These and such as these are the arguments specially applicable to the demonstration that no motion of translation and therefore no motion of combined translation and rotation can be everlasting and continuous.° But considerations affecting all forms of change may be seen from the following arguments to lead to the same result.
Anything that moves continuously is making for its goal before it reaches it, provided that nothing diverts it from its course: thus, if B is what it comes to, it was making for B, and that not only when it came near to B but from the instant when it first started; since you cannot assign any other instant at which to say ‘now but not before.’ And this holds for the other kinds of change as well. @If, then, the mobile moves from A to C and when it gets there returns to A with a continuous movement, it will be moving from A to A continuously and therefore it will be making for A as soon as it begins to make for C; and since movemoving towards A with its (reverse) motion from C (since it is making for A from the first moment of its motion). Hence it willbe making two contrary movements simultaneously.’— 264a TAS EVAVTLAS, EVAVTLAL YAP AL KAT EVUELAVY. “Apa δὲ καὶ ἐκ τούτου μεταβάλλει ἐν ᾧ οὐκ ἔστιν. εἰ οὖν 99 τοῦτ᾽ ἀδύνατον, ἀνάγκη ἵστασθαι ἐπὶ τοῦ Τ᾿. οὐκ dpa μία ἡ κίνησις" ἡ yap διαλαμβανομένη στάσει οὐ μία.
"Ere δὲ καὶ ἐκ τῶνδε φανερὸν καθόλου μᾶλλον περὶ πάσης κινήσεως. εἰ γὰρ ἅπαν τὸ κινούμενον τῶν εἰρημένων τινὰ κινεῖται κινήσεων καὶ ἠρεμεῖ τῶν ἀντικειμένων ἠρεμιῶν (οὐ γὰρ ἦν ἄλλη παρὰ ravras), τὸ δὲ μὴ ἀεὶ κινούμενον τήνδε τὴν κίνησιν --ολέγω δ᾽ ὅσαι ἕτεραι τῷ εἴδει, καὶ μὴ εἴ τι μόριόν ἐστι τῆς ὅλης---ἀνάγκη πρότερον ἠρεμεῖν τὴν ἀντικειμένην ἠρεμίαν (ἡ γὰρ ἠρεμία στέρησις τῆς κινήσεώς ἐστιν)" εἰ οὖν ἐναντίαι μὲν κινήσεις αἱ Kar εὐθεῖαν, dua δὲ μὴ ἐνδέχεται κινεῖσθαι τὰς 1 [Simplicius 1302. 37-39 here paraphrases an objection which does not appear in our mss., and describes the ob-~ jection in this sentence as the third which Aristotle brings forward (εἶτα καὶ τρίτον ἄλλο ἄτοπον érdye). The paraphrase ἐπὶ τὸ γενέσθαι ἐν ᾧ ἐστι κινηθήσεται- τοῦτο δὲ ἄτοπον. οὐδὲν γὰρ κινεῖται διὰ τὸ γενέσθαι ἐν ᾧ ἐστι. τὸ γὰρ κινούμενον ποθέν ποι κινεῖται Suggests that he read ἅμα δὲ καὶ (εἰς τοῦτο μετα-βάλλει (ἢ κινεῖται) ἐν ᾧ ἐστι xal> ἐκ τούτου, κτλ. The moving object is, ex hypothesi, all the time moving towards A; but* it Is already at A when it starts, and it is absurd that a thing should change its place in order to reach a place it already occupies. But Themistius 230. 19 ff. and Philoponus 846. 20 appear to have had our text.—C.]
« (This sentence is ambiguous. Possible meanings are; () * Its change starts from a position which it does not occupy.’
uppose a man at A throws a stone up to a height C, from which it falls back to A. The stone really begins to fall from C; but if we are to say that the whole motion from A to C and back to A is one continuous motion, we must say that the falling starts from A—a position which the stone does not in fact occupy when the falling-motion begins. (2) ‘ I¢ shifts from a condition in which it is not.’ On reaching the ments to and fro on ‘a straight line are -opposite movements, it will be moving in opposite directions at one and the same time. And moreover it would start its reverse movement from C back to A before it had got to C where it is reversed. All this being impossible, then, it follows that the movement must stop at C. And so the movement is not a single one, for a movement that is severed by cessation is not one but two.
