9

watching over rational flocks. And having established measures of life for those who are completing their mortal existence, he has permitted all men to rehearse here the preludes to the life beyond the present age; for there is, there is even beyond the present age a divine and blessed life, which he taught is stored up in good hopes for those who have contended well, and in .. that for those who have lived temperately and piously the transition and removal from hence to better things will occur, but for those who are convicted in this life, the fitting place is assigned. 6.10 Then, as in the prizes of a contest, having proclaimed various crowns for the victors, he crowns them with one prize of virtue after another.., and for a good emperor adorned with piety he proclaims that greater rewards have been prepared than the prizes, the preludes of which he grants him to celebrate already from this life, with a festival composed of perfect numbers, of tens, of triads, and of threefold monads, 6.11 of which the first triad would be the offspring of the monad, and the monad the mother of numbers, having precedence over all months and seasons and years and every period of time, and might reasonably be called the beginning, foundation, and element of all multitude, the monad being named from 'remaining' (menein), because indeed, while every multitude is decreased and increased by the subtraction and addition of numbers, the monad alone has obtained stability and permanence, being isolated from all multitude and from the numbers generated from it, and bearing an image of the indivisible and distinct substance of other things, by whose power and participation the nature of all existing things is constituted. 6.12 For the monad is the creator of every number, since every multitude is established by the composition and addition of monads, nor is it possible otherwise to conceive of the substance of numbers without the monad; but this would be outside of multitude, and far beyond and superior to every number, making and establishing all things, but never being extended by anything. 6.13 And the triad is akin to this, likewise un-split and indivisible, and the first of the numbers composed of even and odd; for the even number two, having taken a monad, generated the first odd nature of the triad. And the triad first showed forth justice, having taken the lead in equality, as having received an equal beginning, middle, and end. And these things are an image of the mystical and all-holy and royal triad, which, being dependent on the un-begun and ungenerated nature, has received the seeds and the principles and the causes of the substance of all generated things. 6.14 And so the power of the triad might reasonably be considered the beginning of everything. But the decad, having received the limit of all numbers, establishes everything up to itself, reasonably being called complete and all-perfect, since it contains all forms and all measures of all numbers and ratios and concords and harmonies. For monads, when increased by composition, are bounded by the ten; having acquired this as a mother and a fixed limit and boundary, they run around a turning-post as in a racecourse. 6.15 Then having made a second circle and again a third and a fourth and up to the tenth, they complete the hundred from ten decades, and then they run back to the first starting point, and starting again from there and proceeding to the ten and running around the hundred ten times, rushing back through the same turning-posts they run long double courses, circling back from themselves into themselves. 6.16 For the tenth of ten is a monad; and ten monads make one decad; and a decad is the limit of monads, a boundary and a restoring turning-post, a turning-post for the infinity of numbers, but a boundary and end for monads, and at the same time a triad, interwoven with a decad and having gone around the period of ten cycles a third time, generates the most natural number thirty; for what the triad is in monads, this the thirty is in decades. 6.17 And this is the fixed limit of the second great luminary after the sun; for the period of the moon from conjunction to conjunction worked out the cycle of a month, after which again a beginning of coming into being

