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they proclaimed, that each of the numbers is most akin to the lights. That Labeo says that January and February, and April and June, Sextilis and September anciently had twenty-nine days, but March and May, Quintilis and October had thirty-one, whence those with twenty-nine days have the Nones on the fifth day, as being lunar, while those with thirty-one have them on the seventh day, as being solar; but that the Tusci intentionally shortened February, since it appears to have been conceded by the priest Numa to the festivals of the chthonic deities, and it was not right for it to be honored equally with the celestial ones, but rather that the month dedicated to these chthonic deities, who diminish everything, should be diminished, whence also, while all the other months have an odd number, February alone appears to have received an even one. This number belongs to matter, and on account of it the Romans consider the number two unlucky in festivals; they call the second, as it were, "fortunate" in their ancestral way by euphemism, just as they call the Fates, who spare no one, Eumenides and Adrasteia and Parcae. And from the Nones themselves to the Ides themselves they observed only nine intervening days, because the number nine is most akin and suitable to the moon; for this number, according to Xenocrates, generates itself. For the progression up to nine is indefinite and cohabits with multitude. Therefore they called the new moon the Kalends, and the second of the month the fourth or the sixth day, as has been said, before the Nones—let the example be as when the Nones are on the fifth—the third, the third day before the Nones, the fourth, the day before the Nones because the number two is unlucky, the fifth, the Nones, the sixth, the eighth day before the Ides, the seventh, the seventh day before the Ides, the eighth, the sixth day before the Ides, the ninth, the fifth day before the Ides, the tenth, the fourth day before the Ides, the 11th, the third day before the Ides, the 12th, the day before the Ides, the 13th, the Ides; the 14th, if the Nones were on the fifth and the month had 30 days, the 18th day before the Kalends of the following month, but if the Nones were on the fifth and the month had 31 days, similarly the 19th day before the Kalends; but if the Nones were on the seventh and the month had 31 days, the 15th was similarly the 17th day before the Kalends. And in February alone, the 14th was the 16th day before the Kalends of March and so on by subtraction of the number of the Kalends. And