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They also count the birth, when the moon is one degree away from the sun. 3.13 Therefore, as we said, the Romans honored the Kalends as a new moon, and after these, in order, the Nones, and in the third rank, the Ides. For the power of Hecate, that is, of the Moon, is three-formed; for what Apollo is in the sun, this Hecate is in the moon. 3.14 That the number thirty is most natural, for what the triad is in units, this the thirty is in tens; since also the cycle of the month is composed of the four consecutive squares from the unit, 1, 4, 9, 16, whence Heraclitus not without reason calls the month a generation. 3.15 But after the Kalends, we find time is divided in many ways into aeon, into time, into season, into year. An aeon, therefore, is a certain infinite revolution of the heavenly bodies or a complete revolution of the entire heaven itself, while time is the indefinite extension from the aeon. For this reason also Cronus is called the child of Uranus; for time (chronos) proceeds from the movements of the heaven (ouranos). so that season (kairos) is an example of time, and not time itself. 3.16 That a greatest restoration differs from a complete period in that the restoration occurs from the same point to the same point according to length and breadth and depth, while the complete period is accomplished from the convergence of the boundaries; for the ancients say there are three periods for all the planets, greatest, least, and mean, and the greatest of Cronus is fifty-seven years, that of Zeus seventy-nine, of Ares indeed sixty-six- whence Caesar led so many thousands of men, as being most experienced even in this part both in the civil and in the other wars, and he was victorious for good reason- of the Sun one hundred and twenty- for which reason it is impossible for a man to live beyond so many years- of Aphrodite eighty-two and of the Moon one hundred and eight. The least of Cronus is thirty, of Zeus twelve, of Ares fifteen, for which reason also the Romans set the cycle of the so-called indiction to this number, of the Sun nineteen, of Aphrodite eight, of Hermes twenty, and of the Moon twenty-five. The mean of Cronus is forty-three and a half, of Zeus forty-five and a half, of Ares forty and a half, of the Sun sixty-nine and a half, of Aphrodite forty-five, of the Moon sixty-six and a half. And such are the greatest and least and mean periods, but the complete restorations of the planets are thus: Cronus makes his restoration in two hundred sixty-five years, Zeus in four hundred twenty-seven, Ares in two hundred ninety-four, the Sun in one thousand four hundred sixty-one, Aphrodite in one thousand one hundred fifty-one, Hermes in four hundred eighty, the Moon in twenty-five, and the restoration of the universe occurs through one million, seven hundred fifty-three thousand, two hundred years, and then there is a conjunction of all the stars at the thirtieth degree of Cancer or the first of Leo; and in Cancer there would be a flood, but in Leo a conflagration, but not a universal one according to the Stoics, but in any case a partial one; for to them it seems that the entire sensible world is subject to such states and they deem it right to give such a cause, and they say the universe is dried up by infinite time or by the conflagrations of the luminaries in heaven or is dissolved by the floods of waters and falls apart from the wandering moisture and is broken up and loses its cohesion. It is necessary

