Et ulterius, si dividatur potentia, media potentia movebit medietatem mobilis per idem spatium in aequali tempore. Sed hoc intelligendum est, quando potentia est talis quae per divisionem non corrumpitur. Loquitur enim secundum considerationem communem, nondum applicando ad aliquam specialem naturam, sicut et in omnibus quae praemisit. Et ponit exemplum. Si enim accipiatur medietas huius potentiae quae est a, et dicatur e; et accipiatur medietas mobilis quod est b, et dicatur z: sicut a movebat b per c in tempore d, ita e movebit z per idem spatium in aequali tempore; quia et hic etiam servatur eadem proportio virtutis motivae ad corpus ponderosum quod movetur. Unde sequitur quod in aequali tempore fiat motus per aequale spatium, sicut dictum est. Further, if the power be divided, half the power will move half the mobile through the same distance in the given time. However, this must be understood of a mover that is not destroyed by division, for he has been speaking in a general way without making application to the particular natures involved. And he gives an example. Let E be half of power A and let Z be half of mobile B, then, just as A moved B through C in time D, so E will move Z through the same distance in the same amount of time, because the same proportion of motive power to moved body mass is preserved. Hence, it follows that, in an equal time, the motion will traverse an equal distance, as was said. 959. Deinde cum dicit: et si e ipsum z etc., excludit duas falsas comparationes. 959. Then, when he says, but, if E moves Z (250a9), he rejects two false comparisons. Quarum prima est, quod addatur ad mobile, et non addatur ad potentiam moventem. Unde dicit quod si e, quod est medietas motivae potentiae, moveat z, quod est medietas mobilis, in tempore d secundum spatium c; non est necessarium quod ipsa potentia dimidiata, quae est e, moveat mobile quod sit in duplo maius quam z, in aequali tempore secundum medietatem spatii quod est c; quia poterit esse quod dimidia potentia duplum mobile nullo modo movere poterit. Sed si posset movere, teneret haec comparatio. The first consists in adding to the mobile without adding to the motive power. Hence, he says that, if E, which is half the motive power, moves Z, which is half the mobile, a distance C in a time D, it is not necessarily true that the halved power E will move a mobile twice Z through half the distance in the given time, for it could happen that the halved power cannot move the doubled mobile at all. But, if it can move it, the comparison will hold. Secunda falsa comparatio est, quando dividitur movens, et non dividitur mobile. Et hanc excludit ibi: si vero a etc.: dicens quod si potentia movens quae est a, moveat mobile quod est b, in tempore d, per spatium quod est c; non oportet quod medietas moventis moveat totum mobile quod est b, in tempore d, neque etiam per quamcumque partem spatii c, cuius partis sit proportio ad totum spatium c sicut e converso erat quando comparabamus a ad z, idest totam potentiam motivam ad partem mobilis. Illa enim erat conveniens comparatio, sed hic non: quia potest contingere quod medietas moventis non movebit totum mobile per aliquod spatium. Si enim aliqua tota virtus movet totum mobile, non sequitur quod medietas illius virtutis moveat totum mobile, neque per quantumcumque spatium, neque in quocumque tempore: quia sequeretur quod solus unus homo posset movere navem per aliquod spatium, si potentia trahentium dividatur secundum numerum trahentium, et secundum longitudinem spatii per quod omnes simul trahunt navem. The second false comparison occurs when the mover is divided and the mobile is not divided. This he rejects at, if, then, A moves B (250a12), saying that, if the motive power A moves the mobile B through distance C in time D, it does not necessarily follow that half the motive power will move the entire mobile B in time D through a part of distance C such that this part of C is related to the entire distance C as A was related to Z in our other example. For when A was compared with Z, it was a suitable comparison, but in the present case, it is not, for it can happen that half the motive power will not move the whole mobile any distance. For if some whole power moves some whole mobile, it does not follow that half of it will move the same mobile any distance, no matter how much time is allowed. Otherwise, it would follow that a man by himself could move a whole ship a certain distance, if the combined power of the ship haulers is divided by the number of haulers and the distance they haul it be so divided. 