Authors/Thomas Aquinas/physics/L5/lect7

Lecture 7 Numerical unity of motion (continued)

Latin	English
	Lecture 7 Numerical unity of motion (continued)
lib. 5 l. 7 n. 1 Postquam philosophus posuit quod tria requiruntur ad hoc quod sit unus motus simpliciter, scilicet unitas temporis, et rei in qua est motus, et subiecti; hic hoc probare intendit. Cum enim multipliciter dicatur unum simpliciter, uno modo sicut aliquod indivisibile est unum, alio modo sicut continuum est unum; motus non potest dici simpliciter unus sicut indivisibilis, quia nullus motus indivisibilis est. Unde relinquitur quod hoc modo dicatur unus sicut continuus; et quod hoc sit motui esse unum simpliciter, quod est ei esse continuum; et ipsa continuitas motus sufficiat ad eius unitatem. Sequitur enim quod si est continuus, quod sit unus. Quaecumque igitur requiruntur ad continuitatem motus, requiruntur ad eius unitatem.	703. After positing that three things are required in order that a motion be unqualifiedly one, namely, unity of time, unity of that in which the motion takes place and unity of subject, the Philosopher now intends to prove this. Now while there are a number of ways in which things are unqualifiedly one, one being the way in which an indivisible is one and another the way in which a continuum is one, no motion can be unqualifiedly one in the way that an indivisible is one, because no motion is indivisible. Consequently, it remains that a motion is one to the extent that it is continuous and that, insofar an a motion is concerned, to be continuous is to be unqualifiedly one, so that the very continuity of motion suffices for its unity. For if it is continuous, it is one. Accordingly, whatever is required to make a motion be continuous is also required to make it one.
lib. 5 l. 7 n. 2 Ad continuationem autem motus requiruntur tria. Quorum primum est unitas speciei. Non enim omnis motus potest continuari omni motui; sicut etiam in aliis continuis non indifferenter qualecumque contingat esse aliquid, continuari potest cuicumque, qualecumque illud esse contingat: sed illa continuari possunt, quorum ultima contingit esse unum, quod est de ratione continui, ut supra dictum est. Sed quaedam sunt quae nulla ultima habent, ut formae et indivisibilia omnia: et ideo eorum non potest esse continuatio. Quorundam vero sunt aliqua ultima, quae sunt divisibilia et quantitatem habentia, quae sunt aequivoca, idest non convenientia in nomine et ratione: et ista etiam non possunt continuari. Nec etiam potest esse contactus in quibusdam eorum. Non enim potest dici quod linea et ambulatio se contingant, vel quod unum sit eorum ultimum, quod est ea continuari ad invicem. Ex quo patet quod ea quae sunt diversorum generum vel specierum, non possunt continuari ad invicem. Ergo motus qui differunt genere vel specie, possunt esse habiti, idest consequenter ad invicem se habere, sicut aliquis post cursum potest statim febricitare; cursus autem et febricitatio sunt in diversis generibus. Et in eodem genere, scilicet loci mutationis, una loci mutatio est consequenter se habens ad aliam, cum tamen non sit continua; sicut patet in diffusione lampadis, ut puta cum candela de manu in manum transfertur: sunt enim ibi diversi motus non continui. Vel potest intelligi quod motum localem liquoris quo flamma sustentatur, quem appellat diffusionem, consequitur motus localis flammae, quae nomine lampadis significatur. Praedictae igitur mutationes, quia differunt genere vel specie, non sunt continuae, cum non possint habere unum ultimum, quod ponitur esse de ratione continui. Unde possunt quidem motus specie vel genere differentes, esse consequenter se habentes et habiti, idest quodammodo se tangentes, absque aliqua interpolatione temporis, inquantum tempus est continuum. Quod quidem eadem ratione habet continuitatem, qua et motus, scilicet inquantum est ei unum ultimum. Nihil autem prohibet in uno instanti temporis, ad quod continuantur partes eius, terminari unum motum, et incipere alium alterius generis vel speciei; et sic motus illi erunt habiti, sed non continui. Et ideo secundum praemissa sequitur quod ad hoc quod motus sit continuus, requiritur quod sit unus secundum speciem: quae quidem unitas speciei est in motu ex re in qua est motus, inquantum est indivisibilis secundum speciem.	