of being rectilinear is rotatory, the same line of reasoning is still applicable: the time occupied is then measurable by the magnitude of the sector to frank its boundary.
If this view is accepted, the passage 966 a 15-24 will be paraphrased as follows, and its application to the subject in hand, viz. the uniform rotation of the lmited universe, and the agent which causes it, will be obvious.
‘Let A represent the limited motor (capable of causing) B the limited mobile (to pass a point or to frank its Bound: ary) and C illimitable time. Now let D cause E, a part of B (to frank its boundary).
[Note that this does not mean that the motion caused by D is confined to the part E, but that it causes enough movement (in B) for E (and no more) to frank its boundary. | ‘Then the time it takes (2) cannot be as great as (the illimitable time) C; for it will take a longer time for a greater amount (of B) (to frank its boundary). Therefore Z, is not illmitable [see the note on this argument on p. 112]. So taking it in this way (that a part (D) of the motive power (A) can move (B) during a definite stretch (Z) of time), by adding one D to another I shall make up the (finite) A, 266 a πεπερασμένον κινεῖν ἄπειρον χρόνον. τρία ya ἔστι---τὸ κινοῦν, τὸ κινούμενον, τὸ ἐν ᾧ τρίτον 16 (ὁ χρόνος)" ταῦτα δὲ ἢ πάντα ἄπειρα ἣ πάντα πεπερασμένα ἢ ἔνια, οἷον τὰ δύο ἢ τὸ ἕν. ἔστω δὴ τὸ A τὸ κινοῦν, τὸ δὲ κινούμενον B, χρόνος ἄπειρος ἐφ᾽ οὗ IT. τὸ δὴ A κινείτω τι μέρος τῆς B, τὸ ἐφ᾽ οὗ E. οὐ δὴ ἐν ἴσῳ τῷ T+ ἐν πλείονι γὰρ τὸ μεῖζον: ὥστ᾽ οὐκ ἄπειρος 6 χρόνος 6 τὸ Ζ.
1 [τὸ Oxf. Trans.: τοῦ codd.—C.]
and by adding one E to another I shall make up the finite B; but I shall not use up the time by deducting a corresponding length for each such addition, since it is illimitable. Therefore the whole of A (the sum of all the D’s) will take only a finite period of the time C to move the whole of B (the sum of all the E’s, past the point, or to cause the whole of B to frank its boundary). So an illimitable motion can not be imparted to anything by a finite mover. Thus it is clear that a finite mover cannot cause motion during illimitable time.’
To take the example of the ship-hauling. Suppose the point to be passed is represented by a post level with the prow of the ship: if 50 men (D) can haul half the ship (E) past the post in an hour (Z) but are then exhausted and can do no more, 50 other men (another D) can haul the remaining half (another E) past the post in another hour (another Z). Therefore the whole gang of 100 men (A), i.e. both the shifts of 50 men (both the D’s), will take only a finite time (two hours) to move the whole of the ship (B) past the post. But it does not necessarily follow that if the whole gang work together for an hour they will produce the same result as if they work in shifts of 50 men, each shift working for an hour.
* [The argument contemplates a finite mover and a finite moved, each of which is not ἀμερὲς καὶ μηδὲν ἔχον μέγεθος but can be considered as divided into parts operating separately. The difficulties raised about the interpretation turn on the epuarsue fallacy in the phrase ἐν πλείονι γὰρ τὸ μεῖζον, which at first sight seems to mean that the greater force (A) οὕτω δὴ τῇ A προστιθεὶς καταναλώσω τὸ A, Kal τῇ E τὸ B- τὸν δὲ χρόνον οὐ καταναλώσω ἀεὶ fot 4 ξ ~ ἀφαιρῶν ἴσον (ἄπειρος γάρ)" wore ἡ πᾶσα A τὴν ὅλην Β κινήσει ἐν πεπερασμένῳ χρόνῳ τοῦ I. οὐκ ἄρα οἷόν τε ὑπὸ πεπερασμένου κινεῖσθαι οὐδὲν ἄπειρον κίνησιν. ὅτι μὲν οὖν οὐκ ἐνδέχεται τὸ πεπερασμένον ἄπειρον κινεῖν χρόνον, φανερόν. Ὅτι δ᾽ ὅλως οὐκ ἐνδέχεται ἐν πεπερασμένῳ vA ΕΣ > δύ 9 Fon’ ὃ δῆλ μεγέθει ἄπειρον εἶναι δύναμιν, ἐκ τῶνδε δῆλον. ἔστω γὰρ ἀεὶ ἡ πλείων δύναμις ἡ τὸ ἴσον ἐν ἐλάτ- Tovt χρόνῳ ποιοῦσα, οἷον θερμαίνουσα 7 yAvKaivovoa ἢ ῥίπτουσα καὶ ὅλως κινοῦσα. ἀνάγκη apa καὶ ὑπὸ TOU πεπερασμένου μὲν ἄπειρον δ᾽ ἔχοντος A δύναμιν πάσχειν TL TO πάσχον, καὶ πλείω ἢ ὑπ᾽ λλ ᾿ λ 7 A ξ 3 ὃ LAAG A ἄλλου: πλείων yap ἡ ἄπειρος δύναμις. ἀλλὰ μὴν χρόνον γε οὐκ ἐνδέχεται εἶναι οὐδένα. εἰ γάρ ἐστιν ὁ ἐφ᾽ ᾧ Α χρόνος ἐν ᾧ ἡ ἄπειρος ἰσχὺς ἐθέρμηνεν ἢ ἔωσεν, ἐν ᾧ δὲ πεπερασμένη tis 6 AB,* πρὸς 1 [ἐν ᾧ δὲ πεπερασμένη τις 6 AB (sc. χρόνος, cf. τῷ A χρόνῳ, b 1): ἐν ᾧ δ᾽ ὁ (ὁ om. EK) ΑΒ πεπερασμένη τις codd. Ether ἐν τῷ δ᾽ AB πεπερασμένη τις (Oxf. Trans.), or ὁ δ᾽ ΑΒ ἐν ᾧ πεπερασμένη τις is possible. Simplic. 