Authors/Aristotle/physics/liber7

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Chapter 1 1 Ἅπαν τὸ κινούμενον ὑπό τινος ἀνάγκη κινεῖσθαι· εἰ μὲν γὰρ ἐν ἑαυτῷ μὴ ἔχει τὴν ἀρχὴν τῆς κινήσεως, φανερὸν ὅτι ὑφ' ἑτέρου κινεῖται (ἄλλο γὰρ ἔσται τὸ κινοῦν)·	241b24 Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else that moves it.
241b27 εἰ δ' ἐν αὑτῷ, ἔστω [τὸ] εἰλημμένον ἐφ' οὗ τὸ ΑΒ ὃ κινεῖται καθ' αὑτό, ἀλλὰ μὴ <τῷ τῶν> τούτου τι κινεῖσθαι. πρῶτον μὲν οὖν τὸ ὑπολαμβάνειν τὸ ΑΒ ὑφ' ἑαυτοῦ κινεῖσθαι διὰ τὸ ὅλον τε κινεῖσθαι καὶ ὑπ' οὐδενὸς τῶν ἔξωθεν ὅμοιόν ἐστιν ὥσπερ εἰ τοῦ ΚΛ κινοῦντος τὸ ΛΜ καὶ αὐτοῦ κινουμένου εἰ μὴ φάσκοι τις τὸ ΚΜ κινεῖσθαι ὑπό τινος, διὰ τὸ μὴ φανερὸν εἶναι πότερον τὸ κινοῦν καὶ πότερον τὸ κινούμενον·	If on the other hand it has the source of its motion in itself, let AB be taken to represent that which is in motion essentially of itself and not in virtue of the fact that something belonging to it is in motion. Now in the first place to assume that Ab, because it is in motion as a whole and is not moved by anything external to itself, is therefore moved by itself-this is just as if, supposing that KL is moving LM and is also itself in motion, we were to deny that KM is moved by anything on the ground that it is not evident which is the part that is moving it and which the part that is moved.
241b34 εἶτα τὸ μὴ ὑπό τινος κινούμενον (242a.) οὐκ ἀνάγκη παύσασθαι κινούμενον τῷ ἄλλο ἠρεμεῖν, ἀλλ' εἴ τι ἠρεμεῖ τῷ ἄλλο πεπαῦσθαι κινούμενον, ἀνάγκη ὑπό τινος αὐτὸ κινεῖσθαι. τούτου δ' εἰλημμένου πᾶν τὸ κινούμενον κινήσεται ὑπό τινος. ἐπεὶ γὰρ εἴληπται [τὸ] κινούμενον ἐφ' ᾧ τὸ ΑΒ, ἀνάγκη διαιρετὸν αὐτὸ εἶναι· πᾶν γὰρ τὸ κινούμενον διαιρετόν. διῃρήσθω δὴ κατὰ τὸ Γ. τοῦ δὴ ΓΒ μὴ κινουμένου οὐ κινηθήσεται τὸ ΑΒ. εἰ γὰρ κινήσεται, δῆλον ὅτι τὸ ΑΓ κινοῖτ' ἂν τοῦ ΓΒ ἠρεμοῦντος, ὥστε οὐ καθ' αὑτὸ κινηθήσεται καὶ πρῶτον. ἀλλ' ὑπέκειτο καθ' αὑτὸ κινεῖσθαι καὶ πρῶτον. ἀνάγκη ἄρα τοῦ ΓΒ μὴ κινουμένου ἠρεμεῖν τὸ ΑΒ. ὃ δὲ ἠρεμεῖ (45) μὴ κινουμένου τινός, ὡμολόγηται ὑπό τινος κινεῖσθαι, ὥστε πᾶν ἀνάγκη τὸ κινούμενον ὑπό τινος κινεῖσθαι· ἀεὶ γὰρ ἔσται τὸ κινούμενον διαιρετόν, τοῦ δὲ μέρους μὴ κινουμένου ἀνάγκη καὶ τὸ ὅλον ἠρεμεῖν.	In the second place that which is in motion without being moved by anything does not necessarily cease from its motion because something else is at rest, but a thing must be moved by something if the fact of something else having ceased from its motion causes it to be at rest. Thus, if this is accepted, everything that is in motion must be moved by something. For AB, which has been taken to represent that which is in motion, must be divisible since everything that is in motion is divisible. Let it be divided, then, at G. Now if GB is not in motion, then AB will not be in motion: for if it is, it is clear that AG would be in motion while BG is at rest, and thus AB cannot be in motion essentially and primarily. But ex hypothesi AB is in motion essentially and primarily. Therefore if GB is not in motion AB will be at rest. But we have agreed that that which is at rest if something else is not in motion must be moved by something. Consequently, everything that is in motion must be moved by something: for that which is in motion will always be divisible, and if a part of it is not in motion the whole must be at rest.
242a16 ἐπεὶ δὲ πᾶν τὸ κινούμενον ἀνάγκη κινεῖσθαι ὑπό τινος, ἐάν γέ τι κινῆται τὴν ἐν τόπῳ κίνησιν ὑπ' ἄλλου κινουμένου, καὶ πάλιν τὸ κινοῦν ὑπ' ἄλλου κινουμένου κινῆται κἀκεῖνο ὑφ' ἑτέρου καὶ ἀεὶ οὕτως,	Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, and so on continually:
242a20 ἀνάγκη εἶναί τι τὸ πρῶτον κινοῦν, καὶ μὴ βαδίζειν εἰς ἄπειρον· μὴ γὰρ ἔστω, ἀλλὰ γενέσθω ἄπειρον. κινείσθω δὴ τὸ μὲν Α ὑπὸ τοῦ Β, τὸ δὲ Β ὑπὸ τοῦ Γ, τὸ δὲ Γ ὑπὸ τοῦ Δ, καὶ ἀεὶ τὸ ἐχόμενον ὑπὸ τοῦ ἐχομένου. ἐπεὶ οὖν ὑπόκειται τὸ κινοῦν κινούμενον κινεῖν, ἀνάγκη ἅμα γίγνεσθαι τὴν τοῦ κινουμένου καὶ τὴν τοῦ κινοῦντος κίνησιν (ἅμα γὰρ κινεῖ τὸ κινοῦν καὶ κινεῖται τὸ κινούμενον)· φανερὸν <οὖν> ὅτι ἅμα ἔσται τοῦ Α καὶ τοῦ Β καὶ τοῦ Γ καὶ ἑκάστου τῶν κινούντων καὶ κινουμένων ἡ κίνησις. εἰλήφθω οὖν ἡ ἑκάστου κίνησις, καὶ ἔστω τοῦ μὲν Α ἐφ' ἧς Ε, τοῦ δὲ Β ἐφ' ἧς Ζ, τῶν <δὲ> Γ Δ ἐφ' ὧν Η Θ. εἰ γὰρ ἀεὶ κινεῖται ἕκαστον ὑφ' ἑκάστου, ὅμως ἔσται λαβεῖν μίαν ἑκάστου κίνησιν τῷ ἀριθμῷ· πᾶσα γὰρ κίνησις ἔκ τινος εἴς τι, καὶ οὐκ ἄπειρος τοῖς ἐσχάτοις· λέγω δὴ ἀριθμῷ μίαν κίνησιν τὴν ἐκ τοῦ αὐτοῦ εἰς τὸ αὐτὸ τῷ ἀριθμῷ ἐν τῷ αὐτῷ χρόνῳ τῷ ἀριθμῷ γιγνομένην. ἔστι γὰρ κίνησις καὶ γένει καὶ εἴδει καὶ ἀριθμῷ ἡ αὐτή, (242b.) γένει μὲν ἡ τῆς αὐτῆς κατηγορίας, οἷον οὐσίας ἢ ποιότητος, εἴδει δὲ <ἡ> ἐκ τοῦ αὐτοῦ τῷ εἴδει εἰς τὸ αὐτὸ τῷ εἴδει, οἷον ἐκ λευκοῦ εἰς μέλαν ἢ ἐξ ἀγαθοῦ εἰς κακὸν ἀδιάφορον τῷ εἴδει· ἀριθμῷ δὲ ἡ ἐξ ἑνὸς τῷ ἀριθμῷ <εἰς ἓν τῷ ἀριθμῷ> ἐν τῷ αὐτῷ χρόνῳ, οἷον ἐκ τοῦδε τοῦ λευκοῦ εἰς τόδε τὸ μέλαν, ἢ ἐκ τοῦδε τοῦ τόπου εἰς τόνδε, ἐν τῷδε τῷ χρόνῳ· εἰ γὰρ ἐν ἄλλῳ, οὐκέτι ἔσται ἀριθμῷ μία κίνησις, ἀλλ' εἴδει.	then the series cannot go on to infinity, but there must be some first movent. For let us suppose that this is not so and take the series to be infinite. Let A then be moved by B, B by G, G by D, and so on, each member of the series being moved by that which comes next to it. Then since ex hypothesi the movent while causing motion is also itself in motion, and the motion of the moved and the motion of the movent must proceed simultaneously (for the movent is causing motion and the moved is being moved simultaneously) it is evident that the respective motions of A, B, G, and each of the other moved movents are simultaneous. Let us take the motion of each separately and let E be the motion of A, Z of B, and H and O respectively the motions of G and D: for though they are all moved severally one by another, yet we may still take the motion of each as numerically one, since every motion is from something to something and is not infinite in respect of its extreme points. By a motion that is numerically one I mean a motion that proceeds from something numerically one and the same to something numerically one and the same in a period of time numerically one and the same: for a motion may be the same generically, specifically, or numerically: it is generically the same if it belongs to the same category, e.g. substance or quality: it is specifically the same if it proceeds from something specifically the same to something specifically the same, e.g. from white to black or from good to bad, which is not of a kind specifically distinct: it is numerically the same if it proceeds from something numerically one to something numerically one in the same period of time, e.g. from a particular white to a particular black, or from a particular place to a particular place, in a particular period of time: for if the period of time were not one and the same, the motion would no longer be numerically one though it would still be specifically one.