704. Now, in order that a motion be continuous, three things are required. The first of these is oneness in species. For there will not be continuity between one motion and another indiscriminately any more than there is continuity between just any two continuous things chosen at random in any other sphere. There can be continuity only when the extremities of the two things are one—this is implied in the very notion of continuity, as was explained above. Now, some things have no extremities at all; for example, forms and all indivisibles. Therefore, in regard to such things there can be no continuity. Other things have extremities which are divisible and have quantity. Some such things are equivocal, i.e., not agreeing in name and notion. Such things afford no means of forming continuity; indeed, in many cases no contact is possible. For how could a line and walking be in contact, or how could they possess a common extremity, so as to make continuity possible? This shows that continuity is impossible with things that belong to genera or species that are diverse. However, motions that differ generically or specifically can follow one upon the other, as a person immediately after running can start to get a fever—running and getting a fever being in diverse genera. And even in the same genus, e.g., in local motion, one change of place could follow upon another without the motion being continuous, as is evident in the spreading of the lamp (the torch-race), when the torch is passed from hand to hand. In this case we have diverse non-continuous motions. Or the phrase “spreading of the lamp” could refer to the local motion of the flame—which is signified by the word “lamp”—which is moved according to the local motion of the fuel that feeds the flame—such local motion being called spreading. Therefore the changes mentioned in the preceding paragraph, since they differ either generically or specifically, are not continuous, since they cannot have one extremity, which is required for a continuum. Consequently, motions that differ generically or specifically may be consecutive and “had”, i.e., in contact somehow without any time interruption, inasmuch as time is continuous and has its continuity in the same way that motion has, namely, because there is one extremity (joining two parts). Now there is nothing to prevent one motion from being ended and another of an entirely different kind from beginning at the same instant that two parts of time are being joined. In that case the two motions will be contiguous but not continuous. Therefore, according to our premises, it follows that in order that a motion be continuous, it is necessary that it be one in species: this unity of species being in the motion from the thing in which the motion is, insofar as it is incapable of division according to species.
lib. 5 l. 7 n. 3 Secundo requiritur ad continuitatem motus, quod sit unius subiecti: quia diversorum subiectorum motus possunt esse habiti, sed non continui; sicut dictum est de mutatione candelae per motum diversarum manuum.	705. In the second place, continuity of motion requires unity of subject, for the motions of diverse subjects cannot be continuous, though they can be contiguous, as was said about transferring a lamp from hand to hand.
lib. 5 l. 7 n. 4 Tertio requiritur ad continuitatem motus et unitatem, quod sit unus tempore, ad hoc quod non interveniat aliqua immobilitas vel quies. Quia si deficeret aliquod tempus motui, in quo scilicet non moveretur, sequeretur quod in illo quiesceret: si autem quies interponitur, erunt multi motus et non unus; multi enim motus et non unus sunt, quorum quies in medio est. Unde si aliquis motus sit qui intercipiatur quiete, non erit neque unus neque continuus. Intercipitur autem quiete, si tempus sit in medio, ut ostensum est: unde requiritur ad continuitatem motus, quod sit unum tempus continuum. Sed tamen hoc non sufficit; quia motus qui non est unus specie, non est continuus, etiam si tempus non deficiat: quia etsi sit unum secundum tempus, erit alius secundum speciem. Quia necesse est ad hoc quod sit motus unus continuus, quod sit unus secundum speciem, sed non sequitur quod motus qui est unus secundum speciem, sit unus simpliciter. Sic ergo patet quod tria praedicta requiruntur ad hoc quod sit unus motus simpliciter. Et hoc est quod concludit, quod dictum est quis motus sit simpliciter unus.	706. Thirdly, in order that a motion be continuous and one, it must be one as regards the time, so that no period of immobility or rest intervene. For if there is a time in which it was not moving, then it was at rest during that time, and if a state of rest intervenes, the motion is not one but many; for motions that are interrupted by rest are not one but many. Consequently, if a motion is interrupted by rest, it will be neither one nor continuous. But it is interrupted by rest, if there is a time in the middle of it, as was shown. Hence for continuity of motion, there must be one continuous time. But mere continuity of time is not enough, because a motion that is not specifically one is not continuous, even though time is not interrupted: for although it be one in regard to time, it will be other in regard to species. In other words, in order that a motion be one and continuous, it must be specifically one; but it does not follow that a motion specifically one is unqualifiedly one, Thus, it is clear that the three aforementioned things are required in order that a motion be unqualifiedly one. And so he concludes that we have now explained which motion is unqualifiedly one.