1324. 30 (paraphr.) τὸ δὴ πεπερασμένην ἔχον δύναμιν τὸ αὐτὸ κινήσει ἐν πλείονι χρόνῳ τῷ AB perhaps slightly favours the order of words I have adopled.—C.]
in all. But 10-times a finite time is finite and will not exhaust the infinite reserve. Therefore the unit-time in which the 10 colliers (the whole of A) move the 10 sacks (the whole of B) is finite. The principle that the fractional force can deal with a multiple of its proper load, if allowed to take it piecemeal, was stated at 250 a 10 (see note there). So it is not necessary to suppose that D must be a larger fraction of A than E is of B (Simplic. 1822. 8).
taking it in this way (2.e. taking the work as done piecemeal, a fraction at a time), by adding one D to another I shall exhaust the (finite) A, and by adding one E to another I shall exhaust the (finite) B; but I shall not use up the tyme by deducting from it a corresponding length for each such addition, since it is unlimited. Therefore the whole of A (the sum of all the D’s) will take only a finite period of the time C to move the whole of B (the sum of all the E’s). So an unlimited motion cannot be imparted to anything by a finite mover. Thus it is clear that a finite mover cannot cause a motion during unlimited time.
Proceeding next to the general proposition that an unlimited power cannot reside in a limited magnitude we take our line as follows. Let us define the greater power, in every case, as that which produces an equal effect in less time, whether it be heating or sweetening or hurling or, to put it universally, effecting any kind of change. If then a limited subject had unlimited power, the object on which it exercised that power would clearly experience some effect, and that more intense than would be produced by any other, for unlimited power must exceed all other. But it is impossible to assign any period of time that would correspond to this. For let A represent the time in which the unlimited force heats the object or thrusts it to a certain distance, and A+B the time in which a given limited force would produce the Aristotle does not mention the factor of distance (or extent of any sort of change), but unless some finite distance is intended, it is nonsense to say that ‘ it takes longer to move the greater amount.’ I take him to have in view any finite extent, however great.—C.]
266 υταύτην μείζω ἀεὶ λαμβάνων πεπερασμένην ἥξω ποτὲ εἰς τὸ ἐν τῷ A χρόνῳ κεκινηκέναι: πρὸς πε- περασμένον yap ἀεὶ προστιθεὶς ὑπερβαλῶ παντὸς ὡρισμένου, καὶ ἀφαιρῶν ἐλλείψω ὡσαύτως. ἐν ἴσῳ ἄρα χρόνῳ κινήσει ἡ πεπερασμένη τῇ ἀπείρῳ" τοῦτο / δὲ ἀδύνατον. οὐδὲν dpa πεπερασμένον ἐνδέχεται ἄπειρον δύναμιν ἔχειν. Οὐ τοίνυν οὐδὲ ἐν ἀπείρῳ πεπερασμένην. καίτοι ἐνδέχεται ἐν ἐλάττονι μεγέθει πλείω δύναμιν εἶναι" ἀλλ᾽ ἔτι μᾶλλον ἐν μείζονι πλείω. ἔστω δὴ τὸ ἐφ᾽ οὗ ΑΒ ἄπειρον. τὸ δὴ BI’ ἔχει δύναμίν τινα, ἣ ἔν τινι χρόνῳ ἐκίνησε τὴν Δ---ἐν τῷ χρόνῳ ἐφ᾽ ᾧ EZ. ἂν δὴ τῆς BL διπλασίαν λαμβάνω, ἐν ἡμίσει κινήσει χρόνῳ τοῦ EZ (ἔστω γὰρ αὕτη ἡ 1 [πλείω: πλείων JH?. Simplicius 1341. 11 read πλείω, but paraphrases πλείων (ἀλλ᾽ ἐν τῷ μείζονι τοῦ ἐλάττονος κατὰ τὸ αὐτὸ εἶδος ἔτι πλείων ἔσται ἡ δύναμι5). πλείω (ἐνδέχεται εἶναι) can be defended as meaning ‘It is possible for the power to be greater (and therefore 1 am entitled to argue from the case in which it is greater).’—C.]