A further general consideration will establish the point for every kind of ‘movement,’ whether local or not. <A thing susceptible of change, whether of quality, quantity, or position (and we have seen that there are no other ways of changing), is also susceptible of the corresponding stationary and unchanging state. %Also, if a change of any kind alters from time to time—TI mean alters in direction, not merely as to the point it has reached—this adopting of a new direction involves the subject resting from change in the previous direction; for rest from change in any direction means ‘ privation of it.’ ὁ Granted, then, that changes to and fro on the same line are contrary and so cannot go on at the same point C the stone shifts from moving away from A to moving towards A. But if the motion is one and continuous, it was always moving towards A and so was never in the condition of moving away from A. This interpretation would account for μεταβάλλει being used instead of déperar.—C.]
Ὁ [The assumption stated in this sentence can also be interpreted: ‘Ifa thing that is undergoing, otherwise than eternally, some particular change—“ particular’? meaning not some particular part of the whole change, but a change belonging to one of the indivisible species of change—must have been previously in the state of rest opposite to that particular motion.’—C. ] 5 4,6. the absence of change in that direction in a subject naturally capable of such change.
264a 30 ἐναντίας, τὸ ἀπὸ τοῦ A πρὸς τὸ Τ' φερόμενον οὐκ ἂν φέροιτο ἅμα καὶ ἀπὸ τοῦ Τ' πρὸς τὸ A> ἐπεὶ δὲ οὐχ ἅμα φέρεται, κινήσεται δὲ ταύτην τὴν κίνησιν, ἀνάγκη πρότερον ἠρεμῆσαι τὴν πρὸς τῷ T+ αὕτη yap ἦν ἡ ἀντικειμένη ἠρεμία τῇ ἀπὸ τοῦ I’ κινήσει. 264b δῆλον τοίνυν ἐκ τῶν εἰρημένων ὅτι οὐκ ἔστι συνεχὴς ἡ κίνησις. "Ere δὲ καὶ ὅδε 6 λόγος μᾶλλον οἰκεῖος τῶν εἰρημένων. ἅμα γὰρ ἔφθαρται τὸ οὐ λευκὸν καὶ γέγονε λευκόν. εἰ οὖν συνεχὴς ἡ ἀλλοίωσις εἰς λευκὸν καὶ ἐκ λευκοῦ Kal μὴ μένει τινὰ χρόνον, 5 ἅμα ἔφθαρται τὸ od λευκὸν καὶ γέγονε λευκὸν Kal γέγονεν οὐ λευκόν" τριῶν γὰρ ἔσται ὃ αὐτὸς χρόνος. τι οὐκ εἰ συνεχὴς ὁ χρόνος, καὶ ἡ κίνησις, ἃ ἐφεξῆς. πῶς δ᾽ ἂν εἴη τὸ ἔσχατον τὸ αὐτὸ τῶν ἐναντίων, οἷον λευκότητος καὶ μελανίας; Η δ᾽ ἐπὶ τῆς περιφεροῦς ἔσται μία Kal συνεχής" 10 οὐθὲν γὰρ ἀδύνατον συμβαίνει. τὸ yap ἐκ τοῦ A κινούμενον ἅμα κινήσεται εἰς TO A κατὰ τὴν αὐτὴν πρόθεσιν---εἰς ὃ yap ἥξει, Kal κινεῖται εἰς τοῦτο--- ἀλλ᾽ οὐχ ἅμα κινήσεται τὰς ἐναντίας οὐδὲ τὰς ἀντικειμένας" οὐ γὰρ ἅπασα ἡ εἰς τοῦτο τῇ ἐκ τούτου ἐναντία οὐδ᾽ ἀντικειμένη, ἀλλ᾽ ἐναντία μὲν PHYSICS, VIIL. vuit.
time, the movement from A to C cannot be going on simultaneously with the movement from C to A; and since this latter motion, not being simultaneous, has still to occur, the motion towards C must first have stopped at C, this being, as we saw,* the ‘rest’ which is opposite to motion from C. All this makes it plain that the movement which reverses its direction is not continuous.
Or (to generalize by taking an example of a change other than that of locality) suppose that a thing has ceased to be not-white and has become white at one and the same instant. If, then, the alteration to white and the reverse alteration from white are one continuous process and the white does not remain in existence for any time at all, that means that the havingceased to be not-white and the having-become white have occurred at the same moment as the havingbecome not-white: the time of all these three events will be the same.