lib. 5 l. 7 n. 5 Deinde cum dicit: amplius autem dicitur unus et perfectus etc., positis tribus modis principalibus unitatis motus, hic ponit duos alios modos secundarios, qui magis pertinent ad quandam formam unitatis, quam ad ipsam unitatem. Secundum ponit ibi: amplius autem aliter et cetera. Dicit ergo primo, quod sive motus dicatur unus secundum genus sive secundum speciem sive secundum substantiam, sicut qui est numero unus, dicitur unus motus ex hoc quod est perfectus, sicut et in aliis rebus perfectum et totum ad unitatis rationem pertinent. Non enim dicimus unum hominem vel unum calceum, nisi de toto. Quandoque autem dicitur unum etiam de imperfecto, dummodo sit continuum. Et ratio huius est, quia unum potest attendi vel secundum quantitatem, et sic sola continuitas sufficit ad unitatem rei; vel secundum formam substantialem, quae est perfectio totius; et sic perfectum et totum dicitur unum.	707. Then at (523 228 b11) having posited the three principal ways in which a motion is one, he mentions two secondary ways, although these pertain more to a certain form of unity than to unity itself. The second of these is given at 708. He says therefore first (523 228 b11) that whether a motion be one in genus or in species or in substance, i.e., numerically one, it is also called one if it is perfect, just as in other things, “perfect” and “whole” pertain to the notion of unity. For we do not speak of one man or one shoe, unless they are whole. However, there are times when we speak of something imperfect as being one, provided it is continuous. And the reason for this is that unity can be regarded from the viewpoint of quantity, in which sense mere continuity suffices for the unity of a thing, or from the viewpoint of the substantial form, which is the perfection of the whole. Thus, what is perfect and whole is said to be one.
lib. 5 l. 7 n. 6 Deinde cum dicit: amplius autem aliter praeter praedictos etc., ponit alium modum secundarium, prout dicitur motus unus qui est regularis, idest uniformis; sicut etiam in aliis rebus dicitur unum, quod est simile in partibus. Et circa hoc tria facit: primo ponit hunc modum unitatis, secundum quod regularis motus dicitur unus; secundo ostendit in quibus inveniatur regularitas et irregularitas, ibi: est autem et in omni motu etc.; tertio ostendit modos irregularitatis, ibi: irregularitatis autem et cetera. Dicit ergo primo, quod praeter praedictos modos unitatis, dicitur motus unus qui est regularis, idest uniformis. Irregularis enim motus, idest difformis, non videtur esse unus, sed magis motus regularis, idest uniformis; sicut motus qui est totus in directum, est uniformis. Ideo autem motus irregularis non videtur unus, quia est divisibilis in partes dissimiles; indivisibilitas autem pertinet ad rationem unius, quia unum est ens indivisum. Sed tamen motus irregularis est quodammodo unus. Sed unitas motus irregularis et regularis videtur differre secundum magis et minus: quia motus regularis est magis unus quam motus irregularis; sicut et corpus similium partium est magis unum quam corpus dissimilium.	708. Then at (524 228 b15) he gives the other secondary way; that a motion is called one when it is regular, i.e., uniform, just as in other things an object is said to be one, if its parts are alike. About this he does three things: First he posits this mode of unity in the sense that a regular motion is one; Secondly, he shows in which motions regularity and irregularity are found, at 709; Thirdly, he explains the modes of irregularity, at 710. He says therefore that in addition to the above-mentioned rays of being one, a motion is called one, if it, is regular, i.e., uniform. For an irregular or non-uniform motion does not seem to be one, whereas a regular, i.e., uniform motion does (as a motion which is entirely straight is uniform). The reason why an irregular motion does not seem to be one is that it can be divided into parts which are not alike, whereas indivisibility pertains to the notion of unity, because that which is one is undivided. However, an irregular motion is one in a sense. But the unity of irregular and regular motions seem to differ according to more and less: because a regular motion is more perfectly one than an irregular one; just as a body whose part’s are alike is more perfectly one than a body of parts that are not alike.
