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184 a9

200 b12

201 a15

Lecture 1 Need for defining motion and things related to it

Latin	English
	Lecture 1 Need for defining motion and things related to it.
lib. 3 l. 1 n. 1 Postquam philosophus determinavit de principiis rerum naturalium, et de principiis huius scientiae, hic incipit prosequi suam intentionem determinando de subiecto huius scientiae, quod est ens mobile simpliciter. Dividitur ergo in partes duas: in prima determinat de motu secundum se; in secunda de motu per comparationem ad moventia et mobilia, ibi: omne quod movetur etc., libro VII. Prima dividitur in duas: in prima determinat de ipso motu; in secunda de partibus eius, in quinto libro, ibi: transmutatur autem et cetera. Circa primum duo facit: primo dicit de quo est intentio; secundo exequitur, ibi: est quidem igitur et cetera. Circa primum duo facit: primo dicit de quo principaliter intendit; secundo ponit quaedam ei adiuncta, quae ex consequenti intenduntur, ibi: determinantibus autem et cetera.	275. Having settled the question of the principles of natural things (Book I), and that of the principles of this science (Book II), the Philosopher here begins to pursue his original plan, which is to arrive at conclusions concerning the subject of this science, mobile being taken absolutely. The treatment, then, is divided into two parts: In the first he concludes with respect to motion in itself (Books III-VI); In the second he concludes with respect to motion in relation to movers [things moving others] and things movable [things which others move] (Book VII). The first part is divided into two: He concludes in regard to motion itself (Books III-IV); He concludes in regard to its parts (Book V). As to the first, he does two things: He states what is under investigation; He follows it out, at 279. With reference to the first of these, he does two things: He states that concerning which he intends to treat principally; He sets down certain things which adjoin thereto, with which he will be subsequently concerned, at 277.
lib. 3 l. 1 n. 2 Circa primum utitur tali ratione natura est principium motus et mutationis, ut ex definitione in secundo posita patet (quomodo autem differant motus et mutatio, in quinto ostendetur): et sic patet quod ignorato motu, ignoratur natura, cum in eius definitione ponatur. Cum ergo nos intendamus tradere scientiam de natura, necesse est notificare motum.	276. As to the first [189 200 b12] he uses the following argument: Nature is the principle of motion and change, as is evident from the definition set down in Book II. (But how motion and change differ, will be shown in Book V.) And thus it is evident that if one does not know motion, one does not know nature, since the former [motion] is placed in the definition of the latter [nature]. Since, therefore, we intend to present the science of nature, we must make motion understood.
lib. 3 l. 1 n. 3 Deinde cum dicit: determinantibus autem etc., adiungit quaedam quae concomitantur motum: et utitur duabus rationibus, quarum prima talis est. Quicumque determinat de aliquo, oportet quod determinet ea quae consequuntur ipsum: subiectum enim et accidentia in una scientia considerantur. Sed motum consequitur infinitum intranee, quod sic patet. Motus enim est de numero continuorum, quod infra patebit in sexto: infinitum autem cadit in definitione continui. Et addit primo, quia infinitum quod est in additione numeri, causatur ex infinito quod est in divisione continui. Et quod infinitum cadat in definitione continui, ostendit quia multoties definientes continuum utuntur infinito; utpote cum dicunt quod continuum est quod est divisibile in infinitum. Et dicit multoties, quia invenitur etiam alia definitio continui, quae ponitur in praedicamentis: continuum est cuius partes ad unum terminum communem copulantur. Differunt autem hae duae definitiones. Continuum enim, cum sit quoddam totum, per partes suas definiri habet: partes autem dupliciter comparantur ad totum, scilicet secundum compositionem, prout ex partibus totum componitur; et secundum resolutionem, prout totum dividitur in partes. Haec igitur definitio continui data est secundum viam resolutionis; quae autem ponitur in praedicamentis, secundum viam compositionis. Sic igitur patet quod infinitum consequitur motum intranee. Quaedam autem consequuntur motum extrinsece, sicut exteriores quaedam mensurae, ut locus et vacuum et tempus. Nam tempus est mensura ipsius motus: mobilis vero mensura est locus quidem secundum veritatem, vacuum autem secundum opinionem quorundam: et ideo subiungit quod motus non potest esse sine loco, vacuo et tempore. Nec impedit quod non omnis motus est localis; quia nihil movetur nisi in loco existens: omne enim corpus sensibile est in loco, et huius solius est moveri. Motus etiam localis est primus motuum, quo remoto removentur alii, ut infra patebit in octavo. Sic igitur patet quod praedicta quatuor consequuntur motum, unde pertinent ad considerationem philosophi naturalis propter rationem praedictam.	