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of the moon's courses, swift, medium, and slow, for which reason the poets also call Hecate—that is, the Moon—Trioditis, he divided the month into three festivals. For the Moon is three-formed, and how this is so, must be learned from the oracle; it speaks thus: I am this many-phased, heaven-roaming maiden, bull-eyed, three-headed, harsh, with golden arrows, Phoebe, of infinite art, light-bringing to mortals, Eileithyia, bearing the three-fold tokens of a three-ranked nature. For, as Aristotle says, she makes her course swifter toward the winter solstice, slower toward the summer one, and regular toward the equinox. The first festival of the month, then, is that called Kalendae by the Romans, and Neomenia by the Greeks. And the first of the month is the "new" day among the Attics, and the last is the "old" day. The ancients named them Kalendae from a Greek meaning, from the high priest calling the council in the so-called Calabra Basilica, and announcing whether the festival of the Nones should be celebrated on the fifth day or on the half-moon, from which they observed the middle of the month. For in the months that still even now preserve the lunar festivals, he announced the Nones for the fifth day, on which day, at the thirteenth day and some degrees, it is likely that not the midpoint of the light, but of the lunar body, coincides. For the number thirteen is composed of the first two squares of four and nine—even and odd—having as sides for the even the material form, the dyad, and for the odd the active idea, the triad. This number, therefore, became for the ancients the observance of the greatest and most perfect of festivals. For the fifteenth day, within six degrees, is properly the middle of the month. For it is the midpoint of the light itself. Whence they have considered it a festival of Zeus, that is, of the Sun, by whom we agree the Moon is illuminated. And in the solar months, they announced the Nones for the seventh day; for the number seven belongs to the Sun, as was said before. For it is clear that the shortest period of the moon is twenty-seven days and some hours, but that of its light is nearly thirty, so that the middle return of the lunar body is the thirteenth day, while the middle of the month for the light, that is, the fifteenth day. The Neomenia, then, is first, from which it is the custom for the Romans to proclaim the second festival, that is, the Nones; and there are either four or six days between the Neomenia and the Nones, so that the total, including the Neomenia