8

the lesser part is deficient by one, and the greater part is excessive by one. So that the number two is not pure, first, because it is empty and not solid, and that which is not full is not pure; and it is the beginning of infinity and inequality; of infinity because of matter, of inequality because of the oblong numbers; whence the ancients take the dyad as matter and otherness. And Pherecydes and his followers called the dyad ‘daring,’ and they call it ‘impulse’ and ‘opinion,’ because the true and the false are in opinion. For matter is ever-agitated and unstable and subject to many changes, suffering evil and enduring of toils, having by nature the divisible and the separate; for the axis, coming through the middle of the whole heaven, first indicates the division into two and the departure from the one, and it is the cause of all perceptible motion and is entirely separate from the intelligibles. Numa, finding these things to be so, forbade the dual number to the Romans in their festivals; for the Romans do not count by saying ‘before two,’ as they do ‘before four’ and ‘three’; just as the Athenians formerly removed the second day of Boedromion, as Plutarch says in his Symposium. 2.8 They dedicated the third day to Pyroeis—this would be Ares among the Greeks—that is, to the aerial and generative fire, which ignites the nature of the whole sensible world and does not allow it to be idle, at once drying and heating with a rush. They say Ares is the child of Hera, that is, from the airy the transparent and fine-particled fire; whence the mythologers couple Aphrodite sometimes with Hephaestus, the chthonic fire, and sometimes with Ares, the aerial fire; for through these the whole sensible world is brought to life, as has been said. And the power of the triad is very great, even in the sensible realm; for the number corresponding to it has bestowed upon created things generation, growth, and nourishment. And it has not been said simply: ‘but all things have been divided in three,’ since there are also three heavenly bodies, the aetherial, the astral, and the stony. And the triad is the beginning of the odd numbers, whence three is also called a proper number, not admitting apportionment or division. That the triad rules all numbers, as it happens to be the beginning of all odd numbers, which are fulfilling and never lacking. And according to Orpheus, the first three principles of generation sprang forth, Night and Earth and Heaven, and there are three kinds of gods in generation, the celestial, the terrestrial, and that which is between these. And three are the most principal parts of the soul: the rational, the spirited, the