§7.1#2ἔστι γὰρ κίνησις καὶ γένει καὶ εἴδει καὶ ἀριθμῷ ἡ αὐτή, 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·
For motion can be the same in genus, in species, and in number. Those same in genus are of the same category, as substance or quality; those same in species are from what is the same in species to what is the same in species, as from white to black, or from good to bad, where there is no difference in species; those same in number are from what is one in number to what is one in number, occurring in the same time, as from this white to this black, or from this place to that place, in this time.
εἰ γὰρ ἐν ἄλλῳ, οὐκέτι ἔσται ἀριθμῷ μία κίνησις, ἀλλʼ εἴδει.
For if it occurs in another time, it will no longer be one in number, but only in species.
εἴρηται δὲ περὶ τούτων ἐν τοῖς πρότερον.
But these things have been discussed in our earlier works.
εἰλήφθω δὲ καὶ ὁ χρόνος ἐν
κεκίνηται τὴν αὑτοῦ κίνησιν τὸ Α, καὶ ἔστω ἐφʼ ᾧ Κ. πεπερασμένης δʼ οὔσης τῆς τοῦ Α κινήσεως καὶ ὁ χρόνος ἔσται πεπερασμένος.
And let the time also be taken in which A has performed its own motion, and let it be represented by K. Since the motion of A is finite, the time also will be finite.
ἐπεὶ δὴ ἄπειρα τὰ κινοῦντα καὶ τὰ κινούμενα, καὶ ἡ κίνησις ἡ ΕΖΗΘ ἡ ἐξ ἁπασῶν ἄπειρος ἔσται·
Since, then, the movers and the things moved are infinite, the motion EZHΘ, which is made up of all of them, will also be infinite.
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.
For it is possible that the motion of A, of B, and of the others should be equal, and it is possible that the motions of the others should be greater, so that whether they are equal or greater, in both cases the whole motion is infinite; for we assume what is possible.
ἐπεὶ δʼ 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 δʼ ἀδύνατον.
And since both A and each of the others are in motion simultaneously, the whole motion will occur in the same time as the motion of A; but the motion of A is in a finite time, so that there would be an infinite motion in a finite time, which is impossible.
οὕτω
μὲν οὖν δόξειεν ἂν δεδεῖχθαι τὸ ἐξ ἀρχῆς, οὐ μὴν ἀποδείκνυται διὰ τὸ μηδὲν δείκνυσθαι ἀδύνατον·
In this way, then, the original thesis might seem to have been demonstrated; yet it is not actually proved, because nothing impossible is demonstrated.
ἐνδέχεται γὰρ ἐν πεπερασμένῳ χρόνῳ ἄπειρον εἶναι κίνησιν, μὴ ἑνὸς ἀλλὰ πολλῶν.
For it is possible that in a finite time there should be an infinite motion, not of one thing but of many.
ὅπερ συμβαίνει καὶ ἐπὶ τούτων· ἕκαστον γὰρ κινεῖται τὴν ἑαυτοῦ κίνησιν, ἅμα δὲ πολλὰ κινεῖσθαι οὐκ ἀδύνατον.
And this is indeed what happens in these cases; for each is performing its own motion, and it is not impossible for many things to be in motion simultaneously.
ἀλλʼ 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, ὥστʼ εἶναί τι ἐξ ἁπάντων ἕν.
But if that which moves primarily in respect of place and bodily motion must either touch or be continuous with that which is moved, as we see in all cases, then the things moved and the movers must be continuous with or touch one another, so that there is some one thing made up of all of them.
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.
Whether this is finite or infinite makes no difference for our present purpose; for in any case the motion will be infinite since the things are infinite, if indeed they can be equal to or greater than one another; for what is possible we shall assume as actual.
εἰ οὖν τὸ μὲν ἐκ τῶν ΑΒΓΔ ἢ πεπερασμένον ἢ ἄπειρόν τί ἐστιν, κινεῖται δὲ τὴν ΕΖΗΘ κίνησιν ἐν τῷ χρόνῳ τῷ Κ, οὗτος δὲ πεπέρανται, συμβαίνει ἐν πεπερασμένῳ χρόνῳ πειρον διιέναι ἢ τὸ πεπερασμένον ἢ τὸ ἄπειρον.
If, then, the thing composed of ABCD is either finite or some infinite thing, and it performs the motion EZHΘ in the time K, and this time is finite, it follows that in a finite time either the finite or the infinite traverses the infinite.
ἀμφοτέρως δὲ ἀδύνατον· ὥστε ἀνάγκη ἵστασθαι καὶ εἶναί τι πρῶτον κινοῦν καὶ κινούμενον.
But in both ways this is impossible; so that there must be a stop, and there must be some first mover and thing moved.
οὐδὲν γὰρ διαφέρει τὸ συμβαίνειν ἐξ ὑποθέσεως τὸ ἀδύνατον· ἡ γὰρ ὑπόθεσις εἴληπται ἐνδεχομένη, τοῦ δʼ ἐνδεχομένου τεθέντος οὐὐὲν προσήκει γίγνεσθαι διὰ τοῦτο ἀδύνατον.
For it makes no difference that the impossible follows from a hypothesis; for the hypothesis has been assumed as possible, and when a possibility is posited, no impossible consequence ought to result because of it.