Authors/Thomas Aquinas/physics/L8/lect19

Lecture 19 Proper reasons why circular motion can be continuous, and why it is the first

Latin	English
	Lecture 19 Proper reasons why circular motion can be continuous, and why it is the first
lib. 8 l. 19 n. 1 Postquam philosophus ostendit quod nullus motus localis potest esse continuus praeter circularem, hic ostendit quod motus circularis potest esse continuus et primus. Et primo ostendit hoc per proprias rationes; secundo per rationes logicas et communes, ibi: rationabiliter autem accidit et cetera. Circa primum duo facit: primo ostendit quod motus circularis sit continuus; secundo quod sit primus, ibi: quod autem lationum et cetera. Circa primum duo facit: primo ponit duas rationes ad ostendendum quod motus circularis potest esse continuus; secundo ex eisdem rationibus concludit quod nullus alius motus potest esse continuus, ibi: manifestum autem et ex hac divisione et cetera.	1129. After showing that no local motion but a circular one can be continuous, the Philosopher now shows that a circular motion can be continuous and first. First of all he shows this with proper arguments; Secondly, with logical and common arguments, (L. 20). About the first he does two things: First he shows that a circular motion is continuous; Secondly, that it is the first, at 1134. About the first he does two things: First he gives two arguments to prove that circular motion can be continuous; Secondly, from the same arguments he concludes that no other motion can be continuous, at 1132.
lib. 8 l. 19 n. 2 Quod autem motus circularis possit esse unus continuus, prima ratione sic probat. Illud dicitur esse possibile, ad quod nullum sequitur impossibile; nullum autem sequitur impossibile, si dicamus quod motus circularis sit in perpetuum continuus. Quod patet ex hoc quod in motu circulari, illud quod movetur ex aliquo, puta a, simul movetur in idem signum secundum eandem positionem, idest secundum eundem processum mobilis, eodem ordine partium servato. Quod in motu reflexo non contingit; quia cum aliquid retrocedit, disponitur secundum contrarium ordinem partium in movendo: quia vel oportet quod pars mobilis quae in primo motu erat prior, in reflexione fiat posterior; vel oportet quod illa pars mobilis quae in primo motu aspiciebat ad unam differentiam loci, puta dextrum vel sursum, in reflexione aspiciat ad contrarium. Sed in motu circulari servatur eadem positio, dum aliquid movetur ad id a quo recedit. Sic ergo poterit dici quod etiam a principio sui motus, dum recedebat ab a, movebatur ad hoc ad quod tandem perveniet, scilicet ad ipsum a. Nec propter hoc sequitur hoc impossibile, quod simul moveatur motibus contrariis aut oppositis, sicut sequebatur in motu recto. Non enim omnis motus qui est ad aliquem terminum, est contrarius aut oppositus motui qui est ex illo eodem termino; sed ista contrarietas invenitur in linea recta, secundum quam attenditur contrarietas in loco. Non enim attenditur contrarietas inter duos terminos secundum lineam circularem, quaecumque pars sit circumferentiae; sed secundum diametrum. Contraria enim sunt quae maxime distant: maxima autem distantia inter duos terminos non mensuratur secundum lineam circularem, sed secundum lineam rectam. Possunt enim inter duo puncta infinitae lineae curvae describi, sed non nisi una linea recta: id autem quod est unum, est mensura in quolibet genere. Sic igitur patet quod si sit aliquis circulus, et dividatur per medium, et sit diameter eius ab; motus qui est per diametrum ab a in b, est contrarius motui qui est per eundem diametrum a b in a. Sed motus qui est per semicirculum ab a in b, non est contrarius motui qui est per alium semicirculum a b in a. Contrarietas autem erat quae impediebat quod motus reflexus non posset esse continuus, ut ex superioribus rationibus apparet. Nihil ergo prohibet, contrarietate sublata, motum circularem esse continuum, et tamen nullo tempore deficere. Et huius ratio est, quia motus circularis habet suum complementum per hoc quod est ab eodem in idem; et sic per hoc non impeditur eius continuatio. Sed motus rectus habet suum complementum per hoc quod est ab eodem in aliud: unde si ab illo alio revertatur in idem a quo inceperat moveri, non erit unus motus continuus, sed duo.	1130. But that a circular motion can be one continuous motion he proves at (890 264 b9) with his first argument: That from which nothing impossible follows is said to be possible. But nothing impossible follows from the statement that a circular motion is forever continuous. This is plain from the fact that, in a circular motion, that which is being moved from somewhere, e.g., from A, is at the same time being moved to the same point “according to the same position,” i.e., according to the same progress of the mobile, the same order of parts having been maintained. This, however, does not happen in a reflex motion, because when something turns back, it is disposed according to a contrary order of parts in its motion. For either that part of the mobile to the fore in the first motion must be at the rear in the reflexion, or that part which was facing one difference of place, for example, the right or above, in reflexion must face a contrary direction. But in a circular motion the same position is maintained, while a thing is being moved toward the point from which it departed. Consequently, it could be said that even from the very beginning of its motion, while it was departing from A, it was being moved toward that which it would finally reach, namely, the very same A. Nor does this lead to the impossibility of being moved with contrary or opposite motions at one and the same