when it was a bissextile year, they called both the 25th and the 26th the sixth day before the Kalends of March, which has also been said. March, May, July, October have the Nones on the seventh day, but all the rest on the fifth. It pleased Caesar, however, even after the solar regulation of the months, to leave the lunar festivals in the months. And so much for the seeming anomaly of the months having the Nones on the fifth and seventh days. 3.11 Among the ancients, the new moon was celebrated in honor of Hera, who is the Moon, the Nones in the name of Zeus, and the Ides again in the name of Zeus; and they called the first of the moon the new moon and both Romans and Greeks celebrated it, but neither was it despised among the Hebrews, as the melodist says: “Blow the trumpet at the new moon.” And it is not at all difficult to say briefly from what the ancients have said what the new moon is and why its power appears to be honored by all, being observed, to speak the truth, in the nature of things. And Antigonus is a witness to this, saying that ants rest on the new moons; it is therefore impossible to see an ant working on the new moons, as has also been said by Archelaus. And the name of the new moon is honorable, as we were saying, as the cause of the renewal of the entire sensible world; for since all things in the sensible world undergo increase and decrease, such a nature of the moon has been ordained by the creator, holding together the whole of sensation; and this is clear from the nature of the waters and the animals in them and from the humors in us;

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ἐκήρυττον, ὅτι ἑκάτερος τῶν ἀριθμῶν οἰκειότατος τοῖς φωσίν. ὅτι ὁ Λαβεών φησι τὸν Ἰανουάριον καὶ Φεβρουάριον, Ἀπρίλλιόν τε καὶ Ἰούνιον, Σεξτίλιον Σε πτέμβριον ἀπὸ ἐννέα καὶ εἴκοσιν ἡμερῶν τὸ πάλαι λαχεῖν, Μάρτιον δὲ καὶ Μάϊον, Κυντίλλιόν τε καὶ Ὀκτώβριον ἀπὸ μιᾶς καὶ τριάκοντα, ὅθεν τοὺς ἀπὸ ἐννέα καὶ εἴκοσι ἡμερῶν ἕλκοντας πεμπταίας ἔχειν τὰς Νώνας ὡς σεληνιακούς, τοὺς δὲ ἀπὸ μιᾶς καὶ τριάκοντα ἑβδομαίας ὡς ἡλιακούς· τὸν δὲ Φεβρουάριον ἐπίτηδες τοὺς Θούσκους ἐλαττῶσαι, ἐπειδὴ ταῖς τῶν καταχθονίων ἑορταῖς φαίνεται πρὸς τοῦ ἱερέως Νουμᾶ παραχωρηθεὶς καὶ οὐ θεμιτὸν ἦν, ἴσα τοῖς οὐρανίοις αὐτὸν τιμᾶσθαι, μειωθῆναι δὲ μᾶλλον τὸν τοῖσδε τὸ πᾶν ἐλαττοῦσι χθονίοις ἀφωρισμένον, ὅθεν καὶ πάντων τῶν μηνῶν τὸν περιττὸν ἀριθμὸν ἑλκόντων μόνος ὁ Φεβρουάριος τὸν ἄνισον φαίνεται λαχών. ὁ δὲ ἀριθμὸς οὗτος τῆς ὕλης, καὶ δι' αὐτὴν τὸν δυαδικὸν ἀριθμὸν ἐπὶ τῶν ἑορτῶν οἱ Ῥωμαῖοι ἀποφράζονται, σεκοῦνδον αὐτὸν οἱονεὶ εὐτυχῆ πατρίως καλοῦσι κατ' εὐφημισμόν, ὡς Εὐμενίδας