itself, becomes either five or seven. If, then, someone should count forward nine days from the fifth day itself—and this addition is called Nones by the Romans instead of "nine"; for there are so many—he will find the middle of the short lunar return, that is, the thirteenth day; so also in the case of the seventh day, counting nine days after it, he will find the middle of the month for the light, that is, the fifteenth day. They held the Nones as inauspicious days in every case, now as from the fifth day, now as from the half-moon, not enduring that either this or that phase be named, but rather the mid-month day arriving after nine days, that is, the Ides, or else honoring them in another way because of the observation of the lights. That the name of the Kalends is born from a Greek meaning, can be taken from the writing itself; for even now the Romans write Kalendae with the Greek kappa. But it must be known that the Kalends happened to be a festival of Hera, that is, of the Moon; for the natural philosophers, as we said before, considered Zeus to be the Sun, and Hera the Moon, and they referred the Neomenia to her, but the Ides, that is, the middle of the month, to Zeus, or the Sun, calling the Ides "plenilunium," as it were, "full moon." And we find the name of the Ides was introduced, among the civic writers from the appearance (eidos) of the Moon, but among the priests from a certain type of sacrifice, which was called "eidulis." the Nones on the fifth or seventh day after the Kalends

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τῆς σελήνης δρόμων, ὀξέως μέσου καὶ ἀνειμένου, δι' οὓς καὶ Τριοδῖτιν τὴν Ἑκάτην- οἱονεὶ τὴν Σελήνην- οἱ ποιηταὶ καλοῦσι, τρισὶν ἑορταῖς τὸν μῆνα διέλαβε. τρίμορφος γὰρ ἡ Σελήνη, καὶ ὅπως, ἐκ τοῦ χρησμοῦ γνωστέον· λέγει δὲ οὕτως· ἥδ' ἐγώ εἰμι κόρη πολυφάσματος οὐρανόφοιτος ταυρῶπις τρικάρηνος ἀπηνὴς χρυσοβέλεμνος Φοίβη ἀπειροτέχνη φαεσίμβροτος Εἰλήθυια τριστοίχου φύσεως συνθήματα τρισσὰ φέρουσα. ὀξυτέραν γὰρ, ὡς Ἀριστοτέλης φησί, ποιεῖται τὴν πορείαν πρὸς τῷ χειμερινῷ τροπικῷ, βραδυτέραν δὲ τὴν πρὸς τῷ θερινῷ, ὁμαλὴν δὲ τὴν πρὸς τῷ ἰσημερινῷ. πρώτη τοίνυν τοῦ μηνὸς ἑορτή ἐστιν ἡ λεγομένη παρὰ μὲν Ῥωμαίοις Καλένδαι, παρὰ δὲ Ἕλλησι Νεομηνία. καὶ νέα ἡ πρώτη τοῦ μηνὸς παρὰ Ἀττικοῖς, ἕνη δὲ ἡ τελευταία. Καλάνδας δὲ αὐτὰς οἱ παλαιοὶ προσηγόρευσαν ἐξ ἑλληνικῆς σημασίας, ἀπὸ τοῦ καλεῖν τὸν ἀρχιερέα τὴν βουλὴν ἐν τῇ λεγομένῃ Καλαβρᾷ βασιλικῇ, καὶ σημαίνειν, εἴτε χρὴ κατὰ τὴν πεμπταῖαν, εἴτε κατὰ τὴν διχότομον τῆς σελήνης ἐπιτελέσαι τὴν τῶν Νωνῶν ἑορτήν, ἐξ ἧς τὴν μεσομηνίαν ἐπετήρουν. ἐπὶ μὲν γὰρ τῶν μηνῶν τῶν ἔτι καὶ νῦν