And note that the continuity of the time does not involve the continuity of the modification, but only that one modification succeeds the other (and counter) modification. And how can contraries like black and white have as their extreme the same point?
Rotatory motion, on the other hand, we may suppose to be uniform and continuous without any impossible consequences. For a mobile revolving in a circle from point A round to point A again is maintaining one identical tenor in its movement, and so is moving all the time to the same point it is moving from until it actually reaches it; but it will not be undergoing simultaneously two motions that are either contrary or opposite. The motion to a point is not always either contrary or opposite to the 264 15 ἡ ἐπ᾽ εὐθείας (ταύτῃ yap ἐστιν ἐναντία κατὰ τόπον, wr οἷον ἡ κατὰ διάμετρον: ἀπέχει yap πλεῖστον) ἀντι- κειμένη δὲ ἡ κατὰ τὸ αὐτὸ μῆκος. ὥστε οὐδὲν κωλύει συνεχῶς κινεῖσθαι καὶ μηδένα χρόνον δια- λείπειν: ἡ μὲν γὰρ κύκλῳ κίνησίς ἐστιν ἀπὸ τοῦ αὐτοῦ «is αὐτό, ἡ δὲ Kar’ εὐθεῖαν εἰς ἄλλο. καὶ ἡ μὲν ἐν τῷ κύκλῳ οὐδέποτε ἐν τοῖς αὐτοῖς, ἡ δὲ κατ᾽ εὐθεῖαν πολλάκις ἐν τοῖς αὐτοῖς" τὴν μὲν οὖν ἀεὶ ἐν ἄλλῳ καὶ ἄλλῳ γιγνομένην ἐνδέχεται κινεῖσθαι συνεχῶς" τὴν δ᾽ ἐν τοῖς αὐτοῖς πολλάκις οὐκ ἐνδέχεται, ἀνάγκη γὰρ ἅμα κινεῖσθαι τὰς ἀντικειμένας. ὥστ᾽ οὐδ᾽ ἐν τῷ ἡμικυκλίῳ οὐδ᾽ ἐν ἄλλῃ περιφερείᾳ οὐδεμιᾷ ἐνδέχεται συνεχῶς κινεῖ- 1 [Simplicius’s paraphrase (1309. 13) shows that he read ἀπὸ τοῦ αὐτοῦ εἰς αὐτό (though in the lemma (1308. 33) Diels writes ἀφ᾽ ἑαυτοῦ εἰς ἑαυτό), and his lemma reads ἡ δὲ κατ᾽ εὐθεῖαν εἰς ἄλλο. Themistius 231. 24 ἀπ’ αὐτοῦ εἰς αὐτό, ἡ δὲ κατ᾽ εὐθεῖαν ἀπ᾽ αὐτοῦ εἰς ἄλλο (ἀφ᾽ αὑτοῦ εἰς αὑτό.., ad αὑτοῦ conj. Spengler). Our mss. have ἀφ᾽ αὑτοῦ (or ἑαυτοῦ) εἰς τὸ (rd om. FHI) αὐτό (éaurd F), ἡ δὲ κατ᾽ εὐθεῖαν ἀφ᾽ αὑτοῦ (or ἑαυτοῦ) εἰς ἄλλο. The Oxf. Trans. reads ἀφ᾽ αὑτοῦ εἰς αὑτό.. « ἀφ᾽ αὑτοῦ eis ἄλλος. The choice lies between this and Simplicius’s reading.—C.]
* [In the diagram the motions along the diameter (A to B and B to A) are both ‘ opposite’ and ‘ contrary,’ because contraries in place are defined as ‘being C at the maximum distance from each Ζ other,’ and this is true of the points A and B on the line AB. The motions A fp along the arc (A to C and C to A) are not ‘ contrary,’ since A and C are not at the maximum distance; but they are ‘ opposite’ as traversing the same course in opposite directions. But in travelling round the whole circle from A back to A, the mobile is not undergoing two contrary or opposite motions at the same time, although it is all the while travelling both from and to the same point.—C.]