εἴρηται δὲ περὶ τούτων ἐν τοῖς πρότερον. εἰλήφθω δὲ καὶ ὁ χρόνος ἐν ᾧ κεκίνηται τὴν αὑτοῦ κίνησιν τὸ Α, καὶ ἔστω ἐφ' ᾧ Κ. πεπερασμένης δ' οὔσης τῆς τοῦ Α κινήσεως καὶ ὁ χρόνος ἔσται πεπερασμένος. ἐπεὶ δὴ ἄπειρα τὰ κινοῦντα καὶ τὰ κινούμενα, καὶ ἡ κίνησις ἡ ΕΖΗΘ ἡ ἐξ ἁπασῶν ἄπειρος ἔσται· ἐνδέχεται μὲν γὰρ ἴσην εἶναι τὴν τοῦ Α καὶ τοῦ Β καὶ τὴν τῶν ἄλλων, ἐνδέχεται δὲ μείζους τὰς τῶν ἄλλων, ὥστε εἴ τε ἴσαι εἴ τε μείζους, ἀμφοτέρως ἄπειρος ἡ ὅλη· λαμβάνομεν γὰρ τὸ ἐνδεχόμενον. ἐπεὶ δ' ἅμα κινεῖται καὶ τὸ Α καὶ τῶν ἄλλων ἕκαστον, ἡ ὅλη κίνησις ἐν τῷ αὐτῷ χρόνῳ ἔσται καὶ ἡ τοῦ Α· ἡ δὲ τοῦ Α ἐν πεπερασμένῳ· ὥστε εἴη ἂν ἄπειρος ἐν πεπερασμένῳ, τοῦτο δ' ἀδύνατον.	We have dealt with this question above. Now let us further take the time in which A has completed its motion, and let it be represented by K. Then since the motion of A is finite the time will also be finite. But since the movents and the things moved are infinite, the motion EZHO, i.e. the motion that is composed of all the individual motions, must be infinite. For the motions of A, B, and the others may be equal, or the motions of the others may be greater: but assuming what is conceivable, we find that whether they are equal or some are greater, in both cases the whole motion is infinite. And since the motion of A and that of each of the others are simultaneous, the whole motion must occupy the same time as the motion of A: but the time occupied by the motion of A is finite: consequently the motion will be infinite in a finite time, which is impossible.
242b19 οὕτω μὲν οὖν δόξειεν ἂν δεδεῖχθαι τὸ ἐξ ἀρχῆς, οὐ μὴν ἀποδείκνυται διὰ τὸ μηδὲν δείκνυσθαι ἀδύνατον· ἐνδέχεται γὰρ ἐν πεπερασμένῳ χρόνῳ ἄπειρον εἶναι κίνησιν, μὴ ἑνὸς ἀλλὰ πολλῶν. ὅπερ συμβαίνει καὶ ἐπὶ τούτων· ἕκαστον γὰρ κινεῖται τὴν ἑαυτοῦ κίνησιν, ἅμα δὲ πολλὰ κινεῖσθαι οὐκ ἀδύνατον.	It might be thought that what we set out to prove has thus been shown, but our argument so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition: for in a finite time there may be an infinite motion, though not of one thing, but of many: and in the case that we are considering this is so: for each thing accomplishes its own motion, and there is no impossibility in many things being in motion simultaneously.
242b23 ἀλλ' εἰ τὸ κινοῦν πρώτως κατὰ τόπον καὶ σωματικὴν κίνησιν ἀνάγκη ἢ ἅπτεσθαι ἢ συνεχὲς εἶναι τῷ κινουμένῳ, καθάπερ ὁρῶμεν ἐπὶ πάντων, ἀνάγκη τὰ κινούμενα καὶ τὰ κινοῦντα συνεχῆ εἶναι ἢ ἅπτεσθαι ἀλλήλων, ὥστ' εἶναί τι ἐξ ἁπάντων ἕν.	But if (as we see to be universally the case) that which primarily is moved locally and corporeally must be either in contact with or continuous with that which moves it, the things moved and the movents must be continuous or in contact with one another, so that together they all form a single unity:
242b27 τοῦτο δὲ εἴτε πεπερασμένον εἴτε ἄπειρον, οὐδὲν διαφέρει πρὸς τὰ νῦν· πάντως γὰρ ἡ κίνησις ἔσται ἄπειρος ἀπείρων ὄντων, εἴπερ ἐνδέχεται καὶ ἴσας εἶναι καὶ μείζους ἀλλήλων· ὃ γὰρ ἐνδέχεται, ληψόμεθα ὡς ὑπάρχον. εἰ οὖν τὸ μὲν ἐκ τῶν Α Β Γ Δ <ἢ πεπερασμένον ἢ> ἄπειρόν τί ἐστιν, κινεῖται δὲ τὴν ΕΖΗΘ κίνησιν ἐν τῷ χρόνῳ τῷ Κ, οὗτος δὲ πεπέρανται, συμβαίνει ἐν πεπερασμένῳ χρόνῳ ἄπειρον διιέναι ἢ τὸ πεπερασμένον ἢ τὸ ἄπειρον. ἀμφοτέρως δὲ ἀδύνατον· ὥστε ἀνάγκη ἵστασθαι καὶ εἶναί τι πρῶτον κινοῦν καὶ κινούμενον. οὐδὲν γὰρ διαφέρει τὸ συμβαίνειν ἐξ ὑποθέσεως τὸ ἀδύνατον· (243a.) ἡ γὰρ ὑπόθεσις εἴληπται ἐνδεχομένη, τοῦ δ' ἐνδεχομένου τεθέντος οὐδὲν προσήκει γίγνεσθαι διὰ τοῦτο ἀδύνατον.	whether this unity is finite or infinite makes no difference to our present argument; for in any case since the things in motion are infinite in number the whole motion will be infinite, if, as is theoretically possible, each motion is either equal to or greater than that which follows it in the series: for we shall take as actual that which is theoretically possible. If, then, A, B, G, D form an infinite magnitude that passes through the motion EZHO in the finite time K, this involves the conclusion that an infinite motion is passed through in a finite time: and whether the magnitude in question is finite or infinite this is in either case impossible. Therefore the series must come to an end, and there must be a first movent and a first moved: for the fact that this impossibility results only from the assumption of a particular case is immaterial, since the case assumed is theoretically possible, and the assumption of a theoretically possible case ought not to give rise to any impossible result.
Chapter 2 Τὸ δὲ πρῶτον κινοῦν, μὴ ὡς τὸ οὗ ἕνεκεν, ἀλλ' ὅθεν ἡ ἀρχὴ τῆς κινήσεως, ἅμα τῷ κινουμένῳ ἐστί (λέγω δὲ τὸ ἅμα, ὅτι οὐδέν ἐστιν αὐτῶν μεταξύ)· τοῦτο γὰρ κοινὸν ἐπὶ παντὸς κινουμένου καὶ κινοῦντός ἐστιν.	243a3 That which is the first movent of a thing-in the sense that it supplies not 'that for the sake of which' but the source of the motion-is always together with that which is moved by it by 'together' I mean that there is nothing intermediate between them). This is universally true wherever one thing is moved by another.
243a5 ἐπεὶ δὲ τρεῖς αἱ κινήσεις, ἥ τε κατὰ τόπον καὶ ἡ κατὰ τὸ ποιὸν καὶ ἡ κατὰ τὸ ποσόν, ἀνάγκη καὶ τὰ κινοῦντα τρία εἶναι, τό τε φέρον καὶ τὸ ἀλλοιοῦν καὶ τὸ αὖξον ἢ φθῖνον. πρῶτον οὖν εἴπωμεν περὶ τῆς φορᾶς·	And since there are three kinds of motion, local, qualitative, and quantitative, there must also be three kinds of movent, that which causes locomotion, that which causes alteration, and that which causes increase or decrease. Let us begin with locomotion, for this is the primary motion.
243a11πρώτη γὰρ αὕτη τῶν κινήσεων. ἅπαν δὴ τὸ φερόμενον ἢ ὑφ' ἑαυτοῦ κινεῖται ἢ ὑπ' ἄλλου. ὅσα μὲν οὖν αὐτὰ ὑφ' αὑτῶν κινεῖται, φανερὸν ἐν τούτοις ὅτι ἅμα τὸ κινούμενον καὶ τὸ κινοῦν ἐστιν· ἐνυπάρχει γὰρ αὐτοῖς τὸ πρῶτον κινοῦν, ὥστ' οὐδέν ἐστιν ἀναμεταξύ·	Everything that is in locomotion is moved either by itself or by something else. In the case of things that are moved by themselves it is evident that the moved and the movent are together: for they contain within themselves their first movent, so that there is nothing in between.
243a15 ὅσα δ' ὑπ' ἄλλου κινεῖται, τετραχῶς ἀνάγκη γίγνεσθαι· τέτταρα γὰρ εἴδη τῆς ὑπ' ἄλλου φορᾶς, ἕλξις, ὦσις, ὄχησις, δίνησις. ἅπασαι γὰρ αἱ κατὰ τόπον κινήσεις ἀνάγονται εἰς ταύτας·	The motion of things that are moved by something else must proceed in one of four ways: for there are four kinds of locomotion caused by something other than that which is in motion, viz. pulling, pushing, carrying, and twirling. All forms of locomotion are reducible to these.
243a18 ἡ μὲν γὰρ ἔπωσις ὦσίς τίς ἐστιν, ὅταν τὸ ἀφ' αὑτοῦ κινοῦν ἐπακολουθοῦν ὠθῇ, ἡ δ' ἄπωσις, ὅταν μὴ ἐπακολουθῇ κινῆσαν, ἡ δὲ ῥῖψις, ὅταν (243b.) σφοδροτέραν ποιήσῃ τὴν ἀφ' αὑτοῦ κίνησιν τῆς κατὰ φύσιν φορᾶς, καὶ μέχρι τοσούτου φέρηται ἕως ἂν κρατῇ ἡ κίνησις.	Thus pushing on is a form of pushing in which that which is causing motion away from itself follows up that which it pushes and continues to push it: pushing off occurs when the movent does not follow up the thing that it has moved: throwing when the movent causes a motion away from itself more violent than the natural locomotion of the thing moved, which continues its course so long as it is controlled by the motion imparted to it.
243b3 πάλιν ἡ δίωσις καὶ σύνωσις ἄπωσις καὶ ἕλξις εἰσίν· ἡ μὲν γὰρ δίωσις ἄπωσις (ἢ γὰρ ἀφ' αὑτοῦ ἢ ἀπ' ἄλλου ἐστὶν ἡ ἄπωσις), ἡ δὲ σύνωσις ἕλξις (καὶ γὰρ πρὸς αὑτὸ καὶ πρὸς ἄλλο ἡ ἕλξις). ὥστε καὶ ὅσα τούτων εἴδη, οἷον σπάθησις καὶ κέρκισις· ἡ μὲν γὰρ σύνωσις, ἡ δὲ δίωσις.	Again, pushing apart and pushing together are forms respectively of pushing off and pulling: pushing apart is pushing off, which may be a motion either away from the pusher or away from something else, while pushing together is pulling, which may be a motion towards something else as well as the puller.
