§7.1#1Ἅπαν τὸ κινούμενον ὑπό τινος ἀνάγκη κινεῖσθαι·
Everything that is in motion must be moved by something.
εἰ μὲν γὰρ ἐν ἑαυτῷ μὴ ἔχει τὴν ἀρχὴν τῆς κινήσεως. φανερὸν ὅτι ὑφ’ ἑτέρου κινεῖται (ἄλλο γὰρ ἔσται τὸ κινοῦν)· εἰ δʼ ἐν αὐτῶ, ἔστω εἰλημμένον ἐφʼ οὗ τὸ AB ὃ κινεῖται καθʼ αὑτό, ἀλλὰ μὴ τῷ τῶν τούτου τι κινεῖσθαι.
For if it does not have the source of motion in itself, it is clear that it is moved by something else (for that which moves it will be something else); but if it is in itself, let there be taken that which is represented by AB, which moves of itself, and not by the fact that some part of it moves.
πρῶτον μὲν οὖν τὸ ὑπολαμβάνειν τὸ AB ὑφʼ ἑαυτοῦ κινεῖσθαι διὰ τὸ ὅλον τε κινεῖσθαι καὶ ὑπʼ 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·
First of all, then, to suppose that AB is moved by itself because the whole is in motion and is moved by none of the things outside is like as if, when KL moves LM and is itself in motion, one were to deny that KM is moved by anything, on the ground that it is not obvious which is the mover and which is the thing moved.
εἶτα τὸ μὴ ὑπό τινος κινούμενον οὐκ ἀνάγκη παύσασθαι κινούμενον τῷ ἄλλο ἠρεμεῖν, ἀλλʼ εἴ τι ἠρεμεῖ τῷ ἄλλο πεπαῦσθαι κινούμενον, ἀνάγκη ὑπό τινος αὐτὸ κινεῖσθαι, τούτου δʼ εἰλημμένου πᾶν τὸ κινούμενον κινήσεται ὑπό τινος.
Secondly, that which is not moved by something does not necessarily cease from being in motion because something else is at rest; but if something is at rest because something else has ceased to be in motion, it must be moved by something. If this is assumed, everything that is in motion will be moved by something.
ἐπεὶ γὰρ εἴληπται κινούμενον ἐφʼ ᾧ τὸ AB, ἀνάγκη διαιρετὸν αὐτὸ εἶναι· πᾶν γὰρ τὸ κινούμενον διαιρετόν.
For since AB has been taken as being in motion, it must be divisible; for everything that is in motion is divisible.
διῃρήσθω δὴ κατὰ τὸ Γ. τοῦ δὴ ΓΒ μὴ κινουμένου οὐ κινηθήσεται τὸ ΑΒ·
Let it, then, be divided at C.
εἰ γὰρ κινήσεται, δῆλον ὅτι τὸ ΑΓ κινοῖτ᾿ ἂν τοῦ ΓΒ ἠρεμοῦντος, ὥστε οὐ καθʼ αὐτὸ κινηθήσεται καὶ πρῶτον.
Now if CB is not in motion, AB will not be in motion; for if it is in motion, it is clear that AC would be in motion while CB is at rest, so that it will not be in motion of itself and primarily.
ἀλλʼ ὑπέκειτο καθʼ αὑτὸ κινεῖσθαι καὶ πρῶτον.
But it was assumed to be in motion of itself and primarily.
ἀνάγκη ἄρα τοῦ ΓΒ μὴ κινουμένου ἠρεμεῖν τὸ AB. ὃ δὲ ἠρεμεῖ 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.
Therefore, if CB is not in motion, AB must be at rest. But that which is at rest when something is not in motion is agreed to be moved by something; so that everything that is in motion must be moved by something; for that which is in motion will always be divisible, and if the part is not in motion, the whole also must be at rest.
ἐπεὶ δὲ πᾶν τὸ κινούμενον
ἀνάγκη κινεῖσθαι ὑπό τινος, ἐόν γέ τι κινῆται τὴν ἐν τόπῳ κίνησιν ὑπʼ ἄλλου κινουμένου, καὶ πάλιν τὸ κινοῦν ὑπ᾿ ἄλλου κινουμένου κινῆται κἀκεῖνο ὑφʼ ἑτέρου καὶ ἀεὶ οὕτως, ἀνάγκη εἶναί τι τὸ πρῶτον κινοῦν, καὶ μὴ βαδίζειν εἰς ἄπειρον· μὴ γὰρ ἔστω, ἀλλὰ γενέσθω ἄπειρον.
And since everything that is in motion must be moved by something, if indeed anything is moved with the motion in place by something that is itself moved by another, and that mover again is moved by another that is in motion, and that by another, and so on always, there must be some first mover, and no regression to infinity; for let it not be so, but let it proceed to infinity.
κινείσθω δὴ τὸ μὲν Α ὑπὸ τοῦ Β. τὸ δὲ Β ὑπὸ τοῦ Γ, τὸ δὲ Γ ὑπὸ τοῦ Δ, καὶ ἀεὶ τὸ ἐχ όμενον ὑπὸ τοῦ ἐχομένου.
Let A, then, be moved by B, B by C, C by D, and always the contiguous by the contiguous.
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)·
Since, then, the mover is assumed to cause motion while being in motion, the motion of the thing moved and that of the mover must occur simultaneously (for the mover moves and the thing moved is moved simultaneously).
φανερὸν ⟨οὖν⟩ ὅτι ἅμα ἔσται τοῦ Α καὶ τοῦ Β καὶ τοῦ Γ καὶ ἑκάστου τῶν κινούντων καὶ κινουμένων ἡ κίνησις.
It is clear, then, that the motion of A, of B, of C, and of each of the movers and things moved will be simultaneous.
εἰλήφθω οὖν ἡ ἑκάστου κίνησις, καὶ ἔστω τοῦ μὲν Α ἐφ᾿ ἧς Ε, τοῦ δὲ Β ἐφʼ ἧς Ζ, τῶν δὲ ΓΔ ἐφ᾿ ὧν ΗΘ. εἰ γὰρ ἀεὶ κινεῖται ἕκαστον ὑφʼ ἑκάστου, ὅμως ἔσται λαβεῖν μίαν ἑκάστου κίνησιν τῷ ἀριθμῷ· πᾶσα γὰρ κίνησις ἔκ τινος εἴς τι, καὶ οὐκ ἄπειρος τοῖς ἐσχάτοις·
Let the motion of each, then, be taken, and let that of A be E, that of B be Z, and those of CD be H and Θ. For even if each is always moved by each, nevertheless it will be possible to take one motion of each, which is one in number; for every motion is from something to something, and is not infinite in its extremes.
λέγω δὴ ἀριθμῷ μίαν κίνησιν τὴν ἐκ τοῦ αὐτοῦ εἰς τὸ αὐτὸ τῷ ἀριθμῷ ἐν τῷ αὐτῷ χρόνῳ τῷ ἀριθμῷ γιγνομένην.
By a motion one in number I mean that which proceeds from the same to the same in number, and occurs in the same time in number.