PHYSICS, VIII. vir.
motion from that same point: the two motions are contrary if they are on the same straight line— along the diameter of the circle, for instance, the one motion is in the local sense ἡ contrary’ to the other, in that the two ends of the diameter are at the greatest possible distance from each other—while the two motions are opposiie only if, in going from and to the same point, they traverse the same line. So there is nothing to prevent the movement of rotation from being perpetual and without interruption; because in a circular movement the mobile is always going to the same point that it is coming from, but in a movement on a straight line it is always going to the point opposite to that which it is coming from. Also on a circle the progress of the movement is never at the same points, whereas the rectilinear movement is at the same points repeatedly. So the movement that is always going forward to another and another may be continuous, but a movement which is at the same points repeatedly cannot, for that would involve moving in opposite directions at one and the same time. Thus it is impossible to move continuously upon a semi-circumference, or any other arc whatever, for that would ὃ (The Oxf. Trans. renders ἐν τοῖς αὐτοῖς ‘ localized within fixed limits,’ following Themistius 231. 25 and others, who explain that whereas the straight line (or the arc) has an ‘actual’ beginning and end, between which the motion must oscillate, there are no such limits anywhere on the circumference of a circle. But 240 a 33 τὰ μέρη (the parts of a rotating sphere) οὐκ ἔστιν ἐν τῷ αὐτῷ οὐδένα χρόνον, εἶτα καὶ τὸ ὅλον μεταβάλλει ἀεὶ εἰς ἕτερον suggests that ἐν. τοῖς αὐτοῖς means ἡ αὖ the same points °"—the movement is always going on to ‘another and another’ point of its progress, whereas a vibratory rectilinear movement recurs to the same points again and again.—C. | 264b σθαι" πολλάκις yap ἀνάγκη ταὐτὰ κινεῖσθαι Kal τὰς ἐναντίας μεταβάλλειν μεταβολάς" οὐ yap συνάπτει τῇ ἀρχῇ τὸ πέρας. ἡ δὲ τοῦ κύκλου συνάπτει, καὶ ἔστι μόνη τέλειος. Φανερὸν δὲ καὶ ἐκ ταύτης τῆς διαιρέσεως ὅτι 80 οὐδὲ τὰς ἄλλας ἐνδέχεται κινήσεις εἶναι συνεχεῖς. ἐν ἁπάσαις γὰρ ταὐτὰ συμβαΐίνει κινεῖσθαι πολλάκις, οἷον ἐν ἀλλοιώσει τὰ μεταξύ, καὶ ἐν τῇ τοῦ ποσοῦ τὰ ava μέσον μεγέθη, καὶ ἐν γενέσει Kat φθορᾷ ε f δὲ ‘ ὃ / λί b>) λλὰ ὡσαύτως" οὐδὲν γὰρ διαφέρει ὀλίγα 7 πολλὰ 25a ποιῆσαι ἐν ols ἐστιν ἡ μεταβολή, οὐδὲ μεταξὺ θεῖναί τι ἢ ἀφελεῖν: ἀμφοτέρως yap συμβαΐνει ταὐτὰ κινεῖσθαι πολλάκις. Δῆλον οὖν ἐκ τούτων ὅτι οὐδ᾽ of φυσιολόγοι καλῶς λέγουσιν of πάντα τὰ αἰσθητὰ κινεῖσθαι δ φάσκοντες ἀεί: κινεῖσθαι γὰρ ἀνάγκη τούτων τινὰ τῶν κινήσεων, καὶ μάλιστα κατ᾽ ἐκείνους ἐστὶν ἀλλοιοῦσθαι" ῥεῖν γάρ φασιν ἀεὶ καὶ φθίνειν, ἔτι δὲ καὶ τὴν γένεσιν καὶ τὴν φθορὰν ἀλλοίωσιν λέγουσιν. ὁ δὲ λόγος viv εἴρηκε καθόλου περὶ πάσης κινήσεως ὅτι κατ᾽ οὐδεμίαν κίνησιν ἐν- δέχεται κινεῖσθαι συνεχῶς, ἔξω τῆς κύκλῳ, ὥστε 10 οὔτε κατ᾽ ἀλλοίωσιν οὔτε κατ᾽ αὔξησιν.
α Which, as we have seen, must break the continuity.
> Which is a term you would not apply to mere changes of local position.
PHYSICS, VIII. vir.
involve recurrent retracing of the course and a series of changes in opposite directions,? inasmuch as on no such are can the extreme limit of departure from the starting-point coincide with that starting-point itself; whereas in the movement on a complete circumference that coincidence is realized, so that it alone is self-completing and re-entrant.
