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he places nature in the divine; for its highest part is being, its middle part is life, and its lowest part is intellect. But perhaps someone will say: what communion have sensible things with the intelligible triad? It should be known, then, that Timaeus hands down three triads, and Proclus is a witness in his Outline of Plato's Philosophy, stating that the summit of the intelligibles, being an intelligible triad, is also a monad; for it can be a henad, having in itself the cause and being of all powers, as Parmenides says. For all intelligible things are contained in the triad, and every divine number has proceeded in this order, as the Chaldean himself says in the Oracles: 'for in the bosoms of this triad all things have been sown,' and again: 'for from this triad the Father mixed every spirit.' For this reason, the Pythagoreans posit the triad among numbers, and among figures the right-angled triangle, as an element of the generation of the wholes. There is, then, one measure, according to which the incorporeal and intelligible cosmos was constituted; a second measure, according to which the sensible heaven was fixed, having obtained a fifth and more divine substance, unchangeable and immutable; and a third, according to which the things under the moon were created, which from the four powers are subject to generation and corruption. 2.9 They dedicated the fourth day to Stilbon, one of the planets so called according to the Egyptians, which equally at one time moistens and at another dries, being rarefied by the swift motion around the sun; the Greeks prefer this to be Hermes. To him, then, those who philosophize dedicated the tetrad, as the overseer of mixed souls; for the supports of the soul are four: intellect, knowledge, opinion, sensation. For the soul of man, as Pythagoras said, is a right-angled quadrilateral. But Archytas gives the definition of the soul not in a quadrilateral, but in a circle: "for this reason the soul is that which moves itself, and the first mover must be this, and this is a circle or a sphere." And so it is in the case of the intelligible, and no less can one see it in the case of the sensible in the generations of animals; for first there is the casting of the seed, second the distribution into kinds, third growth, and fourth perfection. But indeed there are four turnings of the sun, by which existing things are preserved: two equinoxes, the summer and winter solstice. And there are four primary phases of the moon itself, like roots and principles: conjunction, full moon, two half-moons, with each phase altering the