lib. 5 l. 7 n. 7 Deinde cum dicit: est autem et in omni motu etc., ostendit in quibus motibus inveniatur regularitas et irregularitas. Et dicit quod in omni genere vel specie motus, invenitur regulare et non regulare: quia potest aliquid alterari regulariter, sicut quando tota alteratio est uniformis; et potest aliquid ferri, idest secundum locum moveri, in magnitudine regulari, idest uniformi, sicut si feratur aliquid per circulum aut per lineam rectam; et similiter est in augmento et decremento.	709. Then at (525 228 b19) he shows in which motions irregularity and regularity are found. And he says that they are found in every genus and species of motion: for some things can be altered in a regular manner, as when the entire alteration is uniform, and some things can be moved along a magnitude that is regular and uniform, as things that are in circular motion or in rectilinear motion. The same is true of growing and decreasing.
lib. 5 l. 7 n. 8 Deinde cum dicit: irregularitatis autem differentia etc., accedit ad determinandum de motu irregulari. Et primo assignat modos irregularitatis; secundo ostendit quomodo motus irregularis sit unus, quod supra dixerat, ibi: unus igitur et cetera. Circa primum duo facit: primo assignat duos modos irregularitatis in motu; secundo infert quasdam conclusiones ex dictis, ibi: unde neque species et cetera. Dicit ergo primo quod differentia quae facit irregularitatem motus, aliquando est ex parte rei in qua movetur, ut patet praecipue in motu locali: quia impossibile est quod motus sit regularis vel uniformis, qui non transit per magnitudinem regularem, idest uniformem. Dicitur autem magnitudo regularis vel uniformis, cuius quaelibet pars uniformiter sequitur ad aliam partem, et sic quaelibet pars potest supponi alteri parti, ut patet in linea circulari, et etiam in linea recta. Magnitudo autem irregularis est, cuius non quaelibet pars sequitur uniformiter ad aliam partem; sicut patet in duabus lineis facientibus angulum, quarum una applicatur alteri non in directum, sicut partes unius lineae sibi invicem in directum applicantur. Et ideo motus circularis est regularis, et similiter motus rectus: sed motus reflexi aut obliqui, quia faciunt angulum, non sunt regulares nec in magnitudine regulari; vel quicumque alius motus sit per quamcumque magnitudinem, cuius quaecumque pars non conveniat cuicumque parti per uniformitatem applicationis, vel cuius una pars non convenienter possit contingere aliam partem. Si enim illa pars quae continet angulum, supponatur illi parti quae angulum non continet, non erit conveniens contactus.	710. Then at (526 228 b21) he approaches the task of deciding about irregular motion. First he mentions ways of being irregular; Secondly, he shows how an irregular motion is one, at 713. About the first he does two things: First he assigns two ways in which irregularity is present in motions; Secondly, he draws certain conclusions from all this, at 712. He says therefore first (526 228 b21) that the variations that make for irregularity in motion are caused sometimes from the thing in respect to which there is motion, as is evident especially in local motions for it is impossible for a motion to be regular and uniform unless it passes over a magnitude that is regular, i.e., uniform. Now a magnitude is said to be regular or uniform when each part of it follows its neighbor in a uniform manner, so that any part could be superimposed upon any other, as is clear in the case of arcs or straight lines. But a magnitude is irregular, if one part does not uniformly follow another, as is evident in two lines that form an angle, of which one part does not fit perfectly over the other in the way that one part of a line fits perfectly over another, Therefore, a circular motion is regular and so is a rectilinear one: but reflexed or oblique motions, whose path forms an angle, are not regular and do not take place on a uniform magnitude; likewise any motion on a magnitude that is not such that any part of it taken at random fits on any other taken at random, For if the part (of the motion) that contains the angle is superimposed on a part that does not form an angle, they will not match,
lib. 5 l. 7 n. 9 Secunda differentia irregularitatem faciens est, non ex parte loci, neque ex parte temporis, neque in quod quo, idest neque ex parte eius quod dicit quo, idest ex parte cuiuscumque rei in qua fit motus (non enim est solum motus in ubi, sed in qualitate et quantitate): vel potest hoc referri ad subiectum in quo est motus. Sed iste secundus modus irregularitatis accipitur in eo quod ut, idest ex diversitate modi motus. Determinatur enim iste secundus modus irregularitatis velocitate et tarditate: quia ille motus dicitur regularis, cuius est eadem velocitas per totum; irregularis autem, cuius una pars est velocior altera.	711. The second difference that makes for irregularity is found neither in the place nor in the time nor in the goal (for the goal of a motion is not merely a place but also quality or quantity) but in the manner of the motion, For in some cases the motion is differentiated by swiftness and slowness; because a motion that has the same velocity throughout is said to be uniform, while one in which one part is swifter than another is said to be irregular.