243b13 ὁμοίως δὲ καὶ αἱ ἄλλαι συγκρίσεις καὶ διακρίσεις—ἅπασαι γὰρ ἔσονται διώσεις ἢ συνώσεις—πλὴν ὅσαι ἐν γενέσει καὶ φθορᾷ εἰσιν. ἅμα δὲ φανερὸν ὅτι οὐδ' ἔστιν ἄλλο τι γένος κινήσεως ἡ σύγκρισις καὶ διάκρισις· ἅπασαι γὰρ διανέμονται εἴς τινας τῶν εἰρημένων. ἔτι δ' ἡ μὲν εἰσπνοὴ ἕλξις, ἡ δ' ἐκπνοὴ ὦσις.	e may similarly classify all the varieties of these last two, e.g. packing and combing: the former is a form of pushing together, the latter a form of pushing apart. The same is true of the other processes of combination and separation (they will all be found to be forms of pushing apart or of pushing together), except such as are involved in the processes of becoming and perishing. (At same time it is evident that there is no other kind of motion but combination and separation: for they may all be apportioned to one or other of those already mentioned.) Again, inhaling is a form of pulling, exhaling a form of pushing:
243b12 ὁμοίως δὲ καὶ ἡ πτύσις, καὶ ὅσαι ἄλλαι διὰ τοῦ σώματος ἢ ἐκκριτικαὶ ἢ ληπτικαὶ κινήσεις· αἱ μὲν γὰρ ἕλξεις εἰσίν, αἱ δ' ἀπώσεις. δεῖ δὲ καὶ τὰς ἄλλας τὰς κατὰ τόπον ἀνάγειν· ἅπασαι γὰρ πίπτουσιν εἰς τέσσαρας ταύτας. τούτων δὲ πάλιν ἡ ὄχησις καὶ ἡ δίνησις εἰς ἕλξιν καὶ ὦσιν. ἡ μὲν γὰρ ὄχησις κατὰ τούτων τινὰ τῶν τριῶν τρόπων ἐστίν (τὸ μὲν γὰρ ὀχούμενον κινεῖται κατὰ συμβεβηκός, ὅτι ἐν κινουμένῳ ἐστὶν ἢ ἐπὶ κινουμένου τινός, τὸ δ' ὀχοῦν ὀχεῖ ἢ ἑλκόμενον ἢ (244a.) ὠθούμενον ἢ δινούμενον, ὥστε κοινή ἐστιν ἁπασῶν τῶν τριῶν ἡ ὄχησις)·	and the same is true of spitting and of all other motions that proceed through the body, whether secretive or assimilative, the assimilative being forms of pulling, the secretive of pushing off. All other kinds of locomotion must be similarly reduced, for they all fall under one or other of our four heads. And again, of these four, carrying and twirling are to pulling and pushing. For carrying always follows one of the other three methods, for that which is carried is in motion accidentally, because it is in or upon something that is in motion, and that which carries it is in doing so being either pulled or pushed or twirled; thus carrying belongs to all the other three kinds of motion in common.
244a2 ἡ δὲ δίνησις σύγκειται ἐξ ἕλξεώς τε καὶ ὤσεως· ἀνάγκη γὰρ τὸ δινοῦν τὸ μὲν ἕλκειν τὸ δ' ὠθεῖν· τὸ μὲν γὰρ ἀφ' αὑτοῦ τὸ δὲ πρὸς αὑτὸ ἄγει.	And twirling is a compound of pulling and pushing, for that which is twirling a thing must be pulling one part of the thing and pushing another part, since it impels one part away from itself and another part towards itself.
244a4 ὥστ' εἰ τὸ ὠθοῦν καὶ τὸ ἕλκον ἅμα τῷ ὠθουμένῳ καὶ τῷ ἑλκομένῳ, φανερὸν ὅτι τοῦ κατὰ τόπον κινουμένου καὶ κινοῦντος οὐδέν ἐστι μεταξύ.	If, therefore, it can be shown that that which is pushing and that which is pushing and pulling are adjacent respectively to that which is being pushed and that which is being pulled, it will be evident that in all locomotion there is nothing intermediate between moved and movent.
244a7 ἀλλὰ μὴν τοῦτο δῆλον καὶ ἐκ τῶν ὁρισμῶν· ὦσις μὲν γάρ ἐστιν ἡ ἀφ' αὑτοῦ ἢ ἀπ' ἄλλου πρὸς ἄλλο κίνησις, ἕλξις δὲ ἡ ἀπ' ἄλλου πρὸς αὑτὸ ἢ πρὸς ἄλλο, ὅταν θάττων ἡ κίνησις ᾖ [τοῦ ἕλκοντος] τῆς χωριζούσης ἀπ' ἀλλήλων τὰ συνεχῆ· οὕτω γὰρ συνεφέλκεται θάτερον.	But the former fact is clear even from the definitions of pushing and pulling, for pushing is motion to something else from oneself or from something else, and pulling is motion from something else to oneself or to something else, when the motion of that which is pulling is quicker than the motion that would separate from one another the two things that are continuous: for it is this that causes one thing to be pulled on along with the other.
244a11 (τάχα δὲ δόξειεν ἂν εἶναί τις ἕλξις καὶ ἄλλως· τὸ γὰρ ξύλον ἕλκει τὸ πῦρ οὐχ οὕτως. τὸ δ' οὐθὲν διαφέρει κινουμένου τοῦ ἕλκοντος ἢ μένοντος ἕλκειν· ὁτὲ μὲν γὰρ ἕλκει οὗ ἔστιν, ὁτὲ δὲ οὗ ἦν.)	(It might indeed be thought that there is a form of pulling that arises in another way: that wood, e.g. pulls fire in a manner different from that described above. But it makes no difference whether that which pulls is in motion or is stationary when it is pulling: in the latter case it pulls to the place where it is, while in the former it pulls to the place where it was.)
244a14 ἀδύνατον δὲ ἢ ἀφ' αὑτοῦ πρὸς ἄλλο ἢ ἀπ' ἄλλου πρὸς αὑτὸ κινεῖν (244b.) μὴ ἁπτόμενον, ὥστε φανερὸν ὅτι τοῦ κατὰ τόπον κινουμένου καὶ κινοῦντος οὐδέν ἐστι μεταξύ.	Now it is impossible to move anything either from oneself to something else or something else to oneself without being in contact with it: it is evident, therefore, that in all locomotion there is nothing intermediate between moved and movent.
244b2 ἀλλὰ μὴν οὐδὲ τοῦ ἀλλοιουμένου καὶ τοῦ ἀλλοιοῦντος. τοῦτο δὲ δῆλον ἐξ ἐπαγωγῆς· ἐν ἅπασι γὰρ συμβαίνει ἅμα εἶναι τὸ ἔσχατον ἀλλοιοῦν καὶ τὸ πρῶτον ἀλλοιούμενον·	Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be proved by induction: for in every case we find that the respective extremities of that which causes and that which undergoes alteration are adjacent.
<ὑπόκειται γὰρ ἡμῖν τὸ τὰ ἀλλοιούμενα κατὰ τὰς παθητικὰς καλουμένας ποιότητας πάσχοντα ἀλλοιοῦσθαι. ἅπαν γὰρ σῶμα σώματος διαφέρει τοῖς αἰσθητοῖς ἢ πλείοσιν ἢ ἐλάττοσιν ἢ τῷ μᾶλλον καὶ ἧττον τοῖς αὐτοῖς·> ἀλλὰ μὴν καὶ ἀλλοιοῦται τὸ ἀλλοιούμενον ὑπὸ τῶν εἰρημένων. ταῦτα γάρ ἐστι πάθη τῆς ὑποκειμένης ποιότητος· ἢ γὰρ θερμαινόμενον ἢ γλυκαινόμενον ἢ πυκνούμενον ἢ ξηραινόμενον ἢ λευκαινόμενον ἀλλοιοῦσθαί φαμεν, ὁμοίως τό τε ἄψυχον καὶ τὸ ἔμψυχον λέγοντες, καὶ πάλιν τῶν ἐμψύχων τά τε μὴ αἰσθητικὰ τῶν μερῶν καὶ αὐτὰς τὰς αἰσθήσεις. ἀλλοιοῦνται γάρ πως καὶ αἱ αἰσθήσεις· ἡ γὰρ αἴσθησις ἡ κατ' ἐνέργειαν κίνησίς ἐστι διὰ τοῦ σώματος, πασχούσης τι τῆς αἰσθήσεως. καθ' ὅσα μὲν οὖν τὸ ἄψυχον ἀλλοιοῦται, καὶ τὸ ἔμψυχον, καθ' ὅσα δὲ τὸ ἔμψυχον, οὐ κατὰ ταῦτα πάντα τὸ ἄψυχον (οὐ γὰρ ἀλλοιοῦται κατὰ τὰς αἰσθήσεις)· καὶ τὸ μὲν λανθάνει, τὸ δ' οὐ (245a.) λανθάνει πάσχον. οὐδὲν δὲ κωλύει καὶ τὸ ἔμψυχον λανθάνειν, ὅταν μὴ κατὰ τὰς αἰσθήσεις γίγνηται ἡ ἀλλοίωσις. εἴπερ οὖν ἀλλοιοῦται τὸ ἀλλοιούμενον ὑπὸ τῶν αἰσθητῶν, ἐν ἅπασί γε τούτοις φανερὸν ὅτι ἅμα ἐστὶ τὸ ἔσχατον ἀλλοιοῦν καὶ τὸ πρῶτον ἀλλοιούμενον·	For our assumption is that things that are undergoing alteration are altered in virtue of their being affected in respect of their so-called affective qualities, since that which is of a certain quality is altered in so far as it is sensible, and the characteristics in which bodies differ from one another are sensible characteristics: for every body differs from another in possessing a greater or lesser number of sensible characteristics or in possessing the same sensible characteristics in a greater or lesser degree. But the alteration of that which undergoes alteration is also caused by the above-mentioned characteristics, which are affections of some particular underlying quality. Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white: and we make these assertions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts that have no power of sense-perception and of the senses themselves. For in a way even the senses undergo alteration, since the active sense is a motion through the body in the course of which the sense is affected in a certain way. We see, then, that the animate is capable of every kind of alteration of which the inanimate is capable: but the inanimate is not capable of every kind of alteration of which the animate is capable, since it is not capable of alteration in respect of the senses: moreover the inanimate is unconscious of being affected by alteration, whereas the animate is conscious of it, though there is nothing to prevent the animate also being unconscious of it when the process of the alteration does not concern the senses. Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration it is evident that the respective extremities of that which causes and that which undergoes alteration are adjacent.
