§6.5#2λέγεται δὲ τὸ ἐν ᾧ πρώτῳ μεταβέβληκε διχῶς, τὸ
μὲν ἐν ᾧ πρώτῳ ἐπετελέσθη ἡ μεταβολή (τότε γὰρ ἀληθὲς εἰπεῖν ὅτι μεταβέβληκεν, τὸ δʼ ἐν ᾧ πρώτῳ ἤρξατο μεταβάλλειν.
"That in which first it has changed" is spoken of in two ways: on the one hand, the first [time] in which the change was completed (for then it is true to say that it has changed); on the other hand, the first [time] in which it began to change.
τὸ μὲν οὖν κατὰ τὸ τέλος τῆς μεταβολῆς πρῶτον λεγόμενον ὑπάρχει τε καὶ ἔστιν (ἐνδέχεται γὰρ ἐπιτελεσθῆναι μεταβολὴν καὶ ἔστι μεταβολῆς τέλος, ὃ δὴ καὶ δέδεικται ἀδιαίρετον ὄν διὰ τὸ πέρας εἶναι)· τὸ δὲ κατὰ τὴν ἀρχὴν ὅλως οὐκ ἔστιν· οὐ γὰρ ἔστιν ἀρχὴ μεταβολῆς, οὐδʼ ἐν πρώτῳ τοῦ χρόνου μετέβαλλεν.
Now, that which is called first in respect of the end of the change exists and is (for it is possible for a change to be completed, and there is an end of change, which indeed has been shown to be indivisible because it is a limit); but that which is called first in respect of the beginning does not exist at all; for there is no beginning of change, nor was there a first part of time in which it was changing.
ἔστω γὰρ πρῶτον ἐφʼ ᾧ τὸ ΑΔ. τοῦτο δὴ ἀδιαίρετον μὲν οὐκ ἔστιν·
For let the first [time] be AD.
συμβήσεται γὰρ ἐχόμενα εἶναι τὰ νῦν.
This is indeed not indivisible; for it would follow that the "nows" are adjacent.
ἔτι δʼ εἰ ἐν τῷ ΓΑ χρόνῳ παντὶ ἠρεμεῖ (κείσθω γὰρ ἠρεμοῦν, καὶ ἐν τῷ Α ἠρεμεῖ, ὥστʼ εἰ ἀμερές ἐστι τὸ ΑΔ, ἅμα ἠρεμήσει καὶ μεταβεβληκὸς ἔσται· ἐν μὲν γὰρ τῷ Α ἠρεμεῖ, ἐν δὲ τῷ Δ μεταβέβληκεν.
Moreover, if it is at rest during the whole time CA (for let it be assumed to be at rest, and it is also at rest at A), so that if AD is partless, it will be at rest and have changed at the same time; for at A it is at rest, and at D it has changed.
ἐπεὶ δʼ οὐκ ἔστιν ἀμερές, ἀνάγκη διαιρετὸν εἶναι καὶ ἐν ὁτῳοῦν τῶν τούτου μεταβεβληκέναι·
But since it is not partless, it must be divisible and have changed in any part of it whatsoever.
διαιρεθέντος γὰρ τοῦ ΑΔ, εἰ μὲν ἐν μηδετέρῳ μεταβέβληκεν, οὐδʼ ἐν τῷ ὅλῳ· εἰ δʼ ἐν ἀμφοῖν μεταβάλλει καὶ ἐν τῷ παντί, εἴτʼ ἐν θατέρῳ μεταβέβληκεν, οὐκ ἐν τῷ ὅλῳ πρώτῳ.
For when AD is divided, if it has changed in neither part, it has not changed in the whole either; but if it is changing in both parts, it is also changing in the whole; and if it has changed in one of the two parts, it has not changed in the whole as the first.
ὥστε ἀνάγκη ἐν ὁτῳοῦν μεταβεβληκέναι.
Consequently, it must have changed in any part of it whatsoever.
φανερὸν τοίνυν ὅτι οὐκ ἔστιν ἐν πρώτῳ μεταβέβληκεν· ἄπειροι γὰρ αἱ διαιρέσεις.
It is manifest, therefore, that there is no first [time] in which it has changed; for the divisions are infinite.
οὐδὲ δὴ τοῦ μεταβεβληκότος ἔστιν τι πρῶτον ὃ μεταβέβληκεν.
Nor, indeed, of that which has changed is there any first part that has changed.
ἔστω γὰρ τὸ ΔΖ πρῶτον μεταβεβληκὸς τοῦ ΔΕ· πᾶν γὰρ δέδεικται διαιρετὸν τὸ μεταβάλλον.
For let ΔZ be the first part of ΔE that has changed; for everything that changes has been shown to be divisible.
