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that one might ever grant that there were humans before the moon; but that he says the Arcadians and Sicyonians came into being before the formulation of the months. 3.2 The ancients numbered the month according to the lunar course, whence a month (*mēn*) is also named from the moon (*mēnē*), that is, *selēnē*; and *selēnē* from having an ever new light (*selas*). For a month is the time the sun would have completed, in which the light from the sun's center, being carried to the moon and traveling around, returns to the same place from which it began its circuit; whence also, honoring the new moon from conjunction to conjunction, they calculated the year to be three hundred and fifty-four days, so as to assign twenty-nine and a half days to each month. 3.3 That Timaeus defines the cosmos as now generated with respect to cause, now ungenerated; ungenerated because of the intelligible powers in it, but generated as being visible and tangible and at the same time having a body. 3.4 The decad is the cycle and limit of every number; for revolving around it and turning, as around a turning-post, the numbers run their long course. For it is the limit of their infinity; for having counted from the monad up to it and it alone, and stopping at it, we turn back again to the monad. That the decad is comprehensive of every number, nature is a witness, having provided man with no more than ten fingers, nor indeed fewer. So, then, it is also possible to find in the nature of the year that, being completed, it turns back again into itself, just like the number ten; and for this reason it was named *eniautos*, from its moving in itself; for it is a circle revolving upon itself. And the circle is a plane figure contained by one line, and for this reason a shape is called circular which begins from itself and ends in itself, which is indeed characteristic of time, which turns back into itself and is nowhere terminated. Whence also the Egyptians, according to sacred tradition, engrave a serpent devouring its own tail on the pyramids. For they suppose an abyss and a serpent in it, from which they will that the perceptible gods and the whole perceptible universe came to be. Moreover, it is also their custom to inscribe in their temples a circle placed on a straight line, because the year becomes its own beginning and end. For this reason the Pythagoreans called the head of time not the first, but one. 3.5 The Egyptians are said to have reckoned the year as four months, whence they also record that some among them once lived for a thousand years; and Hesiod and Hecataeus, Hellanicus and Acusilaus and Ephorus and Nicolaus say that long-lived men lived for periods even exceeding a thousand years, and not only they, as souls attached to heroic bodies, but also certain men, as Diogenes asserts in his work *On Thule*. The Arcadians reckoned the year as three months, the Sicyonians as six, the Latins as thirteen, and among the Romans in ancient times the year was established to have ten months, but later two others were added by King Numa, January for the sake of honoring the intelligibles, and February for the material things. But later Gaius Caesar, from the teaching of the Egyptians, ordained the time to be three hundred and sixty-five and a quarter days, and the months to have, some thirty days, others thirty-one, and February twenty-eight; for antiquity reckoned all the twelve months of the solar year as having thirty days, and they added the five and a quarter days in a thirteenth month. And a year is the time in which the sun, starting from any solstice or equinox, from any point on the diameter of the circle, arrives at the same point.