time, as followed in rectilinear motion. For not every motion to some terminal is contrary or opposite to one from the same terminal, but such contrariety is present in the straight line, according to which, contrariety in place is gauged. For contrariety between two termini is not forthcoming according to a circular line, whatever part of the circumference be taken, but according to the diameter. Contraries, indeed, are things most far apart; but the greatest distance between two termini is not measured according to a circular line, but according to a straight line. For between two points an infinite number of curves can be described but only one straight line, But the measure in any genus is that which is one. Consequently, it is plain that if one takes a circle, and it be divided in half, and AB be its diameter, a motion through the diameter from A to B is contrary to a motion over the same diameter from B to A. But a motion over the semicircle from A to B is not contrary to a motion from B to A over the other semicircle. But it was contrariety that prevented a reflex motion from being continuous, as appears from the reasons given above. Nothing, therefore, once contrariety has been removed, prevents a circular motion from being continuous and also not failing at any time. And the reason for this is that a circular motion is completed by the fact that it is from the same to the same, and thus its continuity is not impaired by this. But a rectilinear motion is completed by its being from one thing to another; hence, if it returns from that other to the same from which it began, it will be not one continuous motion, but two.
lib. 8 l. 19 n. 3 Deinde cum dicit: et qui quidem etc., ponit secundam rationem, dicens quod motus circularis non est in eisdem; sed motus rectus multoties est in eisdem. Quod sic intelligendum est. Si enim aliquid moveatur ab a in b per diametrum, et iterum a b in a per eundem diametrum, necesse est quod per eadem media redeat per quae prius transierat: et sic pluries per eadem fertur. Sed si aliquid moveatur ab a in b per semicirculum, et iterum a b in a per alium semicirculum, quod est circulariter moveri, manifestum est quod non redit ad idem per eadem media. Est autem de ratione oppositorum, quod circa idem considerentur: et sic manifestum est quod moveri ab eodem in idem secundum motum circularem, est absque oppositione; sed moveri ab eodem in idem secundum motum reflexum, est cum oppositione. Sic igitur patet quod motus circularis, qui non redit ad idem per eadem media, sed semper pertransit aliud et aliud, potest esse unus et continuus, quia non habet oppositionem: sed ille motus, reflexus scilicet, qui dum redit in idem, pluries in eisdem mediis fit pertranseundo, non potest esse in perpetuum continuus; quia necesse esset quod aliquid simul moveretur contrariis motibus, ut supra ostensum est. Et ex eadem ratione concludi potest, quod neque motus qui est in semicirculo, neque in quacumque alia circuli portione, potest esse in perpetuum continuus; quia in his motibus necesse est quod multoties pertranseantur eadem media, et quod moveantur contrariis motibus, quasi debeat fieri reditus ad principium. Et hoc ideo, quia neque in linea recta, neque in semicirculo, neque in quacumque circuli portione, copulatur finis principio, sed distant ab invicem principium et finis: sed in solo circulo finis copulatur principio. Et ideo solus motus circularis est perfectus: unumquodque enim perfectum est ex hoc quod attingit suum principium.	1131. Then at (891 264 b18) he gives the second argument, saying that a circular motion does not exist in identical things, but a rectilinear motion is very often in identical things. Now what this means is that, if something is moved from A to B across a diameter, and again from B to A across the same diameter, it has to return across the same middles through which it previously travelled, Consequently, it is being carried over the same middle a number of times. But if something is moved through a semicircle from A to B, and again from B to A through the other semicircle—and this is motion in the circular manner—it is clear that it does not return to the same point over the same middles. Now, it is of the nature of opposites that they be considered with relation to the same thing. And thus it is clear that to be moved from the same to the same with a circular motion is without opposition, but to be moved from the same to the same with a reflex motion is with opposition. In this way it is plain that a circular motion which does not return to the same over the same middles, but always goes over something other, can be one and continuous, because it does not have opposition. But that motion, namely, the reflex motion, which, in returning to the same, traverses more than once the same middles, cannot be forever continuous, because that would require something being moved with contrary motions at one and the same time, as was proved above. And from the same argument it can be concluded that a motion confined to a semicircle, or to any portion of a circle, cannot be continuous in perpetuity, because such motions require repeated traversing of the same middles and involve being moved with contrary motions, as though a return to the beginning should be made. The reason is because the end is not joined to the beginning when you are dealing with a straight line, or a semicircle, or an arc of a circle; rather the beginning and end are apart. It is only in a circle that the end is joined to the beginning. And for this reason only a circular motion is a perfect motion, since a thing is perfect from attaining its principle.
