§6.5#1Επεὶ δὲ πᾶν τὸ μεταβάλλον ἔκ τινος εἴς τι μεταβάλλει, ἀνάγκη τὸ μεταβεβληκός, ὅτε πρῶτον μεταβέβληκεν, εἶναι ἐν μεταβέβληκεν.
And since everything that changes changes from something to something, it is necessary that that which has changed, when it has first changed, is in that into which it has changed.
τὸ γὰρ μεταβάλλον, ἐξ οὗ μεταβάλλει, ἐξίσταται ἢ ἀπολείπει αὐτό, καὶ ἤτοι ταὐτόν ἐστι τὸ μεταβάλλειν καὶ τὸ ἀπολείπειν, ἢ ἀκολουθεῖ τῷ μεταβάλλειν τὸ ἀπολείπειν.
For that which changes departs from or leaves that from which it changes, and either changing and leaving are the same, or leaving follows upon changing.
εἰ δὲ τῷ μεταβάλλειν τὸ ἀπολείπειν, τῷ μεταβεβληκέναι τὸ ἀπολελοιπέναι· ὁμοίως γὰρ ἑκάτερον ἔχει πρὸς ἑκάτερον.
But if leaving follows upon changing, having left follows upon having changed; for each stands in a similar relation to each.
ἐπεὶ οὖν μία τῶν μεταβολῶν ἡ κατʼ ἀντίφασιν, ὅτε μεταβέβληκεν ἐκ τοῦ υὴ ὄντος εἰς τὸ ὄν, ἀπολέλοιπεν τὸ μὴ ὄν.
Since, then, one of the changes is that according to contradiction, when a thing has changed from non-being to being, it has left non-being.
ἔσται ἄρα ἐν τῷ ὄντι· πᾶν γὰρ ἀνάγκη ἢ εἶναι ἢ μὴ εἶναι.
It will therefore be in being; for everything must either be or not be.
φανερὸν οὖν ὅτι ἐν τῇ κατʼ ἀντίφασιν μεταβολῇ τὸ μεταβεβληκὸς ἔσται ἐν ᾧ μεταβέβληκεν.
It is manifest, therefore, that in change according to contradiction that which has changed will be in that into which it has changed.
εἰ δʼ ἐν ταύτῃ, καὶ ἐν ταῖς ἄλλαις· ὁμοίως γὰρ ἐπὶ μιᾶς καὶ τῶν ἄλλων.
And if in this, also in the others; for it is similar in the case of one and of the others.
ἔτι δὲ καὶ καθʼ ἑκάστην λαμβάνο??σι φανερόν, εἴπερ ἀνάγκη τὸ μεταβεβληκὸς εἶναί που ἢ ἔν τινι.
Moreover, it is also manifest to those who take each change individually, if indeed it is necessary that that which has changed must be somewhere or in something.
ἐπεὶ γὰρ ἐξ οὗ μεταβέβληκεν ἀπολέλοιπεν, ἀνάγκη δʼ εἶναί που, ἢ ἐν τούτῳ ἢ ἐν ἄλλῳ ἔσται.
For since it has left that from which it has changed, and it must be somewhere, it will be either in this or in something else.
εἰ μὲν οὖν ἐν ἄλλῳ, οἷον ἐν τῷ Γ, τὸ εἰς τὸ B μεταβεβληκός, πάλιν ἐκ τοῦ Γ μεταβάλλει εἰς τὸ Β· οὐ γὰρ ἦν ἐχόμενον τὸ B, ἡ δὲ μεταβολὴ συνεχής.
If, then, that which has changed into B is in something else, for instance in Γ, it is changing again from Γ into B; for Γ was not adjacent to B, and the change is continuous.
ὥστε τὸ μεταβεβληκός, ὅτε μεταβέβληκεν, μεταβάλλει εἰς ὃ μεταβέβληκεν.
Consequently, that which has changed, at the moment when it has changed, is changing into that into which it has changed.
τοῦτο δʼ ἀδύνατον· ἀνάγκη ἄρα τὸ μεταβεβληκὸς εἶναι ἐν τούτῳ εἰς ὃ μεταβέβληκεν.
But this is impossible; it is necessary, therefore, that that which has changed is in that into which it has changed.
φανερὸν οὖν ὅτι καὶ τὸ γεγονός, ὅτε γέγονεν, ἔσται, καὶ τὸ ἐφθαρμένον οὐκ ἔσται· καθόλου τε γὰρ εἴρηται περὶ πάσης μεταβολῆς, καὶ μάλιστα δῆλον ἐν τῇ κατʼ ἀντίφασιν.
It is manifest, therefore, that also that which has come to be, when it has come to be, will be, and that which has passed away will not be; for this has been said universally of all change, and is most of all manifest in change according to contradiction.
ὅτι
μὲν τοίνυν τὸ μεταβεβληκός, ὅτε μεταβέβληκε πρῶτον, ἐν ἐκείνῳ ἐστίν, δῆλον· ἐν ᾧ δὲ πρώτῳ μεταβέβληκεν τὸ μεταβεβληκός, ἀνάγκη ἄτομον εἶναι.
That, then, that which has changed, when it has first changed, is in that, is manifest; but that in which first that which has changed has changed must be indivisible.
λέγω δὲ πρῶτον ὃ μὴ τῷ ἕτερόν τι αὐτοῦ εἶναι τοιοῦτόν ἐστιν.
And by 'first' I mean that which is such not by virtue of some other part of it being such.
ἔστω γὰρ διαιρετὸν τὸ ΑΓ, καὶ διῃρήσθω κατὰ τὸ B. εἰ μὲν οὖν ἐν τῷ ΑΒ μετα·
For let AC be divisible, and let it be divided at B.
βέβληκεν ἢ πάλιν ἐν τῷ ΒΓ, οὐκ ἂν ἐν πρώτῳ τῷ ΑΓ μεταβεβληκὸς εἴη.
If, then, it has changed in AB, or again in BC, it would not have changed in AC as the first.
εἰ δʼ ἐν ἑκατέρῳ μετέβαλλεν (ἀνάγκη γὰρ ἢ μεταβεβληκέναι ἢ μεταβάλλειν ἐν ἑκατέρῳ, κἂν ἐν τῷ ὅλῳ μεταβάλλοι· ἀλλʼ ἦν μεταβεβληκός.
But if it was changing in each (for it must either have changed or be changing in each), it would also be changing in the whole; but it was assumed to have changed.
ὁ αὐτὸς δὲ λό. γος καὶ εἰ ἐν τῷ μὲν μεταβάλλει, ἐν δὲ τῷ μεταβέβληκεν· ἔσται γάρ τι τοῦ πρώτου πρότερον· ὥστʼ οὐκ ἂν εἴη διαιρετὸν ἐν ᾧ μεταβέβληκεν.
And the same argument holds also if it is changing in the one part and has changed in the other; for there will be something prior to the first; so that that in which it has changed cannot be divisible.
φανερὸν οὖν ὅτι καὶ τὸ ἐφθαρμένον καὶ τὸ γεγονὸς ἐν ἀτόμῳ τὸ μὲν ἔφθαρται τὸ δὲ γέγονεν.
It is manifest, therefore, that both that which has passed away and that which has come to be have passed away and come to be in an indivisible moment.