Epinomis

Name: Epinomis
Author: Plato

Ancient Greek with an independent English translation.

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EpinomisEpinomis · 990b–991a

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Epinomis · 990b–991a

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Ancient Greek

p. 44

Σελήνη μὲν περίοδον τὴν αὑτῆς τάχιστα διέξεισιν, ἄγουσα μῆνα καὶ πανσέληνον πρώτην· δεύτερον δὲ κατανοεῖν δεῖ τὸν ἥλιον, τροπὰς ἄγοντα διὰ πάσης τῆς αὑτοῦ περιόδου, καὶ τούτῳ τοὺς συνδρόμους. ἵνα δὲ μὴ πολλάκις ταὐτὰ περὶ 990c τῶν αὐτῶν διαλεγώμεθα, τὰς ἄλλας ὅσας ἐν τῷ πρόσθεν διεξήλθομεν ὁδοὺς τούτων οὐ ῥᾴδιον συννοεῖν, ἐπὶ δὲ ταῦτα παρασκευάζοντας φύσεις οἵας δυνατὸν εἶναι, χρεὼν πολλὰ προδιδάσκοντα καὶ ἐθίζοντα ἀεὶ διαπονήσασθαι παῖδα ὄντα καὶ νεανίσκον. διὸ μαθημάτων δέον ἂν εἴη· τὸ δὲ μέγιστόν τε καὶ πρῶτον καὶ ἀριθμῶν αὐτῶν ἀλλ’ οὐ σώματα ἐχόντων, ἀλλὰ ὅλης τῆς τοῦ περιττοῦ τε καὶ ἀρτίου γενέσεώς τε καὶ δυνάμεως, ὅσην παρέχεται πρὸς τὴν τῶν ὄντων φύσιν. 990d ταῦτα δὲ μαθόντι τούτοις ἐφεξῆς ἐστιν ὃ καλοῦσι μὲν σφόδρα γελοῖον ὄνομα γεωμετρίαν, τῶν οὐκ ὄντων δὲ ὁμοίων ἀλλήλοις φύσει ἀριθμῶν ὁμοίωσις πρὸς τὴν τῶν ἐπιπέδων μοῖραν γεγονυῖά ἐστιν διαφανής· ὃ δὴ θαῦμα οὐκ ἀνθρώπινον ἀλλὰ γεγονὸς θεῖον φανερὸν ἂν γίγνοιτο τῷ δυναμένῳ συννοεῖν. μετὰ δὲ ταύτην τοὺς τρὶς ηὐξημένους καὶ τῇ στερεᾷ φύσει ὁμοίους· τοὺς δὲ ἀνομοίους αὖ γεγονότας ἑτέρᾳ τέχνῃ ὁμοιοῖ, ταύτῃ ἣν δὴ στερεομετρίαν ἐκάλεσαν 990e οἱ προστυχεῖς αὐτῇ γεγονότες· ὃ δὲ θεῖόν τ’ ἐστὶν καὶ θαυμαστὸν τοῖς ἐγκαθορῶσί τε καὶ διανοουμένοις ὡς περὶ τὸ διπλάσιον ἀεὶ στρεφομένης τῆς δυνάμεως καὶ τῆς ἐξ ἐναντίας ταύτῃ καθ’ ἑκάστην ἀναλογίαν εἶδος καὶ γένος ἀποτυποῦται 991a πᾶσα ἡ φύσις. ἡ μὲν δὴ πρώτη τοῦ διπλασίου κατ’ ἀριθμὸν ἓν πρὸς δύο κατὰ λόγον φερομένη, διπλάσιον δὲ ἡ κατὰ δύναμιν οὖσα· ἡ δ’ εἰς τὸ στερεόν τε καὶ ἁπτὸν πάλιν αὖ

990b 7.Source editor’s annotationἄγοντα scr. recc.: ἀγαγόντα A L O

990c 2.Source editor’s annotationἐπὶ] ἐπεὶ A (ὶ supra εὶ A²) O

990c 3.Source editor’s annotationοἵας Theo et in marg. γρ. L O: δι’ ἃς A O

990c 4.Source editor’s annotationἀεὶ scripsi: δεῖ libri: secl. Stallbaum

990c 6.Source editor’s annotationκαὶ ἀριθμῶν A L O: ἀριθμὸν vulg.: ἀριθμῶν Bekker