960. Deinde cum dicit: propter hoc Zenonis ratio etc., secundum praemissa solvit rationem Zenonis, qui volebat probare quod quodlibet granum milii faciat aliquem sonum, proiectum in terra, quia totus modius milii, quando in terram effunditur, facit aliquem sonum. Sed Aristoteles dicit quod haec Zenonis ratio non est vera, scilicet quod quaelibet pars milii sonet, idest quodlibet granum milii sonum faciat cum cadit in terram: quia nihil prohibet dicere quod granum milii in nullo tempore movet aerem intantum ut faciat sonum, quem aerem movet ad sonum faciendum totius modius cadens. 960. Then, at hence, Zeno’s reasoning (250a19), he uses the foregoing to answer an argument of Zeno, who wished to prove that each grain of millet falling to the earth makes a sound, because an entire bushel of it, when poured to the earth, makes a sound. But Aristotle says that this argument of Zeno is not true that there is no part of the millet that does not make a sound, that is, that each grain of millet makes a sound when it falls to the earth. For there is no reason why any such part should in any length of time move the air to produce a sound as does the whole bushel in falling. Et ex hoc possumus concludere quod non est necessarium, quod si aliqua quantacumque pars existens in toto, movet, quod separatim per se existens movere possit: quia pars in toto non est in actu, sed in potentia, maxime in continuis. Sic enim aliquid est ens, sicut et unum; unum autem est quod est in se indivisum et ab aliis divisum: pars autem prout est in toto, non est divisa in actu, sed in potentia tantum: unde non est actu ens neque una, sed in potentia tantum. Et propter hoc etiam non agit pars, sed totum. And, from this, we can conclude that it is not necessary that, if a part existing in a whole causes a motion, this part, now existing in isolation from the whole, can cause a motion. For in the whole, the part is not actual, but potential, especially in continua. For a thing is a being in the same way that it is one, and one is that which is undivided in itself and divided from others. But a part, precisely as existing in a whole, is not divided from it actually, but only potentially; hence, it is not actually one, but only potentially. For this reason, it is not the part that acts, but the whole. 961. Deinde cum dicit: si vero duo, et utrumque etc., ponit comparationem secundum aggregationem moventium. Et dicit quod si sint duo, et utrumque eorum moveat; quorum utrumque per se moveat tantum mobile in tanto tempore per tantum spatium: quando coniunguntur istae duae potentiae moventium, movebunt illud quod est coniunctum ex ponderibus motis, per aequale spatium in aequali tempore: quia in hoc etiam servatur eadem analogia. 961. Then, at if, on the other hand (250a25), he sets forth a comparison based on an aggregate of movers and says that, if there are two and each of them causes motion, and if each by itself is moving its own mobile a certain distance in a given time, then, when the two are united, they will move the mobiles—which are now joined together—through an equal distance in the same time, for even in this case, the same proportion is maintained. 962. Deinde cum dicit: sic igitur est in alteratione etc., ponit easdem comparationis regulas in aliis motibus. 962. Then, at then, does this hold (250a28), he sets forth the same rules of comparison for other motions. Et circa hoc tria facit: About this, he does three things: primo ostendit divisibilitatem eorum secundum quae attenduntur comparationes motuum; first, he shows that the things according to which the comparison of motions must be judged are divisible; secundo ponit comparationes veras, ibi: in duplo duplum etc.; second, he sets forth the true comparison, at, thus, in twice as much (250b2; [963]); tertio removet comparationes falsas, ibi: si autem alterans etc. third, he rejects some false comparisons, at but if what causes alteration (250b4; [964]). Dicit ergo primo quantum ad augmentum, quod sunt tria, scilicet augens, et id quod augetur, et tempus: et haec tria habent aliquam quantitatem. He first says, therefore (250a28), that there are three things involved in respect to growth: the cause of increase, the thing increased, and the time. These three have a certain quantity. Est etiam quarto accipere quantitatem, secundum quam augens auget, et auctum augetur. Et haec etiam quatuor est accipere in alteratione: scilicet alterans, et quod alteratur, et quantitas passionis secundum quam fit alteratio, quae inest secundum magis et minus, et iterum quantitas temporis in quo fit alteratio; sicut et haec quatuor in motu locali inveniebantur. Also, there is a fourth thing to be considered: the quantity of increase produced by the cause and received by the growing thing. And these four things must be considered also in alteration: the cause of alteration, the thing altered, the amount or degree of alteration (which is present according to more and less), and the amount of time. These four, of course, are the same as are involved in local motion. 