245a5 τῷ μὲν γὰρ συνεχὴς ὁ ἀήρ, τῷ δ' ἀέρι τὸ σῶμα. πάλιν δὲ τὸ μὲν χρῶμα τῷ φωτί, τὸ δὲ φῶς τῇ ὄψει. τὸν αὐτὸν δὲ τρόπον καὶ ἡ ἀκοὴ καὶ ἡ ὄσφρησις· πρῶτον γὰρ κινοῦν πρὸς τὸ κινούμενον ὁ ἀήρ. καὶ ἐπὶ τῆς γεύσεως ὁμοίως· ἅμα γὰρ τῇ γεύσει ὁ χυμός. ὡσαύτως δὲ καὶ ἐπὶ τῶν ἀψύχων καὶ ἀναισθήτων. ὥστ' οὐδὲν ἔσται μεταξὺ τοῦ ἀλλοιουμένου καὶ τοῦ ἀλλοιοῦντος.	Thus the air is continuous with that which causes the alteration, and the body that undergoes alteration is continuous with the air. Again, the colour is continuous with the light and the light with the sight. And the same is true of hearing and smelling: for the primary movent in respect to the moved is the air. Similarly, in the case of tasting, the flavour is adjacent to the sense of taste. And it is just the same in the case of things that are inanimate and incapable of sense-perception. Thus there can be nothing intermediate between that which undergoes and that which causes alteration.
245a11 οὐδὲ μὴν τοῦ αὐξανομένου τε καὶ αὔξοντος· αὐξάνει γὰρ τὸ πρῶτον αὖξον προσγιγνόμενον, ὥστε ἓν γίγνεσθαι τὸ ὅλον. καὶ πάλιν φθίνει τὸ φθῖνον ἀπογιγνομένου τινὸς τῶν τοῦ φθίνοντος. ἀνάγκη οὖν συνεχὲς εἶναι καὶ τὸ αὖξον καὶ τὸ φθῖνον, τῶν δὲ συνεχῶν οὐδὲν μεταξύ.	Nor, again, can there be anything intermediate between that which suffers and that which causes increase: for the part of the latter that starts the increase does so by becoming attached in such a way to the former that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of the thing becoming detached. So that which causes increase and that which causes decrease must be continuous with that which suffers increase and that which suffers decrease respectively: and if two things are continuous with one another there can be nothing intermediate between them.
245a16 φανερὸν οὖν ὅτι τοῦ κινουμένου καὶ (245b.) τοῦ κινοῦντος πρώτου καὶ ἐσχάτου πρὸς τὸ κινούμενον οὐδέν ἐστιν ἀνὰ μέσον.	t is evident, therefore, that between the extremities of the moved and the movent that are respectively first and last in reference to the moved there is nothing intermediate.
Chapter 3 3 Ὅτι δὲ τὸ ἀλλοιούμενον ἅπαν ἀλλοιοῦται ὑπὸ τῶν αἰσθητῶν, καὶ ἐν μόνοις ὑπάρχει τούτοις ἀλλοίωσις ὅσα καθ' αὑτὰ λέγεται πάσχειν ὑπὸ τῶν αἰσθητῶν, ἐκ τῶνδε θεωρητέον.	245b3 Everything, we say, that undergoes alteration is altered by sensible causes, and there is alteration only in things that are said to be essentially affected by sensible things. The truth of this is to be seen from the following considerations.
245b6 τῶν γὰρ ἄλλων μάλιστ' ἄν τις ὑπολάβοι ἔν τε τοῖς σχήμασι καὶ ταῖς μορφαῖς καὶ ἐν ταῖς ἕξεσι καὶ ταῖς τούτων λήψεσι καὶ ἀποβολαῖς ἀλλοίωσιν ὑπάρχειν· ἐν οὐδετέροις δ' ἔστιν.	Of all other things it would be most natural to suppose that there is alteration in figures and shapes, and in acquired states and in the processes of acquiring and losing these: but as a matter of fact in neither of these two classes of things is there alteration.
245b9 τὸ μὲν γὰρ σχηματιζόμενον καὶ ῥυθμιζόμενον ὅταν ἐπιτελεσθῇ, οὐ λέγομεν ἐκεῖνο ἐξ οὗ ἐστιν, οἷον τὸν ἀνδριάντα χαλκὸν ἢ τὴν πυραμίδα κηρὸν ἢ τὴν κλίνην ξύλον, ἀλλὰ παρωνυμιάζοντες τὸ μὲν χαλκοῦν, τὸ δὲ κήρινον, τὸ δὲ ξύλινον. τὸ δὲ πεπονθὸς καὶ ἠλλοιωμένον προσαγορεύομεν· ὑγρὸν γὰρ καὶ θερμὸν καὶ σκληρὸν τὸν χαλκὸν λέγομεν καὶ τὸν κηρόν	In the first place, when a particular formation of a thing is completed, we do not call it by the name of its material: e.g. we do not call the statue 'bronze' or the pyramid 'wax' or the bed 'wood', but we use a derived expression and call them 'of bronze', 'waxen', and 'wooden' respectively. But when a thing has been affected and altered in any way we still call it by the original name: thus we speak of the bronze or the wax being dry or fluid or hard or hot.
245b15 (καὶ οὐ μόνον οὕτως, ἀλλὰ καὶ τὸ ὑγρὸν καὶ τὸ θερμὸν χαλκὸν λέγομεν), ὁμωνύμως τῷ πάθει προσαγορεύοντες τὴν (246a.) ὕλην. ὥστ' εἰ κατὰ μὲν τὸ σχῆμα καὶ τὴν μορφὴν οὐ λέγεται τὸ γεγονὸς ἐν ᾧ ἐστι τὸ σχῆμα, κατὰ δὲ τὰ πάθη καὶ τὰς ἀλλοιώσεις λέγεται, φανερὸν ὅτι οὐκ ἂν εἶεν αἱ γενέσεις ἀλλοιώσεις.	And not only so: we also speak of the particular fluid or hot substance as being bronze, giving the material the same name as that which we use to describe the affection. Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a thing's affections or alterations we still call it by the name of its material, it is evident that becomings of the former kind cannot be alterations.
246a4 ἔτι δὲ καὶ εἰπεῖν οὕτως ἄτοπον ἂν δόξειεν, ἠλλοιῶσθαι τὸν ἄνθρωπον ἢ τὴν οἰκίαν ἢ ἄλλο ὁτιοῦν τῶν γεγενημένων· ἀλλὰ γίγνεσθαι μὲν ἴσως ἕκαστον ἀναγκαῖον ἀλλοιουμένου τινός, οἷον τῆς ὕλης πυκνουμένης ἢ μανουμένης ἢ θερμαινομένης ἢ ψυχομένης, οὐ μέντοι τὰ γιγνόμενά γε ἀλλοιοῦται, οὐδ' ἡ γένεσις αὐτῶν ἀλλοίωσίς ἐστιν.	Moreover it would seem absurd even to speak in this way, to speak, that is to say, of a man or house or anything else that has come into existence as having been altered. Though it may be true that every such becoming is necessarily the result of something's being altered, the result, e.g. of the material's being condensed or rarefied or heated or cooled, nevertheless it is not the things that are coming into existence that are altered, and their becoming is not an alteration.
246a9 ἀλλὰ μὴν οὐδ' αἱ ἕξεις οὔθ' αἱ τοῦ σώματος οὔθ' αἱ τῆς ψυχῆς ἀλλοιώσεις. αἱ μὲν γὰρ ἀρεταὶ αἱ δὲ κακίαι τῶν ἕξεων· οὐκ ἔστι δὲ οὔτε ἡ ἀρετὴ οὔτε ἡ κακία ἀλλοίωσις, ἀλλ' ἡ μὲν ἀρετὴ τελείωσίς τις (ὅταν γὰρ λάβῃ τὴν αὑτοῦ ἀρετήν, τότε λέγεται τέλειον ἕκαστον—τότε γὰρ ἔστι μάλιστα [τὸ] κατὰ φύσιν—ὥσπερ κύκλος τέλειος, ὅταν μάλιστα γένηται κύκλος καὶ ὅταν βέλτιστος), ἡ δὲ κακία φθορὰ τούτου καὶ ἔκστασις· ὥσπερ οὖν οὐδὲ τὸ τῆς οἰκίας τελείωμα λέγομεν ἀλλοίωσιν (ἄτοπον γὰρ εἰ ὁ θριγκὸς καὶ ὁ κέραμος ἀλλοίωσις, ἢ εἰ θριγκουμένη καὶ κεραμουμένη ἀλλοιοῦται ἀλλὰ μὴ τελειοῦται ἡ οἰκία), τὸν αὐτὸν τρόπον καὶ ἐπὶ τῶν ἀρε(246b.) τῶν καὶ τῶν κακιῶν καὶ τῶν ἐχόντων ἢ λαμβανόντων· αἱ μὲν γὰρ τελειώσεις αἱ δὲ ἐκστάσεις εἰσίν, ὥστ' οὐκ ἀλλοιώσεις.	Again, acquired states, whether of the body or of the soul, are not alterations. For some are excellences and others are defects, and neither excellence nor defect is an alteration: excellence is a perfection (for when anything acquires its proper excellence we call it perfect, since it is then if ever that we have a thing in its natural state: e.g. we have a perfect circle when we have one as good as possible), while defect is a perishing of or departure from this condition. So as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose that the coping or the tiling is an alteration or that in receiving its coping or its tiling a house is altered and not perfected), the same also holds good in the case of excellences and defects and of the persons or things that possess or acquire them: for excellences are perfections of a thing's nature and defects are departures from it: consequently they are not alterations.
246b3 ἔτι δὲ καί φαμεν ἁπάσας εἶναι τὰς ἀρετὰς ἐν τῷ πρός τι πὼς ἔχειν. τὰς μὲν γὰρ τοῦ σώματος, οἷον ὑγίειαν καὶ εὐεξίαν, ἐν κράσει καὶ συμμετρίᾳ θερμῶν καὶ ψυχρῶν τίθεμεν, ἢ αὐτῶν πρὸς αὑτὰ τῶν ἐντὸς ἢ πρὸς τὸ περιέχον· ὁμοίως δὲ καὶ τὸ κάλλος καὶ τὴν ἰσχὺν καὶ τὰς ἄλλας ἀρετὰς καὶ κακίας. ἑκάστη γάρ ἐστι τῷ πρός τι πὼς ἔχειν, καὶ περὶ τὰ οἰκεῖα πάθη εὖ ἢ κακῶς διατίθησι τὸ ἔχον· οἰκεῖα δ' ὑφ' ὧν γίγνεσθαι καὶ φθείρεσθαι πέφυκεν.	Further, we say that all excellences depend upon particular relations. Thus bodily excellences such as health and a good state of body we regard as consisting in a blending of hot and cold elements within the body in due proportion, in relation either to one another or to the surrounding atmosphere: and in like manner we regard beauty, strength, and all the other bodily excellences and defects. Each of them exists in virtue of a particular relation and puts that which possesses it in a good or bad condition with regard to its proper affections, where by 'proper' affections I mean those influences that from the natural constitution of a thing tend to promote or destroy its existence.