σι Θ σι Θ 4 [A is supposed to be some period of time, however short, and the limited force must, of course, take a longer time (A+B). I can now reduce the excess of A+B over A to nothing (or less than nothing) if I augment the limited force by adding any constant amount as often as is required. Each addition will subtract a corresponding fraction from the time B and so I can cut down A+B to A (or to less than A). But then a force that, however augmented, is still limited will do the work in the time allowed for the unhmited force, which is impossible. (This paragraph has been partly re-written).—C. | Ὁ [Literally, ‘ It is true that the greater power may reside in the lesser body (a seed contains enough to produce a large tree; so why should not the converse be true, and the greatest of all bodies—an infinite body—contain less than an infinite ower? Simplicius); but still more is it possible that the arger body should contain the greater power ’ (or ‘ that the same effect. Then if I increase this given force by equal increments successively I shall sooner or later arrive at the point at which the effect will have been successive additions I can make the power exceed any given limit, and by corresponding subtractions can make the time fall short of any). In this way the limited power will take the same time as the unlimited in effecting the movement. But this is impossible. Therefore no limited body can have unlimited power.
It follows also that the power of an unlimited body cannot be limited, although ὃ there may be cases in which the smaller body has the greater power, as well as the more obvious cases in which the greater power accompanies the greater size. For let AB B ς Α ΟΝ er ZO FE μι represent the unlimited body. Then the section BC will have a certain power, which would take a certain time to move Ὁ. Let EZ represent that time. Then, by the inverse ratio, twice BC will produce the same effect in half ἘΖ ὁ (GZ). So by continuing the larger the body, the greater the power it contains,’ if two bodies of the same kind are compared).—C. | ¢ [ἔστω γὰρ αὕτη ἡ ἀναλογία, ‘for let us assume that proportion,’ viz. 2:1, doubling the force and halving the time, for the sake of argument. Any other would do as well,—C. ] 266b ἀναλογία), ὥστ᾽ ἐν τῷ ZO κινήσει. οὐκοῦν οὕ- τω λαμβάνων ἀεὶ τὴν μὲν ΑΒ οὐδέποτε διέξειμι, τοῦ χρόνου δὲ τοῦ δοθέντος ἀεὶ ἐλάττω λήψομαι. 15 ἄπειρος ἄρα ἡ δύναμις ἔσται. πάσης γὰρ πε- περασμένης ὑπερβάλλει δυνάμεως" πάσης δὲ πε- περασμένης δυνάμεως ἀνάγκη πεπερασμένον εἶναι καὶ τὸν χρόνον" εἰ γὰρ ἔν τινι ἡ τοσηδί, ἡ μείζων ἐν ἐλάττονι μὲν ὡρισμένῳ δὲ κινήσει χρόνῳ, κατὰ τὴν ἀντιστροφὴν τῆς ἀναλογίας. ἄπειρος δὲ πᾶσα 29 δύναμις, ὥσπερ καὶ πλῆθος καὶ μέγεθος τὸ ὑπε- ρβάλλον παντὸς ὡρισμένου. ἔστι δὲ καὶ ὧδε δεῖξαι τοῦτο: ληψόμεθα γὰρ δή τινα δύναμιν τὴν αὐτὴν τῷ γένει τῇ ἐν τῷ ἀπείρῳ μεγέθει, ἐν πεπερασ- μένῳ μεγέθει οὖσαν, ἣ καταμετρήσει τὴν ἐν τῷ ἀπείρῳ πεπερασμένην δύναμιν.