277. Then [196 201 a15] he adds certain things which accompany motion. And he employs two sets of reasons [for including them], the first of which is as follows [the second at no. 2778, below]: Whoever determines something, must determine those things which follow upon it—for the subject and its accidents [Properties] are considered in a single science. But the infinite follows upon motion intrinsically, as the following makes plain: Motion is of the number of continuous things, as will be evident below in Book VI (l.6). But “infinite” enters into the definition of “continuum.” And he [Aristotle] adds “first of all,” because the infinite which is found in the addition of number, is caused from the infinite which is in the division of the continuum. And that the infinite enters [first of all] into the definition of the continuum, he shows from the fact that those defining the continuum often use “infinite”—as, for example, when they say that the “continuum” is that which is “divisible to infinity.” And he [Aristotle] says “often,” since there is also found another definition of the continuum, which is given in the Predicaments [or Categories]: the “continuum” is that “whose parts are joined at a common boundary.” Now these two definitions differ. For the continuum, since it is a certain whole, is properly defined through its parts. But parts are compared to the whole in a twofold way, namely, as its components, i.e., according to composition, insofar as the whole is composed out of the parts; and as its resolutes, i.e., according to resolution, insofar as the whole is divided into the parts. The present definition, therefore, of the continuum , is given according to the mode of resolution [division into parts]; while that which is set down in the Predicaments is according to the mode of composition [composition out of parts]. Hence it is clear that the infinite follows upon motion intrinsically. But there are some things which follow upon motion extrinsically, as certain external measures: such as place, and the void, and time. For time is the measure of motion itself; while the measure of the mobile thing is indeed place according to truth, but the void according to the opinion of some. And therefore he adds that motion cannot be without place, the void, and time. Nor does the fact that not all motion is local affect this; since nothing is moved which is not in place. For every sensible body is in place, and to it [sensible body] alone does it belong to be moved. Likewise, local motion is the first of motions, which, when it is removed, the other motions are removed, as will be evident below in Book VIII (l.14). It is thus clear that the four above-mentioned properties are consequent upon motion; whence they pertain to the consideration of the natural philosopher for the aforesaid reason.
lib. 3 l. 1 n. 4 Et etiam propter aliam quam consequenter subiungit, quia praedicta sunt communia omnibus rebus naturalibus. Unde cum determinandum sit in scientia naturali de omnibus rebus naturalibus, praedeterminandum est de quolibet istorum: quia speculatio quae est de propriis, est posterior ea quae est de communibus, ut in principio dictum est. Sed inter haec communia prius determinandum est de motu; quia alia consequuntur ad ipsum, ut dictum est.	278. This is also true for yet another reason which he [Aristotle] adds subsequently: namely, because the aforesaid are common to all natural things. Accordingly, since it is the task of natural science to reach conclusions concerning all natural things, one must therefore first determine concerning each of these [four]. For the speculation which is directed toward proper things, comes after that which is of common things, as was stated in the beginning [Book I, l.1, no. 6]. But among all these common things, one must first reach conclusions concerning motion itself, because the other things follow upon it as was stated [in the preceding no].
lib. 3 l. 1 n. 5 Deinde cum dicit: est quidem igitur aliquid etc., exequitur propositum. Et primo determinat de motu et infinito, quod intranee motum consequitur; secundo de aliis tribus, quae consequuntur ipsum extrinsece, in quarto libro, ibi: similiter autem necesse et cetera. Prima dividitur in duas: in prima determinat de motu; in secunda de infinito, ibi: quoniam autem de natura et cetera. Circa primum duo facit: primo praemittit quaedam ad investigandum definitionem motus; secundo definit motum, ibi: diviso autem secundum unumquodque et cetera. Circa primum duo facit: primo enim praemittit quasdam divisiones: quia via ad inveniendum definitiones convenientissima est per divisiones, ut patet per philosophum in II Poster. et in VII Metaphys.; secundo ostendit quod motus in praedictas divisiones cadit, ibi: non est autem motus et cetera.	279. Then [191 200 b26] he puts his plan into execution: He reaches conclusions concerning motion, and the infinite, which follows motion intrinsically; He does the same for the other three, which follow motion extrinsically, and this he does in Book IV. The first treatment is divided into two parts: He concludes with respect to motion; He does the same for the infinite, at 326. With respect to the first of these, he does two things: He prefaces his treatment with certain considerations requisite for investigating the definition of motion; He defines motion, at 283. As to the first of these, he does two things: He sets down in advance certain divisions, since the most suitable path towards finding definitions is through division, as is clear from the Philosopher in Posterior Analytics II (l.14 ff.), and in Metaphysics VII (l.12); He shows that motion falls within the aforesaid divisions, at 281.
