regarding the explanation of the Platonic psychogony, this we now discharge for you as a kind of debt. For Plato's statement that the division of these seven circles occurred "according to the double and triple interval," "each of the intervals being three of either kind," is somewhat difficult as regards the wording, but nevertheless signifies that the division occurred according to each interval of the double and triple intervals, there being three of either kind (for in four terms there are three intervals), which is the same as "along the length," so that in each of the seven circles all the intervals and all the ratios are present; for according to the number of the double and triple intervals, being six, he cut the circles in six ways. These things being presupposed, we say (and the argument is Greek) that the soul of the universe, having the principles of all things within the cosmos, has prior to these also the principles of the whole parts of the cosmos, I mean, of the sphere of the fixed stars and of the wandering sphere, whence the circle of the Different of the seven circles has comprehended within itself the primary causes. 11 But if someone should ask why a proper circle of Substance has not come into being as one of Sameness and of Difference, we shall resolve it, that of these there is an opposition, but substance is common to the whole soul. The Pythagorean doctrine says that the division into six is most proper to the soul, they who assign by analogy the monad to a point, the dyad to a line, the triad to a plane, the tetrad to a body, the pentad to the qualified, the hexad to the ensouled, and the heptad to the intellectual. The remainder, however, was demonstrated to you mathematically earlier in the letter. And there is such a thing also in the universe; for from each of the spheres certain effluences descend to the regions under the earth and certain mixed dregs of the elements themselves, having much that is disorderly and dark and material, but nevertheless contributing to the whole composition and harmony of the cosmos. Plato, positing the cause of these things in the whole soul, has called it a remainder, which is indeed significant of the lowest nature. And the rank of souls in relation to daimonic beings holds the rank of the remainder, and the heroic in relation to the daimonic holds the epogdoic ratio because of the unstained form of life, but the souls of the many would hold the rank of the remainder in relation to them. And the soul is also the first even-odd; for it is intermediate between the indivisible and the divisible, of which the odd is proper to the former, and the even to the latter. And to say that all the epitrites were filled up by the epogdoic interval with the remainder, shows that the terminations of the ratios ended in more partial hypostases. And there are seven terms, because the soul has obtained an intermediate hypostasis between the indivisible and the divisible, and it imitates the former through the triad of terms, but has taken up the latter through the tetrad. Since also the whole soul through its whole self is hebdomadic; for if the demiurgic mind is a monad, and the soul proceeds first from mind, it has the ratio of a heptad to it; for the heptad is paternal and motherless. And of the three means, the geometric binds together all that is substantial of souls, the harmonic binds together sameness, and the arithmetic binds together difference. And the geometric is an image of good order, the harmonic of justice, and the arithmetic of peace. You have therefore from us sufficiently, O my friend, unless someone might say ambitiously and excessively, the account of the things you sought. 12 Explanation of the Platonic Charioteering of Souls and the Army of the Gods in the Phaedrus These Platonic sayings: "The great leader in heaven, Zeus, driving a winged chariot, goes first, ordering all things and caring for them; and he is followed by an army of gods and spirits, arranged in eleven divisions; for Hestia alone remains in the house of the gods," were previously put to me by one of the learned and received a treatment

