That local movement in general takes precedence of other forms of change is testified by all who have treated of motion: they all assign as the principles of change just the very things that exemplify local motion. For ‘resolution’ and ‘combination’ are local movements; and ‘attraction’ and ‘repulsion’? likewise, inasmuch as the one severs and the other combines. Anaxagoras ὁ too says that Intelligence, the first mover, severed things out. And it is the same with those ὁ who allege no suchlike cause, but declare that things move because of the void; for they too say that the movement or change of natural substance ὁ is the local one, for the motion which the void makes possible is local, just as if it came about in a place; whereas changes other than local are never regarded by these thinkers as affecting the primary substances but always as derivative; for growth and qualitive change they consider as caused by the combination and resolution of the atoms. It motion; cf. 230 b 24. Hence, as the Oxf. Trans. notes, the middle ἀφίστηται, ‘ removes itself.’—C.
> (The Love and Strife of Empedocles.—C. ] ¢ (Frag. 13, καὶ ὅσον ἐκίνησεν ὁ Νοῦς, πᾶν τοῦτο διεκρίθη, and Frag. 12.—C.]
4 (Leucippus and Democritus.—C.]
6 [τὴν φύσιν, τουτέστι τὰ φυσικὰ Kal πρῶτα καὶ ἄτομα σώματα, ARISTOTLE 66" 80 φασίν. τὸν αὐτὸν δὲ τρόπον καὶ ὅσοι διὰ πυκνότητα ἢ μανότητα κατασκευάζουσι γένεσιν καὶ φθοράν" συγκρίσει γὰρ καὶ διακρίσει ταῦτα διακοσμοῦσιν. ἔτι δὲ παρὰ τούτους οἱ τὴν ψυχὴν αἰτίαν ποιοῦντες κινήσεως" τὸ γὰρ αὐτὸ ἑαυτὸ κινοῦν ἀρχὴν εἶναί φασι τῶν κινουμένων, κινεῖ δὲ τὸ ζῷον καὶ πᾶν 2668 τὸ ἔμψυχον τὴν κατὰ τόπον ἕαυτὸ κίνησιν. καὶ κυρίως δὲ κινεῖσθαί φαμεν μόνον τὸ κινούμενον κατὰ τόπον: ἂν δ᾽ ἠρεμῇ μὲν ἐν τῷ αὐτῷ, ad- ξάνηται δὲ ἢ φθίνῃ ἢ ἀλλοιούμενον τυγχάνῃ, πῇ κινεῖσθαι, ἁπλῶς δὲ κινεῖσθαι οὔ φαμεν.
Ὅτι μὲν οὖν ἀεί τε κίνησις ἦν καὶ ἔσται τὸν ἅ- παντα χρόνον, καὶ τίς ἀρχὴ τῆς ἀιδίου κινήσεως, ἔτι δὲ τίς πρώτη κίνησις, καὶ τίνα κίνησιν ἀΐδιον ἐνδέχεται μόνην εἶναι, καὶ τὸ κινοῦν πρῶτον ὅτι ἀκίνητον, εἴρηται.
σι α [Anaximenes, with whom Aristotle would group Thales and Heracleitus. Cf. 187 a 12 ff.—C.| ὃ [Plato (Phaedrus 245 c) and his school.—C.]
CHAPTER X ARGUMENT [ The Prime Mover is without parts or magnitude. To prove this, some premises must first be established (266 a 10-12): (1) Nothing finite can cause a motion that will occupy an unlimited time. This can be shown by considering the work as done piecemeal by a fraction of the finite mover (a 12-24).
(2) A finite magnitude cannot contain an infinite force; for it can be shown that otherwise a finite and an infinite force would take the same time to effect the same movement PHYSICS, VIII. τα. χα.
is the same too with those * who get genesis and dissolution out of density and rarity, for it is by draw- ing together and separating apart that they get these dispositions. And yet again those ὃ who think the soul is the cause of motion take their place in the same rank, for they declare that the self-moving is the principle and initiator of the movements of all things that move, and the movement which an animal or other living creature produces in itself is local movement. And in fact it is only what is moving in the sense of changing its place that we primarily and properly say is ‘ moving’; if it abides in the same place but grows or contracts or changes its qualities we say that it is moving ‘in a way,’ but not just that ‘it is moving.’
We have now said what needed saying in demon- stration of the fact that movement always was and always will be throughout time, and to show what is the principle of this everlasting motion, and what is the nature of the primary movement, and what is the only movement that can possibly be eternal, and that the prime mover is itself motionless.