α (Or, ‘but each time (I make such an addition) I shall obtain a smaller fraction of the time allowed (i.e. the whole time EZ); for as the additions to BC form the series 1, 2, 3, 4,,..n, so the time-fractions form the series 1, 4, 4, 1 oe 2, never reaching 0). Hence the force (in the unlimited body AB) must be unlimited. For it exceeds any limited force; and any limited force (BC or any multiple of BC in the series) must correspond to a limited time (EZ or the corresponding fraction of EZ in the series); for if a definite force takes a definite time, a greater force must, according to the inverse ratio, take a correspondingly smaller fraction of time, but still a definite fraction (which will never dwindle to 0). But (the time corresponding to AB must accordingly be less than any finite amount, and the corresponding force must exceed any definite amount; and) any force—just as any number or magnitude—that exceeds any definite amount is unlimited.’ The last sentence is ungrammatical, equivalent to Simplicius’s paraphrase (1342. 32) ἄπειρος δὲ πᾶσα δύναμις ὑπερβάλλουσα παντὸς ὡρισμένου ὥσπερ καὶ πλῆθος καὶ μέγεθος.
aim, * aim, * like additions I shall never come to the end of AB, “but I shall sometime come to the multiple of BC which will move D in less than any given period of time. The motive power of AB then has no limit, for it exceeds any limited power you may choose. Again, the time taken by a limited force to effect the movement must itself be limited, for if so much force can effect it in so much time, then a greater force will effect it in a less, but still definite, time, in the inverse ratio; but an unlimited force (as with an unlimited number or size) must exceed any limited force.2 An alternative proof is as follows. We shall take a certain definite force of the same kind as that supposed to be in the infinite body, and let this foree we take reside in a limited body and be an exact measure of the force supposed to reside in the unlimited body.° > And unless the force could increase above any assignable limit the time could not decrease below any assignable limit. Therefore the smallness of the time taken by a limited force is itself limited.
¢ (This argument is left incomplete. Since the force (F) supposed to be in the unlimited body AB is finite, we can take a force (Ε΄) which will be an exact measure (say one-third) of F, and let it reside in a finite body (CD). The two forces are to be ‘ of the same kind’ and will of course reside in bodies of the same kind (¢.g. the weights of two lumps of gold or of any substance with a fixed specific gravity); accordingly the forces will vary directly as the magnitudes of the bodies. Therefore, since ἘΠ is one-third of F, the magnitude of CD is one-third (or in any case some definite fraction) of the magnitude of AB. But that is impossible unless AB is of limited size. Therefore AB—the body containing a limited force—cannot be unlimited. Simplicius introduces a needless complication by not seeing that καταμετρεῖν means ‘to be an exact measure of,’ as at 233 Ὁ 8 and elsewhere.
σι Ὅτι μὲν οὖν οὐκ ἐνδέχεται ἄπειρον εἶναι δύναμιν ἐν πεπερασμένῳ μεγέθει, οὐδὲ πεπερασμένην ἐν ἀπείρῳ, ἐκ τούτων δῆλον.
Περὶ δὲ τῶν φερομένων καλῶς ἔχει διαπορῆσαί τινα ἀπορίαν πρῶτον. εἰ γὰρ πᾶν τὸ κινούμενον κινεῖται ὑπὸ τινός, ὅσα μὴ αὐτὰ ἑαυτὰ κινεῖ, πῶς κινεῦται ἔνια συνεχῶς μὴ ἁπτομένου τοῦ κινήσαντος, οἷον τὰ ῥιπτούμενα; εἰ δ᾽ ἅμα κινεῖ καὶ ἄλλο τι ὁ κινήσας, οἷον τὸν ἀέρα, ὃς κινούμενος κινεῖ, ὁμοίως ἀδύνατον τοῦ πρώτου μὴ ἁπτομένου μηδὲ κινοῦντος κινεῖσθαι, ἀλλ᾽ ἅμα πάντα καὶ κινεῖσθαι καὶ πεπαῦσθαι ὅταν τὸ πρῶτον κινοῦν παύσηται, καὶ εἰ ποιεῖ, ὥσπερ ἡ λίθος, οἷον κινεῖν ὃ ἐκίνησεν. ἀνάγκη δὴ τοῦτο μὲν λέγειν, ὅτι τὸ πρῶτον κινῆσαν ποιεῖ [οἷόν τε κινεῖν] ἢ τὸν ἀέρα τοιοῦτον" ἢ τὸ ὕδωρ ἤ τι ἄλλο ὃ πέφυκε κινεῖν καὶ κινεῖσθαι" ἀλλ᾽ 1 {Hither τοιοῦτον must be cut out cS by the Oxf. Trans.), though it is in all mss. and in Simplicius 1345. 28, or οἷόν τε κινεῖν (οἷον καὶ κινεῖν Ἐὶ: οἷόν τι καὶ κινεῖν ΕἾ removed as a gloss on τοιοῦτον: ‘the first agent makes the air (an agent) of the kind just described’ (by οἷον κινεῖν in the previous sentence). The intrusion of οἷόν re κινεῖν is easily explained; but why should τοιοῦτον be inserted?—C.]
* Because if you break the contact of the original magnet with the first bar of iron all the others instantly lose their power; whereas in the case of missiles each successive secondary agent becomes active as the previous one ceases to be so. So the power is not exhausted all at once when the first link in the chain ceases to exercise it, but is transmitted with gradually waning intensity to each successive link. [Cf. Plato, Jon 533 p, where Socrates tells Ion the rhapsode that when he recites there is a divine power of inspiration moving his hearers through him, * like the power in the stone which Euripides calls the Magnesian stone We have now proved that an unlimited force cannot reside in a limited magnitude, and also that the force residing in an unlimited magnitude cannot itself be limited.