lib. 3 l. 1 n. 6 Circa primum ponit tres divisiones: quarum prima est quod ens dividitur per potentiam et actum. Et haec quidem divisio non distinguit genera entium: nam potentia et actus inveniuntur in quolibet genere. Secunda divisio est prout ens dividitur secundum decem genera: quorum unum est hoc aliquid, idest substantia, aliud quantum vel quale, aut aliquod aliorum praedicamentorum. Tertia divisio est unius generis entium, scilicet eius quod est ad aliquid. Nam motus aliquo modo ad hoc genus pertinere videtur, inquantum movens refertur ad mobile. Ad huius igitur tertiae divisionis intellectum, considerandum est quod, cum relatio habeat debilissimum esse, quia consistit tantum in hoc quod est ad aliud se habere, oportet quod super aliquod aliud accidens fundetur; quia perfectiora accidentia sunt propinquiora substantiae, et eis mediantibus alia accidentia substantiae insunt. Maxime autem super duo fundatur relatio, quae habent ordinem ad aliud, scilicet super quantitatem et actionem: nam quantitas potest esse mensura etiam alicuius exterioris; agens autem transfundit actionem suam in aliud. Relationes igitur quaedam fundantur super quantitatem; et praecipue super numerum, cui competit prima ratio mensurae, ut patet in duplo et dimidio, multiplici et submultiplici, et in aliis huiusmodi. Idem etiam et simile et aequale fundantur super unitatem, quae est principium numeri. Aliae vero relationes fundantur super actionem et passionem: vel secundum ipsum actum, sicut calefaciens dicitur ad calefactum; vel secundum hoc quod est egisse, sicut pater refertur ad filium quia genuit; vel secundum potentiam agendi, sicut dominus ad servum quia potest eum coercere. Hanc igitur divisionem manifeste expressit philosophus in V Metaphys.; sed hic breviter tangit, dicens quod ad aliquid aliud quidem est secundum superabundantiam et defectum; quod quidem fundatur super quantitatem, ut duplum et dimidium: aliud autem secundum activum et passivum, et motivum et mobile, quae ad invicem referuntur, ut patet per se.	280. With respect to the first of these, he sets down three divisions: The first of these is that being is divided by potency and act. Now this division does not distinguish beings into genera—for potency and act are found in every genus. The second division is of being as divided according to the ten genera: the first of these is “this something,” i.e., substance; others are: how much [i.e., quantity ], or how [quality], or some other of the Predicaments. The third division is of one genus of beings, namely, of the one which is “to something” [relation]. For motion seems in a certain way to pertain to this genus, insofar as the mover is referred to the movable thing. In order to understand this third division, one must consider that, since relation has the weakest existence—consisting alone, as it does, in the fact of being something referred to something else—it is necessary that it be grounded on some other accident. For the more perfect accidents are closer to the substance, and it is through them as intermediates that the other accidents inhere in the substance. Now relation is founded chiefly upon two accidents which have an order to something else, namely, upon quantity and action. [or quantity may be a measure even of something external to it; while the agent transfuses its action into something other than itself. Accordingly, certain relations are founded upon quantity; and especially upon that species of quantity which is number, to which the basic notion of measure pertains, as—is evident in “double and half,” “multiple and submultiple [fraction]” and other such. Similarly, “same,” “like,” and “equal” are founded upon unity, which is the principle of number. Still other relations are founded upon action and passion: either according to existing act [in the present], as something is said to be “heating” in relation to that which is heated; or according to “having acted” [in the past], as a father is referred to a son because he because he engendered him; or else according to the possibility of acting [in the future], as master is related to a servant because he is able to make him do something. Now the Philosopher clearly explains this division in Metaphysics V (l.17); but he here touches on it briefly, saying that one sort of “to something” [relation] is that according to “excess and defect,” which sort, indeed, is founded on quantity, as in the case of “double and half”; while the other is according to “active and passive,” and “mover and movable,” which are referred to each other, as is self-evident.