πρὸς τὴν ἐξήγησιν τῆς Πλατωνικῆς ψυχογονίας, τοῦτο δή σοι νῦν ὥσπερ τι χρέος διαλυόμεθα. τὸ γὰρ «κατὰ τὴν τοῦ διπλασίου καὶ τριπλασίου διάστασιν» εἰρημένον τῷ Πλάτωνι «ἑκάστην τῶν διαστάσεων οὐσῶν ἑκατέρων τριῶν» γεγονέναι τὴν σχίσιν τῶν ἑπτὰ τούτων κύκλων ἐστὶ μὲν ὅσον γε κατὰ τὴν λέξιν ὑποδύσκολον, σημαίνει δὲ ὅμως, ὅτι κατὰ ἑκάστην διάστασιν τῶν διπλασίων καὶ τριπλασίων διαστάσεων, οὐσῶν ἑκατέρων τριῶν (ἐν γὰρ τέτταρσιν ὅροις αἱ διαστάσεις τρεῖς) ἡ σχίσις γέγονεν, ὅ ἐστι τῷ κατὰ μῆκος ταὐτόν, ἵν' ἑκάστῳ τῶν ἑπτὰ κύκλων ἐνῶσιν αἱ διαστάσεις πᾶσαι καὶ οἱ λόγοι πάντες· κατὰ γὰρ τὸν ἀριθμὸν τῶν τοῦ διπλασίου καὶ τριπλασίου διαστάσεων ἓξ οὐσῶν ἑξαχῇ τοὺς κύκλους ἔτεμε. τούτων δὲ προειλημμένων φαμέν (ὁ δὲ λόγος Ἑλληνικός) τὴν τοῦ παντὸς ψυχὴν λόγους ἔχουσαν πάντων τῶν ἐγκοσμίων ἔχειν πρὸ τούτων καὶ τῶν ὅλων τοῦ κόσμου μερίδων, αὐτῆς, λέγω, τῆς ἀπλανοῦς καὶ τῆς πλανωμένης, ὅθεν ὁ θατέρου κύκλος τῶν ἑπτὰ κύκλων τὰς πρωτουργοὺς αἰτίας ἐν ἑαυτῷ περιείληφεν. 11 εἰ δὲ μὴ καὶ τῆς οὐσίας ἴδιός τις γέγονε κύκλος ὡς τῆς ταυτότητος καὶ τῆς ἑτερότητος, διαλύσομεν, εἴ τις ἐρωτῴη, ὅτι τούτων μέν ἐστιν ἀντίθεσις, ἡ δὲ οὐσία κοινὴ τῆς πάσης ἐστὶ ψυχῆς. τὴν δὲ εἰς ἓξ διαίρεσιν οἰκειοτάτην εἶναι τῇ ψυχῇ ὁ τῶν Πυθαγορείων λόγος φησίν, ἀνάλογον ταττόντων σημείῳ μὲν μονάδα, γραμμῇ δὲ δυάδα, τῷ δὲ ἐπιπέδῳ τριάδα, τῷ δὲ σώματι τετράδα, τῷ δὲ πεποιωμένῳ τὴν πεντάδα, τῷ δὲ ἐμψυχωμένῳ τὴν ἑξάδα, τῷ δὲ νοερῷ τὴν ἑπτάδα. Τὸ μέντοι γε λεῖμμα ἄνω μὲν τῆς ἐπιστολῆς μαθηματικῶς ἀπεδείχθη σοι. ἔστι δὲ καὶ ἐν τῷ παντὶ τοιοῦτον· ἀφ' ἑκάστης γὰρ τῶν σφαιρῶν ἀπόρροιαί τινες καθήκουσιν εἰς τὰ ὑπὸ γῆν καὶ αὐτῶν τῶν στοιχείων συμμιγεῖς τινες ὑποστάθμαι, πολὺ μὲν τὸ ταραχῶδες ἔχουσαι καὶ σκοτεινὸν καὶ ἔνυλον, συντελοῦσαι δὲ ὅμως πρὸς τὴν ὅλην τοῦ κόσμου σύστασιν καὶ ἁρμονίαν. τούτων δὴ τὴν αἰτίαν ἐν τῇ ὅλῃ ψυχῇ τιθεὶς ὁ Πλάτων λεῖμμα κέκληκεν αὐτήν, ὃ δὴ τῆς ἐσχάτης φύσεώς ἐστι σημαντικόν. καὶ ὁ τῶν ψυχῶν δὲ λόγος πρὸς τὰ δαιμόνια ζῷα τὸν τοῦ λείμματος ἐπέχει λόγον, καὶ τὰ ἡρωϊκὰ δὲ πρὸς τὰ δαιμόνια τὸν ἐπόγδοον ἔχει λόγον διὰ τὸ ἄχραντον τῆς ζωῆς εἶδος, τὰ δὲ τῶν πολλῶν ἔχοι ἂν πρὸς ἐκεῖνα τὸν τοῦ λείμματος. ἔστι δὲ καὶ πρώτη ἀρτιοπέριττος ἡ ψυχή· μέση γάρ ἐστι τῶν ἀμερῶν καὶ τῶν μεριστῶν, ὧν τοῖς μὲν τὸ περιττὸν οἰκεῖον, τοῖς δὲ τὸ ἄρτιον. τὸ δὲ φάναι, ὅτι τὰ ἐπίτριτα πάντα συνεπληροῦτο τῷ τοῦ ἐπογδόου διαστήματι μετὰ τοῦ λείμματος, ἐμφαίνει, ὅτι τῶν λόγων αἱ ἀποπερατώσεις εἰς μερικωτέρας ὑποστάσεις κατέληξαν. ἑπτὰ δέ εἰσιν ὅροι, διότι μέσην ἔλαχεν ὑπόστασιν ἡ ψυχὴ τῶν τε ἀμερίστων καὶ τῶν μεριστῶν, καὶ ἐκεῖνα μὲν μιμεῖται διὰ τῆς τριάδος τῶν ὅρων, ταῦτα δὲ προείληφε διὰ τῆς τετράδος. ἐπεὶ καὶ ὅλη δι' ὅλης ἑαυτῆς ἡ ψυχὴ ἑβδομαδική ἐστιν· εἰ γὰρ μονὰς ὁ δημιουργικὸς νοῦς, ἡ δὲ ψυχὴ πρώτως ἀπὸ νοῦ πρόεισιν, ἑβδομάδος ἔχει λόγον πρὸς αὐτόν· πατρικὴ γὰρ καὶ ἀμήτωρ ἡ ἑβδομάς. τῶν δὲ μεσοτήτων τριῶν οὐσῶν ἡ μὲν γεωμετρικὴ τὸ οὐσιῶδες πᾶν συνδεῖ τῶν ψυχῶν, ἡ δὲ ἁρμονικὴ τὴν ταυτότητα, ἡ δὲ ἀριθμητικὴ τὴν ἑτερότητα. καὶ ἡ μὲν γεωμετρικὴ εὐνομίας εἰκών, ἡ δὲ ἁρμονικὴ δίκης, ἡ δὲ ἀριθμητικὴ εἰρήνης. ἔχεις οὖν αὐτάρκως παρ' ἡμῶν, ὦ φιλότης, εἰ μή τις ἂν εἴποι καὶ φιλοτίμως καὶ περιττῶς, τὸν περὶ ὧν ἐζήτησας λόγον. 12 Ἐξήγησις τῆς Πλατωνικῆς ἐν τῷ Φαίδρῳ διφρείας τῶν ψυχῶν καὶ στρατείας τῶν θεῶν Τὰ Πλατωνικὰ ταῦτα ῥητά «ὁ μὲν δὴ μέγας ἡγεμὼν ἐν οὐρανῷ Ζεὺς ἐλαύνων πτηνὸν ἅρμα πρῶτος πορεύεται, διακοσμῶν πάντα καὶ ἐπιμελούμενος· τῷ δ' ἕπεται στρατιὰ θεῶν τε καὶ δαιμόνων κατὰ ἕνδεκα μέρη κεκοσμημένη· μένει γὰρ Ἑστία ἐν θεῶν οἴκῳ μόνη» καὶ πρότερόν μοι προεβλήθη παρά του τῶν λογίων καὶ ἔτυχε διαίτης