But before discussing rotating bodies it will be well to examine a certain question concerning bodies in locomotion. If everything that is in motion is being moved by something, how comes it that certain things, missiles for example, that are not self-moving nevertheless continue their motion without a break when no longer in contact with the agent that gave them motion? Even if that agent at the same time that he puts the missile in motion also sets something else (say air) in motion, which something when itself in motion has power to move other things, still when the prime agent has ceased to be in contact with this secondary agent and has therefore ceased to be moving it, it must be just as impossible for it as for the missile to be in motion: missile and secondary agent must all be in motion simultaneously, and must have ceased to be in motion the instant the prime mover ceases to move them; and this holds good even if the prime agent is like the magnet, which has power to confer upon the iron bar it moves the power of moving another iron bar. We are forced, therefore, to suppose that the prime mover conveys to the air (or water, or other such intermediary as is naturally capable both of moving and conveying motion) a power of conveying motion, but that this though it is generally known as the stone of Heracles. ‘This not only attracts rings that are made of iron, but puts into them the power of producing the same effect as the stone and attracting other rings in their turn. Sometimes there is quite a long chain of rings hanging from one another; but all the power they have depends on the stone.’—C.]
VOL. II QE 417 27a ody ἅμα παύεται κινοῦν Kal κινούμενον, ἀλλὰ κινούμενον μὲν ἅμα, ὅταν ὁ κινῶν παύσηται κινῶν, κινοῦν δὲ ἔτι ἐστίν" διὸ κινεῖ τι ἄλλο ἐχόμενον. καὶ ἐπὶ τούτου 6 αὐτὸς λόγος" παύεται δὲ ὅταν ἀεὶ ἐλάττων ἡ δύναμις τοῦ κινεῖν ἐγγίγνηται τῷ 10 ἐχομένῳ, τέλος δὲ παύεται ὅταν μηκέτι ποιήσῃ τὸ πρότερον κινοῦν ἀλλὰ κινούμενον μόνον. ταῦτα δ᾽ ἀνάγκη ἅμα παύεσθαι--τὸ μὲν κινοῦν τὸ δὲ κινούμενον---καὶ τὴν ὅλην κίνησιν. αὕτη μὲν οὖν ἐν τοῖς ἐνδεχομένοις ὁτὲ μὲν κινεῖσθαι ὁτὲ δ᾽ ἠρεμεῖν ἐγγίγνεται ἡ κίνησις: καὶ οὐ συνεχής, ἀλλὰ φαίνεται: ἢ yap ἐφεξῆς ὄντων ἢ ἁπτομένων 13 ἐστίν, οὐ γὰρ ἕν τὸ κινοῦν ἀλλ᾽ ἐχόμενα ἀλλήλων" \ διὸ Kal ἐν ἀέρι καὶ ἐν ὕδατι γίγνεται ἡ τοιαύτη κίνησις, ἣν λέγουσί τινες ἀντιπερίστασιν εἶναι. ἀδύνατον δὲ ἄλλως τὰ ἀπορηθέντα λύειν, εἰ μὴ τὸν εἰρημένον τρόπον. ἡ δ᾽ ἀντιπερίστασις ἅμα πάντα κινεῖσθαι ποιεῖ καὶ κινεῖν, ὥστε καὶ παύεα [ Literally, ‘ And so it (the intermediary) moves something else consecutive with it. And of this again the same thing is true (that it ceases to be moved itself but moves the next thing); παύεται δέ (Sc. κινοῦν), but this imparting of motion by the intermediary does come to an end in any case in which the moving power gets continually less as it is imparted to each successive member of the series.’—C.]
‘ Elasticity’ is the nearest equivalent. Cf. 215 a 15 [Vol. I. p. 350 note a, where Simplicius’s definition of antiperistasis is quoted. The Oxford Trans. renders it by mutual replacement’ and refers to Plato, Timaeus 59 a, "9 B, c,E,80c. This last sentence and the following may be more literally rendered: ‘ That is why movement of the kind described occurs in air and water (their continuous structure being suited to transmit motion in this way). Some describe power is not exhausted when the intermediary ceases to be moved itself. Thus the intermediary will cease to be moved itself as soon as the prime mover ceases to move it, but will still be able to move something else. *Thus this something else will be put in motion after the prime mover’s action has ceased, and. will itself continue the series. The end of it all will approach as the motive power conveyed to each successive secondary agent wanes, till at last there comes one which can only move its neighbour without being able to convey motive force to it. At this point the last active intermediary will cease to convey motion, the passive intermediary that has no active power will cease to be in motion, and the missile will come to a stand, at the same instant. Now this movement occurs in things that are sometimes in motion and sometimes stationary, and it is not continuous, though it appears to be. For there is a succession of contiguous agents, since there is no one motor concerned but a series, one following upon another. And so there comes about both in air and water the kind of motion that some have called ant:-peristasis.° But whereas the only possible solution of the problem it suggests is that which has just been explained, the theory of those who call it antsperistasis would involve the simultaneity of the action of every motor and the passion of every mobile in the series, and the simultaneity of their cessation.