CHAPTER X ARGUMENT (continued) (3) A finite force cannot reside in an infinite magnitude. Proofs of this (Ὁ 6-24).
Summary of these results (b 25-27).
Before proceeding to the conclusion, a problem of locomotion must be solved: How can a missile continue in motion after it has left the thrower’s hand? The original agent imparts to an intermediary (air or water) a motive force which is gradually exhausted. The theory that the effect is produced ARISTOTLE ARGUMENT (contenued) by ‘ mutual replacement ’ in the intermediary will not account Sor the observed fact (Ὁ 27-267 a 20).
To resume the main argument: The single continuous motion which we have seen must exist in the world can be caused only by a mover which rs not moved or changed in any way. This mover must be felt at the circumference, rather 266a10 Ore δὲ τοῦτ᾽ ἀμερὲς ἀναγκαῖον εἶναι καὶ μηδὲν ἔχειν μέγεθος, viv λέγωμεν, πρῶτον περὶ τῶν προτέρων αὐτοῦ διορίσαντες. Τούτων δ᾽ ἕν μὲν ἔστιν ὅτι οὐχ οἷόν τε οὐδὲν 4 {I have substituted for Dr. Wicksteed’s rendering of this paragraph an interpretation published in the Classacal Quarterly, xxvi. (1932) p. 52.—C.]
Dr. Wicksteed (supported, as he thought, by Aquinas) explained the use of the phrase ἐν πλείονι yap τὸ μεῖζον here by supposing that Aristotle is thinking of the time it takes for a mobile to pass a certain point, or in other words, to frank its boundary, not of the time it takes to advance a - certain distance for, if the [2 whole and all its parts move with a uniform motion, it Pe te te da! takes no longer for the whole to advance a certain distance than for any part of it to do so, but it does take longer for the greater bulk of the whole to frank its boundary than for the lesser bulk of the part to do so.
Now in any time however short there can be movement, and whenever there is any movement some portion of the mobile will frank its boundary: in a longer time a greater portion, and in a shorter time a lesser portion. Thus the time during which a limited force causes uniform motion in a limited mobile is proportionate to (and can be measured by) the magnitude of that portion of the mobile that it causes to frank its boundary.
If the mobile, instead of being rectangular as in the first diagram, is circular or spherical, and the movement instead PHYSICS, VIII. x.
ARGUMENT (continued) than at the centre, of the spherical universe; for there the motion is quickest (a 20—b 9).
If the mover were rtself in motion, the motion it caused could not be continuous (Ὁ 9-17).
The Prime Mover cannot, then, be either a finite or an infinite magnitude. Therefore it has no parts or magnitude LeT us now go on to show that the first mover must necessarily be unsusceptible of partition, and so not dimensional. This will involve the antecedent establishment of certain theorems, the first of which is as follows.
“Tt is impossible for a limited motor to cause a 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 uni- verse, 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 move- ment (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, ARISTOTLE ARISTOTLE 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 correspond- ing 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 illimit- able 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 remain- ing 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 separ- ately. 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) 20 25 80 ARISTOTLE 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 yAvKai- vovoa 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 ex- haust 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).
PHYSICS, VIII. x.
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 sweeten- ing or hurling or, to put it universally, effecting any kind of change. If then a limited subject had un- limited 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.]
ARISTOTLE 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 1 Θ σι 1 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 PHYSICS, VIII. x.
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 pro- portion,’ viz. 2:1, doubling the force and halving the time, for the sake of argument. Any other would do as well,—C. ] ARISTOTLE 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, * PHYSICS, VIII. x.
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 assign- able 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 need- less complication by not seeing that καταμετρεῖν means ‘to be an exact measure of,’ as at 233 Ὁ 8 and elsewhere.
80 σι ARISTOTLE 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 trans- mitted 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 PHYSICS, VIII. x.
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, there- fore, 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 ARISTOTLE 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 7 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 anti- peristasis 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 PHYSICS, VIII. x.
PHYSICS, VIII. x.
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 some- thing 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 con- tinuous, 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 antsperi- stasis 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. More- over, 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 simultane- ously; whereas, etc.’ (see next note).—C.]
ARISTOTLE 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.
PHYSICS, VIII. x.
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 re- solved 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 ex- hausted (for suchlike conveying of motion is not toil- some); 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 ARISTOTLE 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.]