This analysis also makes it plain that none of the other kinds of change can be sustained in continuity, for all such changes do in fact retrace their movement repeatedly. In the case of change of quality all the intermediate stages would have to be retraced in the inverse order, and in quantitive changes the intermediate magnitudes, and analogously in genesis and evanishment; for it makes no difference whether the recognized intermediary states are many or few, or whether we interpolate new ones or eliminate the accepted ones, since in any case the change must make its progress recurrently through them in the reverse direction if it is to be sustained.
From all this it follows that the physicists who say that all objects of sense are in uninterrupted motion and change are mistaken. For the motion or change they speak of must be one or another of those we have just shown to be intermittent; and indeed the thinkers in question lay special stress on one of these very changes, namely the qualitive one; for they say that all things are in a state of flux ὃ and decay, and moreover they regard genesis and dissolution as mere qualitive modifications. But our present argument has shown, of all motions in general, that there is no kind of sustained motion or change that can be continuous except that of rotation; and this excludes both qualitive and quantitive change.
20a Ὅτι μὲν οὖν οὔτ᾽ ἄπειρός ἐστι μεταβολὴ οὐδεμία οὔτε συνεχὴς ἔξω τῆς κύκλῳ φορᾶς, ἔστω τοσαῦθ᾽ ἡμῖν εἰρημένα.
CHAPTER ΙΧ [The priority of rotation to all other forms of locomotion is easily shown. We may dismiss as compound and derivative all species of locomotion except the rectilinear and the circular, and of these the circular is prior, (1) as being simpler and more complete and capable of never coming to an end (265 a 13-27). Also (2) on a circumference there is not (as on a straight line) any definite starting-point or finishing-point forthe motion. The centre is the only beginning, middle, and end, and the rotating body moves round, not towards, the centre. Hence a sphere as a whole does not change its place, though it moves continuously (a 27-b 8). (8) Rotation must be primary because it is the measure of all other motions, and conversely it must be the measure because primary (Ὁ 8~11). (4) Rotation is the only motion that can continue with a uniform velocity. Physical bodies moving in a straight line increase their velocity as they approach their proper place (and decrease their velocity as they are Sorced away from it) (Ὁ 11-16).
265013 Ore δὲ τῶν φορῶν ἡ κυκλοφορία πρώτη, δῆλον. πᾶσα γὰρ φορὰ (ὥσπερ καὶ πρότερον εἴπομεν) ἢ 15 κύκλῳ 7 ἐπ᾽ εὐθείας ἣ μιεκτή. ταύτης δ᾽ ἀνάγκη προτέρας εἶναι ἐκείνας" ἐξ ἐκείνων γὰρ συνέστηκεν. τῆς δ᾽ εὐθείας ἡ κύκλῳ: ἁπλῆ γὰρ καὶ τέλειος μᾶλλον. ἄπειρον μὲν yap οὐκ ἔστιν εὐθεῖαν φέρεα (Consequently, from this point onwards, all movements from place to place except rectilinear movement may be PHYSICS, VIII. virr.-1x.
Let this then suffice in proof that there can be no movement sustained without limit or continuously except rotatory locomotion.
CHAPTER Ix ARGUMENT (continued) The primacy of locomotion over all other forms of change is supported by the testimony of all physical philosophers. Empedocles’ Love and Strife and Anaxagoras’ Mind cause change of all kinds by ‘combining’ or ‘ separating’ (i.e. moving in space) material particles. The Atomists attribute only locomotion to their primary bodies or atoms. The Ionians explain the formation of a differentiated cosmos by ‘condensation’ and ‘ rarifaction ’ (i.e. bringing matter more or less closely together). The Platonists make the self~ moving soul the princeple of all kinds of change, and selfmotion means locomotion. Finally in common usage locomotion is the strict and proper sense of * motion ’—the term we have used to cover locomotion, change of quality, and change of quantity (b 16-266 a 5). ala of conclusions reached in Chaps. I.-LX. (a 6-9).