963. Deinde cum dicit: in duplo duplum etc., ponit comparationes veras. Et dicit quod si aliqua potentia secundum hos motus moveat tantum in tanto tempore, in duplo tempore movebit duplum: et si moveat duplum, hoc erit in duplo tempore. Et similiter movebit eadem potentia medium in medio tempore: aut si moveat in medio tempore, erit dimidium quod est motum. Aut si sit dupla potentia, in aequali tempore movebit duplum. 963. Then, at thus, in twice as much (250b2), he sets forth the true comparison and says that, if a power moves some amount in a given time according to these motions, then it will move twice the amount in twice the time; and if it moves twice the amount, it will be in twice the time. Likewise, the same power will move half the amount in half the time, or if it moves in half the time, then the motion will be half the amount. Or, if there is twice the power, it will move something twice the amount in an equal time. 964. Deinde cum dicit: si autem alterans etc., excludit falsam comparationem. Et dicit quod si aliqua potentia moveat motu alterationis et augmenti tantum in tanto tempore, non necesse est quod medietas potentiae moveat medietatem in eodem tempore, aut in medio tempore tantundem: sed forte continget quod nihil augmentabit vel alterabit, sicut et in gravi, idest sicut dictum est quod dimidiata potentia non potest movere totum pondus, neque per totum spatium, neque per aliquam eius partem. 964. Then, at but if what causes alteration (250b4), he dismisses a false comparison and says that, if what causes alteration or increase causes a certain amount of increase or alteration respectively in a certain amount of time, it does not necessarily follow that half the force will alter or increase half the object or some given amount in half the time, for it may happen that there will be no alteration or increase at all, as is the case with weight, that is, the case being the same as with the locally mobile that has weight. Est enim intelligendum, quod hoc quod dicit: in medio medium, aut in aequali duplum, ly duplum et medium (quod in accusativo ponitur) non accipitur pro dimidio vel duplo ipsius mobilis, sed pro dimidio et duplo ex parte rei in qua est motus, scilicet qualitatis aut quantitatis, quae ita se habent in istis duobus motibus, sicut longitudo spatii in motu locali: alioquin non similiter esset in istis motibus et in motu locali. In motu enim locali, dictum est quod si tanta potentia movet tantum mobile, medietas movebit medietatem mobilis: hic autem dicitur quod medietas forte nihil movebit. Sed intelligendum est de toto mobili integro: quia virtus motiva dimidiata non movebit ipsum, neque per tantam quantitatem aut qualitatem, neque per eius medium. It should be observed that, when Aristotle says that half will be moved in half or double will be moved in an equal, the words “double” and “half” (which are in the accusative case) refer not to the mobile, but to that in which there is motion—that is, the quality or the quantity, which are related to alteration and growth as length of distance is related to local motion. For in local motion, it was said that, if a certain power moves a certain mobile, half will move half the mobile, but here it is said that half might not move anything. But it must be understood that we are speaking of an integral mobile whole, which will not be moved by a halved motive power to any amount of quantity or degree of quality, much less to half. Liber 8 Book 8 Theta (Θ) Nature of the First Motion and First Mover Lectio 1 Lecture 1 Utrum motus aliquando esse indeperit, et aliquando deficiat: aut e contrario neque unquam incepit, neque unquam deficiet—opiniones ad utramque partem utilitas huius considerationis Whether or not motion began or will end Utrum autem factus sit aliquando motus, cum non esset prius, et corrumpitur iterum sic quod moveri nihil sit: It remains to consider the following question. Was there ever a becoming of motion before which it had no being, and is it corruption again so as to leave nothing in motion? aut neque factus est neque corrumpitur, sed erat semper et erit; et