9

λογικοῖς θρέμμασιν ἐπισκοπούμενος. μέτρα τε ζωῆς τοῖς τὸν θνητὸν διανύουσι βίον διαθεσμοθετήσας, προεμμελετᾶν ἐν τῷδε τὰ προοίμια τῆς ὑπὲρ τὸν νῦν αἰῶνα ζωῆς ἅπασιν ἀνθρώποις συγκεχώρηκεν· εἶναι γάρ, εἶναι καὶ ὑπὲρ τὸν παρόντα αἰῶνα θείαν καὶ μακαρίαν ζωήν, ἣν τοῖς εὖ διηγωνισμένοις ἐν ἀγαθῶν ἐλπίσι τεταμιεῦσθαι ἐδίδαξεν, καὶ ἐν .. τοῖς μὲν σωφρόνως καὶ εὐσεβῶς βεβιωκόσιν τὴν ἐνθένδε ἐπὶ τὰ κρείττω μετάβασίν τε καὶ μετοικίαν γενήσεσθαι, τοῖς δὲ ἐληλεγμένοις ἐν τῷδε χῶρον ἀπονεῖμαι τὸν προσήκοντα. 6.10 εἶθ' ὡς ἐν ἀγῶνος ἄθλοις παντοίους τοῖς νενικηκόσιν ἀναγορεύσας στεφάνους, ἄλλους ἐφ' ἑτέροις .. ἀρετῶν βραβείοις στεφανοῖ, βασιλεῖ δ' ἀγαθῷ θεοσεβείᾳ κοσμησαμένῳ μείζονα προητοιμάσθαι κηρύττει τῶν ἐπάθλων τὰ γέρα, ὧν τοῖς προοιμίοις ἐντεῦθεν ἤδη πανηγυρίζειν δίδωσιν, ἑορτῇ τελείων ἐξ ἀριθμῶν συγκειμένῃ, δεκάδων τριάδων μονάδων τε τριπλασιόνων, 6.11 ὧν ἡ μὲν πρώτη τριὰς μονάδος ἂν γένοιτο ἔκγονος, μονὰς δὲ μήτηρ ἀριθμῶν, μηνῶν ἁπάντων καὶ ὡρῶν καὶ ἐνιαυτῶν πάσης τε χρόνων περιόδου πρεσβεύουσα, ἤδη καὶ παντὸς πλήθους ἀρχὴ καταβολή τε καὶ στοιχεῖον εἰκότως ἂν ῥηθείη, μονὰς παρὰ τὸ μένειν ὠνομασμένη, ὅτι δή, μειουμένου καὶ αὐξομένου παντὸς πλήθους κατὰ τὴν τῶν ἀριθμῶν ὑφαίρεσίν τε καὶ προσθήκην, μόνη μονὰς στάσιν καὶ μονὴν εἴληφε, μεμονωμένη πληθύος ἁπάσης καὶ τῶν ἐξ αὐτῆς γεννωμένων ἀριθμῶν, φέρουσά τε εἰκόνα τῆς ἀμερίστου καὶ διακεκριμένης τῶν ἄλλων οὐσίας, ἧς δυνάμει καὶ μετοχῇ ἡ τῶν ὄντων ἁπάντων συνέστηκε φύσις. 6.12 μονὰς γὰρ παντὸς δημιουργὸς ἀριθμοῦ, ἐπείπερ κατὰ σύνθεσιν καὶ προσθήκην μονάδων πᾶν πλῆθος κρατύνεται, οὐδ' ἔστιν ἄλλως δίχα μονάδος οὐσίαν ἀριθμῶν ἐπινοῆσαι· αὕτη δ' ἐκτὸς ἂν εἴη πλήθους πορρωτάτω τε καὶ κρείττων ἀριθμοῦ παντός, πάντα ποιοῦσα καὶ ὑφισταμένη, τεινομένη δὲ ὑπ' οὐδενὸς πώποτε. 6.13 τριὰς δὲ ταύτῃ συγγενής, ἄσχιστος ὡσαύτως καὶ ἀδιαίρετος, καὶ πρώτη τῶν ἐξ ἀρτίων καὶ περιττῶν ἀριθμῶν συνεσταμένων· ἄρτιος γὰρ ὁ δύο μονάδα προσλαβὼν τριάδος πρώτην περιττὴν ἐγέννησε φύσιν. πρώτη δὲ τριὰς δικαιοσύνην ἀνέδειξεν ἰσότητος καθηγησαμένη, ὡς ἂν ἀρχὴν καὶ μεσότητα καὶ τελευτὴν ἴσην ἀπολαβοῦσα. εἰκὼν δὲ ταῦτα μυστικῆς καὶ παναγίας καὶ βασιλικῆς τριάδος, ἣ τῆς ἀνάρχου καὶ ἀγεννήτου φύσεως ἠρτημένη τῆς τῶν γεννητῶν ἁπάντων οὐσίας τὰ σπέρματα καὶ τοὺς λόγους καὶ τὰς αἰτίας ἀπείληφεν. 6.14 καὶ τριάδος μὲν δύναμις ἄρα παντὸς εἰκότως ἂν ἀρχὴ νομισθείη. δεκὰς δὲ τὸ πάντων ἀριθμῶν πέρας ἀπολαβοῦσα μέχρις αὐτῆς τὸ πᾶν ἵστησιν, πλήρης καὶ παντέλειος ὠνομασμένη εἰκότως, ἅτε δὴ πάσας ἰδέας καὶ πάντα μέτρα πάντων ἀριθμῶν λόγων τε καὶ συμφωνιῶν καὶ ἁρμονιῶν περιέχουσα. μονάδες γοῦν αὐξηθεῖσαι κατὰ σύνθεσιν τοῖς δέκα περιορίζονται· μητέρα ταύτην καὶ πῆξαι ὅρον τε καὶ περιγραφὴν κτησάμεναι ὥσπερ ἐν περιδρόμῳ καμπτῆρα περιθέουσιν. 6.15 εἶτα κύκλον ἐργασάμεναι δεύτερον καὶ πάλιν τρίτον καὶ τέταρτον καὶ μέχρι τῶν δέκα τὸν ἑκατὸν ἐκ δεκάδων δέκα πληροῦσι, κἄπειτα ἐπὶ τὴν πρώτην ἀνατρέχουσιν ἀφετηρίαν, κἀντεῦθεν πάλιν ἀρξάμεναι καὶ ἐπὶ τὸν δέκα προελθοῦσαι δεκάκις τε τὸν ἑκατὸν ἀμφιδραμοῦσαι, παλίσσυτοι διὰ τῶν αὐτῶν καμπτήρων μακροὺς δολιχεύουσι διαύλους ἐξ αὐτῶν εἰς ἑαυτὰς ἀνακυκλούμεναι. 6.16 τῶν γοῦν δέκα τὸ δέκατον μονάς· δέκα δὲ μονάδες μίαν ἀποφαίνουσι δεκάδα· δεκὰς δὲ πέρας μονάδων, ὅρος καὶ καμπτὴρ ἀποκαταστατικός, καμπτὴρ μὲν τῆς ἀπειρίας τῶν ἀριθμῶν ὅρος δὲ καὶ τέλος μονάδων, ὁμοῦ δὲ τριὰς δεκάδι συμπλα κεῖσα τρίτον τε περιελθοῦσα τὴν τῶν δέκα κύκλων περίοδον φυσικώτατον ἀριθμὸν γεννᾷ τὸν τριάκοντα· ὃ γὰρ ἐν μονάσι τριάς, τοῦτο ἐν δεκάσι τριακοντάς. 6.17 ὅρος τε πάγιος οὗτος τοῦ δευτέρου μεθ' ἥλιον μεγάλου φωστῆρος· σελήνης γοῦν περίοδος ἀπὸ συνόδου ἐπὶ σύνοδον μηνὸς κύκλον ἀπειργάζετο, μεθ' ὃν αὖθις ἀρχὴν γενέσεως