§158καὶ μὴν καὶ περὶ τοῦ μορίου γε ἑκάστου ὁ αὐτὸς λόγος· καὶ γὰρ τοῦτο ἀνάγκη μετέχειν τοῦ ἑνός.
And indeed, the same argument holds also concerning each part; for this too must participate in the one.
εἰ γὰρ ἕκαστον αὐτῶν μόριόν ἐστι, τό γε ἕκαστον εἶναι ἓν δήπου σημαίνει, ἀφωρισμένον μὲν τῶν ἄλλων, καθʼ αὑτὸ δὲ ὄν, εἴπερ ἕκαστον ἔσται. ὀρθῶς.
For if each of them is a part, "being each" surely signifies being one, separated from the others and being by itself, if indeed it is to be "each." Correct.
μετέχοι δέ γε ἂν τοῦ ἑνὸς δῆλον ὅτι ἄλλο ὂν ἢ ἕν· οὐ γὰρ ἂν μετεῖχεν, ἀλλʼ ἦν ἂν αὐτὸ ἕν.
But it would participate in the one, clearly, as being other than one; for otherwise it would not participate, but would be the one itself.
νῦν δὲ ἑνὶ μὲν εἶναι πλὴν αὐτῷ τῷ ἑνὶ ἀδύνατόν που.
But as it is, for anything except the one itself to be one is, I suppose, impossible.
ἀδύνατον.
Impossible.
μετέχειν δέ γε τοῦ ἑνὸς ἀνάγκη τῷ τε ὅλῳ καὶ τῷ μορίῳ.
But both the whole and the part must participate in the one.
τὸ μὲν γὰρ ἓν ὅλον ἔσται, οὗ μόρια τὰ μόρια· τὸ δʼ αὖ ἕκαστον ἓν μόριον τοῦ ὅλου, ὃ ἂν ᾖ μόριον ὅλου.
For the one will be a whole, of which the parts are parts; and each, on the other hand, will be one part of the whole, of whatever whole it is a part.
οὕτως.
Thus.
οὐκοῦν ἕτερα ὄντα τοῦ ἑνὸς μεθέξει τὰ μετέχοντα αὐτοῦ;
Then the things participating in the one will participate as being other than the one?
πῶς δʼ οὔ;
How could they not?
τὰ δʼ ἕτερα τοῦ ἑνὸς πολλά που ἂν εἴη· εἰ γὰρ μήτε ἓν μήτε ἑνὸς πλείω εἴη τἆλλα τοῦ ἑνός, οὐδὲν ἂν εἴη.
But the things other than the one would, I suppose, be many; for if the others than the one were neither one nor more than one, they would be nothing.
οὐ γὰρ οὖν.
Indeed they would.
ἐπεὶ δέ γε πλείω ἑνός ἐστι τά τε τοῦ ἑνὸς μορίου καὶ τὰ τοῦ ἑνὸς ὅλου μετέχοντα, οὐκ ἀνάγκη ἤδη πλήθει ἄπειρα εἶναι αὐτά γε ἐκεῖνα τὰ μεταλαμβάνοντα τοῦ ἑνός;
But since the things participating in the part of the one and in the whole of the one are more than one, is it not already necessary that those very things which take part in the one are infinite in multitude?
πῶς;
How?
ὧδε ἴδωμεν.
Let us look at it this way.
ἄλλο τι οὐχ ἓν ὄντα οὐδὲ μετέχοντα τοῦ ἑνὸς τότε, ὅτε μεταλαμβάνει αὐτοῦ, μεταλαμβάνει;
Do they not take part in it at that time when they take part, being other than one and not yet participating in the one?
δῆλα δή.
Clearly so.
οὐκοῦν πλήθη ὄντα, ἐν οἷς τὸ ἓν οὐκ ἔνι;
Are they not, then, multitudes in which the one is not present?
πλήθη μέντοι.
Multitudes, indeed.
τί οὖν;
What then?
εἰ ἐθέλοιμεν τῇ διανοίᾳ τῶν τοιούτων ἀφελεῖν ὡς οἷοί τέ ἐσμεν ὅτι ὀλίγιστον, οὐκ ἀνάγκη καὶ τὸ ἀφαιρεθὲν ἐκεῖνο, εἴπερ τοῦ ἑνὸς μὴ μετέχοι, πλῆθος εἶναι καὶ οὐχ ἕν;
If we should wish to subtract in thought from such things the very least we can, must not that which is subtracted, if it does not participate in the one, also be a multitude and not one?
ἀνάγκη.
It is necessary.
οὐκοῦν οὕτως ἀεὶ σκοποῦντες αὐτὴν καθʼ αὑτὴν τὴν ἑτέραν φύσιν τοῦ εἴδους ὅσον ἂν αὐτῆς ἀεὶ ὁρῶμεν ἄπειρον ἔσται πλήθει;
Then, by always looking in this way at the other nature of the form itself by itself, will not as much of it as we always see be infinite in multitude?
παντάπασι μὲν οὖν.
Absolutely.
καὶ μὴν ἐπειδάν γε ἓν ἕκαστον μόριον μόριον γένηται, πέρας ἤδη ἔχει πρὸς ἄλληλα καὶ πρὸς τὸ ὅλον, καὶ τὸ ὅλον πρὸς τὰ μόρια.
And indeed, when each part becomes one part, they already have a limit in relation to one another and to the whole, and the whole in relation to the parts.
κομιδῇ μὲν οὖν.
Quite so.
τοῖς ἄλλοις δὴ τοῦ ἑνὸς συμβαίνει ἐκ μὲν τοῦ ἑνὸς καὶ ἐξ ἑαυτῶν κοινωνησάντων, ὡς ἔοικεν, ἕτερόν τι γίγνεσθαι ἐν ἑαυτοῖς, ὃ δὴ πέρας παρέσχε πρὸς ἄλληλα· ἡ δʼ ἑαυτῶν φύσις καθʼ ἑαυτὰ ἀπειρίαν.
Thus, for the others than the one, it turns out that, from the association of the one and themselves, as it seems, something else arises in them, which indeed provides a limit in relation to one another; whereas their own nature, by itself, provides infinity.
φαίνεται.
It seems so.
οὕτω δὴ τὰ ἄλλα τοῦ ἑνὸς καὶ ὅλα καὶ κατὰ μόρια ἄπειρά τέ ἐστι καὶ πέρατος μετέχει.
Thus, indeed, the others than the one, both as wholes and by parts, are both infinite and participate in limit.
πάνυ γε.
Quite so.
οὐκοῦν καὶ ὅμοιά τε καὶ ἀνόμοια ἀλλήλοις τε καὶ ἑαυτοῖς;
Are they not, then, both like and unlike to one another and to themselves?
πῇ δή;
In what way, then?
ἧι μέν που ἄπειρά ἐστι κατὰ τὴν ἑαυτῶν φύσιν πάντα, ταὐτὸν πεπονθότα ἂν εἴη ταύτῃ.
Insofar, I suppose, as they are all infinite according to their own nature, in this respect they would have experienced the same thing.
πάνυ γε.
Quite so.
καὶ μὴν ᾗ γε ἅπαντα πέρατος μετέχει, καὶ ταύτῃ πάντʼ ἂν εἴη ταὐτὸν πεπονθότα.
And indeed, insofar as they all participate in limit, in this respect too they would all have experienced the same thing.
πῶς δʼ οὔ;
How could they not?