lib. 3 l. 1 n. 7 Deinde cum dicit: non est autem motus praeter res etc., ostendit quomodo motus reducitur ad praedictas divisiones. Et circa hoc duo facit: primo ostendit quod motus non est praeter genera rerum in quibus contingit esse motum; secundo quod dividitur sicut genera rerum dividuntur, ibi: unumquodque autem et cetera. Circa primum considerandum est quod, cum motus, sicut infra patebit, sit actus imperfectus; omne autem quod est imperfectum, sub eodem genere cadit cum perfecto, non quidem sicut species, sed per reductionem (sicut materia prima est in genere substantiae); necesse est quod motus non sit praeter genera rerum in quibus contingit esse motum. Et hoc est quod dicit, quod motus non est praeter res, idest praeter genera rerum in quibus est motus, ita quod sit aliquid extraneum, vel aliquid commune ad haec genera. Et hoc manifestat per hoc quod omne quod mutatur, mutatur vel secundum substantiam, vel secundum quantitatem, vel secundum qualitatem, vel secundum locum, ut in quinto ostendetur. His autem generibus non est accipere aliquod commune univocum, quod non contineatur sub aliquo praedicamento, sed sit genus eorum: sed ens est commune ad ea secundum analogiam, ut in IV Metaphys. ostendetur. Unde etiam manifestum est quod neque motus neque mutatio sunt extra praedicta genera; cum nihil sit extra ea, sed sufficienter dividant ens. Quomodo autem motus se habeat ad praedicamentum actionis vel passionis, infra ostendetur.	281. Then [192 200 b32] he shows how motion is reduced to the aforesaid [three] divisions. And as to this he does two things: He shows that motion is not outside the genera of things in which motion occurs; He shows that motion is divided as the genera of things are divided, at 282. As to the first of these, it should be observed that since motion, as will be evident below (lesson following, nos. 285, 287; l.3, no. 296), is an imperfect act, and since everything which is imperfect falls under the same genus with that which is perfect in respect to it—not, indeed, as a species, but by reduction (as prime matter is by reduction in the genus of “substance”) necessarily motion is not outside the genera of things in which motion occurs. And this is what he [Aristotle] states, namely, that motion is not “outside of things,” i.e., outside the genera of things in which motion is found, in such a way as to be something extraneous to, or something common to, these genera. And he makes this plain by the fact that whatever is changed, is changed either according to substance, or quantity, or quality, or place, as will be shown in Book V. Now there is not to be found in these genera some common univocal element which would not be found under some predicament but would be their genus; but being is common to them according to analogy, as will be shown in Metaphysics IV (l.1). Whence it is also plain that neither motion nor change is outside the aforesaid genera, since nothing is outside the latter and they sufficiently divide being. But, as to the question of how motion is related to the predicament of action or passion, this will be explained below (l.5).
lib. 3 l. 1 n. 8 Deinde cum dicit: unumquodque autem dupliciter etc., ostendit quod motus dividitur sicut genera rerum. Manifestum est enim quod in omnibus generibus contingit aliquid esse dupliciter, vel sicut perfectum, vel sicut imperfectum. Cuius ratio est, quia privatio et habitus est prima contrarietas, quae in omnibus contrariis salvatur, ut in X Metaphys. dicitur. Unde, cum omnia genera dividantur contrariis differentiis, oportet in omnibus generibus esse perfectum et imperfectum: sicut in substantia aliquid est ut forma, et aliquid ut privatio; et in qualitate aliquid est ut album quod est perfectum, et aliquid ut nigrum, quod est quasi imperfectum; et in quantitate, aliquid est quantitas perfecta et aliquid imperfecta; et in loco aliquid est sursum, quod est quasi perfectum, et aliquid deorsum, quod est quasi imperfectum; vel leve et grave, quae ponuntur in ubi, ratione inclinationis. Unde manifestum est quod quot modis dividitur ens, tot modis dividitur motus. Differunt enim species motus secundum diversa genera entium; ut augmentum, quod est motus in quantitate, a generatione, quae est motus in substantia. Differunt etiam species motus secundum perfectum et imperfectum in eodem genere: nam generatio est motus in substantia ad formam, corruptio vero ad privationem; et in quantitate augmentum ad quantitatem perfectam, diminutio ad imperfectam. Quare autem non assignentur duae species in qualitate et in ubi ostendetur in quinto.	282. Then [193 201 a3] he shows that motion is divided as the genera of things are divided, For it is plain that in all the genera a thing may be present in two ways, either as something perfect, or as something imperfect. The reason for this is that privation and possession is the prime contrariety, which is found in all the contraries, as is stated in Metaphysics X (l.6). Whence, since all the genera are divided through contrary differences, it is necessary that in all there be the perfect and the imperfect: as in “substance” something is as form and something is as privation; and in “quality” there is something such as white, which is perfect, and something such as black, which is, as it were, imperfect; and in “quantity” one thing is perfect quantity, another imperfect; and in “place” something is above, which is, as it were, perfect, and something is below, which is, so to speak, imperfect; or else there is light and heavy, which are placed in “where” [place] by virtue of the inclination [to a certain place] which is in them. Hence it is plain that according to the divisions of being, there are corresponding divisions of motion. For the species of motion differ according to the different genera of being—as “increase,” which is motion in quantity, differs from “generation,” which is motion in substance. The species of motion likewise differ according to perfect and imperfect in the same genus: for “generation” is motion in substance toward form, while “corruption” is motion toward privation; and in quantity, “increase” is toward perfect quantity, “diminution” toward imperfect. But as to the question of why there are not assigned two kinds in quality and where [place], this will be explained in Book V (l.4).