lib. 8 l. 19 n. 4 Deinde cum dicit: manifestum autem et ex hac divisione etc., ostendit ex eadem ratione quod in nullo alio genere potest esse aliquis motus continuus. Et primo ostendit propositum; secundo infert quoddam corollarium ex dictis, ibi: manifestum igitur ex his et cetera. Dicit ergo primo, quod etiam ex ista distinctione quae ponitur inter motum circularem et alios motus locales, manifestum est quod nec in aliis generibus motus contingit esse aliquos motus in infinitum continuos: quia in omnibus aliis generibus motus, si debeat aliquid moveri ab eodem in idem, sequitur quod multoties pertranseat eadem. Sicut in alteratione oportet quod pertranseat medias qualitates: ex calido enim transitur in frigidum per tepidum; et si debeat rediri ex frigido in calidum, oportet quod per tepidum transeatur. Et idem apparet in motu qui est secundum quantitatem: quia si quod movetur de magno in parvum, iterum redeat ad magnum, oportet quod bis sit in media quantitate. Et simile est etiam in generatione et corruptione: si enim ex igne fiat aer, et iterum ex aere fiat ignis, oportet quod medias dispositiones bis transeat (sic enim medium potest poni in generatione et corruptione, secundum quod accipitur cum transmutatione dispositionum). Et quia media transire contingit in diversis mutationibus diversimode, subiungit quod nihil differt vel pauca vel multa media facere, per quae aliquid moveatur de extremo in extremum; neque accipere aliquod medium positive, ut pallidum inter album et nigrum, vel remotive, ut inter bonum et malum quod neque bonum neque malum est: quia qualitercumque media se habeant, semper accidit quod eadem multoties pertranseantur.	1132. Then at (892 264 b28) he proves from the same argument that in no other genus of motion can there be continuous motion. First he proves the proposition; Secondly, he draws a corollary from what was said, at 1133. He says therefore First (892 264 b28) that also from this distinction between circular motion and other local motions, it is plain that neither in the other genera of motion can there be any infinitely continuous motions, because in all the other genera of motion if anything is to be moved from the same to the same, it follows that the same will be repeatedly traversed. For example, in alteration the intermediate qualities must be passed through—for the passage from hot to cold is through tepid, and if a return is to be made from cold to hot, tepid must be traversed again. The same is apparent in a motion according to quantity—for if that which is moved from large to small, should return again to large, the intermediate quantity must be traversed twice. Generation and corruption present a similar situation—for if air comes to be from fire, and then again fire from air, the intermediate dispositions must be traversed twice (for a middle may be placed in generation and ceasing-to-be, insofar as taken along with the dispositional changes). And because the intermediates are traversed in different ways in changes that are diverse, he adds that it makes no difference whether many or few intermediates are introduced through which something is moved from one extreme to the other, or whether the intermediate is taken in a positive sense, as pallid between white and black, or in a remotive sense, as, between good and evil, that which is neither good nor evil-for, be they what they may, it always happens that the same are traversed a number of times.
lib. 8 l. 19 n. 5 Deinde cum dicit: manifestum igitur etc., concludit ex praemissis, quod antiqui naturales non bene dixerunt, ponentes omnia sensibilia semper moveri: quia oporteret quod moverentur secundum aliquem praedictorum motuum, de quibus ostendimus quod non possunt esse in perpetuum continui; et maxime quia, secundum quod illi dicunt, motus semper continuus est alteratio. Dicunt enim quod omnia semper defluunt et corrumpuntur; et adhuc dicunt quod generatio et corruptio nihil est aliud quam alteratio: et sic dum dicunt omnia semper corrumpi, dicunt omnia semper alterari. Probatum est autem per rationem supra inductam, quod nullo motu contingit semper moveri nisi circulari: et sic relinquitur quod neque secundum alterationem, neque secundum augmentum, possunt omnia semper moveri, ut illi dicebant. Ultimo autem principale intentum epilogando concludit, scilicet quod nulla mutatio possit esse infinita et continua nisi circularis.	1133. Then at (893 265 a2) he concludes from the foregoing that the early natural philosophers did not phrase the matter well when they said that all sensible things are forever in motion, because that would necessitate their being moved with respect to one of the aforesaid motions, concerning which we have shown that they cannot be forever continuous; and especially because they said that the ever-continuous motion is alteration. For they assert that all things are always perishing and ceasing to be, and yet they say that generation and ceasing-to-be are nothing more than alteration, and so in saying that all things are forever ceasing to be, they are saying that all things are forever being altered. But it was proved in the argument given above that nothing can be moved forever except by a circular motion. Thus it remains that neither according to alteration, nor growth, can all things be forever in motion, as they said. Finally, he concludes by way of summary to the chief proposition, namely, that no change can be infinite and continuous except a circular one.