τὰς σεληνιακὰς σωζόντων ἑορτὰς πεμπταίας τὰς Νώνας ἐσήμαινε, καθ' ἃς ἐπὶ τῆς τρισκαιδεκάτης καὶ μοιρῶν τινων, οὐ τὴν τοῦ φωτός, ἀλλὰ τὴν τοῦ σεληνιακοῦ σώματος εἰκός ἐστι συντρέχειν μεσότητα. ὁ γὰρ τῶν δεκατριῶν ἀριθμὸς συνέστηκεν ἐκ τῶν πρώτων δυοῖν τετραγώνων τοῦ τέσσαρα καὶ τοῦ ἐννέα-ἀρτίου τε καὶ περιττοῦ- πλευρὰς ἐχόντων τοῦ μὲν ἀρτίου τὸ ὑλικὸν εἶδος δυάδα, τοῦ δὲ περιττοῦ τὴν δραστήριον ἰδέαν τριάδα. οὗτος οὖν ὁ ἀριθμὸς ἡ μεγίστη καὶ τελειοτάτη τῶν ἑορτῶν γέγονε τοῖς ἀρχαίοις ἐπιτήρησις. ἡ γὰρ πεντεκαιδεκάτη παρὰ μοίρας ἓξ κυρίως ἐστὶν ἡ μεσομηνία. αὐτοῦ γὰρ τοῦ φωτός ἐστιν ἡ μεσότης. ὅθεν καὶ ∆ιὸς αὐτὴν ἑορτὴν οἷον Ἡλίου νενομίκασι, δι' οὗ σύμφαμεν φωτίζεσθαι τὴν Σελήνην. ἐπὶ δὲ τῶν ἡλιακῶν μηνῶν ἑβδομαίας τὰς Νώνας ἐσήμαινον· ὁ γὰρ ἕβδομος ἀριθμὸς Ἡλίου ἐστίν, ὡς ἔμπροσθεν εἴρηται. δῆλον γὰρ τὴν μὲν ἐλαχίστην τῆς σελήνης περίοδον εἴκοσι καὶ ἑπτὰ ἡμερῶν εἶναι καὶ ὡρῶν τινων, τοῦ δὲ φωτὸς ἐγγὺς τριάκοντα, ὡς καὶ ἡ μὲν τοῦ σεληνιακοῦ σώματος μέση ἀποκατάστασις ἡ τρισκαιδεκάτη ἐστίν, ἡ δὲ τοῦ φωτὸς μεσομηνία ἤτοι ἡ πεντεκαιδεκάτη. πρώτη τοίνυν ἡ νεομηνία, ἐξ ἧς ἔθος Ῥωμαίοις προκαλεῖν τὴν δευτέραν ἑορτήν, τουτέστι τὰς Νώνας· εἰσὶ δὲ μέσαι ἀπὸ τῆς νεομηνίας ἄχρι τῶν Νωνῶν ἢ τέσσαρες ἢ ἕξ, ὡς γίγνεσθαι τὰς πάσας σὺν καὶ αὐτῇ τῇ νεομηνίᾳ ἢ πέντε ἢ ἑπτά. εἴ τις οὖν ἀπὸ τῆς πεμπταίας καὶ αὐτῆς ἐννέα προσεπιλογίσεται ἡμέρας-αὕτη δὲ ἡ προσθήκη παρὰ Ῥωμαίοις Νῶναι καλεῖται ἀντὶ τοῦ ἐννέα· τοσαῦται γάρ εἰσιν-εὑρήσει τὴν ἐκ μικρᾶς σεληνιακῆς ἀποκατάστασιν μέσην, τουτέστι τὴν τρισκαιδεκάτην· οὕτως καὶ ἐπὶ τῆς ἑβδομαίας μετ' αὐτῆς ἀριθμῶν τὰς ἐννέα εὑρήσει τὴν τοῦ φωτὸς μεσομηνίαν, τουτέστι τὴν πεντεκαιδεκάτην. ἀποφράδας δὲ πάντως τὰς Νώνας εἶχον, νῦν μὲν ὡς ἀπὸ τῆς πεμπταίας νῦν δὲ ὡς ἀπὸ διχοτόμου, μηδὲ ὠνομάσθαι ἢ ταύτην ἢ ἐκείνην τὴν φάσιν ὑπομένοντες, ἀλλὰ τὴν μετὰ ἐννέα ἡμέ ρας ἐπιφοιτῶσαν μεσομηνίαν, τουτέστι τὰς Εἰδούς, ἢ καὶ ἄλλως τιμῶντες διὰ τὴν τῶν φώτων ἐπιτήρησιν. ὅτι δὲ ἐξ ἑλληνικῆς σημασίας τίκτεται τὸ τῶν Καλενδῶν ὄνομα, ἐξ αὐτῆς ἐστι λαβεῖν τῆς γραφῆς· ἔτι γὰρ καὶ νῦν τῷ ἑλληνικῷ κάππα τὰς Καλένδας γράφουσιν οἱ Ῥωμαῖοι. ἰστέον δέ, ὅτι αἱ Καλένδαι Ἥρας ἑορτὴ ἐτύγχανον, τουτέστι Σελήνης· οἱ γὰρ φυσικοί, ὡς ἔφθημεν εἰπόντες, ∆ία μὲν τὸν Ἥλιον, Ἥραν δὲ τὴν Σελήνην ἐνόμιζον εἶναι, καὶ τὴν μὲν νεομηνίαν αὐτῇ, τὰς δὲ Εἰδούς, τουτέστι τὴν μεσομηνίαν, ∆ιὶ ἤγουν Ἡλίῳ ἀνέφερον, πληνιλούνιον τὰς Εἰδοὺς καλοῦντες οἱονεὶ πληροσέληνον. τὸ δὲ τῶν Εἰδῶν ὄνομα παρὰ μὲν τοῖς πολιτικοῖς ἐκ τοῦ εἴδους τῆς Σελήνης, παρὰ δὲ τοῖς ἱερεῦσιν ἀπὸ θυσίας τινὸς τρόπου, ἥτις εἴδουλις ὠνομάζετο, εὑρίσκομεν εἰσενηνεγμένον. πεμπταίας δὲ ἢ ἑβδομαίας τὰς Νώνας μετὰ τὰς Καλένδας