Ir is easy to show that rotation is the primary form of locomotion. Local movement, as already said, is always either rectilinear’ or rotatory, or a combination of the two, and the things combined necessarily take precedence of the combination formed out of them.* And, of the two comparatively simple movements, rotation takes precedence of rectilinear motion, as being the simpler and more self-completing. For no mobile can travel all along dismissed as derivative, and it will be enough to show that rotation is prior to rectilinear motion.—C. ] 265a σθαι τὸ γὰρ οὕτως ἄπειρον οὐκ ἔστιν. ἀλλ᾽ οὐδ᾽ el ἦν, ἐκινεῦτ᾽ ἂν οὐδέν: οὐ yap γίγνεται TO a- 90 δύνατον, διελθεῖν δὲ τὴν ἄπειρον ἀδύνατον. ἡ δ᾽ ἐπὶ THs πεπερασμένης εὐθείας ἀνακάμπτουσα μὲν συνθετὴ καὶ δύο κινήσεις, μὴ ἀνακάμπτουσα δὲ ἀτελὴς καὶ φθαρτή: πρότερον δὲ καὶ φύσει καὶ λόγῳ καὶ χρόνῳ τὸ τέλειον μὲν τοῦ ἀτελοῦς, τοῦ φθαρτοῦ δὲ τὸ ἄφθαρτον. ἔτι προτέρα ἣν ἐν- δέχεται ἀίδιον εἶναι τῆς μὴ ἐνδεχομένης" τὴν μὲν οὖν κύκλῳ ἐνδέχεται ἀΐδιον εἶναι, τῶν δ᾽ ἄλλων οὔτε φορὰν οὔτ᾽ ἄλλην οὐδεμίαν: στάσιν γὰρ δεῖ γίγνεσθαι, εἰ δὲ στάσις, ἔφθαρται ἡ κίνησις. Εὐλόγως δὲ συμβέβηκε τὸ τὴν κύκλῳ μίαν εἶναι καὶ συνεχῆ, καὶ μὴ τὴν ἐπ᾽ εὐθείας. τῆς μὲν γὰρ ἐπ᾽ εὐθείας ὥρισται καὶ ἀρχὴ καὶ τέλος καὶ μέσον, καὶ πάντ᾽ ἔχει ἐν αὑτῇ, ὥστ᾽ ἔστιν ὅθεν ἄρξεται τὸ κινούμενον καὶ οὗ τελευτήσει (πρὸς γὰρ τοῖς πέρασιν ἠρεμεῖ πᾶν, ἢ ὅθεν 7 οὗν)" τῆς δὲ περιφεροῦς ἀόριστα---τί γὰρ μᾶλλον ὁποιονοῦν πέρας τῶν ἐπὶ τῆς γραμμῆς; ὁμοίως γὰρ ἕκαστον καὶ ἀρχὴ καὶ α {Nothing can actually travel a rectilinear distance longer than the diameter of the spherical universe.—C.]
> [The rectilinear movement is ‘ incomplete and must come to an end ᾿ in either case, for the movement which returns on itself is nothing but two movements of which this is true. It can go no farther when it has reached one extreme or the other; and it is incomplete or imperfect in that it cannot ‘ knit the end to the beginning ’ (264 Ὁ 27): for the straight line can always be extended, whereas the circle 1s once for all complete. Cf. De caelo 286 Ὁ 19.—C.]
5. [ἄφθαρτον here seems to mean ‘ capable of not coming to an end’ (rather than ‘ incapable of coming to an end’), as the opposite of φθαρτόν * incapable of not coming to an end’; for rotation can stop, but need not; whereas rectilinear PHYSICS, VIII. rx.
a straight line that has no limit; in the first place because there is no such line,* and in the second place because, even if there were, no mobile would effect the transit over it, for the impossible does not happen, and it is impossible to traverse to the end that which has no limit. And as to movement on a finite straight line, if it returns upon itself it is compound and consists of two movements, and if it does not return upon itself it has no intrinsic completeness and must be broken οἵ Now that which is fully developed precedes that which is undeveloped, alike in nature, in definition, and in time; and that which is capable of not being broken off ὁ in like manner precedes that which must be broken off. Again, that which can be eternal precedes that which cannot, and movement of rotation can be eternal, whereas no other movement or change, whether local or of any other kind, can be so. For in all these other cases the movement must stop, that is, be broken off and put an end to.
Nor is it anything strange that rotation should be uniform and continuous and rectilinear motion not. Motion on a straight line has a definite beginning, middle, and end, all of which it contains in itself in such a way that the mobile has a defined startingplace and goal (for the limit of a movement, whether it be its whither or its whence, always implies cessation). Motion round a circumference, on the other hand, has no such defined elements; for why should any one point on the line rather than another be regarded as a limit? Any point on the circumference is indifferently a potential beginning, middle, or end movement must stop. The next sentence puts it more strongly: rotation is capable of never coming to an end.—C.]
