§53ΤΙ. τὰ δὲ κινούμενα ἄλλα ἄλλοσε ἀεὶ φέρεσθαι διακρινόμενα, ὥσπερ τὰ ὑπὸ τῶν πλοκάνων τε καὶ ὀργάνων τῶν περὶ τὴν τοῦ σίτου κάθαρσιν σειόμενα καὶ ἀνικμώμενα τὰ μὲν πυκνὰ καὶ βαρέα ἄλλῃ, τὰ δὲ μανὰ καὶ κοῦφα εἰς ἑτέραν ἵζει φερόμενα ἕδραν·
TI. And the things in motion, being separated, were carried in different directions, just as the things shaken and winnowed by fans and other instruments used for the cleaning of corn; the dense and heavy particles settle in one place, while the rare and light are carried to another seat.
τότε οὕτω τὰ τέτταρα γένη σειόμενα ὑπὸ τῆς δεξαμενῆς, κινουμένης αὐτῆς οἷον ὀργάνου σεισμὸν παρέχοντος, τὰ μὲν ἀνομοιότατα πλεῖστον αὐτὰ ἀφʼ αὑτῶν ὁρίζειν, τὰ δὲ ὁμοιότατα μάλιστα εἰς ταὐτὸν συνωθεῖν, διὸ δὴ καὶ χώραν ταῦτα ἄλλα ἄλλην ἴσχειν, πρὶν καὶ τὸ πᾶν ἐξ αὐτῶν διακοσμηθὲν γενέσθαι.
At that time, in this way, the four classes being shaken by the receptacle, which itself moved like an instrument that provides shaking, separated the most dissimilar elements furthest from one another, and pushed the most similar closest together; and for this very reason, these elements came to occupy different spaces even before the universe was formed and decorated out of them.
καὶ τὸ μὲν δὴ πρὸ τούτου πάντα ταῦτʼ εἶχεν ἀλόγως καὶ ἀμέτρως·
Indeed, before this, all these things were in an irrational and measureless condition.
ὅτε δʼ ἐπεχειρεῖτο κοσμεῖσθαι τὸ πᾶν, πῦρ πρῶτον καὶ ὕδωρ καὶ γῆν καὶ ἀέρα, ἴχνη μὲν ἔχοντα αὑτῶν ἄττα, παντάπασί γε μὴν διακείμενα ὥσπερ εἰκὸς ἔχειν ἅπαν ὅταν ἀπῇ τινος θεός, οὕτω δὴ τότε πεφυκότα ταῦτα πρῶτον διεσχηματίσατο εἴδεσί τε καὶ ἀριθμοῖς.
But when the ordering of the universe was undertaken, fire first, and water, earth, and air—possessing indeed some traces of themselves, yet being in every way in such a state as is natural for everything to be when god is absent—being then by nature in this state, he first fashioned them with forms and numbers.
τὸ δὲ ᾗ δυνατὸν ὡς κάλλιστα ἄριστά τε ἐξ οὐχ οὕτως ἐχόντων τὸν θεὸν αὐτὰ συνιστάναι, παρὰ πάντα ἡμῖν ὡς ἀεὶ τοῦτο λεγόμενον ὑπαρχέτω·
And that god constructed them to be as beautiful and best as possible from what was not in that state, let this remain as our constant premise in everything we say.
νῦν δʼ οὖν τὴν διάταξιν αὐτῶν ἐπιχειρητέον ἑκάστων καὶ γένεσιν ἀήθει λόγῳ πρὸς ὑμᾶς δηλοῦν, ἀλλὰ γὰρ ἐπεὶ μετέχετε τῶν κατὰ παίδευσιν ὁδῶν διʼ ὧν ἐνδείκνυσθαι τὰ λεγόμενα ἀνάγκη, συνέψεσθε.
But now, I must attempt to explain to you the disposition and generation of each of them by an unusual argument; yet, since you participate in those educational paths through which it is necessary to demonstrate what is said, you will follow.
πρῶτον μὲν δὴ πῦρ καὶ γῆ καὶ ὕδωρ καὶ ἀὴρ ὅτι σώματά ἐστι, δῆλόν που καὶ παντί· τὸ δὲ τοῦ σώματος εἶδος πᾶν καὶ βάθος ἔχει.
First, then, that fire, earth, water, and air are bodies is clear to everyone; and every form of body also possesses depth.
τὸ δὲ βάθος αὖ πᾶσα ἀνάγκη τὴν ἐπίπεδον περιειληφέναι φύσιν· ἡ δὲ ὀρθὴ τῆς ἐπιπέδου βάσεως ἐκ τριγώνων συνέστηκεν.
And depth, in turn, must of necessity contain flat surfaces; and the straight base of a flat surface is composed of triangles.
τὰ δὲ τρίγωνα πάντα ἐκ δυοῖν ἄρχεται τριγώνοιν, μίαν μὲν ὀρθὴν ἔχοντος ἑκατέρου γωνίαν, τὰς δὲ ὀξείας·
Now all triangles start from two triangles, each having one right angle and the others acute.
ὧν τὸ μὲν ἕτερον ἑκατέρωθεν ἔχει μέρος γωνίας ὀρθῆς πλευραῖς ἴσαις διῃρημένης, τὸ δʼ ἕτερον ἀνίσοις ἄνισα μέρη νενεμημένης.
One of these has on each side a part of a right angle divided by equal sides (isosceles right triangle); the other has it distributed into unequal parts by unequal sides (scalene right triangle).
ταύτην δὴ πυρὸς ἀρχὴν καὶ τῶν ἄλλων σωμάτων ὑποτιθέμεθα κατὰ τὸν μετʼ ἀνάγκης εἰκότα λόγον πορευόμενοι· τὰς δʼ ἔτι τούτων ἀρχὰς ἄνωθεν θεὸς οἶδεν καὶ ἀνδρῶν ὃς ἂν ἐκείνῳ φίλος ᾖ.
This we hypothesize as the principle of fire and of the other bodies, proceeding according to the probable account accompanied by necessity; but the principles still higher than these are known to god and to whichever of men is friendly to him.
δεῖ δὴ λέγειν ποῖα κάλλιστα σώματα γένοιτʼ ἂν τέτταρα, ἀνόμοια μὲν ἑαυτοῖς, δυνατὰ δὲ ἐξ ἀλλήλων αὐτῶν ἄττα διαλυόμενα γίγνεσθαι·
We must then state what are the four most beautiful bodies that could be generated, unlike one another, yet capable of being generated from one another when some of them are dissolved.
τούτου γὰρ τυχόντες ἔχομεν τὴν ἀλήθειαν γενέσεως πέρι γῆς τε καὶ πυρὸς τῶν τε ἀνὰ λόγον ἐν μέσῳ.
For if we succeed in this, we shall have the truth about the generation of earth and fire and the intermediate elements in proportion.
τόδε γὰρ οὐδενὶ συγχωρησόμεθα, καλλίω τούτων ὁρώμενα σώματα εἶναί που καθʼ ἓν γένος ἕκαστον ὄν.
For we will not concede to anyone that there are any more beautiful visible bodies than these, each existing as a single class.
τοῦτʼ οὖν προθυμητέον, τὰ διαφέροντα κάλλει σωμάτων τέτταρα γένη συναρμόσασθαι καὶ φάναι τὴν τούτων ἡμᾶς φύσιν ἱκανῶς εἰληφέναι.
Therefore, we must be eager to harmonize these four classes of bodies that excel in beauty, and to assert that we have adequately grasped their nature.