ἅμα δέ πως ἐπιστήσας καὶ διαλιπών οἷον εἶπον ὦ Εὔστροφε, πεπόνθαμεν, ὀλίγου παρελθόντες τὸν Ὅμηρον, ὡς οὐχὶ πρῶτον εἰς πέντε νείμαντα μερίδας τὸν κόσμον, ὃς τὰς μὲν ἐν μέσῳ τρεῖς ἀποδέδωκε τοῖς τρισὶ θεοῖς, δύο δὲ τὰς ἄκρας ὄλυμπον καὶ γῆν, ὧν ἡ μέν ἐστι τῶν κάτω πέρας ἡ δὲ τῶν ἄνω, κοινὰς καὶ ἀνεμήτους ἀφῆκεν. ἀλλʼ ἀνοιστέος ὁ λόγος ὡς Εὐριπίδης φησίν. οἱ γὰρ τὴν τετράδα σεμνύναντες οὐ φαύλως διδάσκουσιν, ὅτι τῷ ταύτης λόγῳ πᾶν σῶμα γένεσιν ἔσχηκεν. ἐπεὶ γὰρ ἐν μήκει καὶ πλάτει βάθος λαβόντι πᾶν τὸ στερεόν ἐστι, καὶ μήκους μὲν προϋφίσταται στιγμὴ κατὰ μονάδα ταττομένη, μῆκος δʼ ἀπλατὲς ἡ γραμμὴ καλεῖται καὶ μῆκος ἐστιν, ἡ δʼ ἐπὶ πλάτος γραμμῆς κίνησις ἐπιφανείας γένεσιν ἐν τριάδι παρέσχε, βάθους δὲ τούτοις προσγενομένου διὰ τεττάρων εἰς στερεὸν ἡ αὔξησις προβαίνει· παντὶ δῆλον, ὅτι μέχρι δεῦρο τὴν φύσιν ἡ τετρὰς προαγαγοῦσα, μέχρι τοῦ σῶμα τελειῶσαι καὶ παρασχεῖν ἁπτὸν ὄγκον καὶ ἀντίτυπον, εἶτʼ ἀπολέλοιπεν ἐνδεᾶ τοῦ μεγίστου. τὸ γὰρ ἄψυχον ὡς ἁπλῶς εἰπεῖν ὀρφανὸν καὶ ἀτελὲς καὶ πρὸς οὐδʼ ὁτιοῦν, μὴ χρωμένης ψυχῆς, ἐπιτήδειον· ἡ δὲ τὴν ψυχὴν ἐμποιοῦσα κίνησις ἢ διάθεσις, μεταβολῇ διὰ πέντε γιγνομένη, τῇ φύσει τὸ τέλειον ἀποδίδωσι, καὶ τοσούτῳ κυριώτερον ἔχει τῆς τετράδος λόγον, ὅσῳ τιμῇ διαφέρει τοῦ ἀψύχου τὸ ζῷον. ἔτι δʼ ἰσχύσασα μᾶλλον ἡ τῶν πέντε συμμετρία καὶ δύναμις οὐκ εἴασεν εἰς ἄπειρα γένη προελθεῖν τὸ ἔμψυχον, ἀλλὰ πέντε τῶν ζώντων ἁπάντων ἰδέας παρέσχεν. εἰσὶ γὰρ θεοὶ δήπου καὶ δαίμονες καὶ ἥρωες καὶ μετὰ τούτους τὸ τέταρτον ἄνθρωποι γένος, ἔσχατον δὲ καὶ πέμπτον τὸ ἄλογον καὶ θηριῶδες;. ἔτι δʼ εἰ τὴν ψυχὴν αὐτὴν κατὰ φύσιν διαιροῖς, πρῶτον αὐτῆς καὶ ἀμαυρότατόν ἐστι τὸ θρεπτικὸν δεύτερον δὲ τὸ αἰσθητικὸν, εἶτα τὸ ἐπιθυμητικὸν εἶτʼ ἐπὶ τούτῳ τὸ θυμοειδές· εἰς δὲ τὴν τοῦ λογιστικοῦ δύναμιν ἐξικομένη καὶ τελεώσασα τὴν φύσιν ὥσπερ ἐν ἄκρῳ τῷ πέμπτῳ καταπέπαυται.