energy; for from conjunction to the half-moon it moistens, from this to the full moon it heats, from this to the second half-moon it dries, and from this to the conjunction it cools. Whence I think those who have occupied themselves with agriculture safely sow and plant around the conjunctions or full moons, as the air is then moister and moved toward the generation of other things; but around the half-moons they cut whatever wood is workable and they gather the fruits for storage, as it is in a drier season. And these things are so in the case of sensible and intelligible things. But concerning its dignity according to number, the fourth number is a square. For it alone is by nature generated equally equal times equal-parted from the same things both by composition and by power—composition, then, from two and two, and power from twice two—displaying a most beautiful form of harmony, which has happened to none of the other numbers, whence it is also called effective; for if the numbers from the monad up to the tetrad are added in sequence, they produce a decad. 2.10 They dedicated the fifth to Phaethon, the most temperate of all the planets; the Greeks theologize him as life-giving Zeus. Whence they also mythically wish him to have been born in Crete, in which nothing mortal grows, nor is a wolf or an owl found, as Antigonus says. And he is called heavenly according to the circulatory substance in the pentad, from which they say the heaven was formed according to Aristotle. For the pentad, having received the tetrad which has the account of matter in a certain way and is a substrate for things from

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φύσιν ἐν τῷ θείῳ τίθεται· ἔστι γὰρ αὐτοῦ τὸ μὲν ἀκρότατον οὐσία, τὸ δὲ μέσον ζωή, τὸ δὲ ἔσχατον νοῦς. ἄλλ' ἴσως ἐρεῖ τις· ποία κοινωνία τοῖς αἰσθητοῖς πρὸς τὴν νοητὴν τριάδα; ἰστέον τοίνυν, ὅτι τρεῖς τριάδας ὁ Τίμαιος παραδίδωσι, καὶ μάρτυς ὁ Πρόκλος ἐν ὑποτυπώσει τῆς Πλάτωνος φιλοσοφίας φάσκων, ὅτι ἡ τῶν νοητῶν ἀκρότης, τριὰς οὖσα νοητή, καὶ μονάς ἐστιν· ἑνὰς γὰρ τυγχάνειν δύναται, ἐν ἑαυτῇ τὴν πασῶν δυνάμεων αἰτίαν ἔχουσα καὶ οὐσίαν, ὥς φησιν ὁ Παρμενίδης. πάντα γὰρ τὰ νοητὰ ἐν τῇ τριάδι περιέχεται, καὶ πᾶς ὁ θεῖος ἀριθμὸς ἐν τῇ τάξει ταύτῃ προελήλυθεν, ὡς καὶ αὐτὸς ὁ Χαλδαῖος ἐν τοῖς λογίοις· τῆσδε γὰρ ἐν τριάδος κόλποις ἔσπαρται ἅπαντα, καὶ πάλιν· τῆσδε γὰρ ἐκ τριάδος πᾶν πνεῦμα πατὴρ ἐκέρασσε. διὰ μὲν τοῦτο οἱ Πυθαγόρειοι τριάδα μὲν ἐν ἀριθμοῖς, ἐν δὲ σχήμασι τὸ ὀρθογώνιον τρίγωνον ὑποτίθενται στοιχεῖον τῆς τῶν ὅλων γενέσεως. ἓν μὲν οὖν μέτρον ἐστί, καθ' ὃ συνέστη ὁ ἀσώματος καὶ νοητὸς κόσμος· δεύτερον δὲ μέτρον, καθ' ὃ ἐπάγη ὁ αἰσθητὸς οὐρανός, πέμπτην λαχὼν καὶ θειοτέραν οὐσίαν, ἄτρεπτον καὶ ἀμετάβολον· τρίτον δὲ καθ' ὃ ἐδημιουργήθη τὰ ὑπὸ σελήνην, ἐκ τῶν τεσσάρων δυνάμεων γένεσιν καὶ φθορὰν ἐπιδεχόμενα. 