Authors/Thomas Aquinas/physics/L8/lect20

Lecture 20 Dialectical reasons why circular motion is continuous and first. Confirmation from the ancients

Latin	English
	Lecture 20 Dialectical reasons why circular motion is continuous and first. Confirmation from the ancients
lib. 8 l. 20 n. 1 Postquam philosophus ostendit per proprias rationes, quod motus circularis est continuus et primus; hic ostendit idem per quasdam logicas et communes rationes. Et ponit tres rationes. Circa quarum primam dicit, quod rationabiliter accidit quod motus circularis sit unus et continuus in perpetuum, non autem motus rectus. Quia in recto determinatur principium, medium et finis, et omnia haec tria est assignare in ipsa linea recta: et ideo est in ipsa linea unde incipiat motus, et ubi finiatur; quia omnis motus quiescit apud terminos, scilicet vel a quo vel ad quem (has enim duas quietes supra in quinto distinxerat). Sed in linea circulari termini non sunt distincti: nulla enim est ratio quare unum punctum signatum in linea circulari, sit magis terminus quam aliud; quia unumquodque similiter est et principium et medium et finis. Et sic quodammodo quod movetur circulariter, semper est in principio et in fine, inquantum scilicet quodlibet punctum signatum in circulo potest accipi ut principium vel finis: et quodammodo nunquam est in principio vel fine, inquantum scilicet nullum punctum circuli est principium vel finis in actu. Unde sequitur quod sphaera quodammodo movetur, et quodammodo quiescit: quia sicut in sexto dictum est, sphaera dum movetur semper obtinet eundem locum secundum subiectum, et quantum ad hoc quiescit; alium tamen et alium secundum rationem, et quantum ad hoc movetur. Ideo autem in ipsa linea circulari non distinguitur principium, medium et finis, quia haec tria pertinent ad centrum; a quo sicut a principio procedunt lineae ad circumferentiam, et ad ipsum terminantur lineae a circumferentia protractae; et est etiam medium totius magnitudinis secundum aequidistantiam ad omnia signa circumferentiae. Et ideo, quia principium et finis circularis magnitudinis est extra circulationem, scilicet in centro, ad quod non pertingit quod circulariter movetur; non est assignare in motu circulari ubi quiescat illud quod fertur, cum pervenerit ad ipsum: quia quod circulariter movetur, semper fertur circa medium, sed non fertur ad ultimum, quia non fertur ad medium quod est principium et ultimum. Et propter hoc, totum quod sphaerice movetur, quodammodo semper quiescit, et quodammodo continue movetur, ut dictum est. Ex his ergo quae dicta sunt, sic ratio extrahi potest. Omnis motus qui nunquam est in principio et fine, est continuus: sed motus circularis est huiusmodi: ergo et cetera. Et per idem medium probatur quod motus rectus non possit esse continuus.	1136. After proving with proper reasons that a circular motion is continuous and first, the Philosopher now proves the same with certain logical and common reasons. And he gives three arguments. With respect to the First (896 265 a27) he says that it is reasonable that a circular motion but not a straight one be one and forever continuous. For in a straight motion there are determined a beginning, middle, and end, and all three of these can be designated in a straight line, Therefore in a straight line there exist that whence the motion begins, and where it ends, since all motion rests at its termini, namely, the terminus from which or to which (he having distinguished these two states of rest in Book V). But in a circular line the termini are not distinct, for there is no reason why in a circle some designated point should be a terminus more than another, since each and every one alike is a beginning and an intermediate and an end. Consequently, the things which are moved circularly are in a sense always in the beginning and in the end, insofar, namely, as any point at all in a circle may be taken as a beginning or end, while in another sense, they are never in the beginning or end, inasmuch as no point in the circle is a beginning or end in act. Hence it follows that a sphere is in one sense in motion and in another sense at rest, because, as was said in Book VI, while the sphere is being moved it always keeps the same place as to subject, and in this respect it is at rest; but yet the place is always other and other in conception, and in this respect it is being moved. Now, the reason why a beginning, intermediate and end are not distinguished in a circular line is that these three belong to the center, from which, as from a beginning, lines proceed to the circumference and at which lines drawn from the circumference end. Moreover, it is the middle of the entire magnitude by virtue of its equidistance to all the points of the circumference. And therefore, since the beginning and end of a circular magnitude are outside its circularity—for they are in the center which is never reached by a thing moving circularly—no place can be assigned at which a thing in circular motion should be at rest, because anything in circular motion is always carried about the middle but not to what is ultimate, because it is not carried to the middle, which is the beginning and the ultimate. On this account, a whole that is being moved in a spherical manner is in one sense always at rest and in another in continuous motion, as has been said. From all this the following argument may be extracted: Every motion that is never in its beginning and end is continuous. But a circular motion is of this kind. Therefore, etc, And with this same middle term, it is proved that a straight motion cannot be continuous.