265 b μέσον καὶ τέλος----ὦ στ᾽ ἀεί TE TWa" εἶναι ἐν ἀρχῆ Oo καὶ ev τέλει καὶ μηδέποτε. διὸ κινεῖται καὶ ἠρεμεῖ πὼς ἡ σφαῖρα: τὸν αὐτὸν γὰρ κατέχει τόπον. αἴ- τιον δ᾽ ὅτι πάντα συμβέβηκε ταῦτα τῷ κέντρῳ--- καὶ γὰρ ἀρχὴ καὶ μέσον τοῦ μεγέθους καὶ τέλος ἐστίν---ὥὦοστε, διὰ τὸ ἔξω εἶναι τοῦτο τῆς περι- φερείας, οὐκ ἔστιν ὅπου τὸ φερόμενον ἠρεμήσει ὡς διεληλυθός" ἀεὶ γὰρ φέρεται περὶ τὸ μέσον, ἀλλ᾽ οὐ πρὸς τὸ ἔσχατον. διὰ δὲ τοῦτο μένει ἀεί τε ἠρεμεῖ πως τὸ ὅλον καὶ κινεῖται συνεχῶς.
Συμβαίνει δ᾽ ἀντιστρόφως" καὶ γὰρ ὅτι μέτρον τῶν κινήσεων ἡ περιφορά ἐστι, πρώτην ἀναγκαῖον αὐτὴν εἶναι (ἅπαντα γὰρ μετρεῖταν τῷ πρώτῳ)" καὶ διότι πρώτη, μέτρον ἐστὶ τῶν ἄλλων.
1 {τινα om. EK. Themistius’s paraphrase is (232. 32) ἀεὶ οὖν ἐν ἀρχῇ καὶ del ἐν τέλει, ignoring καὶ μηδέποτε. If τινὰ is omitted, the subject of εἶναι is τὴν περιφερῆ κίνησιν.---( 2 [The reading of the Tauchnitz edition διὰ δὲ τὸ τοῦτο (se. τὸ μέσον) μένειν might be supported by Themistius 233. 3 ἐπεὶ τοίνυν οὐκ ἐπὶ τὸ πέρας ἀλλὰ περὶ τὸ πέρας κινεῖται, τοῦτο δὲ ἀεὶ ἐν ταὐτῷ μένει, xrdr., Philop. 849. 16 περὶ τὸ ἔδιον κέντρον ἀκίνητον μένον, Simplic. 1316. 22 μένοντος ἀεὶ τοῦ περὶ ὃ ἡ κίνησις γίνεται. All three commentators feel the need to mention that the centre does not move. E obtains this sense by reading διὸ (in the late sense of ‘because’ = διότι) for διὰ, But the other mss. read διὰ δὲ τοῦτο μένει ‘for this reason the sphere stays where it is,’ i.e. does not move from place to place. The point here is, not that the awis is stationary while the ‘rest of the sphere moves round it, but that the sphere is stationary as a whole (ἠρεμεῖ πως τὸ ὅλον), and all the time it is revolving ‘occupies the same place’ (rév αὐτὸν κατέχει τόπον, ]. 2).—C.]
σ [ria (if itshould be retained αὖ 411) is ambiguous. Other possible meanings are: (1) ‘So that you can say that there’ are always some parts of the rotating body at a starting- PHYSICS, VIII. rx.
of a movement of rotation, so that any points you take are at beginning-and-end places potentially but none of them actually. And thus a rotating sphere is moving in one sense, and (since as the frame of reference for internal positions it is constant) at rest in another.? The reason of which is that all the elements which are distinct in a straight line are attributes of the centre in a circle or sphere; for the centre is alike the beginning and middle and end of the measure of ¢ a circular magnitude, so that, none of these limits being on the periphery, there is no position on that periphery at which the mobile must rest as having passed through to the end of its movement, for it is always being carried round the centre and never to any extreme point; and therefore the whole sphere is stationary and motionless in one sense, and moves continuously in another.