appetitive. And Aristotle hands down three forms of intellect: the material, that which is by disposition, and that from without; from which also come three ideas: nature, learning, practice. And of music itself, which moves all things, according to Theophrastus there are three divisions: grief, pleasure, enthusiasm. But indeed, the motions of a body are also three: locomotion, law, progression. And the constitutions of spheres are also three: center, diameter, circumference. And the motions of the stars are also three: direct motion, retrograde motion, acronychal rising. And there are three differences of bodies: for some are material, some aerial, and some empyrean, as the Chaldean hands down. And there are three dimensions of each figure: breadth, depth, length. And three are the circles that define the width of the zodiac: the summer tropic, the winter tropic, the equinoctial. And three are the super-terrestrial centers: rising, setting, mid-heaven. And one could say many things about the triad in the sensible realm, and the entire cosmos is said to be constituted from three powers: arithmetical, geometrical, harmonical; for the intelligible has surpassed the present investigation. For we know that the triad initiated the procession of divine things and wrought for them their eternal stability in the same form, as Ocellus the Pythagorean says in these words: “The triad first constituted beginning, middle, and end.” For the odd and finalizing equality is demiurgic according to the tetragonal nature; for the divine is characterized by these three things: the desirable, the sufficient, the perfect. Furthermore, both the Socrates in the Phaedrus, and indeed the one in the Republic, hand down that the intelligible some third

8

ἐλάττονα ἔχει ἑνί, τὴν δὲ μείζω περιττοτέραν ἑνί. ὥστε ὁ δύο ἀριθμὸς οὐ καθαρός, πρῶτον μέν, ὅτι κενός ἐστι καὶ οὐ ναστός, τὸ δὲ μὴ πλῆρες οὐ καθαρόν, ἀρχὴ δὲ ἀπειρίας καὶ ἀνισότητος· ἀπειρίας μὲν διὰ τὴν ὕλην, ἀνισότητος δὲ διὰ τοὺς ἑτερομήκεις· ὅθεν οἱ παλαιοὶ ὡς ὕλην καὶ ἑτερότητα τὴν δυάδα παραλαμβάνουσι. τόλμαν δὲ καὶ οἱ περὶ Φερεκύδην ἐκάλεσαν τὴν δυάδα, καὶ ὁρμὴν καὶ δόξαν καλοῦσιν, ὅτι τὸ ἀληθὲς καὶ ψευδὲς ἐν δόξῃ ἐστί. πανσόβητος γὰρ ἡ ὕλη καὶ ἄστατος καὶ πολυμετάβολος, κακοπαθής τε καὶ πόνων ὑπομονητική, κατὰ φύσιν τὸ μεριστὸν καὶ διεστὼς ἔχουσα· ὁ γὰρ ἄξων μέσος διὰ παντὸς ἥκων τοῦ οὐρανοῦ πρῶτος τὴν εἰς δύο τομὴν καὶ ἀπὸ τοῦ ἑνὸς ἀπόστασιν ὑποφαίνει, αἴτιος δὲ τῆς πάσης τοῦ αἰσθητοῦ κινήσεως καὶ πάντη τῶν νοητῶν κεχωρισμένος. ταῦθ' οὕτως ἔχοντα ὁ Νουμᾶς εὑρὼν Ῥωμαίοις τὸν δυικὸν ἀριθμὸν ἀπηγόρευσεν ἐν ταῖς ἑορταῖς· οὐδὲ γὰρ ἀριθμοῦσιν οἱ Ῥωμαῖοι, ὥσπερ πρὸ τεσσάρων καὶ τριῶν, οὕτω καὶ πρὸ δύο λέγοντες· ὡς