it as ‘‘ mutual replacement,” but (though mutual replacement may in fact occur) the difficulty under discussion cannot be solved otherwise than in the way described above. Moreover, the process of mutual replacement involves that all the members of the series receive motion and impart it simultaneously and consequently cease to do so simultaneously; whereas, etc.’ (see next note).—C.]
267220 σθαι: νῦν δὲ φαίνεταί τι ἕν κινούμενον συνεχῶς" ὑπὸ τίνος οὖν; οὐ γὰρ ὑπὸ τοῦ αὐτοῦ. Επεὶ δ᾽ ἐν τοῖς οὖσιν ἀνάγκη κίνησιν εἶναι συνεχῆ, αὕτη δὲ pia ἐστίν, ἀνάγκη δὲ THY μίαν μεγέθους τέ τινος εἶναι (οὐ γὰρ κινεῦται τὸ ἀμέγεθες) καὶ ἑνὸς καὶ ὑφ᾽ ἑνός (οὐ yap ἔσται συνεχής, ἀλλ 25 ἐχομένη ἑτέρα ἑτέρας καὶ διῃρημένη), τὸ δὲ κινοῦν εἰ ἕν, ἢ κινού -νον κινεῖ ἢ ἀκίνητον OV" εἰ μὲν δὴ κινούμενον, συνακολουθεῖν δεήσει καὶ μεταβάλλειν 267b αὐτό, ἅμα δὲ κινεῖσθαι ὑπό τινος" ὥστε στήσεται καὶ ἥξει εἰς τὸ κινεῖσθαι ὑπὸ ἀκινήτου. τοῦτο γὰρ οὐκ ἀνάγκη συμμεταβάλλειν, ἀλλ᾽ ἀεί τε δυνήσεται κινεῖν (ἄπονον γὰρ καὶ τὸ οὕτω κινεῖν) καὶ ὁμαλὴς αὕτη ἡ κίνησις ἢ μόνη ἢ μάλιστα' οὐ γὰρ ἔχει μετα- ὃ βολὴν τὸ κινοῦν οὐδεμίαν. δεῖ δὲ οὐδὲ τὸ κινού- μενον πρὸς ἐκεῖνο ἔχειν μεταβολήν, ἵνα ὁμοία ἦ ἡ κίνησις. ἀνάγκη δ᾽ ἢ ἐν μέσῳ ἢ ἐν κύκλῳ εἶναι" "ν ὔ Ἂ αὗται γὰρ at ἀρχαί. ἀλλὰ τάχιστα κινεῖται τὰ α (Literally, ‘Whereas the appearance that is in fact resented (and has to be explained) is that of a single thing the missile) kept in motion continuously (after the originator of the movement, the thrower, has ceased to cause motion). What then keeps it in motion? Not the same agent (but one or more intermediaries which do not simultaneously cease to move and to be moved).’—C.]
δ Τ take this qualification to refer to the heavenly spheres, or the bodies they bear upon them, which being subject to the influence of other immaterial beings (which the primum mobile is not) change their relations to the prime motion and are therefore uniform with reference to their own axes but not with reference to the prime axis.
α Whereas the fact is that the supposed continuity of the movement of the single mobile which sets us inquiring after the motor is only apparent; for in fact it is not impelled by one and the same motor throughout its course.
Now we have seen that there must be a continuous movement somewhere in the sum of things, and that it must be uniform, and that such uniform motion must be that of some dimensional magnitude (for that which is not dimensional cannot move), and that such magnitude must be unitary and must be kept in motion by a unitary motor (for otherwise the motion would not be continuous, but would be resolved into a series of successive motions), and that this single motor must itself be either in motion or unmoving. Now if it is in motion (and is therefore a physical magnitude) it will have to follow up that which it is moving, and therefore be itself locally changing, and moreover must be referred back tc some motor that causes its motion. This leaves us where we were, and the perpetual recession can only be arrested by supposing a motor that is not in motion. Such a motor need not undergo any change to preserve a constant relation with the mobile, but can exercise its kinetic power without ever being exhausted (for suchlike conveying of motion is not toilsome); and such motion or change as it directly causes must be uniform either uniquely or in the primary and supreme sense, for the motor is subject to no change. And for the motion to be uniform, the disposition of the mobile to the motor must also be without change.° Now the action of this unmoving cause must be felt either at the centre or the periphery, for these are the determining principles; and since the swiftest 261} ἐγγύτατα τοῦ κινοῦντος, τοιαύτη δ᾽ ἡ τοῦ κύκλου κίνησις" ἐκεῖ ἄρα τὸ κινοῦν.