246b10 ἐπεὶ οὖν τὰ πρός τι οὔτε αὐτά ἐστιν ἀλλοιώσεις, οὔτε ἔστιν αὐτῶν ἀλλοίωσις οὐδὲ γένεσις οὐδ' ὅλως μεταβολὴ οὐδεμία,	Since then, relatives are neither themselves alterations nor the subjects of alteration or of becoming or in fact of any change whatever,
246b12 φανερὸν ὅτι οὔθ' αἱ ἕξεις οὔθ' αἱ τῶν ἕξεων ἀποβολαὶ καὶ λήψεις ἀλλοιώσεις εἰσίν, ἀλλὰ γίγνεσθαι μὲν ἴσως αὐτὰς καὶ φθείρεσθαι ἀλλοιουμένων τινῶν ἀνάγκη, καθάπερ καὶ τὸ εἶδος καὶ τὴν μορφήν, οἷον θερμῶν καὶ ψυχρῶν ἢ ξηρῶν καὶ ὑγρῶν, ἢ ἐν οἷς τυγχάνουσιν οὖσαι πρώτοις. περὶ ταῦτα γὰρ ἑκάστη λέγεται κακία καὶ ἀρετή, ὑφ' ὧν ἀλλοιοῦσθαι πέφυκε τὸ ἔχον· ἡ μὲν γὰρ ἀρετὴ ποιεῖ ἢ ἀπαθὲς ἢ ὡδὶ παθητικόν, ἡ δὲ κακία παθητικὸν ἢ ἐναντίως ἀπαθές.	it is evident that neither states nor the processes of losing and acquiring states are alterations, though it may be true that their becoming or perishing is necessarily, like the becoming or perishing of a specific character or form, the result of the alteration of certain other things, e.g. hot and cold or dry and wet elements or the elements, whatever they may be, on which the states primarily depend. For each several bodily defect or excellence involves a relation with those things from which the possessor of the defect or excellence is naturally subject to alteration: thus excellence disposes its possessor to be unaffected by these influences or to be affected by those of them that ought to be admitted, while defect disposes its possessor to be affected by them or to be unaffected by those of them that ought to be admitted.
246b20 ἐπὶ τῶν τῆς ψυχῆς ἕξεων· ἅπασαι γὰρ καὶ αὗται τῷ πρός τι πὼς ἔχειν, καὶ αἱ μὲν ἀρεταὶ τελειώσεις, αἱ δὲ κακίαι ἐκστάσεις. ἔτι δὲ ἡ μὲν ἀρετὴ εὖ διατίθησι πρὸς τὰ οἰκεῖα πάθη, ἡ δὲ κακία κακῶς. ὥστ' οὐδ' αὗται ἔσονται ἀλλοιώσεις· οὐδὲ δὴ αἱ ἀποβολαὶ καὶ αἱ λήψεις αὐτῶν. γίγνεσθαι δ' αὐτὰς ἀναγκαῖον ἀλλοιουμένου τοῦ αἰσθητικοῦ μέρους. ἀλλοιωθήσεται δ' ὑπὸ τῶν αἰσθητῶν·	And the case is similar in regard to the states of the soul, all of which (like those of body) exist in virtue of particular relations, the excellences being perfections of nature and the defects departures from it: moreover, excellence puts its possessor in good condition, while defect puts its possessor in a bad condition, to meet his proper affections. Consequently these cannot any more than the bodily states be alterations, nor can the processes of losing and acquiring them be so, though their becoming is necessarily the result of an alteration of the sensitive part of the soul, and this is altered by sensible objects:
ἅπασα γὰρ ἡ ἠθικὴ ἀρετὴ περὶ ἡδονὰς καὶ λύπας τὰς σωματικάς, αὗται δὲ ἢ ἐν τῷ πράττειν ἢ ἐν τῷ μεμνῆσθαι ἢ ἐν τῷ ἐλπίζειν. αἱ μὲν οὖν ἐν τῇ πράξει κατὰ τὴν αἴσθησίν εἰσιν, ὥσθ' ὑπ' αἰσθητοῦ τινὸς κινεῖσθαι, αἱ δ' ἐν τῇ μνήμῃ καὶ ἐν τῇ ἐλπίδι ἀπὸ ταύτης εἰσίν· ἢ γὰρ οἷα ἔπαθον μεμνημένοι ἥδονται, ἢ ἐλπίζοντες οἷα μέλλουσιν. ὥστ' ἀνάγκη πᾶσαν τὴν τοιαύτην ἡδονὴν ὑπὸ τῶν αἰσθητῶν γίγνεσθαι. ἐπεὶ δ' ἡδονῆς καὶ λύπης ἐγγιγνομένης καὶ ἡ κακία καὶ ἡ ἀρετὴ ἐγγίγνεται (περὶ ταύτας γάρ εἰσιν), αἱ δ' ἡδοναὶ καὶ αἱ λῦπαι ἀλλοιώσεις τοῦ αἰσθητικοῦ, φανερὸν ὅτι ἀλλοιουμένου τινὸς ἀνάγκη καὶ ταύτας ἀποβάλλειν καὶ λαμβάνειν. ὥσθ' ἡ μὲν γένεσις αὐτῶν μετ' ἀλλοιώσεως, αὐταὶ δ' οὐκ εἰσὶν ἀλλοιώσεις.	for all moral excellence is concerned with bodily pleasures and pains, which again depend either upon acting or upon remembering or upon anticipating. Now those that depend upon action are determined by sense-perception, i.e. they are stimulated by something sensible: and those that depend upon memory or anticipation are likewise to be traced to sense-perception, for in these cases pleasure is felt either in remembering what one has experienced or in anticipating what one is going to experience. Thus all pleasure of this kind must be produced by sensible things: and since the presence in any one of moral defect or excellence involves the presence in him of pleasure or pain (with which moral excellence and defect are always concerned), and these pleasures and pains are alterations of the sensitive part, it is evident that the loss and acquisition of these states no less than the loss and acquisition of the states of the body must be the result of the alteration of something else. Consequently, though their becoming is accompanied by an alteration, they are not themselves alterations.
247b1 (247b.) ἀλλὰ μὴν οὐδ' αἱ τοῦ νοητικοῦ μέρους ἕξεις ἀλλοιώσεις, οὐδ' ἔστιν αὐτῶν γένεσις. πολὺ γὰρ μάλιστα τὸ ἐπιστῆμον ἐν τῷ πρός τι πὼς ἔχειν λέγομεν. ἔτι δὲ καὶ φανερὸν ὅτι οὐκ ἔστιν αὐτῶν γένεσις· τὸ γὰρ κατὰ δύναμιν ἐπιστῆμον οὐδὲν αὐτὸ κινηθὲν ἀλλὰ τῷ ἄλλο ὑπάρξαι γίγνεται ἐπιστῆμον.	Again, the states of the intellectual part of the soul are not alterations, nor is there any becoming of them. In the first place it is much more true of the possession of knowledge that it depends upon a particular relation. And further, it is evident that there is no becoming of these states. For that which is potentially possessed of knowledge becomes actually possessed of it not by being set in motion at all itself but by reason of the presence of something else: i.e. it is when it meets with the particular object that it knows in a manner the particular through its knowledge of the universal.
247b7 ὅταν γὰρ γένηται τὸ κατὰ μέρος, ἐπίσταταί πως τὰ καθόλου τῷ ἐν μέρει. πάλιν δὲ τῆς χρήσεως καὶ τῆς ἐνεργείας οὐκ ἔστι γένεσις, εἰ μή τις καὶ τῆς ἀναβλέψεως καὶ τῆς ἁφῆς οἴεται γένεσιν εἶναι· τὸ γὰρ χρῆσθαι καὶ τὸ ἐνεργεῖν ὅμοιον τούτοις.	(Again, there is no becoming of the actual use and activity of these states, unless it is thought that there is a becoming of vision and touching and that the activity in question is similar to these.)
247b9 ἡ δ' ἐξ ἀρχῆς λῆψις τῆς ἐπιστήμης γένεσις οὐκ ἔστιν οὐδ' ἀλλοίωσις· τῷ γὰρ ἠρεμῆσαι καὶ στῆναι τὴν διάνοιαν ἐπίστασθαι καὶ φρονεῖν λεγόμεθα, εἰς δὲ τὸ ἠρεμεῖν οὐκ ἔστι γένεσις· ὅλως γὰρ οὐδεμιᾶς μεταβολῆς, καθάπερ εἴρηται πρότερον. ἔτι δ' ὥσπερ ὅταν ἐκ τοῦ μεθύειν ἢ καθεύδειν ἢ νοσεῖν εἰς τἀναντία μεταστῇ τις, οὔ φαμεν ἐπιστήμονα γεγονέναι πάλιν (καίτοι ἀδύνατος ἦν τῇ ἐπιστήμῃ χρῆσθαι πρότερον), οὕτως οὐδ' ὅταν ἐξ ἀρχῆς λαμβάνῃ τὴν ἕξιν· τῷ γὰρ καθίστασθαι τὴν ψυχὴν ἐκ τῆς φυσικῆς ταραχῆς φρόνιμόν τι γίγνεται καὶ ἐπιστῆμον. διὸ καὶ τὰ παιδία οὔτε μανθάνειν δύνανται οὔτε κατὰ τὰς αἰσθήσεις (248a.) ὁμοίως κρίνειν τοῖς πρεσβυτέροις· πολλὴ γὰρ ἡ ταραχὴ καὶ ἡ κίνησις. καθίσταται δὲ καὶ ἠρεμίζεται πρὸς ἔνια μὲν ὑπὸ τῆς φύσεως αὐτῆς, πρὸς ἔνια δ' ὑπ' ἄλλων, ἐν ἀμφοτέροις δὲ ἀλλοιουμένων τινῶν τῶν ἐν τῷ σώματι, καθάπερ ἐπὶ τῆς χρήσεως καὶ τῆς ἐνεργείας, ὅταν νήφων γένηται καὶ ἐγερθῇ. φανερὸν οὖν ἐκ τῶν εἰρημένων ὅτι τὸ ἀλλοιοῦσθαι καὶ ἡ ἀλλοίωσις ἔν τε τοῖς αἰσθητοῖς γίγνεται καὶ ἐν τῷ αἰσθητικῷ μορίῳ τῆς ψυχῆς, ἐν ἄλλῳ δ' οὐδενὶ πλὴν κατὰ συμβεβηκός.	And the original acquisition of knowledge is not a becoming or an alteration: for the terms 'knowing' and 'understanding' imply that the intellect has reached a state of rest and come to a standstill, and there is no becoming that leads to a state of rest, since, as we have said above, change at all can have a becoming. Moreover, just as to say, when any one has passed from a state of intoxication or sleep or disease to the contrary state, that he has become possessed of knowledge again is incorrect in spite of the fact that he was previously incapable of using his knowledge, so, too, when any one originally acquires the state, it is incorrect to say that he becomes possessed of knowledge: for the possession of understanding and knowledge is produced by the soul's settling down out of the restlessness natural to it. Hence, too, in learning and in forming judgements on matters relating to their sense-perceptions children are inferior to adults owing to the great amount of restlessness and motion in their souls. Nature itself causes the soul to settle down and come to a state of rest for the performance of some of its functions, while for the performance of others other things do so: but in either case the result is brought about through the alteration of something in the body, as we see in the case of the use and activity of the intellect arising from a man's becoming sober or being awakened. It is evident, then, from the preceding argument that alteration and being altered occur in sensible things and in the sensitive part of the soul, and, except accidentally, in nothing else.