Note also this reciprocal relation. It is rotation (of the farthest heavenly sphere) that is the measure (in time) of all movements,? wherefore it must be primary, for itis by what is primary in their kind that all things are standardized or measured. And again it is because rotation is primary that it is the measure of all other kinds of movement or change.
point or at a goal, or you can equally well say that they are never at either.’ (2) ‘ So that we can say of certain things (sc. things that rotate about an axis) both that they are always and that they never are at a starting-point and at a finishing-point ’ (Oxf. Trans.).—C.]
ὃ See Introd. to Bk. IV., Vol. I. p. 270.
¢ [ΟΕ the space traversed’ (Oxf. Tr.). Simplic. 1315. 12, the centre is ‘ beginning’ in that the circumference is everywhere’ at an equal distance from it; ‘end’ in that all radii from the circumference end in it.—C.]
4 (Cf. 223 Ὁ 18, uniform rotation is the best measure, because the easiest to count.—C.]
VOL. II 2D 401 25b "Eire δὲ καὶ ὁμαλῇ ἐνδέχεται εἶναι τὴν κύκλῳ μόνην. τὰ γὰρ ἐπ᾽ εὐθείας ἀνωμαλῶς ἀπὸ τῆς ἀρχῆς φέρεται καὶ πρὸς τὸ τέλος: πάντα yap ὅσῳπερ av ἀφίστηται πλεῖον τοῦ ἠρεμοῦντος, 15 φέρεται θᾶττον: τῆς δὲ κύκλῳ μόνης οὔτ᾽ ἀρχὴ οὔτε τέλος ἐν αὐτῇ πέφυκεν, ἀλλ᾽ ἐκτός. Ort δ᾽ ἡ κατὰ τόπον φορὰ πρώτη τῶν κινήσεων, ’ μαρτυροῦσι πάντες ὅσοι περὶ κινήσεως πεποίηνται A κι a μνείαν: τὰς yap ἀρχὰς αὐτῆς ἀποδιδόασι τοῖς κι- 20 νοῦσι τοιαύτην κίνησιν. διάκρισις γὰρ καὶ σύγ- / lon κρισις κινήσεις κατὰ τόπον εἰσίν, οὕτω δὲ κινοῦσιν ἡ Φιλία καὶ τὸ Νεῖκος---τὸ μὲν yap διακρίνει τὸ δὲ συγκρίνει αὐτῶν---καὶ τὸν Νοῦν δέ φησιν Ava€aydpas διακρίνειν τὸν κινήσαντα πρῶτον. ὁμοίως δὲ Kal ὅσοι τοιαύτην μὲν οὐδεμίαν αἰτίαν 85 λέγουσι, διὰ δὲ τὸ κενὸν κινεῖσθαί φασι: Kal yap οὗτοι τὴν κατὰ τόπον κίνησιν κινεῖσθαι τὴν φύσιν λέγουσιν: ἡ γὰρ διὰ τὸ κενὸν κίνησις φορὰ ἔστιν Os ev τόπῳ. τῶν δ᾽ ἄλλων οὐδεμίαν ὑπάρχειν τοῖς πρώτοις ἀλλὰ τοῖς ἐκ τούτων οἴονται: αὐξά- νεσθαι γὰρ καὶ φθίνειν καὶ ἀλλοιοῦσθαι ovyKpwe- μένων καὶ διακρινομένων τῶν ἀτόμων σωμάτων 1. [φορὰ ἔστιν ὡς ἐν τόπῳ, * (15) in a sense motion in space’ ——‘in a sense,’ because Aristotle does not admit the exist-~ ence of empty space or of motion through it: φορά ἐστιν ws ἐν τόπῳ EK: φορά ἐστι καὶ ὡς ἐν τόπῳ cett. Bekker (translated by Dr. Wicksteed). (I assume that when ἐστι was understood as the copula with φορά, καί was inserted to help out—rather inadequately—the remaining ὡς ἐν τόπῳ): φορά ἐστιν ἐν τόπῳ Simplic. 1319. 7 (paraphr.).—C.]
* [In the case of natural (but not of ‘ violent ’ or unnatural) PHYSICS, VIII. rx.
Again, it is rotation only that can be uniform; for natural movements on the straight are never uniform as they pass from the beginning to the end, for in them the mobile moves more rapidly in proportion as it is further from the position of rest,* whereas in rotation, and in rotation alone, the beginning and end are not inherent in the path of motion but external to it.
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, 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.]
[ 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 drawing 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 demonstration 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.
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 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 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