10 ἔχει δ᾽ ἀπορίαν εἰ ἐνδέχεταί τι κινούμενον κινεῖν συνεχῶς, ἀλλὰ μὴ--ὥἦσπερ τὸ ὠθοῦν πάλιν καὶ πάλιν---τῷ ἐφεξῆς εἶναι συνεχῶς. ἢ yap αὐτὸ δεῖ ὠθεῖν ἢ ἕλκειν (ἢ ἄμφω), ἢ ἕτερόν τι ἐκδεχόμενον ἄλλο παρ᾽ ἄλλου, ὥσπερ πάλαι ἐλέχθη ἐπὶ τῶν an \ ῥιπτουμένων. εἰ δὲ διαιρετὸς ὧν 6 ἀὴρ ἢ τὸ ὕδωρ 15 κινεῖ, ἀλλ᾽ ὡς ζἄλλος)" ἀεὶ κινούμενος: ἀμφοτέρως 1 [κύκλου HK Simplic. 1354. 8: ὅλου cett.—C.]
2 [ἀλλ᾽ ws «ἄλλος»:- ἄλλος F: ἄλλον ἘΠῚ; ἀλλ᾽ ὡς cett. The uncertainty of the readings in this sentence leaves it doubtful how it is related to its neighbours. Simplicius 1356. 12 apparently read ὥσπερ πάλαι ἐλέχθη ἐπὶ τῶν ῥιπτουμένων, εἰ διαιρετὸς (or διαιρετὸς γὰρ: E has γὰρ) ὧν ὁ ἀὴρ καὶ (sic) τὸ ὕδωρ κινεῖ, ἀλλ᾽ ὡς ἄλλος ἀεὶ κινούμενος. ἀμφοτέρως δ᾽ κτλ., ‘as we said in the case of missiles, since the air or the water causes the motion as being divisible into parts. But (it causes the motion only) inasmuch as one part of it after another is set in motion (and moves the next)’; for his paraphrase εἴπερ διαιρετὸς ὧν ὁ ἀὴρ καὶ τὸ ὕδωρ, τούτεστιν εὐδιαίρετα καὶ εὐκίνητα, κινεῖ" πῶς δὲ κινεῖ ὁ ἀήρ; ἄλλος ἀεὶ καὶ ἄλλος κινούμενος καὶ οὕτως κινῶν seems explicable only if he read (as the beginning of a new sentence) ἀλλ᾽ ὡς ἄλλος (or, less probably, ἀλλὰ πῶς; ὡς GAdos). It is another question whether his reading is right. The reading attributed to him by the Oxf. Trans. ἐπὶ τῶν ῥιπτουμένων, εἰ διαιρετὸς ὧν ὁ ἀὴρ ἢ (sic) τὸ ὕδωρ κινεῖ ἄλλος ἀεὶ κινούμενος, may be preferred. In printing εἰ δὲ διαιρετὸς κτλ. as a separate sentence I am providing a text which suits Dr. Wicksteed’s view of the course of the argument.—C.]
* (Literally, ‘ circle,” 1.6. circumference (ταχεῖα δὲ ἡ τοῦ κύκλου κίνησις, τουτέστι τῆς περιφερείας, Simplic. 1354. 7). In a revolving sphere the motion of a point on any circle inscribed on its surface in a plane at right angles to its axis is faster than that of any point in the same plane that is nearer to the axis. And if the universe is conceived as a movements must be those of the parts closest to the moving force, and the movement of the outermost sphere @ is such, it is there that the motive influence is felt.
The question arises, however, whether it may not be possible for a motor which itself is in motion to cause a continuous movement in something else, not with the specious continuity of a succession of thrusts, but genuinely. Well, in such a case either (i.) the prime motor itself must all the time directly thrust or draw ὃ the mobile (or both thrust and draw it),° or (ii.) there must be some continuous succession of intermediaries other than the prime motor, as we just now supposed to be the fact in the case of missiles, and if these intermediaries are constituted by an easily divisible substance, such as air or water, what is causing the movement at any time will be the particular division of that substance which at the time being is in motion. In both cases (i.) and (ii.), therefore, the movement is not one and unbroken, nest of material spheres, each of a certain thickness, the motion will be quickest in the outermost sphere. Simplicius records a discussion as to what ‘ circle’ is here meant and where the Prime Mover can be. He ends with the suggestion μήποτε δὲ ἐν τῷ κύκλῳ λέγων ἐν τῷ ὅλῳ οὐρανῷ λέγει (1355. 38). This discussion may account for the variant ὅλου here. Cf. De gen. et corr. 336 Ὁ 8 ἡ τοῦ ὅλου (se. οὐρανοῦ) φορά, meaning the motion of the First Heaven, as carrying with it re whole system of concentric spheres (Joachim, ad loc.), > (Cf. 243 a 15 ff. where it was shown that all forms of locomotion of things that are moved by something else can be reduced to pushing or pulling. A twirling motion is a combination of pulling and pushing: the man turning a millstone is both thrusting away part of the stone and drawing towards himself another part.—C.]