ὁ δὲ χρόνος ἐν ᾧ τὸ ΔΖ μεταβέβληκεν ἔστω ἐφʼ ᾧ ΘΙ. εἰ οὖν ἐν τῷ παντὶ τὸ ΔΖ μεταβέβληκεν ἐν τῷ ἡμίσει ἔλαττον ἔσται τι μεταβεβληκὸς καὶ πρότερον τοῦ ΔΖ, καὶ πάλιν τούτου ἄλλο, κἀκείνου ἕτερον, καὶ αἰεὶ οὕτως.
And let the time in which ΔZ has changed be ΘI. If, then, ΔZ has changed in the whole time, in half the time there will be some smaller part that has changed, and prior to ΔZ; and again another part prior to this, and another prior to that, and always so.
ὥστʼ οὐθὲν ἔσται πρῶτον τοῦ μεταβάλλοντος ὃ μεταβέβληκεν.
Consequently, there will be no first part of the changing thing that has changed.
ὅτι μὲν οὖν οὔτε τοῦ μεταβάλλοντος οὔτʼ ἐν ᾧ μεταβάλλει
χρόνῳ πρῶτον οὐθέν ἐστιν, φανερὸν ἐκ τῶν εἰρημένων·
That, then, there is no first part either of the changing thing or of the time in which it changes, is manifest from what has been said.
αὐτὸ δὲ ὃ μεταβάλλει ἢ καθʼ ὃ μεταβάλλει, οὐκέθʼ ὁμοίως ἕξει.
But the changing thing itself, or that in respect of which it changes, will no longer be in a similar case.
τρία γάρ ἐστιν ἃ λέγεται κατὰ τὴν μεταβολήν, τό τε μεταβάλλον καὶ ἐν καὶ εἰς ὃ μεταβάλλει, οἷον ὁ ἄνθρωπος καὶ ὁ χρόνος καὶ τὸ λευκόν.
For there are three things spoken of in connection with change: that which changes, that in which it changes, and that into which it changes, for example, the man, the time, and the white.
ὁ μὲν οὖν ἄνθρωπος καὶ ὁ χρόνος διαιρετοί, περὶ δὲ τοῦ λευκοῦ ἄλλος λόγος.
The man and the time are divisible, but concerning the white there is another argument.
πλὴν κατὰ συμβεβηκός γε πάντα διαιρετά· ᾧ γὰρ συμβέβηκεν τὸ λευκὸν ἢ τὸ ποιόν, ἐκεῖνο διαιρετόν ἐστιν·
Except, indeed, that accidentally all things are divisible; for that to which the white or the quality belongs is divisible.
ἐπεὶ ὅσα γε καθʼ αὐτὰ λέγεται διαιρετὰ καὶ μὴ κατὰ συμβεβηκός, οὐδʼ ἐν τούτοις ἔσται τὸ πρῶτον, οἷον ἐν τοῖς μεγέθεσιν.
But in the case of those things which are said to be divisible in themselves and not accidentally, there will not be a first in these either, for instance in magnitudes.
ἔστω γὰρ τὸ ἐφʼ ΑΒ μέγεθος, κεκινήσθω δʼ ἐκ τοῦ B εἰς τὸ Γ πρῶτον.
For let the magnitude be AB, and let it have moved from B to Γ as the first.
οὐκοῦν εἰ μὲν ἀδιαίρετον ἔσται τὸ ΒΓ, ἀμερὲς ἀμεροῦς ἔσται ἐχόμενον· εἰ δὲ διαιρετόν, ἔσται τι τοῦ Γ πρότερον, εἰς ὃ μεταβέβληκεν, κἀκείνου πάλιν ἄλλο, καὶ ἀεὶ οὕτως διὰ τὸ μηδέποτε ὑπολείπειν τὴν διαίρεσιν.
If, then, BΓ is indivisible, a partless thing will be adjacent to a partless thing; but if it is divisible, there will be something prior to Γ into which it has changed, and again another prior to that, and always so because the division never fails.
ὥστʼ οὐκ ἔσται πρῶτον εἰς ὃ μεταβέβληκεν.
Consequently, there will be no first into which it has changed.
ὁμοίως δὲ καὶ ἐπὶ τῆς τοῦ ποσοῦ μεταβολῆς· καὶ γὰρ αὕτη ἐν συνεχεῖ ἐστιν.
And likewise also in the case of change of quantity; for this also is in a continuous thing.
φανερὸν οὖν ὅτι ἐν μόνῃ τῶν κινήσεων τῇ κατὰ τὸ ποιὸν ἐνδέχεται ἀδιαίρετον καθʼ αὑτὸ εἶναι.
It is manifest, therefore, that only in the case of change of quality is it possible for there to be something indivisible in itself.