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ὅτι πρὸ τῆς σελήνης ἀνθρώπους ἄν τις δοίη ποτέ· ἀλλ' ὅτι πρὸ διατυπώσεως τῶν μηνῶν Ἀρκάδας φησὶ καὶ Σικυωνίους γενέσθαι. 3.2 Τὸν μῆνα κατὰ τὸν σεληνιακὸν δρόμον ἠρίθμουν οἱ παλαιοί, ἔνθεν καὶ μὴν προσαγορεύεται ἀπὸ τῆς μήνης, τουτέστι τῆς σελήνης· σελήνη δὲ ἀπὸ τοῦ σέλας ἀεὶ νέον ἔχειν. μὴν γάρ ἐστι χρόνος ὁπόσον ἂν ὁ ἥλιος διηνυκὼς εἴη, ἐν ᾧ τὸ ἀπὸ τοῦ ἡλιακοῦ κέντρου φῶς ἐπὶ τὴν σελήνην φερόμενον καὶ περιοδεῦσαν εἰς τὸν αὐτὸν ἀποκαταστῇ τόπον ὅθεν ἤρξατο περιοδεύειν· ὅθεν καὶ ἀπὸ συνόδου εἰς σύνοδον τὴν νεομηνίαν τιμῶντες συνελογίζοντο τὸν ἐνιαυτὸν τεσσάρων καὶ πεντήκοντα καὶ τριακοσίων ἡμερῶν εἶναι, ὥστε ἑκάστῳ μηνὶ περιβάλλειν ἐννέα καὶ εἴκοσι πρὸς τῇ ἡμισείᾳ ἡμέρας. 3.3 Ὅτι Τίμαιος νῦν μὲν γεννητὸν κατ' αἰτίαν, νῦν δὲ ἀγέννητον τὸν κόσμον ὁρίζεται· ἀγέννητον μὲν διὰ τὰς ἐν αὐτῷ νοητὰς δυνάμεις, γεννητὸν δὲ οἷα ὁρατὸν ἁπτόν τε ἅμα καὶ σῶμα ἔχοντα. 3.4 Κύκλος παντὸς ἀριθμοῦ ἐστιν ἡ δεκὰς καὶ πέρας· περὶ αὐτὴν γὰρ εἰλούμενοι καὶ κατακάμπτοντες ὥσπερ καμπτῆρα δολιχεύουσιν οἱ ἀριθμοί. ὅρος γάρ ἐστι τῆς ἀπειρίας αὐτῶν· ἀπὸ γὰρ μονάδος ἄχρις αὐτῆς καὶ μόνης ἀριθμήσαντες καὶ στάντες ἐπ' αὐτὴν αὖθις ἐπὶ τὴν μονάδα ἀναστρέφομεν. ὅτι δὲ παντὸς ἀριθμοῦ συνεκτικὴ ἡ δεκάς, μάρτυς ἡ φύσις, μὴ πλείους τῶν δέκα δακτύλων ἀλλὰ μηδὲ ἐλάττους ἀνθρώπῳ παρασχοῦσα. οὕτως ἄρα καὶ ἐπὶ τῆς τοῦ ἐνιαυτοῦ φύσεως ἔστιν εὑρεῖν, ὅτι συμπληρούμενος αὖθις, ὥσπερ ὁ δέκα ἀριθμός, εἰς ἑαυτὸν ἀναστρέφει· καὶ ταύτῃ ἐνιαυτὸς ὠνομάσθη, παρὰ τὸ ἐν ἑαυτῷ κινεῖσθαι αὐτόν· κύκλος γάρ ἐστιν ἐφ' ἑαυτὸν εἰλούμενος. ὁ δὲ κύκλος ἐπίπεδον σχῆμά ἐστιν ὑπὸ μιᾶς γραμμῆς περιεχόμενον, καὶ ταύτῃ κυκλικὸν ὀνομάζεται σχῆμα ἀφ' ἑαυτοῦ ἀρχόμενον καὶ εἰς ἑαυτὸ καταλῆγον, ὁ δὴ ἴδιον τοῦ χρόνου εἰς ἑαυτὸν ἀναστρέφοντος καὶ μηδαμοῦ περατουμένου. ὅθεν καὶ Αἰγύπτιοι καθ' ἱερὸν λόγον δράκοντα οὐρηβόρον ταῖς πυραμίσιν ἐγγλύφουσιν. ἄβυσσον γὰρ ὑποτίθενται καὶ δράκοντα ἐν αὐτῇ, ἐξ οὗ τοὺς αἰσθητοὺς θεοὺς καὶ αὐτὸ δὲ τὸ πᾶν αἰσθητὸν γενέσθαι βούλονται. ἔτι μὴν ἔθος αὐτοῖς καὶ κύκλον ἐπ' εὐθείας χιούμενον τοῖς ἱεροῖς ἐγγράφειν, διὰ τὸ τὸν ἐνιαυτὸν ἀρχὴν ἑαυτοῦ γίνεσθαι καὶ πέρας. διὰ τοῦτο τὴν κεφαλὴν τοῦ χρόνου οἱ Πυθαγόρειοι οὐχὶ πρώτην ἀλλὰ μίαν ὠνόμασαν. 3.5 Αἰγύπτιοι δὲ λέγονται ἀριθμῆσαι τὸν ἐνιαυτὸν τεσσάρων μηνῶν, ὅθεν καὶ χιλιετεῖς τινας βιῶναί ποτε παρ' αὐτοῖς ἀναγράφουσιν· Ἡσίοδος δὲ καὶ Ἑκαταῖος, Ἑλλάνικος καὶ Ἀκουσίλαος καὶ Ἔφορος καὶ Νικόλαός φασιτοὺς μακραίωνας καὶ ὑπὲρ χιλίους διαζῆσαι χρόνους, καὶ οὐκ αὐτοὺς μόνους ὡς ἡρωικὰς ἀνημμένους ψυχάς, ἀλλὰ καὶ ἀνθρώπους τινάς, ὡς ∆ιογένης ἐν τοῖς ὑπὲρ Θούλην ἀξιοῖ. οἱ δὲ Ἀρκάδες τριῶν μηνῶν, Σικυώνιοι δὲ ἕξ, Λατῖνοι τριῶν καὶ δέκα τὸν ἐνιαυτὸν ἠρίθμουν, παρὰ δὲ Ῥωμαίοις τὸ παλαιὸν δέκα μῆνας ἐτετύπωτο τὸν ἐνιαυτὸν ἔχειν, ὕστερον δὲ πρὸς τοῦ βασιλέως Νουμᾶ καὶ ἕτεροι δύο προσετέθησαν, τιμῆς μὲν ἕνεκα τῶν νοητῶν ὁ Ἰανουάριος, τῶν ὑλικῶν δὲ ὁ Φεβρουάριος. Καῖσαρ δὲ ὕστερον ὁ Γάϊος ἐκ τῆς τῶν Αἰγυπτίων διδαχῆς διετάξατο τόν τε χρόνον εἶναι τριακοσίων ἑξήκοντα πέντε τετάρτου ἡμερῶν, καὶ τοὺς μῆνας τοὺς μὲν ἀπὸ τριάκοντα ἔχειν ἡμερῶν, τοὺς δὲ ἀπὸ τριάκοντα ἑνός, τὸν δὲ Φεβρουάριον εἰκοσιοκτώ· ἡ γὰρ παλαιότης τοὺς δυοκαίδεκα μῆνας τοῦ ἡλιακοῦ ἐνιαυτοῦ ἀπὸ τριάκοντα ἡμερῶν πάντας ἠρίθμησεν, τὰς δὲ πέντε τέταρτον ἡμέρας ἐν τρισκαιδεκάτῳ μηνὶ ἐπέβαλλεν. ἐνιαυτὸς δέ ἐστι χρόνος ἐν ᾧ ἂν ὁ ἥλιος ἀπὸ τροπῆς ἰσημερίας ἡστινοσοῦν ἀρξάμενος ἀφ' οἵου δήποτε σημείου τῶν ἀπὸ τοῦ διαμέτρου κύκλου ἐπὶ τὸ αὐτὸ σημεῖον ἀφίκηται.