lib. 8 l. 19 n. 6 Deinde cum dicit: quod autem lationum etc., probat quod motus circularis sit primus motuum, duabus rationibus: quarum prima talis est. Omnis motus localis, ut prius dictum est, aut est circularis aut rectus aut commixtus. Circularis autem et rectus sunt priores commixto, quia ex illis constituitur. Inter illos autem duos, circularis est prior recto: circularis enim est simplicior et perfectior recto. Quod sic probat. Motus enim rectus non potest procedere in infinitum. Hoc enim esset dupliciter. Uno modo sic quod esset magnitudo per quam transit motus rectus infinita: quod est impossibile. Sed etiam si esset aliqua magnitudo infinita, nihil moveretur ad infinitum. Quod enim impossibile est esse, nunquam fit aut generatur; impossibile est autem transire infinitum; nihil ergo movetur ad hoc quod infinita pertranseat. Non ergo potest esse motus rectus infinitus super magnitudinem infinitam. Alio modo posset intelligi motus rectus infinitus, super magnitudine finita per reflexionem. Sed motus qui est reflexus non est unus, ut supra probatum est, sed est compositus ex duobus motibus. Si autem super linea recta finita non fiat reflexio, erit motus imperfectus et corruptus: imperfectus quidem, quia possibile est ei fieri additionem; corruptus autem, quia cum pervenerit ad terminum magnitudinis, cessabit motus. Sic ergo patet quod motus circularis qui non est compositus ex duobus, et qui non corrumpitur cum venit ad terminum (cum sit idem eius principium et finis), est simplicior et perfectior quam motus rectus. Perfectum autem est prius imperfecto, et similiter incorruptibile corruptibili, et natura et ratione et tempore, sicut supra ostensum est, cum probabatur loci mutationem esse priorem aliis motibus. Necesse est ergo motum circularem esse priorem recto.	1134. Then at (894 265 a13) he proves with two arguments that circular motion is the first of motions. The first argument is this: Every local motion, as stated above, is either circular, or straight, or a combination of the two. But circular and straight are prior to the combination. which is composed of them. But between these two, the circular is prior to the straight, for the circular is simpler and more perfect than the straight. And this he proves as follows: Straight motion cannot go on infinitely. For this would occur in two ways: First in such a way that the magnitude traversed by the straight motion would be infinite—which is impossible. But even if there were some infinite magnitude, nothing would be moved to infinity. For what is impossible to be, never comes to be or is generated; but it is impossible to traverse the infinite; therefore, nothing is moved toward the end of traversing the infinite. Therefore, there cannot be an infinite straight motion over an infinite magnitude. In a second way, an infinite straight motion can be understood as being a reflex motion over a finite magnitude. But a reflex motion is not one, as was proved above, but is a composition of two motions. But if a reflexion does not occur upon a finite straight line, the motion will be imperfect and destroyed: imperfect, because further addition can be made to it; destroyed, because when the terminus of the magnitude is reached, the motion will cease. From all this it is clear that a circular motion which is not composed of two, and which is not destroyed when it comes to a terminus (for its beginning and terminus are identical), is simpler and more perfect than a straight motion. Now the perfect is prior to the imperfect, and likewise the imperishable is prior to the perishable, in nature and notion and time, as was shown above when it was proved that local change is prior to other motions. Therefore, it is necessary that circular motion be prior to straight.
lib. 8 l. 19 n. 7 Deinde cum dicit: amplius prior etc., ponit secundam rationem: quae talis est. Motus qui potest esse perpetuus, est prior eo qui perpetuus esse non potest; quia perpetuum est prius non perpetuo, et tempore et natura. Circularis autem motus potest esse perpetuus, et nullus aliorum motuum, cum oporteat eis succedere quietem: ubi autem quies supervenerit, corrumpitur motus. Relinquitur ergo quod motus circularis sit prior omnibus aliis motibus. Haec autem quae in hac ratione supponit, ex superioribus patent.	1135. Then at (895 265 a24) he gives the second argument, which is this; A motion which can be perpetual is prior to one that cannot be perpetual, because the perpetual is prior to the non-perpetual, both in time and in nature. But a circular motion and no other can be perpetual, for the others must be followed by rest, and where rest intervenes, motion is destroyed. What is left, therefore, is that circular motion is prior to all the other motions. (The premises of this argument are plain from what has been said previously.)