5 And this alternative (i.) has been shown to be impossible.
δ᾽ οὐχ οἷόν τε μίαν εἶναι, ἀλλ᾽ ἐχομένην. μόνη ἄρα συνεχὴς ἣν κινεῖ TO ἀκίνητον" ἀεὶ yap ὁμοίως ἔχον καὶ πρὸς TO κινούμενον ὁμοίως ἕξει Kal συνεχῶς. Διωρισμένων δὲ τούτων, φανερὸν ὅτι ἀδύνατον TO πρῶτον κινοῦν καὶ ἀκίνητον ἔχειν τι μέγεθος. εἰ γὰρ μέγεθος ἔχει, ἀνάγκη ἦτοι πεπερασμένον \ ον αὐτὸ εἶναι ἢ ἄπειρον. ἄπειρον μὲν οὖν ὅτι οὐκ ἐνδέχεται μέγεθος εἶναι, δέδεικται πρότερον" ἐν τοῖς Φυσικοῖς: ὅτι δὲ τὸ πεπερασμένον ἀδύνατον ἔχειν δύναμιν ἄπειρον, Kal ὅτι ἀδύνατόν ὑπὸ πε- περασμένου κινεῖσθαΐ τι ἄπειρον χρόνον, δέδεικται a5 viv. τὸ δέ ye πρῶτον κινοῦν ἀΐδιον κινεῖ κίνησιν καὶ ἄπειρον χρόνον. φανερὸν τοίνυν ὅτι ἀδιαίρετόν ἐστι καὶ ἀμερὲς καὶ οὐδὲν ἔχον μέγεθος.
but successional. The only continuous movement, therefore, is that which is caused by the motionless motor, which ever maintains its own uniformity of disposition and will therefore maintain a uniform and continuous relation to the mobile.
All these points being established, it is clear that the prime and motionless motor cannot have magnitude. For if it had magnitude it must either be limited or unlimited. Now we have shown already, in our discourse on Physics, that there cannot be an unlimited magnitude; and now we have further proved that a limited body cannot exert unlimited force and that nothing can be kept in motion for an unlimited time by a limited agent. But the prime motor causes an everlasting motion and maintains it through time without limit. It is manifest, therefore, that this prime motor is not divisible, has no parts, and is not dimensional.
Note —The references to Volume 1. are wn roman, those to Volume II. in italre.
ABOVE and BELOW, Relative, ABSTRACT: see Concrete ABSTRACTION, i. 119, 1213 see ACCIDENT, i. 141-163 ACCIDENTAL: see Incidental ACHILLES, ii. 181, 183 See also Bisection ACTUALITY, ACTUALIZATION = Realization, i. 89, 198-197, ADDITION of terms, ‘Limited and Illimitable, i. 247-251 AFTER: see Before AGENT: see Mover AIR— Relation to Water, 1. 49, 327, Substantiality of, 1. 331, 361 AMBIGUOUS: see Verbal Ambiguity ANAX AGORAS— on the Unlimited, i. 221, 228, on the Void, 1. 331 ANAXIMANDER on Unity and Multipheity, i. 41 ANTIPERISTASIS, ti. 419 ANTIPHON— on Squaring the circle, i. 19 on Substantive existence, i. 111 ANTITHESIS— Nature of Primary Antithesis or Antitheses, i. 41, 51-67 Antithetical Principles need something to work on, 1. 61, Antithetical Terms, 11, 221 See also Extremes APART, Definition of, ti. 35 ARRIVAL(‘ has arnived at’ ), Legitimate use of term, ii. 373- 379 ARROW, The Flying, ti. 181-185 ART: Analogy with aera i. 125, 173 of Making, i 123, 1 of Using, i. 128,1 ΤῊΣ ARTIFICIAL PRODUCTS: see Natural Products ASHES, Water poured on to, i. 333, ASTRONOMY, Relation to mathematics and physics, i. 119, 121 ATOMS— ΤΟΣ barat and Resolution of of Matter, and Atomic Magnialso Indivisible ἘΠΕ ee na REPULSION, of ee Part, of the Whole, i. 295; Potential and actual, i. 367-371; AYTOMATON, Meaning and scope