lib. 5 l. 7 n. 10 Deinde cum dicit: unde neque species motus etc., concludit duo corollaria ex praemissis. Quorum primum est, quod velocitas et tarditas non sunt species motus, neque differentiae specificae, quia consequuntur omnes species motus; quia velocitate et tarditate determinatur regularitas et irregularitas, quae consequuntur quamlibet speciem motus, ut supra dictum est. Nulla autem species vel differentia consequitur omnem speciem sui generis. Secundum corollarium est, quod velocitas et tarditas non sunt idem quod gravitas et levitas: quia utrumque istorum habet motum semper ad idem; sicut motus terrae, quae est gravis, semper est ad ipsam, idest ad locum ipsius, qui est deorsum, et motus ignis semper est ad ipsum, idest ad locum proprium, qui est sursum. Velocitas autem et tarditas se habent ad diversos motus, ut dictum est.	712. Then at (527 228 b28) he draws two conclusions from the foregoing. The first of which is that swiftness and slowness are neither species of motion nor specific differences, because they can be found in all types of motion, since they determine regularity and irregularity, which follow upon each species of motion, as was said above. And no species or difference is common to every species of a genus. The second corollary is that swiftness and slowness are not the same as heaviness and lightness, because each of the latter has its own motion, for the motion of earth, which is heavy, is always toward a downward place and the motion of fire is always toward an upward. On the other hand, swiftness and slowness are common to diverse motions, as was said.
lib. 5 l. 7 n. 11 Deinde cum dicit: unus igitur irregularis est etc., ostendit quomodo motus irregularis sit unus; secundo infert quoddam corollarium ex dictis, ibi: si autem omnem unum et cetera. Dicit ergo primo, quod motus irregularis potest dici unus, inquantum est continuus; sed minus dicitur unus quam regularis; sicut et linea habens angulum, minus dicitur una quam linea recta. Et hoc maxime apparet in motu reflexivo: quia quasi videntur duo motus. Ex hoc autem quod est minus unus, apparet quod aliquid habet de multitudine: quia ex hoc aliquid est minus, quod habet admixtionem contrarii, sicut minus album habet aliquid admixtum de nigro, ad minus secundum quandam appropinquationem. Et sic patet quod motus irregularis et est unus, inquantum est continuus, et est quodammodo multiplex, inquantum est minus unus.	713. Then at (528 229 a1) he shows how an irregular motion is one; Secondly, he draws a corollary at 714. He says therefore first that an irregular motion can be said to be one insofar as it is continuous, but it is less perfectly one than a regular motion, just as a line having an angle is less perfectly one than a straight line. This is especially clear in a reflected motion, which seems to be, as it were, two motions. Now, since an irregular motion is less perfectly one, it appears to share in the notion of multitude, for a thing is said to be less, because it has an admixture of the contrary, as what is less perfectly white has an admixture of black, at least in being closer to black than a perfectly white object is.
lib. 5 l. 7 n. 12 Deinde cum dicit: si autem omnem etc., concludit ex immediate dictis quod supra proposuerat; scilicet quod motus qui sunt diversi secundum speciem, non possunt continuari. Omnem enim motum unum contingit esse regularem, et iterum non regularem. Sed motus qui est compositus ex diversis motibus secundum speciem, non potest esse regularis. Quomodo enim esset regularis motus compositus ex alteratione et loci mutatione? Necesse est enim ad hoc quod motus sit regularis, quod partes conveniant ad invicem. Ergo relinquitur quod motus diversi, qui non consequuntur se invicem eiusdem speciei existentes, non sunt unus motus et continuus; quod supra positum est et per exempla manifestatum.	714. Then at (529 229 a3) he concludes from the immediately foregoing the conclusion which he had previously proposed; namely, that motions which are specifically diverse cannot form a continuity. For every motion that is one can be either irregular or regular. But a motion that is composed of specifically distinct motions cannot be regular. For how could a regular motion be composed of alteration and local motion? For in order that a motion be regular its parts must agree. Consequently, the conclusion is that diverse motions that are consecutive but not all of the same species do not form a motion that Is one and continuous, as was stated above and explained by examples.