2.9 Τὴν δὲ τετάρτην ἡμέραν Στίλβοντι, ἑνὶ τῶν πλανήτων κατ' Αἰγυπτίους οὕτω καλουμένῳ, ἀνέθεντο, ὃς ἐξ ἴσου ποτὲ μὲν ὑγραίνει ποτὲ δὲ ξηραίνει, πνευματούμενος ὑπὸ τῆς περὶ τὸν ἥλιον ὀξυκινησίας· Ἑρμοῦ δὲ τοῦτον Ἕλληνες εἶναι βούλονται. αὐτῷ τοίνυν τὴν τετράδα οἱ φιλοσοφοῦντες ἀνέθεντο ὡς ἐφόρῳ τῶν μιγάδων ψυχῶν· τὰ γὰρ τῆς ψυχῆς στηρίγματα τέσσαρά ἐστι, νοῦς ἐπιστήμη δόξα αἴσθησις. ψυχὰ γὰρ ἀνθρώπου, ὡς Πυθαγόρας ἔφη, ἔστι τετράγωνον ὀρθογώνιον. Ἀρχύτας δὲ τῆς ψυχῆς τὸν ὅρον οὐκ ἐν τετραγώνῳ, ἀλλ' ἐν κύκλω ἀποδίδωσι, «διὰ τοῦτο ψυχὰ τὸ αὑτὸ κινοῦν, ἀνάγκα δὲ τὸ πρῶτον κινοῦν, κύκλος δὲ τοῦτο ἢ σφαῖρα». καὶ οὕτω μὲν ἐπὶ τοῦ νοητοῦ, οὐδὲν δὲ ἧττον κἀπὶ τοῦ αἰσθητοῦ ἐστι συνιδεῖν ἐν ταῖς τῶν ζώων γενέσεσι· πρῶτον μὲν γάρ ἐστι σπέρματος καταβολή, δεύτερον δὲ ἡ εἰς τὰ γένη διανομή, τρίτον αὔξησις, καὶ τέταρτον τελείωσις. ἀλλὰ μὴν τέσσαρές τε ἡλίου τροπαί, καθ' ἃς τὰ ὄντα συντηρεῖται, ἰσημερίαι δύο, θερινὴ καὶ χειμερινὴ τροπή. τέσσαρες δὲ καὶ αὐτῆς τῆς σελήνης αἱ πρῶται φάσεις ὥσπερ ῥίζαι καὶ ἀρχαί, σύνοδος πανσέληνος διχότομοι δύο, ἑκάστης φάσεως ἀλλοιούσης τὴν ἐνέργειαν· ἀπὸ μὲν γὰρ συνόδου ἕως διχοτόμου ὑγραίνει, ἀπὸ δὲ ταύτης ἕως πανσελήνου θερμαίνει, ἀπὸ δὲ ταύτης ἕως τῆς δευτέρας διχοτόμου ξηραίνει, ἐκ δὲ ταύτης ἕως ἐπὶ σύνοδον ψύχει. ἔνθεν οἶμαι τοὺς περὶ γεωργίαν ἐσχολακότας ἀσφαλῶς σπείρειν μὲν καὶ φυτεύειν περὶ συνόδους ἢ πανσελήνους, οἷα δὴ ἐν ὑγροτέρῳ τηνικαῦτα τῷ ἀέρι καὶ πρὸς γένεσιν ἄλλων κεκινημένῳ· περὶ δὲ τὰς διχοτόμους ὕλην τε, ὅση ἐργάσιμος, κόπτουσι καὶ τοὺς πρὸς ἀπόθεσιν καρποὺς συγκομίζουσιν, οἷα δὴ ἐν ξηροτέρᾳ τῇ ὥρᾳ. καὶ ταῦτα μὲν ἐπὶ τῶν αἰσθητῶν καὶ νοητῶν. περὶ δὲ τοῦ κατ' ἀριθμὸν ἀξιώματος ὁ τέταρτος ἀριθμὸς τετράγωνός ἐστι. μόνος γὰρ ἰσάκις ἶσος ἰσομερὴς ἐκ τῶν αὐτῶν καὶ συνθέσει καὶ δυνάμει πέφυκε γεννᾶσθαι, σύνθεσιν μὲν οὖν ἐκ δυεῖν καὶ δυεῖν, δύναμιν δὲ ἐκ τοῦ δὶς δύο, πάγκαλόν τι συμφωνίας εἶδος ἐπιδεικνύμενος, ὃ μηδενὶ τῶν ἄλλων ἀριθμῶν συμβέβηκεν, ὅθεν καὶ ἀποτελεσματικὸς καλεῖται· εἰ γὰρ ἀπὸ μονάδος μέχρι τετράδος ἑξῆς συντεθεῖεν ἀριθμοί, δεκάδα ἀποτελοῦσιν. 2.10 Τὴν δὲ πέμπτην Φαέθοντι, τῷ πάντων πλανήτων εὐκρατοτάτῳ ἀνέθεντο· ∆ία δὲ αὐτὸν Ἕλληνες ζωογόνον θεολογοῦσιν. ὅθεν καὶ ἐν Κρήτῃ τεχθῆναι μυθικῶς αὐτὸν βούλονται, ἐν ᾗ θανάσιμον οὐδὲν φύεται, ἀλλ' οὐδὲ λύκος ἢ γλαὺξ εὑρίσκεται, ὥς φησιν Ἀντίγονος. καὶ οὐράνιος δὲ καλεῖται κατὰ τὴν ἐν πεν τάδι κυκλοφορικὴν οὐσίαν, ἐξ ἧς φασιν ἀποτελεσθῆναι τὸν οὐρανὸν κατὰ τὸν Ἀριστοτέλην. ἡ γὰρ πεντὰς παραλαβοῦσα τὴν τετράδα ὕλης λόγον ἔχουσαν τρόπον τινὰ καὶ ὑποκείμενον τοῖς ἐξ