καὶ Ἀθηναῖοι τὸ πρὶν τὴν δευτέραν ἐξῄρουν τοῦ Βοηδρομιῶνος, ὡς Πλούταρχος ἐν Συμποσίῳ φησί. 2.8 Τὴν δὲ τρίτην ἡμέραν ἀνέθεντο Πυρόεντι- Ἄρης δ' ἂν εἴη οὗτος παρ' Ἕλλησι-τουτέστι τῷ ἀερίῳ καὶ γονίμῳ πυρί, ὅπερ ἐξάπτει τὴν τοῦ παντὸς αἰσθητοῦ φύσιν καὶ ἀργεῖν οὐκ ἐᾷ, ξηραῖνον ἅμα καὶ ῥοιζηδὸν θερμαῖνον. Ἥρας δὲ παῖδά φασι τὸν Ἄρεα, τουτέστιν ἐκ τοῦ ἀερώδους τὸ διειδὲς καὶ λεπτομερὲς πῦρ· ὅθεν οἱ μυθικοὶ ζευγνύουσι τὴν Ἀφροδίτην ποτὲ μὲν Ἡφαίστῳ, τῷ χθονίῳ πυρί, ποτὲ δὲ Ἄρεϊ, τῷ ἀερίῳ· διὰ γὰρ τούτων τὸ πᾶν αἰσθητὸν ζωογονεῖται, ὡς εἴρηται. μεγίστη δὲ ἡ τῆς τριάδος καὶ κατ' αἴσθησιν δύναμις· ὁ γὰρ κατ' αὐτὴν ἀριθμὸς τοῖς γεννητοῖς ἐπιδέδωκε γένεσιν αὔξησιν τροφήν. καὶ οὐχ ἁπλῶς εἴρηται· τριχθὰ δὲ πάντα δέδασται, τριῶν ὄντων καὶ αὐτῶν τῶν οὐρανίων σωμάτων, τοῦ τε αἰθερώδους, ἀστρώδους τε καὶ λιθώδους. καὶ τῶν περιττῶν ἀριθμῶν ἀρχὴ ἡ τριάς, ὅθεν καὶ ἰδικὸς ἀριθμὸς ὁ τρία καλεῖται, μερισμὸν ἢ διαίρεσιν οὐκ ἐπιδεχόμενος. ὅτι πάντων ἄρχει τῶν ἀριθμῶν ἡ τριάς, ὡς ἀρχὴ τυγχάνουσα τῶν περιττῶν πάντων, πληρούν των καὶ μηδέποτε λειπομένων. καὶ τρεῖς πρῶται κατ' Ὀρφέα ἐξεβλάστησαν ἀρχαὶ τῆς γενέσεως, νὺξ καὶ γῆ καὶ οὐρανός, θεῶν δὲ τῶν ἐν γενέσει τρία γένη, οὐράνιον καὶ ἐπίγειον καὶ τὸ μεταξὺ τούτων. τρία δὲ καὶ τῆς ψυχῆς τὰ κυριώτατα, λογικὸν θυμικὸν ἐπιθυμητικόν. τρία δὲ καὶ νοῦ εἴδη Ἀριστοτέλης παραδίδωσι, τὸν ὑλικόν, τὸν καθ' ἕξιν, τὸν θύραθεν· ἐξ ὧν καὶ τρεῖς ἰδέαι, φύσις μάθησις ἄσκησις. καὶ αὐτῆς δὲ τῆς πάντα κινούσης μουσικῆς κατὰ τὸν Θεόφραστον τομαὶ τρεῖς, λύπη ἡδονὴ ἐνθουσιασμός. ἀλλὰ μὴν καὶ σώματος τρεῖς αἱ κινήσεις, φορὰ νόμος πρόβασις. τρεῖς δὲ καὶ σφαιρῶν αἱ συστάσεις, κέντρον διάμετρον περιφερές. τρεῖς δὲ καὶ κινήσεις τῶν ἀστέρων, προποδισμὸς ὑποποδισμὸς ἀκρωνυχία. τρεῖς δὲ σωμάτων διαφοραί· τὰ μὲν γάρ ἐστιν ὑλικά, τὰ δὲ ἀέρια, τὰ δὲ ἐμπύρια, ὡς ὁ Χαλδαῖος παραδίδωσι. τρία δὲ καὶ ἑκάστου κινήματα σχήματος, πλάτος βάθος μῆκος. τρεῖς δὲ καὶ οἱ τὸ ζῳδιακὸν πλάτος ὁρίζοντες κύκλοι, θερινὸς τροπικός, χειμερινὸς τροπικός, ἰσημερινός. τρία δὲ καὶ τὰ ὑπέργεια κέντρα, ἀνατολὴ δύσις μεσουρά νημα. καὶ πολλὰ ἄν τις εἴποι περὶ τῆς κατ' αἴσθησιν τριάδος, καὶ ὁ σύμπας κόσμος ἐκ τριῶν δυνάμεων συστῆναι λέγεται, ἀριθμητικῆς γεωμετρικῆς ἁρμονικῆς· ἡ γὰρ νοητὴ ὑπερβέβηκε τὴν παροῦσαν ἐξέτασιν. ἴσμεν γάρ, ὅτι ἡ τριὰς τὴν τῶν θείων πρόοδον ἐκίνησε καὶ στάσιν αὐτοῖς τὴν αἰώνιον ἀπειργάσατο ἐν τῷ αὐτῷ εἴδει, ὥς φησιν ὁ Πυθαγόρειος Ὤκελλος ῥήμασι τούτοις· «ἡ τριὰς πρώτη συνέστησεν ἀρχήν, μεσότητα καὶ τελευτήν.» ἡ γὰρ περιττὴ καὶ περαίνουσα ἰσότης δημιουργός ἐστι κατὰ τὴν τετράγωνον φύσιν· τὸ γὰρ θεῖον τρισὶ τούτοις χαρακτηρίζεται, τῷ ἐφετῷ, τῷ ἱκανῷ, τῷ τελείῳ. ἔτι μὴν καὶ ὁ ἐν Φαίδρῳ Σωκράτης, ἀλλὰ μὴν καὶ ὁ ἐν Πολιτείᾳ παραδίδωσιν, ὅτι τὸ νοητὸν τρίτην τινὰ