990c 6.Source editor’s annotationσώματα L Theo et in marg. γρ. O: σώματος A O

990d 3.Source editor’s annotationὁμοίωσις O² (ι supra ει): ὁμοιώσεις A O

990d 6.Source editor’s annotationτρὶς Bekker: τρεῖς libri

990d 8.Source editor’s annotationὁμοιοῖ A O: ὁμοίᾳ L O²

990d 8.Source editor’s annotationστερεομετρίαν Theo L²: γεωμετρίαν A O

990e 2.Source editor’s annotationὡς περὶ O² (ὶ supra εὶ): ὡσπερεὶ A O

991a 3.Source editor’s annotationδ’ εἰς in marg. A²: δὶς A L O

Epinomis

p. 45

The moon goes through its own circuit most quickly, bringing on the month and the full moon, first;¹ second, one must apprehend the sun, bringing on the turnings through the whole of its circuit, and those that run along with it.² And so that we may not often 990c discuss the same things about the same things: the other routes of these, all that we went through before, are not easy to understand; but, preparing for these things natures such as there can be, one must labor at it always, teaching him much beforehand and accustoming him while he is a boy and a young man.³ Therefore there would be need of subjects of learning; and the greatest and first is also that of numbers themselves, but not of numbers that have bodies, but of the whole coming into being and power of the odd and the even, as much as it contributes to the nature of the things that are. 990d And for one who has learned these, next after them is what they call by a very ridiculous name, geometry; but it is a making alike, become evident, of numbers that are not like one another by nature, with respect to the portion of plane figures;⁴ and this, to one able to understand it, would become manifest as a wonder that has come into being not human but divine. After this, the numbers three times increased and like the solid nature; and those that, again, have come to be unlike, one makes like by another craft, the one that 990e those who have met with it have called stereometry.⁵ And what is divine and wonderful to those who see into it and think about it is how, as the power, and the power opposite to it, turn always about the double, in each proportion 991a the whole of nature stamps out form and kind.⁶ The first proportion, then, that of the double in number, is carried along as one to two in ratio, and the one that is by power is double; and the one into the solid and tangible is, again,

1.First: prōtēn, which agrees in form with “full moon”, is taken with the “second” that follows: the moon is learned first, the sun second (interpretation).

2.Turnings: tropai, the solstices.

3.Always: aei, Burnet’s correction; the manuscripts have dei, “must”, which Stallbaum deletes.

4.Geometry: the word means “land-measuring”. A making alike: numbers whose ratio is not that of two squares, such as 1 and 2, are made alike as the areas of squares whose sides cannot be measured by one another; compare Theaetetus 147d–148b (interpretation).

5.Three times increased: numbers of three dimensions, products of three factors, such as cubes (interpretation); tris, “three times”, is Bekker’s correction for the manuscripts’ treis, “three”. Stereometry: “solid-measuring”, the reading of Theon of Smyrna and a corrector of L; A and O have geōmetria, “geometry”.

6.Power: dunamis, also the mathematicians’ word for a square. The double: the ratio 2:1, which gives 1:2 in numbers, 1:4 in squares and 1:8 in cubes (interpretation).

About This Reading Edition

The complete Epinomis, 973a–992e: the Athenian stranger, Clinias, and Megillus examine wisdom, number, the soul, and the ordered heavens. Burnet’s Greek faces a new Diotimos Editions English translation, with an introduction, key words, outline, glossary, critical apparatus, and linked translator notes. Transmitted under Plato’s name, the dialogue’s authorship is disputed; the supplied Introduction presents the question without deciding it.

Historical Text and Translation

Greek: Epinomis, transmitted under Plato’s name, with disputed authorship, in John Burnet, Platonis Opera, volume V, part II (Oxford, 1907; a later impression printed by John Johnson, issued 1936–1945). The words were taken from the Perseus Digital Library transcription and checked against the printed pages by the supplied edition; Burnet’s lineation and critical apparatus are retained. The digital Greek transcription and its modifications are attributed to the Perseus Digital Library, Tufts University, under CC BY-SA 4.0. English translation and editorial matter: Diotimos Editions, 2026.

About Diotimos Editions

This historical edition credits Diotimos Editions as its English translator.

Rights

The ancient Greek work and Burnet’s printed edition are in the public domain. The Perseus digital Greek transcription and its modifications are reused under CC BY-SA 4.0. The new English translation and editorial matter are credited to Diotimos Editions, 2026; no open license is stated in the supplied edition.