on an argument. The principle of this argument is that, since three things are involved in a magnitude that is traversed, namely, a beginning, a middle, and an end, the middle is both, when compared to both. For in respect to the end, the middle is a beginning, and in respect to the beginning, it is an end. Consequently, while it is one as to subject, it is two in conception. Another principle to be taken is that what is in potency is other than what is in act. Keeping these things in mind, it should be considered, from what has been said, that each sign, i.e., each designated point between termini of a line ever which something is being moved, is potentially a middle, but it is not one unless a division with respect to the motion takes place in such a way that at a given point the thing in motion stops and then resumes its motion at that point. Now, in this way that middle will become an actual beginning and an actual end, i.e., the beginning of the subsequent (inasmuch as the mobile resumes its motion from it) and an end of the first motion (inasmuch as the first motion was terminated there by reason of rest). For let there be a line at whose beginning is A, at whose middle is B, and at whose end is C. Then let something be moved from A to B and stop there; then let it begin to be moved from B and be carried along to C. In this example, it is plain that B is actually the end of the prior motion and the beginning of the subsequent one. But if something be moved continuously from A to C without any interval of rest, it is not possible to say that the mobile has “come to be,” i.e., has arrived at, or has “ceased to be,” i.e., has left, either the point A or the point B. Only this can be said, namely, that it is in A or in B at a certain “now.” (But not at a certain time, unless we should perchance say that a thing is somewhere in time because it is there in some “now” of time. And so what is being moved continuously from A to C in some time will be in B at an instant which is a divider of time. In this way, it will be said to be in B in that entire time, in the sense that we speak of something being moved in a day because it is in motion in a part of that day.) And because it seemed doubtful that what is in motion does not arrive at and leave each determinate point of a magnitude which is traversed by a continuous motion, he shows this. He says, then, that if someone grants that the mobile arrives at and then leaves some assigned point in the magnitude, it follows that it is at rest there. For it is impossible that in the same instant a mobile arrive at and leave this point B, because to arrive somewhere and to leave there are contraries, which cannot exist in the same instant. Therefore, it must be at other and other “now’s” that the mobile arrives at and leaves a given point of the magnitude. But between any two “now’s” is an intermediate time. Therefore, it will follow that the mobile, A, rests in B. For anything that is somewhere for a time is there before and after. And the same must be said for all the other “signs” or points, because the same reasoning applies to all. Hence it is plain that what is being carried along continuously over a magnitude is at no time arriving at, or departing from, any intermediate point. For when it is said that the mobile is “at” this point, or is “coming to be” in it or is “approaching” it, all these expressions imply that that point is a terminus of the motion. And when it is said that it “leaves” or “departs,” a beginning of motion is implied. But a designated point of a magnitude is not actually a middle or a beginning or an end, because the motion neither begins nor ends there; rather, it is these potentially only, because the motion could begin or end there. Hence the mobile neither arrives at nor leaves an intermediate point, but it is said to be there absolutely in a “now.” For the existence of a mobile at some point of the magnitude is compared to the whole motion as the “now” is compared to time.
lib. 8 l. 16 n. 7 Sed cum mobile quod est a, utatur ipso b ut medio, principio et fine in actu, necesse est quod ibi stet, propter hoc quod facit ipsum movendo et stando unum signum esse duo, scilicet principium et finem, sicut etiam contingit in intelligendo. Possumus enim simul intelligere unum punctum ut est unum subiecto: sed si seorsum intelligamus ipsum ut principium, seorsum autem ut finem, non simul hoc continget. Ita et cum id quod movetur, utitur aliquo signo ut uno, non erit ibi nisi in uno nunc. Si autem utitur eo ut duobus, scilicet ut principio et fine in actu, necesse erit quod sit ibi in duobus nunc, et per consequens in tempore medio, et ita quiescet. Manifestum est ergo quod id quod continue movetur ab a in c, in medio b neque affuit neque abfuit, idest neque accessit neque abscessit: sed a primo signo, quod est a, abfuit vel abscessit, quasi a principio in actu; in ultimo autem signo, quod est c, affuit vel accessit, quia ibi perficitur motus, et mobile quiescit. Et est attendendum quod in praemissis ponitur a quandoque quidem pro mobili, quandoque vero pro principio magnitudinis.	1110. But when the mobile A uses B as an actual middle, beginning and end, then it must be at a stop there, because by moving and stopping it makes that one point to be two, namely, a beginning and an end, as happens also in understanding. For we can simultaneously understand one point as it is one in subject, but if we consider it separately as a beginning and separately as an end, this will not take place simultaneously. So too, when that which is being moved uses a point as one, it will be there only in the one “now.” But if it uses it as two, namely, as a beginning and end in act, it will be there for two “now’s,” and, consequently, for a middle time between them. And so it will be at rest. Therefore, it is plain that what is being moved continuously from A to C was neither present nor away from the intermediate B, i.e., it neither arrived at it nor departed from it; but it was away from and left, the first point A, as the actual beginning; and it was present in, or arrived at, the final point C, because there the motion is finished, and the mobile rests. It should be remarked that in the foregoing, “A” was sometimes taken as the mobile, and sometimes as the beginning of the magnitude.
lib. 8 l. 16 n. 8 Ex istis autem patet quod motus reflexus, sive in circulari sive in recta magnitudine, non potest esse continuus, sed intercidit quies media; quia idem signum est quod actu fit finis primi motus et principium reflexionis. Sed in motu circulari mobile non utitur aliquo signo ut principio vel fine in actu, sed quolibet signo magnitudinis utitur ut medio: et ideo motus circularis potest esse continuus, non autem reflexus.	1111. From all these things it is clear that a reflected motion, whether it occurs along a circular or a straight magnitude, cannot be continuous, but a rest intervenes, because the same point is actually the end of the first motion and beginning of the reflexed one. But in a circular motion the mobile does not use any point as an actual beginning and end, but each point is used as an intermediate. Therefore, a circular motion can be continuous, but a reflexed one cannot.