§6.6#1Ἐπεὶ δὲ τὸ μεταβάλλον ἅπαν ἐν χρόνῳ μεταβάλλει, λέγεται δʼ ἐν χρόνῳ μεταβάλλειν καὶ ὡς ἐν πρώτῳ καὶ ὡς καθʼ ἕτερον, οἷον ἐν τῷ ἐνιαυτῷ ὅτι ἐν τῇ ἡμέρᾳ μεταβάλλει, ἐν πρώτῳ χρόνῳ μεταβάλλει τὸ μεταβάλλον, ἐν ὁτῳοῦν ἀνάγκη τούτου μεταβάλλειν.
Since everything that changes changes in time, and changing in time is spoken of both as in a first [time] and as in respect of another (for instance, changing in a year because it changes in a day), when the changing thing changes in a first time, it must change in any part of this whatsoever.
δῆλον μὲν οὖν καὶ ἐκ τοῦ ὁρισμοῦ (τὸ γὰρ πρῶτον οὕτως ἐλέγομεν, οὐ μὴν ἀλλὰ καὶ ἐκ τῶνδε φανερόν.
This, then, is clear from the definition (for we used to mean "first" in this way), but it is also manifest from the following.
ἔστω γὰρ ἐν ᾧ πρώτῳ κινεῖται τὸ κινούμενον ἐφʼ ᾧ XP, καὶ διῃρήσθω κατὰ τὸ Κ· πᾶς γὰρ χρόνος διαιρετός.
For let the first time in which the moving thing moves be XP, and let it be divided at K; for all time is divisible.
ἐν δὴ τῷ ΧΚ χρόνῳ ἤτοι κινεῖται ἢ οὐ κινεῖται, καὶ πάλιν ἐν τῷ KP ὡσαύτως.
Now in the time XK it either moves or does not move, and likewise again in KP.
εἰ μὲν οὖν ἐν μηδετέρῳ κινεῖται, ἠρεμοίη ἂν ἐν τῷ παντί (κινεῖσθαι γὰρ ἐν μηθενὶ τῶν τούτου κινούμενον ἀδύνατον)· εἰ δʼ ἐν θατέρῳ μόνῳ κινεῖται, οὐκ ἂν ἐν πρώτῳ κινοῖτο τῷ ΧΡ· καθʼ ἕτερον γὰρ ἡ κίνησις.
If, then, it moves in neither, it would be at rest in the whole (for it is impossible for a moving thing to move in none of its parts); but if it moves in only one of the two parts, it would not be moving in XP as the first; for its motion is in respect of another.
ἀνάγκη ἄρα ἐν ὁτῳοῦν τοῦ ΧΡ κινεῖσθαι. δεδει.
Therefore, it must be moving in any part of XP whatsoever.
γμένου δὲ τούτου φανερὸν ὅτι πᾶν τὸ κινούμενον ἀνάγκη κεχινῆσθαι πρότερον.
This having been proved, it is manifest that everything that moves must have moved prior.
εἰ γὰρ ἐν τῷ XP πρώτῳ χρόνῳ τὸ ΚΛ κεκίνηται μέγεθος, ἐν τῷ ἡμίσει τὸ ὁμοταχῶς κινούμενον καὶ ἅμα ἀρξάμενον τὸ ἣμισυ ἔσται κεκινημένον.
For if in the first time XP it has moved [through] magnitude KL, in half the time another thing moving at equal speed and having started at the same time will have moved [through] half [the magnitude].
εἰ δὲ τὸ ὁμοταχὲς ἐν τῷ αὐτῷ χρόνῳ κεκίνηταί τι, καὶ θάτερον ἀνάγκη ταὐτὸ κεκινῆσθαι μέγεθος, ὥστε κεκινημένον ἔσται τὸ κινούμενον.
And if that which moves at equal speed has moved some amount in the same time, the other also must have moved the same magnitude, so that the moving thing will have moved.
ἔτι δὲ εἰ ἐν τῷ παντὶ χρόνῳ τῷ XP κεκινῆσθαι λέγομεν, ἢ ὅλως ἐν ὁτῳοῦν χρόνῳ, τῷ λαβεῖν τὸ ἔσχατον αὐτοῦ νῦν (τοῦτο γάρ ἐστι τὸ ὁρίζον, καὶ τὸ μεταξὺ τῶν νῦν χρόνος, κἂν ἐν τοῖς ἄλλοις ὁμοίως λέγοιτο κεκινῆσθαι.
Moreover, if we say that it has moved in the whole time XP, or generally in any time whatsoever, by taking its last "now" (for this is what limits it, and what is between the "nows" is time), then in other [times] also it would likewise be said to have moved.
τοῦ δʼ ἡμίσεος ἔσχατον ἡ διαίρεσις.
But the limit of the half is the division.
ὥστε καὶ ἐν τῷ ἡμίσει κεκινημένον ἔσται καὶ ὅλως ἐν ὁτῳοῦν τῶν μερῶν· ἀεὶ γὰρ ἅμα τῇ τομῇ χρόνος ἔστιν ὡρισμένος ὑπὸ τῶν νῦν.
Consequently, it will also have moved in the half, and generally in any of its parts whatsoever; for along with the division there is always a time limited by "nows".
εἰ οὖν ἅπας μὲν χρόνος διαιρετός, τὸ δὲ μεταξὺ τῶν νῦν χρόνος, ἅπαν τὸ μεταβάλλον ἄπειρα ἔσται μεταβεβληκός.
If, therefore, all time is divisible, and what is between the "nows" is time, everything that changes will have changed infinitely many times.
ἔτι δʼ εἰ τὸ συνεχῶς μεταβάλλον καὶ μὴ φθαρὲν μηδὲ πεπαυμένον τῆς μεταβολῆς ἢ μεταβάλλειν ἢ μεταβεβληκέναι ἀναγκαῖον ἐν ὁτῳοῦν, ἐν δὲ τῷ νῦν οὐκ ἔστιν μεταβάλλειν, ἀνάγκη μεταβεβληκέναι καθʼ ἕκαστον τῶν νῦν· ὥστʼ εἰ τὰ νῦν ἄπειρα, πᾶν τὸ μεταβάλλον ἄπειρα ἔσται μεταβεβληκὔς.
Moreover, if that which is continuously changing and has not perished nor ceased from change must either be changing or have changed in any [time] whatsoever, and it is not possible to be changing in the "now", it must have changed at each of the "nows"; consequently, if the "nows" are infinite, everything that changes will have changed infinitely many times.
οὐ μόνον δὲ τὸ μεταβάλλον ἀνάγκη μεταβεβληκέναι,
ἀλλὰ καὶ τὸ μεταβεβληκὸς ἀνάγκη μεταβάλλειν πρότερον· ἅπαν γὰρ τὸ ἔκ τινος εἴς τι μεταβεβληκὸς ἐν χρόνῳ μεταβέβληκεν.
And not only must that which is changing have changed, but also that which has changed must have been changing prior; for everything that has changed from something to something has changed in time.