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ff. On stereometry in the age of Plato see Rothlauf l.c. pp. 69—74, Cantor l.c. pp. 194—202, Tannery Rev. Phil. X (1880) pp. 523 ff. The most famous stereometrical problem of Plato's time was the so-called ‘Delian problem’ or duplication of the cube, and it is highly probable that Plato had this question in his mind when he wrote the present chapter. A dramatic poet, whom Valckenaer supposed to be Euripides, had already made allusion to it in the lines μικρόν γ᾽ ἔλεξας βασιλικοῦ σηκὸν τάφου: | διπλάσιος ἔστω. τοῦ καλοῦ (v.l. κύβου) δὲ μὴ σφαλεὶς | δίπλαζ᾽ ἕκαστον κῶλον ἐν τάχει τάφου (Nauck Trag. Gr. Fr. p. 676). The story runs that the Delians, having been commanded by an oracle to double a certain altar, were in great perplexity, διαπεμψαμένους δὲ τοὺς παρὰ τῷ Πλάτωνι ἐν Ἀκαδημίᾳ γεωμέτρας ἀξιοῦν αὑτοῖς εὑρεῖν τὸ ζητούμενον (Eratosthenes, quoted by Eutocius in Archimed. III pp. 102 ff. Heiberg. See also Plut. de gen. Socr. 7. 579 B—D and de εἰ ap. Delphos 6. 386 E f., and Johannes Philop. quoted by Sturm Das Delische Problem p. 10). Plato favourably entertained their application, and the students of the Academy set to work with extraordinary enthusiasm. A remarkable stimulus was thereby given to the study of stereometry, and the Delian problem was successfully solved. The anecdote may of course be apocryphal, but we have not the smallest reason for rejecting it. The memory of such incidents is usually cherished with peculiar care in the history of a College, and Eratosthenes (276—194 B.C.) was born only seventy-one years after Plato's death. In any case the duplication of the cube may well have seemed in Plato's time a question of the first importance for the purposes of stereometrical science, for, as Tannery remarks (l.c. p. 256), the duplication of the square, which had already been discovered (Men. 82 B ff.), was believed to be the key to plane problems, and so it was probably surmised that the διπλασιασμὸς τοῦ κύβου would give the solution of a whole series of solid problems. English readers will find a short account of this classical ἀπορία with some of its ancient solutions in Rouse Ball's Math. Recreations and Problems pp. 154 ff. The most elaborate and exhaustive history of the problem and its solutions in antiquity is that of Sturm Das Delische Problem 1896. ἐμοὶ γοῦν. Schneider and others write ἔμοιγ᾽ οὖν (see cr. n.), but οὖν is too strongly illative for this passage. Cf. I 335 E note τὸ γὰρ περὶ κτλ. Cf. 526 C note and Xenophon there quoted, esp. § 4 ἐκέλευε δὲ καὶ ἀστρολογίας ἐμπείρους γίγνεσθαι, καὶ ταύτης μέντοι μέχρι τοῦ νυκτός τε ὥραν καὶ μηνὸς καὶ ἐνιαυτοῦ δύνασθαι γιγνώσκειν κτλ. and infra τὰς ὥρας τῶν εἰρημένων διαγιγνώσκοντες. The ana logy of this passage suggests that in Plato καὶ (‘both’) μηνῶν καὶ ἐνιαυτῶν depends on ὥρας, which is the accusative plural: cf. Laws 812 B εὐαισθήτους δεῖν γεγονέναι περί τε τοὺς ῥυθμοὺς κτλ. Practical astronomy will enable one to tell both the time of month and the time of year by looking at the moon and the sun. For ὥρας μηνῶν cf. also, besides the passage of Xenophon just quoted, Eur. Alc. 449 f. Σπάρτᾳ κυκλὰς ἁνίκα Καρνείου περινίσσεται ὥρα | μηνός κτλ. Schneider and the English translators take ὥρας as genitive and parallel with μηνῶν κτλ., but it is difficult to see what εὐαισθητοτέρως ἔχειν περὶ ἐνιαυτῶν can mean: for ἐπιμέλειαν ποιεῖσθαι ἐνιαυτοῦ καὶ ὡρῶν in VI 488 D is quite different. Schleiermacher translates the passage correctly. εὐαισθητοτέρως. For this form of the comparative adverb see I 343 E note ἡδὺς εἶ: ‘you amuse me.’ See I 337 D note μὴ δοκῇς κτλ. The usefulness of ‘useless’ studies is a fundamental principle in Plato's theory; and (as Schneider points out) ὅτι ἐν τούτοις κτλ. is intended to shew that liberal studies are in the highest and truest sense useful. τὸ δ᾽ ἔστιν. I 340 D note χαλεπόν. Cobet's παγχάλεπον (after Nicom. Introd. Ar. III 7) is a wholly gratuitous change: see App. VII. ἑκάστου. Every human being has an ὄργανον ψυχῆς viz. νοῦς: it is indeed the possession of νοῦς which makes him at once truly human and therewithal divine (VI 501 B note). The genitive is much more expressive than ἑκάστῳ, which Herwerden proposes: cf. 518 C note, and for the combination of genitives V 449 A note ἐκκαθαίρεται κτλ.: ‘is purged and rekindled.’ In passages like this Plato hurls his metaphors about with Shakespearian vehemence and profusion. Cf. II 365 C note, and see the admirable remarks on metaphor by the author of the treatise περὶ ὕψους 32. 4 πλήθους καὶ τόλμης μεταφορῶν—τὰ εὔκαιρα καὶ σφοδρὰ πάθη καὶ τὸ γενναῖον ὕψος εἶναί φημι ἴδιά τινα ἀλεξιφάρμακα, ὅτι τῷ ῥοθίῳ τῆς φορᾶς ταυτὶ πέφυκεν ἅπαντα τἄλλα παρασύρειν καὶ προωθεῖν, μᾶλλον δὲ καὶ ὡς ἀναγκαῖα πάντως εἰσπράττεσθαι τὰ παράβολα, καὶ οὐκ ἐᾷ τὸν ἀκροατὴν σχολάζειν περὶ τὸν τοῦ πλήθους ἔλεγχον διὰ τὸ συνενθουσιᾶν τῷ λέγοντι. The eye of soul is purged of its blindness: its smouldering fires flame forth afresh. To translate “‘is polished’ like a soiled mirror” (J. and C.), besides being wrong, falls far below the level of Plato's ὕψος. The chiasmus in ἐκκαθαίρεται—τυφλούμενον adds to the literary effect. On other readings in this passage see App. VII.
The Republic of Plato. James Adam. 1902. Cambridge. Cambridge University Press.
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