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ἀριθμοῦσι καὶ τὴν γένναν, ὅταν μίαν μοῖραν ἀποστῇ ἡ σελήνη τοῦ ἡλίου. 3.13 Τὰς τοίνυν Καλένδας ὡς ἐλέγομεν οἷα νεομηνίαν ἐτίμησαν Ῥωμαῖοι, μετὰ δὲ ταύτας καθεξῆς τὰς Νώνας, καὶ κατὰ τρίτην τάξιν τὰς Εἰδούς. τρίμορφος μὲν γὰρ ἡ τῆς Ἑκάτης, ἤτοι τῆς Σελήνης, δύναμις· ὃ γὰρ Ἀπόλλων ἐν ἡλίῳ, τοῦτο Ἑκάτη ἐν σελήνῃ. 3.14 Ὅτι ὁ τριάκοντα ἀριθμὸς φυσικώτατός ἐστιν, ὃ γὰρ ἐν μονάσι τριάς, τοῦτο ἐν δεκάσι τριακοντάς· ἐπεὶ καὶ ὁ τοῦ μηνὸς κύκλος συνέστηκεν ἐκ τεσσάρων τῶν ἀπὸ μονάδος ἑξῆς τετραγώνων, αʹ δʹ θʹ ιςʹ, ὅθεν οὐκ ἀπὸ σκοποῦ Ἡράκλειτος γενεὰν τὸν μῆνα καλεῖ. 3.15 Μετὰ δὲ τὰς Καλένδας εὑρίσκομεν πολλαχῶς τὸν χρόνον διαιρεῖσθαι εἰς αἰῶνα εἰς χρόνον εἰς καιρὸν εἰς ἐνιαυτόν. αἰὼν τοίνυν ἐστὶν ἄπειρός τις τῶν οὐρανίων σωμάτων περιπόλησις ἢ αὐτοῦ τοῦ παντὸς οὐρανοῦ παντελὴς ἀνακύκλησις, χρόνος δὲ ἡ ἐξ αἰῶνος ἀόριστος ἔκτασις. ταύτῃ καὶ Κρόνος παῖς Οὐρανοῦ λέγεται· ὁ γὰρ χρόνος ἐκ τῶν τοῦ οὐρανοῦ κινήσεων πρόεισιν. ὥστε καιρός ἐστι χρόνου παράδειγμα, καὶ οὐκ αὐτὸς ὁ χρόνος. 3.16 Ὅτι διαφέρει μεγίστη ἀποκατάστασις τελείας περιόδου τῷ τὴν μὲν ἀποκατάστασιν ἀπὸ τοῦ αὐτοῦ ση μείου ἐπὶ τὸ αὐτὸ σημεῖον γίνεσθαι κατὰ μῆκος καὶ πλάτος καὶ βάθος, τὴν δὲ τελείαν περίοδον ἐκ τῆς συναγωγῆς τῶν ὁρίων ἀποτελεῖσθαι· τρεῖς γὰρ εἶναί φασιν οἱ ἀρχαῖοι περιόδους πάντων τῶν πλανήτων, μεγίστας ἐλαχίστας μέσας, καὶ τὴν μὲν τοῦ Κρόνου μεγίστην ἑπτὰ καὶ πεντήκοντα ἐτῶν, τὴν δὲ ∆ιὸς ἐννέα καὶ ἑβδομήκοντα, Ἄρεός γε μὴν ἓξ πρὸς τοῖς ἑξήκοντα- ὅθεν τοσαύτας χιλιάδας ἀνδρῶν ἐπήγετο ὁ Καῖσαρ ὡς κἂν τούτῳ τῷ μέρει ἐμπειρότατος ἔν τε τῷ ἐμφυλίῳ καὶ ἐν τοῖς ἄλλοις πολέμοις, καὶ εἰκότως ἐκράτει- Ἡλίου δὲ εἴκοσι καὶ ἑκατόν-οὗ δὴ χάριν ἀδύνατον ἄνθρωπον ἐπέκεινα τῶν τοσούτων διαζῆσαι ἐνιαυτῶν- τῆς δὲ Ἀφροδίτης δύο καὶ ὀγδοήκοντα καὶ Σελήνης ὀκτὼ καὶ ἑκατόν. τὴν δὲ ἐλαχίστην Κρόνου τριάκοντα, ∆ιὸς δυοκαίδεκα, Ἄρεος πεντεκαίδεκα, δι' ὃν καὶ τὸν κύκλον τῆς λεγομένης ἐπινεμήσεως οἱ Ῥωμαῖοι εἰς τοῦτο ἔθεντο ἀριθμοῦ, Ἡλίου ἐννεακαίδεκα, Ἀφροδίτης ὀκτώ, Ἑρμοῦ εἴκοσι καὶ Σελήνης πέντε πρὸς τοῖς εἴκοσι. τὴν δὲ μέσην Κρόνου μὲν τριῶν καὶ τεσσαράκοντα πρὸς τῷ ἡμίσει, ∆ιὸς πέντε καὶ τεσσαράκοντα πρὸς τῷ ἡμίσει, Ἄρεος τεσσαράκοντα πρὸς τῷ ἡμίσει, Ἡλίου ἐννέα καὶ ἑξήκοντα πρὸς τῷ ἡμίσει, Ἀφροδίτης πέντε πρὸς τοῖς τεσσαράκοντα, Σελήνης ἓξ καὶ ἑξήκοντα πρὸς τῷ ἡμίσει. καὶ αἱ μὲν μέγισται καὶ ἐλάχισται καὶ μέσαι περίοδοι τοιαῦται, αἱ δὲ τέλειαι ἀποκαταστάσεις τῶν πλανήτων οὕτω· Κρόνος ποιεῖται τὴν ἀποκατάστασιν ἔτεσι πέντε καὶ ἑξήκοντα καὶ δια κοσίοις, Ζεὺς ἑπτὰ καὶ εἴκοσι καὶ τετρακοσίοις, Ἄρης τέσσαρσι καὶ ἐννενήκοντα καὶ διακοσίοις, Ἥλιος ἑνὶ καὶ ἑξήκοντα καὶ τετρακοσίοις καὶ χιλίοις, Ἀφροδίτη ἑνὶ καὶ πεντήκοντα καὶ ἑκατὸν καὶ χιλίοις, Ἑρμῆς ὀγδοήκοντα πρὸς τοῖς τετρακοσίοις, Σελήνη πέντε πρὸς τοῖς εἴκοσιν, ἡ δὲ τοῦ παντὸς ἀποκατάστασις γίνεται δι' ἐτῶν μυριάδων ἑκατὸν ἑβδομήκοντα πέντε καὶ τρισχιλίοις πρὸς τοῖς διακοσίοις, καὶ τότε γίνεται σύνοδος πάντων τῶν ἀστέρων κατὰ τὴν τριακοστὴν μοῖραν τοῦ καρκίνου ἢ τὴν πρώτην τοῦ λέοντος· καὶ ἐπὶ μὲν τοῦ καρκίνου γένοιτ' ἂν κατακλυσμός, ἐπὶ δὲ τοῦ λέοντος ἐκπύρωσις, ἀλλ' οὐ καθολικὴ κατὰ τοὺς Στωικούς, μερικὴ δὲ πάντως· ἐκείνοις γὰρ δοκεῖ τὸ πᾶν αἰσθητὸν τοῖς τοιούτοις ὑπάγεσθαι καταστήμασι καὶ αἰτίαν ἀξιοῦσι διδόναι τοιάνδε, τὸ δὲ πᾶν φασι τῷ ἀπείρῳ χρόνῳ ἢ ταῖς ἐκπυρώσεσι τῶν ἐν οὐρανῷ φωστήρων ἀποξηραίνεσθαι ἢ ταῖς ἐπικλύσεσιν τῶν ὑδάτων διαχεῖσθαι καὶ διαπίπτειν ἀπὸ τῆς ἐπιπλαζούσης ὑγρότητος καὶ ἀναλύεσθαι καὶ τὸ στεγανὸν ἀπολλύειν. ἀνάγκη