καὶ Ἀδράστειαν καὶ Πάρκας κατ' αὐτοὺς τὰς μηδενὸς φειδομένας Μοίρας. ἀπὸ δὲ τῶν Νωνῶν καὶ αὐτῶν ἕως τῶν Εἰδῶν καὶ αὐτῶν μόνας ἐννέα μέσας παρετηρήσαντο, ὅτι οἰκειότατος καὶ προσφυὴς ὁ ἐννέα ἀριθμὸς τῇ σελήνῃ· οὗτος γὰρ ἑαυτὸν γεννᾷ κατὰ Ξενοκράτην. ἀόριστος γὰρ ἡ ἄχρις ἐννεάδος πρόβασις καὶ πλήθει σύνοικος. τὴν μὲν οὖν νεομηνίαν ἔλεγον Καλένδας, τὴν δὲ δευτέραν τοῦ μηνὸς πρὸ τεσσάρων ἢ πρὸ ἕξ, ὡς εἴρηται, Νωνῶν-ἔστω δὲ τὸ παράδειγμα ὥσπερ ὅταν πεμπταῖαι ὦσιν αἱ Νῶναι-τὴν δὲ τρίτην πρὸ τριῶν Νωνῶν, τὴν δὲ τετάρτην πρὸ μιᾶς Νωνῶν διὰ τὸ ἀποφράζεσθαι τὴν δυάδα, τὴν πέμπτην Νώνας, τὴν ἕκτην πρὸ ὀκτὼ Εἰδῶν, τὴν ἑβδόμην πρὸ ἑπτὰ Εἰδῶν, τὴν ὀγδόην πρὸ ἓξ Εἰδῶν, τὴν ἐννάτην πρὸ πέντε Εἰδῶν, τὴν δεκάτην πρὸ τεσσάρων Εἰδῶν, τὴν ιαʹ πρὸ τριῶν Εἰδῶν, τὴν ιβʹ πρὸ μιᾶς Εἰδῶν, τὴν ιγʹ Εἰδούς· τὴν ιδʹ, εἰ μὲν πεμπταῖαι ἦσαν αἱ Νῶναι καὶ ὁ μὴν ἡμερῶν λʹ, πρὸ ιηʹ Καλενδῶν τοῦ ἐπιόντος μηνός, εἰ δὲ πεμπταῖαι μὲν αἱ Νῶναι καὶ ὁ μὴν ἡμερῶν λαʹ, πρὸ ιθʹ Καλενδῶν ὁμοίως· εἰ δὲ αἱ Νῶναι μὲν ἑβδομαῖαι καὶ ὁ μὴν λαʹ ἡμερῶν, τὴν ιεʹ πρὸ ιζʹ Καλενδῶν ὁμοίως. ἐπὶ δὲ τοῦ Φεβρουαρίου μόνου τὴν ιδʹ πρὸ ιςʹ Καλενδῶν Μαρτίων καὶ καθεξῆς καθ' ὑπόβασιν τοῦ ἀριθμοῦ τῶν Καλενδῶν. ἡνίκα δὲ ἂν βίσεξτον ᾖ, τὴν κεʹ καὶ τὴν κςʹ πρὸ ἓξ Καλενδῶν Μαρτίων ἔλεγον, ὃ καὶ εἴρηται. ἔχουσι δὲ ἑβδομαίας μὲν τὰς Νώνας Μάρτιος Μάϊος Ἰούλιος Ὀκτώβριος, πεμπταίας δὲ οἱ λοιποὶ πάντες. ἤρεσε δὲ ὅμως τῷ Καίσαρι καὶ μετὰ τὴν ἡλιακὴν τῶν μηνῶν διατύπωσιν τὰς σεληνιακὰς ἑορτὰς τοῖς μησὶ καταλεῖψαι. καὶ ταῦτα μὲν περὶ τῆς δοκούσης ἀνωμαλίας τῶν πεμπταίας καὶ ἑβδομαίας τὰς Νώνας ἐχόντων μηνῶν. 3.11 Ἑορτάζετο δὲ παρὰ τοῖς παλαιοῖς ἡ μὲν νεο μηνία εἰς τιμὴν Ἥρας, ἥτις ἐστὶ Σελήνη, αἱ δὲ Νῶναι εἰς ὄνομα ∆ιός, αἱ δὲ Εἰδοὶ πάλιν εἰς ὄνομα ∆ιός· ἐκάλουν δὲ νεομηνίαν τὴν πρώτην τῆς σελήνης καὶ ἑόρταζον αὐτῇ καὶ Ῥωμαῖοι καὶ Ἕλληνες, ἀλλ' οὐδὲ παρὰ Ἑβραίοις κατεφρονεῖτο, ὥς φησιν ὁ μελῳδός· «σαλπίσατε ἐν νεομηνίᾳ σάλπιγγι.» χαλεπὸν δὲ οὐδὲν ἐκ τῶν τοῖς ἀρχαίοις εἰρημένων διὰ βραχέων εἰπεῖν ὅ, τί ποτε ἄρα ἐστὶ νεομηνία καὶ τίνος χάριν παρὰ πᾶσι φαίνεται ἡ τῆς νεομηνίας δύναμις τιμωμένη, εἰ τἀληθὲς εἰπεῖν, τῇ φύσει τῶν πραγμάτων ἐνθεωρουμένη. καὶ τούτου μάρτυς Ἀντίγονος, φάσκων τοὺς μύρμηκας ἐν ταῖς νεομηνίαις ἀναπαύεσθαι· ἀδύνατον οὖν ἰδεῖν μύρμηκα ἐν ταῖς νεομηνίαις ἐργαζόμενον, ὡς καὶ Ἀρχελάῳ εἴρηται. καὶ τίμιον τὸ τῆς νεομηνίας ὡς ἐλέγομεν ὄνομα ὡς αἴτιον ἀνανεώσεως τοῦ παντὸς αἰσθητοῦ· τῶν γὰρ ἐν αἰσθήσει πάντων ἐν αὐξήσει καὶ μειώσει τυγχανόντων τοιαύτη τις ὑπὸ τοῦ δημιουργοῦ διατετύπωται ἡ τῆς σελήνης φύσις συνέχουσα τὴν ὅλην αἴσθησιν· καὶ τοῦτο δῆλον ἐκ τῆς τῶν ὑδάτων καὶ τῶν ἐν αὐτοῖς ζώων φύσεως καὶ ἐκ τῶν ἐν ἡμῖν χυμῶν·