lib. 8 l. 20 n. 2 Deinde cum dicit: accidit autem conversim etc., ponit secundam rationem, dicens quod haec duo conversim se sequuntur, scilicet quod motus circularis sit mensura omnium motuum, et quod sit primus motuum: omnia enim mensurantur primo sui generis, ut in X Metaphys. ostenditur. Et sic ista proposito convertibilis est: omne quod est mensura, est primum sui generis; et omne quod est primum, est mensura. Sed motus circularis est mensura omnium aliorum motuum, ut patet ex his quae in fine quarti sunt dicta: ergo motus circularis est primus motuum. Vel si supponatur quod motus circularis sit primus motuum propter supra dictas rationes, concludetur quod sit mensura aliorum motuum.	1137. Then at (897 265 b8) he gives the second argument, saying that these two follow one another conversely, namely, that a circular motion is the measure of all motions and that it is the first of all motions—for all things are measured by what is first in their genus, as is proved in Metaphysics X. Accordingly, this is a convertible proposition: Whatever is a measure is the first in its genus; whatever is first is a measure. But circular motion is the measure of all other motions, as is clear from what was said at the end of Book IV. Therefore, circular motion is the first of motions. On the other hand, if one suppose that a circular motion is the first of motions on account of the arguments given above, it will be concluded that it is the measure of the other motions.
lib. 8 l. 20 n. 3 Tertiam rationem ponit ibi: amplius autem et regularem etc., dicens quod solus motus circularis potest esse regularis: quia quae in linea recta moventur, irregulariter feruntur a principio usque ad finem. Est enim motus irregularis, ut in quinto dictum est, qui non est aequaliter velox per totum: quod necesse est accidere in omni motu recto; quia in motibus naturalibus, quanto aliqua quae moventur plus distant a prima quiete, a qua incipit motus, velocius moventur; in motu autem violento, quanto plus distant ab ultima quiete, ad quam terminatur motus, tanto velocius moventur. Nam motus naturalis intenditur in fine: violentus autem in principio. Hoc autem in motu circulari locum non habet: quia in circulo principium et finis non est natum esse inter ipsam circulationem, quae fit per circumferentiam, sed extra, idest in centro, ut dictum est. Unde nulla est ratio quare intendatur vel remittatur motus circularis quasi per approximationem ad principium vel finem; cum semper aequaliter appropinquat centro, quod est principium et finis. Manifestum est autem ex his quae in quinto dicta sunt, quod motus regularis est magis unus quam irregularis: et sic motus circularis est prior naturaliter quam motus rectus. Quanto enim aliquid est magis unum, tanto naturaliter prius est.	1138. The third argument he gives at (898 265 b11), saying that only a circular motion can be regular, since things in motion in a straight line are being carried along in an irregular manner from beginning to end. For, as was said in Book V, a motion is irregular which is not equally swift throughout, and this must occur in every straight motion, since in natural motions the further things in motion are distant from the first rest, from which the motion started, the swifter they are moved; and in a violent motion, the farther they are distant from the ultimate rest, at which the motion terminates, the swifter they travel. For every natural motion is more intense near the end, but a violent motion at the beginning. But this has no place in a circular motion in place, because in a circle the beginning and end do not exist somewhere in the circling which occurs along the circumference, but outside it, i.e., in the center, as was explained. Hence, there is no reason why a circular motion should be intensified or weakened on account of a nearness to its beginning or end, since it is always equally approaching the center, which is the beginning and ends Now, it is plain from what was said in Book V that a regular motion is more one motion than an irregular one. Consequently, a circular motion is naturally prior to a straight motion. For the more a thing is one, the more it is by nature prior.