Having here stopped a little, and made a small pause between, I said: What a fault, O Eustrophus, were we like to have committed, having almost passed by Homer, as if he were not the first that distributed the world into five parts, who assigned the three which are in the midst to three Gods, and left the two extremes, Olympus and the Earth—of which one is the limit of things above, the other of things below—common and undistributed. But we must, as Euripides says, return to our discourse. For those who magnify the quaternary, or number of four, teach not amiss, that every solid body had its generation by reason of this. For since every solid consists in length and breadth, having withal a depth; and since before length there is extant a point, answerable to unity, and length without breadth is called a line and consists of two; and the motion of a line towards breadth exhibits also the procreation of a superficies in the number three; and the argumentation of this, when depth is added to it, goes on to a solid in the number four; it is manifest to every one, that the quaternary, having carried on Nature hitherto, and even to the perfecting of a body and the exhibiting it tangible, massy, and solid, has yet at last left it wanting the greatest accomplishment. For that which is inanimate is, to speak sincerely, orphan-like, imperfect, and fit for nothing at all, unless there is some soul to use it; but the motion or disposition introducing a soul, being a change made by the number five, adds the consummation to Nature, and has a reason so much more excellent than the quaternary, as an animal differs in dignity from that which is inanimate. Moreover, the symmetry and power of this number five, having obtained greater force, has not permitted the animate body to proceed to infinite sorts, but has exhibited five species of all things that have life. For there are Gods, Genii, and heroes, and then after them the fourth sort is men, and the fifth and last the irrational and brutish animal. Furthermore, if you divide the soul itself according to its nature, its first and most obscure part or faculty is the vegetative, the second the sensitive, then the concupiscible, after that the irascible; and having brought on and perfected Nature in the faculty of the rational, it rests in this fifth, as in the top of all.
τοσαύτας δὲ καὶ τηλικαύτας ἔχοντος τοῦ ἀριθμοῦ δυνάμεις, καλὴ καὶ ἡ γένεσίς ἐστιν, οὐχ ἣν ἤδη διήλθομεν, ἐκ δυάδος οὖσα καὶ τριάδος, ἀλλʼ ἣν ἡ ἀρχὴ τῷ πρώτῳ συνελθοῦσα τετραγώνῳ παρέσχεν. ἀρχὴ μὲν γὰρ ἀριθμοῦ παντὸς ἡ μονάς, τετράγωνος δὲ πρῶτος ἡ τετράς ἐκ δὲ τούτων, ὥσπερ ἰδέας καὶ ὕλης πέρας ἐχούσης, ἡ πεμπάς. εἰ δὲ δὴ καὶ τὴν μονάδα τετράγωνον ὀρθῶς ἔνιοι τίθενται, δύναμιν οὖσαν ἑαυτῆς καὶ περαίνουσαν εἰς ἑαυτήν, ἐκ δυεῖν πεφυκυῖα τῶν πρώτων τετραγώνων ἡ πεμπὰς οὐκ ἀπολέλοιπεν ὑπερβολὴν εὐγενείας.
Now the generation of this number, which has so many and so great faculties, is also beautiful,—not that which we have already discoursed of, from two and three, but that which the first principle joined with the first square has exhibited. For the principle of all number is unity, and the first square is the quaternary; now the quinary is composed of these, as of form and of matter which has attained to perfection. And if it is right, which some hold, that unity is also square, as being the power of itself and terminating in itself; the quinary, being made of the first two squares, could not have a more noble original.
τὸ δὲ μέγιστον ἔφην δέδια μὴ ῥηθὲν πιέζῃ τὸν Πλάτωνα ἡμῶν, ὡς ἐκεῖνος ἔλεγε πιέζεσθαι τῷ τῆς σελήνης ὀνόματι τὸν Ἀναξαγόραν, παμπάλαιον οὖσαν τινα τὴν περὶ τῶν φωτισμῶν δόξαν αὑτοῦ, ἰδίαν ποιούμενον. ἦ γὰρ οὐ ταῦτʼ εἴρηκεν ἐν Κρατύλῳ; πάνυ μὲν οὖν ὁ Εὔστροφος ἔφη, τί δʼ ὅμοιον πέφυκεν οὐ συνορῶ. καὶ μὴν οἶσθα δήπουθεν, ὅτι πέντε μὲν ἐν Σοφιστῇ τὰς κυριωτάτας· ἀποδείκνυσιν ἀρχάς, τὸ ὂν τὸ ταὐτὸν τὸ ἕτερον, τέταρτον δὲ καὶ πέμπτον ἐπὶ τούτοις κίνησιν καὶ στάσιν. ἄλλῳ δʼ αὖ τρόπῳ διαιρέσεως ἐν Φιλήβῳ χρώμενος, ἓν μὲν εἶναί φησι τὸ ἄπειρον ἕτερον δὲ τὸ πέρας· τούτων δὲ μιγνυμένων πᾶσαν συνίστασθαι γένεσιν. αἰτίαν δʼ, ὑφʼ ἧς μίγνυται, τέταρτον γένος τίθεται· καὶ πέμπτον ἡμῖν ὑπονοεῖν ἀπολέλοιπεν, ᾧ τὰ μιχθέντα πάλιν ἴσχει διάκρισιν καὶ διάστασιν. τεκμαίρομαι δὲ ταῦτʼ ἐκείνων ὥσπερ εἰκόνας λέγεσθαι, τοῦ μὲν ὄντος τὸ γιγνόμενον, κινήσεως δὲ τὸ ἄπειρον, τὸ δὲ πέρας τῆς στάσεως, ταὐτοῦ δὲ τὴν μιγνύουσαν ἀρχήν, θατέρου δὲ τὴν διακρίνουσαν. εἰ δʼ ἕτερα ταῦτʼ ἐστί, κἀκείνως ἂν εἴη καὶ οὕτως ἐν πέντε γένεσι καὶ διαφοραῖς. πυθόμενος, φήσει δή τις, ταῦτα πρότερος συνιδὼν Πλάτωνος, δύο Ε καθιέρωσε τῷ θεῷ, δήλωμα καὶ σύμβολον τοῦ ἀριθμοῦ τῶν πάντων ἀλλὰ μὴν καὶ τἀγαθὸν ἐν πέντε γένεσι φανταζόμενον κατανοήσας, ὧν πρῶτόν ἐστι τὸ μέτριον δεύτερον δὲ τὸ σύμμετρον, καὶ τρίτον ὁ νοῦς καὶ τέταρτον αἱ περὶ ψυχὴν ἐπιστῆμαι καὶ τέχναι καὶ δόξαι ἀληθεῖς, πέμπτον εἴ τις ἡδονὴ καθαρὰ καὶ πρὸς τὸ λυποῦν ἄκρατος, ἐνταῦθα λήγει τὸ Ὀρφικὸν ὑπειπών ἕκτῃ δʼ ἐν γενεῇ καταπαύσατε θεσμὸν ἀοιδῆς.