Chapter 4 Ἀπορήσειε δ' ἄν τις πότερόν ἐστι κίνησις πᾶσα πάσῃ συμβλητὴ ἢ οὔ. εἰ δή ἐστιν πᾶσα συμβλητή, καὶ ὁμοταχὲς τὸ ἐν ἴσῳ χρόνῳ ἴσον κινούμενον, ἔσται περιφερής τις ἴση εὐθείᾳ, καὶ μείζων δὴ καὶ ἐλάττων. ἔτι ἀλλοίωσις καὶ φορά τις ἴση, ὅταν ἐν ἴσῳ χρόνῳ τὸ μὲν ἀλλοιωθῇ τὸ δ' ἐνεχθῇ. ἔσται ἄρα ἴσον πάθος μήκει. ἀλλ' ἀδύνατον.	248a10 A difficulty may be raised as to whether every motion is commensurable with every other or not. Now if they are all commensurable and if two things to have the same velocity must accomplish an equal motion in an equal time, then we may have a circumference equal to a straight line, or, of course, the one may be greater or less than the other. Further, if one thing alters and another accomplishes a locomotion in an equal time, we may have an alteration and a locomotion equal to one another: thus an affection will be equal to a length, which is impossible.
248a15 ἀλλ' ἆρα ὅταν ἐν ἴσῳ ἴσον κινηθῇ, τότε ἰσοταχές, ἴσον δ' οὐκ ἔστιν πάθος μήκει, ὥστε οὐκ ἔστιν ἀλλοίωσις φορᾷ ἴση οὐδ' ἐλάττων, ὥστ' οὐ πᾶσα συμβλητή;	But is it not only when an equal motion is accomplished by two things in an equal time that the velocities of the two are equal? Now an affection cannot be equal to a length. Therefore there cannot be an alteration equal to or less than a locomotion: and consequently it is not the case that every motion is commensurable with every other.
248a18 ἐπὶ δὲ τοῦ κύκλου καὶ τῆς εὐθείας πῶς συμβήσεται; ἄτοπόν τε γὰρ εἰ μὴ ἔστιν κύκλῳ ὁμοίως τουτὶ κινεῖσθαι καὶ τουτὶ ἐπὶ τῆς εὐθείας, ἀλλ' εὐθὺς ἀνάγκη ἢ θᾶττον ἢ βραδύτερον, ὥσπερ ἂν εἰ κάταντες, τὸ δ' ἄναντες·	But how will our conclusion work out in the case of the circle and the straight line? It would be absurd to suppose that the motion of one in a circle and of another in a straight line cannot be similar, but that the one must inevitably move more quickly or more slowly than the other, just as if the course of one were downhill and of the other uphill.
248a22 οὐδὲ διαφέρει οὐδὲν τῷ λόγῳ, εἴ τίς φησιν ἀνάγκην εἶναι θᾶττον εὐθὺς ἢ βραδύτερον κινεῖσθαι· ἔσται γὰρ μείζων καὶ ἐλάττων ἡ περιφερὴς τῆς εὐθείας, ὥστε καὶ ἴση. εἰ γὰρ ἐν τῷ Α χρόνῳ (248b.) τὴν Β διελήλυθε τὸ δὲ τὴν Γ, μείζων ἂν εἴη ἡ Β τῆς Γ· οὕτω γὰρ τὸ θᾶττον ἐλέγετο. οὐκοῦν καὶ εἰ ἐν ἐλάττονι ἴσον, θᾶττον· ὥστ' ἔσται τι μέρος τοῦ Α ἐν ᾧ τὸ Β τοῦ κύκλου τὸ ἴσον δίεισι καὶ τὸ Γ ἐν ὅλῳ τῷ Α [τὴν Γ].	Moreover it does not as a matter of fact make any difference to the argument to say that the one motion must inevitably be quicker or slower than the other: for then the circumference can be greater or less than the straight line; and if so it is possible for the two to be equal. For if in the time A the quicker (B) passes over the distance B' and the slower (G) passes over the distance G', B' will be greater than G': for this is what we took 'quicker' to mean: and so quicker motion also implies that one thing traverses an equal distance in less time than another: consequently there will be a part of A in which B will pass over a part of the circle equal to G', while G will occupy the whole of A in passing over G'.
248b4 ἀλλὰ μὴν εἰ ἔστιν συμβλητά, συμβαίνει τὸ ἄρτι ῥηθέν, ἴσην εὐθεῖαν εἶναι κύκλῳ. ἀλλ' οὐ συμβλητά· οὐδ' ἄρα αἱ κινήσεις, ἀλλ' ὅσα μὴ συνώνυμα, πάντ' ἀσύμβλητα.	None the less, if the two motions are commensurable, we are confronted with the consequence stated above, viz. that there may be a straight line equal to a circle. But these are not commensurable: and so the corresponding motions are not commensurable either.
248b6 οἷον διὰ τί οὐ συμβλητὸν πότερον ὀξύτερον τὸ γραφεῖον ἢ ὁ οἶνος ἢ ἡ νήτη; ὅτι ὁμώνυμα, οὐ συμβλητά· ἀλλ' ἡ νήτη τῇ παρανήτῃ συμβλητή, ὅτι τὸ αὐτὸ σημαίνει τὸ ὀξὺ ἐπ' ἀμφοῖν. ἆρ' οὖν οὐ ταὐτὸν τὸ ταχὺ ἐνταῦθα κἀκεῖ, πολὺ δ' ἔτι ἧττον ἐν ἀλλοιώσει καὶ φορᾷ;	But may we say that things are always commensurable if the same terms are applied to them without equivocation? e.g. a pen, a wine, and the highest note in a scale are not commensurable: we cannot say whether any one of them is sharper than any other: and why is this? they are incommensurable because it is only equivocally that the same term 'sharp' is applied to them: whereas the highest note in a scale is commensurable with the leading-note, because the term 'sharp' has the same meaning as applied to both. Can it be, then, that the term 'quick' has not the same meaning as applied to straight motion and to circular motion respectively? If so, far less will it have the same meaning as applied to alteration and to locomotion.
248b12 ἢ πρῶτον μὲν τοῦτο οὐκ ἀληθές, ὡς εἰ μὴ ὁμώνυμα συμβλητά; τὸ γὰρ πολὺ τὸ αὐτὸ σημαίνει ἐν ὕδατι καὶ ἀέρι, καὶ οὐ συμβλητά. εἰ δὲ μή, τό γε διπλάσιον ταὐτό (δύο γὰρ πρὸς ἕν), καὶ οὐ συμβλητά.	Or shall we in the first place deny that things are always commensurable if the same terms are applied to them without equivocation? For the term 'much' has the same meaning whether applied to water or to air, yet water and air are not commensurable in respect of it: or, if this illustration is not considered satisfactory, 'double' at any rate would seem to have the same meaning as applied to each (denoting in each case the proportion of two to one), yet water and air are not commensurable in respect of it.
248b15 ἢ καὶ ἐπὶ τούτων ὁ αὐτὸς λόγος; καὶ γὰρ τὸ πολὺ ὁμώνυμον. ἀλλ' ἐνίων καὶ οἱ λόγοι ὁμώνυμοι, οἷον εἰ λέγοι τις ὅτι τὸ πολὺ τὸ τοσοῦτον καὶ ἔτι, ἄλλο τὸ τοσοῦτον· καὶ τὸ ἴσον ὁμώνυμον, καὶ τὸ ἓν δέ, εἰ ἔτυχεν, εὐθὺς ὁμώνυμον. εἰ δὲ τοῦτο,	But here again may we not take up the same position and say that the term 'much' is equivocal? In fact there are some terms of which even the definitions are equivocal; e.g. if 'much' were defined as 'so much and more','so much' would mean something different in different cases: 'equal' is similarly equivocal; and 'one' again is perhaps inevitably an equivocal term; and if 'one' is equivocal, so is 'two'.
248b21 καὶ τὰ δύο, ἐπεὶ διὰ τί τὰ μὲν συμβλητὰ τὰ δ' οὔ, εἴπερ ἦν μία φύσις;	Otherwise why is it that some things are commensurable while others are not, if the nature of the attribute in the two cases is really one and the same?
248b22 ἢ ὅτι ἐν ἄλλῳ πρώτῳ δεκτικῷ; ὁ μὲν οὖν ἵππος καὶ ὁ κύων συμβλητά, πότερον λευκότερον (ἐν ᾧ γὰρ πρώτῳ, τὸ αὐτό, ἡ ἐπιφάνεια), καὶ κατὰ μέγεθος ὡσαύτως· ὕδωρ δὲ καὶ φωνὴ οὔ· ἐν ἄλλῳ γάρ.	Can it be that the incommensurability of two things in respect of any attribute is due to a difference in that which is primarily capable of carrying the attribute? Thus horse and dog are so commensurable that we may say which is the whiter, since that which primarily contains the whiteness is the same in both, viz. the surface: and similarly they are commensurable in respect of size. But water and speech are not commensurable in respect of clearness, since that which primarily contains the attribute is different in the two cases.
248b25 ἢ δῆλον ὅτι ἔσται οὕτω γε πάντα ἓν ποιεῖν, ἐν ἄλλῳ (249a.) δὲ ἕκαστον φάσκειν εἶναι, καὶ ἔσται ταὐτὸ <τὸ> ἴσον καὶ γλυκὺ καὶ λευκόν, ἀλλ' ἄλλο ἐν ἄλλῳ;	It would seem, however that we must reject this solution, since clearly we could thus make all equivocal attributes univocal and say merely that that contains each of them is different in different cases: thus 'equality', 'sweetness', and 'whiteness' will severally always be the same, though that which contains them is different in different cases.
249a2 ἔτι δεκτικὸν οὐ τὸ τυχὸν <τοῦ τυχόντος> ἐστίν, ἀλλ' ἓν ἑνὸς τὸ πρῶτον.	Moreover, it is not any casual thing that is capable of carrying any attribute: each single attribute can be carried primarily only by one single thing.