lib. 8 l. 20 n. 4 Deinde cum dicit: quod autem secundum locum mutatio etc., ostendit per opiniones antiquorum philosophorum, quod motus localis sit primus motuum. Et dicit quod huic veritati attestantur dicta omnium philosophorum antiquorum, qui de motu fecerunt memoriam; quia principiis attribuunt quod moveant motu locali. Et hoc primo ostendit per opinionem Empedoclis, qui posuit amicitiam et litem prima principia moventia; quorum amicitia congregat, lis vero disgregat: congregatio autem et disgregatio sunt motus locales. Secundo ostendit idem per opinionem Anaxagorae, qui posuit intellectum primam causam moventem; cuius opus, secundum ipsum, est disgregare commixta. Tertio ostendit idem per opinionem Democriti, qui non posuit causam moventem, sed dixit quod omnia moventur propter naturam vacui. Motus autem qui est propter vacuum, est loci mutatio, vel similis loci mutationi: quia vacuum et locus non differunt nisi ratione, ut in quarto dictum est. Et sic dum ponunt res primo moveri propter vacuum, ponunt motum localem naturaliter primum, et nullum aliorum motuum: sed alios motus opinantur consequi ad motum localem. Dicunt enim sequentes Democritum, quod augmentari et corrumpi et alterari contingit per quandam congregationem et disgregationem indivisibilium corporum. Quarto ostendit idem per opiniones antiquorum naturalium, qui ponebant unam causam materialem tantum, vel aquam vel aerem vel ignem, vel aliquid medium. Ex illo enim uno materiali principio constituunt generationem et corruptionem rerum per condensationem et rarefactionem; quae per quandam congregationem et disgregationem complentur. Quinto ostendit idem per opinionem Platonis, qui posuit animam esse primam causam motus. Posuit enim Plato quod movens seipsum, quod est anima, est principium omnium eorum quae moventur. Movere autem seipsum convenit animali et omni animato, secundum eum qui est secundum locum autokinesim, idest per transmutationem localem. Sexto autem ostendit idem per ea quae communiter et vulgariter loquentes dicunt. Illud enim solum proprie dicimus moveri, quod movetur secundum motum localem. Si autem aliquid quiescat in loco, sed moveatur motu augmenti aut decrementi aut alterationis, dicitur quod movetur quodammodo, sed non simpliciter.	1139. Then at (899 265 b16) he shows through the opinions of the early philosophers that local motion is the first of motions. And he says that the statements of all the ancient philosophers who discussed motion attest to this truth, for they declare that the principles of things move with local motion. He refers first to the opinion of Empedocles, who posited friendship and strife as the first moving principles, the former gathering and the latter separating—and gathering and separating are local motions. Secondly, he shows the same thing through the opinion of Anaxagoras, who posited Intellect as the first moving cause, whose work, according to him, is to separate what is commingled. Thirdly, he shows the same thing through the opinion of Democritus, who did not posit a moving cause but said that all things are moved on account of the nature of the void. But a motion that is due to the void is a local motion or one similar to local motion, for void and place differ only in conception, as was said in Book IV. And so, by positing that things are first moved on account of the void, they posit local motion as naturally first and none of the other motions, but they believe that the other motions follow upon local motion. For those who follow Democritus declare that being increased and corrupted and altered occur by a certain assembling and separating of indivisible bodies. Fourthly, he shows the same thing through the opinions of the ancient philosophers of nature who posited only one cause, a material cause, namely, water, or air, or fire, or some intermediate. For from that one material cause they explain the generation and ceasing-to-be of things through condensation and rarefaction, which are completed by a kind of assembling and separation. Fifthly, he shows the same through the opinion of Plato who posited soul as the first cause of motion. For Plato posited that that which moves itself, which is the soul, is the principle of all things that are moved. But self-movement belongs to animals and all animate things, according to autokinesis with respect to place, i.e., per se local transmutation. Sixthly, he shows the same thing through what is commonly and popularly held, For we only say that to be moved in the proper sense which is moved with respect to place. Whereas, if something is at rest in place, but is moved with the motion of growth or decrease or alteration, it is said to be moved in a certain sense but not absolutely.
lib. 8 l. 20 n. 5 Deinde cum dicit: quod quidem igitur semper motus erat etc., epilogat quae dixerat: scilicet quod motus semper fuerit et semper erit, et quod est aliquod primum principium motus perpetui, et quis sit primus motus, et quem motum contingat esse perpetuum, et quod primum movens sit immobile. Haec enim omnia in praecedentibus declarata sunt.	1140. Then at (900 266 a5) he summarizes what he had said, namely, that motion always has been and always will be, and that there is some first principle of perpetual motions and what the first motion is, and which motion happens to be perpetual, and that the first mover is immobile. For all these things have been set forth in what has preceded.