hoc immortale et sine quiete existit in his quae sunt, ut vita quaedam ens natura omnibus subsistentibus? Or are we to say that it never had any becoming and is not corruption, but always was and always will be? Is it in fact an immortal, never-failing property of things that are, a sort of life, as it were, to all naturally constituted things? Esse quidem igitur motum omnes affirmant de natura aliquid dicentes, propter hoc quod mundum faciunt, et de generatione et corruptione est consideratio omnibus ipsis, quam impossibile est esse, nisi sit motus. Now, the existence of motion is asserted by all who have anything to say about nature, because they all concern themselves with the construction of the world and study the question of generation and corruption, which processes could not come about without the existence of motion. Sed quanti quidem infinitos mundos dicunt esse, et quosdam quidem fieri, quosdam autem corrumpi mundorum, semper dicunt esse motum: necessarium enim est generationes et corruptiones ipsorum cum motu esse. But those who say that there is an infinite number of worlds, some of which are in process of generation while others are in process of corruption, assert that there is always motion (for these processes of generation and corruption of the worlds necessarily involve motion). Quicumque autem unum, et non esse semper, et de motu apponunt secundum rationem. But those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion. Si igitur contingit aliquando nihil moveri, dupliciter necesse est hoc accidere. Aut enim sicut Anaxagoras dicit: inquit enim ille, simul omnibus existentibus et quiescentibus infinito tempore, motum fecisse intellectum et disgregasse: If, then, it is possible that, at any time, nothing should be in motion, this must come about in one of two ways: either in the manner described by Anaxagoras, who says that all things were together and at rest for an infinite period of time, and that then mind introduced motion and separated them; aut sicut Empedocles, in parte moveri et iterum quiescere; moveri quidem cum amicitia ex multis faciat unum, aut discordia multa ex uno; quiescere autem in mediis temporibus; or in the manner described by Empedocles, according to whom the universe is alternately in motion and at rest—in motion, when love is making the one out of many or strife is making many out of one, and at rest in the intermediate periods of time. dicens sic: inquantum quidem ex pluribus unum, didicit nasci: inquantum iterum ex uno geminato plurima perficiuntur. Sic fiunt res: et nullo modo ipsius est saeculum unum. Sic autem permutantur, neque simul perficiuntur: sic autem semper sunt immobiles secundum circulum. Hoc enim quod sic permutantur, ab hinc inde dicere ipsum opinandum est. His account is as follows: since one hath learned to spring from manifold, and again one commingled makes manifold arise, thus do things come to be, nor is their era one, nor are they made perfect all at once, and thus they change, but since their motion must alternate be, thus are they always immobile. We must suppose that he means by this that they alternate from the one motion to the other. Considerandum igitur de hoc, quomodo se habet. Praeopere enim non solum ad naturae considerationem scire veritatem, sed ad scientiam de principio primo. We must consider, then, how this matter stands, for the discovery of the truth about it is of importance, not only for the study of nature but also for the investigation of the first principle. 965. Postquam Philosophus in praecedenti libro ostendit quod necesse est ponere primum mobile, et primum motum, et primum motorem; in hoc libro intendit inquirere qualis sit primus motor, et primus motus, et primum mobile. 965. After showing in the preceding book that it is necessary to posit a first mobile, and a first motion, and a first mover, the Philosopher intends in this present book to inquire after a description of the first mover, and first motion, and first mobile. Et dividitur in partes duas: The book is divided into two parts. in prima praemittit quoddam quod est necessarium ad sequentem investigationem, scilicet motum esse sempiternum; In the first, he sets out something necessary to the following investigation: motion is sempiternal. in secunda procedit ad investigationem propositi, ibi: principium autem considerationis etc. In the second part, he proceeds to investigate what is proposed, at our enquiry will resolve (253a22; [1004]). Circa primum tria facit: About the first, he does three things: primo movet dubitationem; first, he raises a problem;