249a3 ἀλλ' ἆρα οὐ μόνον δεῖ τὰ συμβλητὰ μὴ ὁμώνυμα εἶναι ἀλλὰ καὶ μὴ ἔχειν διαφοράν, μήτε ὃ μήτε ἐν ᾧ; λέγω δὲ οἷον χρῶμα ἔχει διαί ρεσιν· τοιγαροῦν οὐ συμβλητὸν κατὰ τοῦτο (οἷον πότερον κεχρωμάτισται μᾶλλον, μὴ κατὰ τὶ χρῶμα, ἀλλ' ᾗ χρῶμα), ἀλλὰ κατὰ τὸ λευκόν.	Must we then say that, if two things are to be commensurable in respect of any attribute, not only must the attribute in question be applicable to both without equivocation, but there must also be no specific differences either in the attribute itself or in that which contains the attribute-that these, I mean, must not be divisible in the way in which colour is divided into kinds? Thus in this respect one thing will not be commensurable with another, i.e. we cannot say that one is more coloured than the other where only colour in general and not any particular colour is meant; but they are commensurable in respect of whiteness.
249a8 οὕτω καὶ περὶ κίνησιν ὁμοταχὲς τῷ ἐν ἴσῳ χρόνῳ κινεῖσθαι ἴσον τοσονδί·	Similarly in the case of motion: two things are of the same velocity if they occupy an equal time in accomplishing a certain equal amount of motion.
249a12 εἰ δὴ τοῦ μήκους ἐν τῳδὶ τὸ μὲν ἠλλοιώθη τὸ δ' ἠνέχθη, ἴση ἄρα αὕτη ἡ ἀλλοίωσις καὶ ὁμοταχὴς τῇ φορᾷ; ἀλλ' ἄτοπον. αἴτιον δ' ὅτι ἡ κίνησις ἔχει εἴδη,	Suppose, then, that in a certain time an alteration is undergone by one half of a body's length and a locomotion is accomplished the other half: can be say that in this case the alteration is equal to the locomotion and of the same velocity? That would be absurd, and the reason is that there are different species of motion.
249a13 ὥστ' εἰ τὰ ἐν ἴσῳ χρόνῳ ἐνεχθέντα ἴσον μῆκος ἰσοταχῆ ἔσται, ἴση ἡ εὐθεῖα καὶ ἡ περιφερής.	And if in consequence of this we must say that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference.
249a13 πότερον οὖν αἴτιον, ὅτι ἡ φορὰ γένος ἢ ὅτι ἡ γραμμὴ γένος; ὁ μὲν γὰρ χρόνος ὁ αὐτός, ἂν δὲ τῷ εἴδει ᾖ ἄλλα, καὶ ἐκεῖνα εἴδει διαφέρει. καὶ γὰρ ἡ φορὰ εἴδη ἔχει, ἂν ἐκεῖνο ἔχῃ εἴδη ἐφ' οὗ κινεῖται	What, then, is the reason of this? Is it that locomotion is a genus or that line is a genus? (We may leave the time out of account, since that is one and the same.) If the lines are specifically different, the locomotions also differ specifically from one another: for locomotion is specifically differentiated according to the specific differentiation of that over which it takes place. (It is also similarly differentiated, it would seem, accordingly as the instrument of the locomotion is different:
249a17 (ὁτὲ δὲ ἐὰν ᾧ, οἷον εἰ πόδες, βάδισις, εἰ δὲ πτέρυγες, πτῆσις. ἢ οὔ, ἀλλὰ τοῖς σχήμασιν ἡ φορὰ ἄλλη;).	thus if feet are the instrument, it is walking, if wings it is flying; but perhaps we should rather say that this is not so, and that in this case the differences in the locomotion are merely differences of posture in that which is in motion.)
249a19 ὥστε τὰ ἐν ἴσῳ ταὐτὸ μέγεθος κινούμενα ἰσοταχῆ, τὸ αὐτὸ δὲ καὶ ἀδιάφορον εἴδει καὶ κινήσει ἀδιάφορον· ὥστε τοῦτο σκεπτέον, τίς διαφορὰ κινήσεως.	We may say, therefore, that things are of equal velocity in an equal time they traverse the same magnitude: and when I call it 'the same' I mean that it contains no specific difference and therefore no difference in the motion that takes place over it. So we have now to consider how motion is differentiated:
249a21 καὶ σημαίνει ὁ λόγος οὗτος ὅτι τὸ γένος οὐχ ἕν τι, ἀλλὰ παρὰ τοῦτο λανθάνει πολλά, εἰσίν τε τῶν ὁμωνυμιῶν αἱ μὲν πολὺ ἀπέχουσαι, αἱ δὲ ἔχουσαί τινα ὁμοιότητα, αἱ δ' ἐγγὺς ἢ γένει ἢ ἀναλογίᾳ, διὸ οὐ δοκοῦσιν ὁμωνυμίαι εἶναι οὖσαι.	and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that in the case of equivocal terms sometimes the different senses in which they are used are far removed from one another, while sometimes there is a certain likeness between them, and sometimes again they are nearly related either generically or analogically, with the result that they seem not to be equivocal though they really are.
249a25 πότε οὖν ἕτερον τὸ εἶδος, ἐὰν ταὐτὸ ἐν ἄλλῳ, ἢ ἂν ἄλλο ἐν ἄλλῳ; καὶ τίς ὅρος; ἢ τῷ κρινοῦμεν ὅτι ταὐτὸν τὸ λευκὸν καὶ τὸ γλυκὺ ἢ ἄλλο—ὅτι ἐν ἄλλῳ φαίνεται ἕτερον, ἢ ὅτι ὅλως οὐ ταὐτό;	When, then, is there a difference of species? Is an attribute specifically different if the subject is different while the attribute is the same, or must the attribute itself be different as well? And how are we to define the limits of a species? What will enable us to decide that particular instances of whiteness or sweetness are the same or different? Is it enough that it appears different in one subject from what appears in another? Or must there be no sameness at all?
249a29 περὶ δὲ δὴ ἀλλοιώσεως, πῶς ἔσται ἰσοταχὴς ἑτέρᾳ ἑτέρα; εἰ δή ἐστι τὸ ὑγιάζεσθαι ἀλλοιοῦσθαι, ἔστι τὸν μὲν ταχὺ τὸν δὲ βραδέως ἰαθῆναι, καὶ ἅμα τινάς, ὥστ' (249b.) ἔσται ἀλλοίωσις ἰσοταχής· ἐν ἴσῳ γὰρ χρόνῳ ἠλλοιώθη.	And further, where alteration is in question, how is one alteration to be of equal velocity with another? One person may be cured quickly and another slowly, and cures may also be simultaneous: so that, recovery of health being an alteration, we have here alterations of equal velocity, since each alteration occupies an equal time.
249b2 ἀλλὰ τί ἠλλοιώθη; τὸ γὰρ ἴσον οὐκ ἔστιν ἐνταῦθα λεγόμενον, ἀλλ' ὡς ἐν τῷ ποσῷ ἰσότης, ἐνταῦθα ὁμοιότης.	But what alteration? We cannot here speak of an 'equal' alteration: what corresponds in the category of quality to equality in the category of quantity is 'likeness'.
249b4 ἀλλ' ἔστω ἰσοταχὲς τὸ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ μεταβάλλον.	However, let us say that there is equal velocity where the same change is accomplished in an equal time.
249b5 πότερον οὖν ἐν ᾧ τὸ πάθος ἢ τὸ πάθος δεῖ συμβάλλειν;	Are we, then, to find the commensurability in the subject of the affection or in the affection itself?
249b6 ἐνταῦθα μὲν δὴ ὅτι ὑγίεια ἡ αὐτή, ἔστιν λαβεῖν ὅτι οὔτε μᾶλλον οὔτε ἧττον ἀλλ' ὁμοίως ὑπάρχει. ἐὰν δὲ τὸ πάθος ἄλλο ᾖ, οἷον ἀλλοιοῦται τὸ λευκαινόμενον καὶ τὸ ὑγιαζόμενον, τούτοις οὐδὲν τὸ αὐτὸ οὐδ' ἴσον οὐδ' ὅμοιον, ᾗ ἤδη ταῦτα εἴδη ποιεῖ ἀλλοιώσεως, καὶ οὐκ ἔστι μία ὥσπερ οὐδ' αἱ φοραί. ὥστε ληπτέον πόσα εἴδη ἀλλοιώσεως καὶ πόσα φορᾶς. εἰ μὲν οὖν τὰ κινούμενα εἴδει διαφέρει, ὧν εἰσὶν αἱ κινήσεις καθ' αὑτὰ καὶ μὴ κατὰ συμβεβηκός, καὶ αἱ κινήσεις εἴδει διοίσουσιν· εἰ δὲ γένει, γένει, εἰ δ' ἀριθμῷ, ἀριθμῷ.	In the case that we have just been considering it is the fact that health is one and the same that enables us to arrive at the conclusion that the one alteration is neither more nor less than the other, but that both are alike. If on the other hand the affection is different in the two cases, e.g. when the alterations take the form of becoming white and becoming healthy respectively, here there is no sameness or equality or likeness inasmuch as the difference in the affections at once makes the alterations specifically different, and there is no unity of alteration any more than there would be unity of locomotion under like conditions. So we must find out how many species there are of alteration and of locomotion respectively. Now if the things that are in motion-that is to say, the things to which the motions belong essentially and not accidentally-differ specifically, then their respective motions will also differ specifically: if on the other hand they differ generically or numerically, the motions also will differ generically or numerically as the case may be.
249b14 ἀλλὰ δὴ πότερον εἰς τὸ πάθος δεῖ βλέψαι, ἐὰν ᾖ τὸ αὐτὸ ἢ ὅμοιον, εἰ ἰσοταχεῖς αἱ ἀλλοιώσεις, ἢ εἰς τὸ ἀλλοιούμενον, οἷον εἰ τοῦ μὲν τοσονδὶ λελεύκανται τοῦ δὲ τοσονδί; ἢ εἰς ἄμφω, καὶ ἡ αὐτὴ μὲν ἢ ἄλλη τῷ πάθει, εἰ τὸ αὐτὸ <ἢ μὴ τὸ> αὐτό, ἴση δ' ἢ ἄνισος, εἰ ἐκεῖνο <ἴσον ἢ> ἄνισον;	But there still remains the question whether, supposing that two alterations are of equal velocity, we ought to look for this equality in the sameness (or likeness) of the affections, or in the things altered, to see e.g. whether a certain quantity of each has become white. Or ought we not rather to look for it in both? That is to say, the alterations are the same or different according as the affections are the same or different, while they are equal or unequal according as the things altered are equal or unequal.