But as for its greatest excellency, I fear, lest being spoken it should press our Plato as much as he himself said Anaxagoras was pressed by the name of the moon, when he made a certain opinion concerning her illuminations, which was very ancient, to be an invention of his own. For has he not said this in his dialogue entitled Cratylus?
Yes indeed, answered Eustrophus; but I see not any thing that has fallen out like it. And yet you know, that in the Sophister he demonstrates five principal beginnings, to wit, that which is, or Ens (τὸ ὄν), the Same, the Different, adding to these, for a fourth and fifth, Motion, and Rest. Again, in his dialogue called Philebus, using another manner of division, he says, that there is one thing Infinite, and another the End; and that all generation consists of these two mixed together. Then he puts the cause by which they are mixed for the fourth kind; and has left us to conjecture the fifth, by which the things that were mixed have again a division and dissipation. Now I am of opinion that these last are delivered as the images or representations of those before,—to wit, the things engendered of Ens, the Infinite of Motion, the End of Rest, the Mixing Principle of the Same, and the Separating Principle of the Different. But if these are different from those, yet both that way and this way these principles are still distinguished into five kinds and differences. Now some one, said he, being persuaded of these things and seeing them before Plato, consecrated to the God two E E, for a mark and symbol of the number of all things. And having perhaps further understood that good also appears in five kinds, of which the first is the mean, the second the commensurate, the third understanding, the fourth the sciences, arts, and true opinions in the soul, and the fifth a certain pleasure, pure and unmixed with sorrow; he stops there, subjoining that of Orpheus: In the sixth age stay your desire of singing.
ἐπὶ τούτοις ἔφην εἰρημένοις πρὸς ὑμᾶς ἓν βραχύ τοῖς περὶ Νίκανδρον ἀείσω ξυνετοῖσι τῇ γὰρ ἕκτῃ τοῦ νέου μηνὸς ὅταν κατάγῃ εἷς τὴν Πυθίαν εἰς τὸ πρυτανεῖον, ὁ πρῶτος ὑμῖν γίγνεται τῶν τριῶν κλήρων εἰς, τὰ πέντε, πρὸς ἀλλήλους ἐκείνης τὰ τρία τοῦ δὲ τὰ δύο βάλλοντες. ἦ γὰρ οὐχ οὕτως ἔχει; καὶ ὁ Νίκανδρος οὕτως εἶπεν ἡ δʼ αἰτία πρὸς ἑτέρους ἄρρητός ἐστι. οὐκοῦν ἔφην ἐγὼ μειδιάσας ἄχρι οὗ τἀληθὲς; ἡμῖν ὁ θεὸς ἱεροῖς γενομένοις γνῶναι παράσχῃ, προσκείσεται καὶ τοῦτο τοῖς ὑπὲρ τῆς πεμπάδος λεγομένοις. τοιοῦτο μὲν καὶ ὁ τῶν ἀριθμητικῶν καὶ ὁ τῶν μαθηματικῶν ἐγκωμίων τοῦ Ε λόγος, ὡς ἐγὼ μέμνημαι, πέρας ἔσχεν.
After what I have spoken to you, I said, Yet one short word to those about Nicander, I’ll sing to men of skill. For on the sixth day of the new moon, when you introduce the Pythia into the Prytaneum, the first of the three lots tends with you towards five, casting neither three, nor two, one to another. For is not this so?
It is so, said Nicander; but the cause is not to be told to others.
Well then, said I smiling, till such time as the God admits us, being consecrated, to know the truth, this also shall be added to those things that have been spoken concerning the quinary. This end, as I remember, had the discourse of the arithmetical and mathematical encomiums of E.
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