249b19 καὶ ἐπὶ γενέσεως δὲ καὶ φθορᾶς τὸ αὐτὸ σκεπτέον. πῶς ἰσοταχὴς ἡ γένεσις; εἰ ἐν ἴσῳ χρόνῳ τὸ αὐτὸ καὶ ἄτομον, οἷον ἄνθρωπος ἀλλὰ μὴ ζῷον· θάττων δ', εἰ ἐν ἴσῳ ἕτερον (οὐ γὰρ ἔχομέν τινα δύο ἐν οἷς ἡ ἑτερότης ὡς ἡ ἀνομοιότης),	And now we must consider the same question in the case of becoming and perishing: how is one becoming of equal velocity with another? They are of equal velocity if in an equal time there are produced two things that are the same and specifically inseparable, e.g. two men (not merely generically inseparable as e.g. two animals). Similarly one is quicker than the other if in an equal time the product is different in the two cases. I state it thus because we have no pair of terms that will convey this 'difference' in the way in which unlikeness is conveyed.
249b23 ἤ, εἰ ἔστιν ἀριθμὸς ἡ οὐσία, πλείων καὶ ἐλάττων ἀριθμὸς ὁμοειδής· ἀλλ' ἀνώνυμον τὸ κοινόν, καὶ τὸ ἑκάτερον [ποιόν· τὸ μὲν ποιόν,] ὥσπερ τὸ πλεῖον πάθος ἢ τὸ ὑπερέχον μᾶλλον, τὸ δὲ ποσὸν μεῖζον.	If we adopt the theory that it is number that constitutes being, we may indeed speak of a 'greater number' and a 'lesser number' within the same species, but there is no common term that will include both relations, nor are there terms to express each of them separately in the same way as we indicate a higher degree or preponderance of an affection by 'more', of a quantity by 'greater.'
Chapter 5 Ἐπεὶ δὲ τὸ κινοῦν κινεῖ τι ἀεὶ καὶ ἔν τινι καὶ μέχρι του (λέγω δὲ τὸ μὲν ἔν τινι, ὅτι ἐν χρόνῳ, τὸ δὲ μέχρι του, ὅτι ποσόν τι μῆκος· ἀεὶ γὰρ ἅμα κινεῖ καὶ κεκίνηκεν, ὥστε ποσόν τι ἔσται ὃ ἐκινήθη, καὶ ἐν ποσῷ),	249b27 Now since wherever there is a movent, its motion always acts upon something, is always in something, and always extends to something (by 'is always in something' I mean that it occupies a time: and by 'extends to something' I mean that it involves the traversing of a certain amount of distance: for at any moment when a thing is causing motion, it also has caused motion, so that there must always be a certain amount of distance that has been traversed and a certain amount of time that has been occupied).
249b30 εἰ δὴ τὸ μὲν Α τὸ κινοῦν, τὸ δὲ Β τὸ κινούμενον, ὅσον δὲ κεκίνηται (250a.) μῆκος τὸ Γ, ἐν ὅσῳ δέ, ὁ χρόνος, ἐφ' οὗ τὸ Δ, ἐν δὴ τῷ ἴσῳ χρόνῳ ἡ ἴση δύναμις ἡ ἐφ' οὗ τὸ Α τὸ ἥμισυ τοῦ Β διπλασίαν τῆς Γ κινήσει, τὴν δὲ τὸ Γ ἐν τῷ ἡμίσει τοῦ Δ· οὕτω γὰρ ἀνάλογον ἔσται.	If, then, A the mover has moved B a distance G in a time D, then in the same time the same force A will move 1/2B twice the distance G, and in 1/2D it will move 1/2B the whole distance for G: thus the rules of proportion will be observed.
250a4 καὶ εἰ ἡ αὐτὴ δύναμις τὸ αὐτὸ ἐν τῳδὶ τῷ χρόνῳ τοσήνδε κινεῖ καὶ τὴν ἡμίσειαν ἐν τῷ ἡμίσει, καὶ ἡ ἡμίσεια ἰσχὺς τὸ ἥμισυ κινήσει ἐν τῷ ἴσῳ χρόνῳ τὸ ἴσον. οἷον τῆς Α δυνάμεως ἔστω ἡμίσεια ἡ τὸ Ε καὶ τοῦ Β τὸ Ζ ἥμισυ· ὁμοίως δὴ ἔχουσι καὶ ἀνάλογον ἡ ἰσχὺς πρὸς τὸ βάρος, ὥστε ἴσον ἐν ἴσῳ χρόνῳ κινήσουσιν.	Again if a given force move a given weight a certain distance in a certain time and half the distance in half the time, half the motive power will move half the weight the same distance in the same time. Let E represent half the motive power A and Z half the weight B: then the ratio between the motive power and the weight in the one case is similar and proportionate to the ratio in the other, so that each force will cause the same distance to be traversed in the same time.
250a9 καὶ εἰ τὸ Ε τὸ Ζ κινεῖ ἐν τῷ Δ τὴν Γ, οὐκ ἀνάγκη ἐν τῷ ἴσῳ χρόνῳ τὸ ἐφ' οὗ Ε τὸ διπλάσιον τοῦ Ζ κινεῖν τὴν ἡμίσειαν τῆς Γ·	But if E move Z a distance G in a time D, it does not necessarily follow that E can move twice Z half the distance G in the same time.
250a12 εἰ δὴ τὸ Α τὴν τὸ Β κινεῖ ἐν τῷ Δ ὅσην ἡ τὸ Γ, τὸ ἥμισυ τοῦ Α τὸ ἐφ' ᾧ Ε τὴν τὸ Β οὐ κινήσει ἐν τῷ χρόνῳ ἐφ' ᾧ τὸ Δ οὐδ' ἔν τινι τοῦ Δ τι τῆς Γ ἀνάλογον πρὸς τὴν ὅλην τὴν Γ ὡς τὸ Α πρὸς τὸ Ε· ὅλως γὰρ εἰ ἔτυχεν οὐ κινήσει οὐδέν· οὐ γὰρ εἰ ἡ ὅλη ἰσχὺς τοσήνδε ἐκίνησεν, ἡ ἡμίσεια οὐ κινήσει οὔτε ποσὴν οὔτ' ἐν ὁποσῳοῦν· εἷς γὰρ ἂν κινοίη τὸ πλοῖον, εἴπερ ἥ τε τῶν νεωλκῶν τέμνεται ἰσχὺς εἰς τὸν ἀριθμὸν καὶ τὸ μῆκος ὃ πάντες ἐκίνησαν.	If, then, A move B a distance G in a time D, it does not follow that E, being half of A, will in the time D or in any fraction of it cause B to traverse a part of G the ratio between which and the whole of G is proportionate to that between A and E (whatever fraction of AE may be): in fact it might well be that it will cause no motion at all; for it does not follow that, if a given motive power causes a certain amount of motion, half that power will cause motion either of any particular amount or in any length of time: otherwise one man might move a ship, since both the motive power of the ship-haulers and the distance that they all cause the ship to traverse are divisible into as many parts as there are men.
250a19 διὰ τοῦτο ὁ Ζήνωνος λόγος οὐκ ἀληθής, ὡς ψοφεῖ τῆς κέγχρου ὁτιοῦν μέρος· οὐδὲν γὰρ κωλύει μὴ κινεῖν τὸν ἀέρα ἐν μηδενὶ χρόνῳ τοῦτον ὃν ἐκίνησεν πεσὼν ὁ ὅλος μέδιμνος. οὐδὲ δὴ τοσοῦτον μόριον, ὅσον ἂν κινήσειεν τοῦ ὅλου εἰ εἴη καθ' αὑτὸ τοῦτο, οὐ κινεῖ. οὐδὲ γὰρ οὐδὲν ἔστιν ἀλλ' ἢ δυνάμει ἐν τῷ ὅλῳ.	Hence Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such a quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially.
250a25 εἰ δὲ τὰ <κινοῦντα> δύο, καὶ ἑκάτερον τῶνδε ἑκάτερον κινεῖ τὸ τοσόνδε ἐν τοσῷδε, καὶ συντιθέμεναι αἱ δυνάμεις τὸ σύνθετον ἐκ τῶν βαρῶν τὸ ἴσον κινήσουσιν μῆκος καὶ ἐν ἴσῳ χρόνῳ· ἀνάλογον γάρ.	If on the other hand we have two forces each of which separately moves one of two weights a given distance in a given time, then the forces in combination will move the combined weights an equal distance in an equal time: for in this case the rules of proportion apply.
250a28 ἆρ' οὖν οὕτω καὶ ἐπ' ἀλλοιώσεως καὶ ἐπ' αὐξήσεως; τὶ μὲν γὰρ τὸ αὖξον, τὶ δὲ τὸ αὐξανόμενον, ἐν ποσῷ δὲ χρόνῳ καὶ ποσὸν τὸ μὲν αὔξει τὸ δὲ αὐξάνεται. καὶ τὸ ἀλλοιοῦν καὶ τὸ ἀλλοιούμενον ὡσαύτως—τὶ καὶ ποσὸν (250b.) κατὰ τὸ μᾶλλον καὶ ἧττον ἠλλοίωται, καὶ ἐν ποσῷ χρόνῳ, ἐν διπλασίῳ διπλάσιον,	Then does this hold good of alteration and of increase also? Surely it does, for in any given case we have a definite thing that cause increase and a definite thing that suffers increase, and the one causes and the other suffers a certain amount of increase in a certain amount of time. Similarly we have a definite thing that causes alteration and a definite thing that undergoes alteration, and a certain amount, or rather degree, of alteration is completed in a certain amount of time:
250b2 καὶ τὸ διπλάσιον ἐν διπλασίῳ· τὸ δ' ἥμισυ ἐν ἡμίσει χρόνῳ (ἢ ἐν ἡμίσει ἥμισυ), ἢ ἐν ἴσῳ διπλάσιον.	thus in twice as much time twice as much alteration will be completed and conversely twice as much alteration will occupy twice as much time: and the alteration of half of its object will occupy half as much time and in half as much time half of the object will be altered: or again, in the same amount of time it will be altered twice as much.
250b4 εἰ δὲ τὸ ἀλλοιοῦν ἢ αὖξον τὸ τοσόνδε ἐν τῷ τοσῷδε αὔξει ἢ ἀλλοιοῖ, οὐκ ἀνάγκη καὶ τὸ ἥμισυ ἐν ἡμίσει καὶ ἐν ἡμίσει ἥμισυ, ἀλλ' οὐδέν, εἰ ἔτυχεν, ἀλλοιώσει ἢ αὐξήσει, ὥσπερ καὶ ἐπὶ τοῦ βάρους.	On the other hand if that which causes alteration or increase causes a certain amount of increase or alteration respectively in a certain amount of time, it does not necessarily follow that half the force will occupy twice the time in altering or increasing the object, or that in twice the time the alteration or increase will be completed by it: it may happen that there will be no alteration or increase at all, the case being the same as with the weight.