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1 Cf. Charm. 166 D, Phaedo 64 C, Soph. 265 A, Apol. 33 A.
4 Lit. “increase” Cf. Pearson, The Grammar of Science, p. 411: “He proceeds from curves of frequency to surfaces of frequency, and then requiring to go beyond these he finds his problem lands him in space of many dimensions.”
5 This is not to be pressed. Plato means only that the progress of solid geometry is unsatisfactory. Cf. 528 D. There may or may not be a reference here to the “Delian problem” of the duplication of the cube (cf. Wilamowitz, Platon, i. p. 503 for the story) and other specific problems which the historians of mathematics discuss in connection with this passage. Cf. Adam ad loc. To understand Plato we need only remember that the extension of geometry to solids was being worked out in his day, perhaps partly at his suggestion, e.g. by Theaetetus for whom a Platonic dialogue is named, and that Plato makes use of the discovery of the five regular solids in his theory of the elements in the Timaeus. Cf. also Laws 819 E ff. for those who wish to know more of the ancient traditions and modern conjectures I add references: Eva Sachs, De Theaeteto Ath. Mathematico,Diss. Berlin, 1914, and Die fünf platonischen Körper(Philolog. Untersuch. Heft 24), Berlin, 1917; E. Hoppe, Mathematik und Astronomie im klass. Altertum, pp. 133 ff.; Rudolf Eberling, Mathematik und Philosophie bei Plato,Münden, 1909, with my review in Class. Phil. v. (1910) p. 114; Seth Demel, Platons Verhältnis zur Mathematik,Leipzig, with my review, Class. Phil. xxiv. (1929) pp. 312-313; and, for further bibliography on Plato and mathematics, Budé, Rep.Introd. pp. lxx-lxxi.
6 Plato is perhaps speaking from personal experience as director of the Academy. Cf. the hint in Euthydem. 290 C.
7 i.e. the mathematicians already feel themselves to be independent specialists.
8 This interpretation is, I think, correct. For the construction of this sentence cf. Isoc. xv. 84. The text is disputed; see crit. note.
10 An eminent modern psychologist innocently writes: “The problem of why geometry gives pleasure is therefore a deeper problem than the mere assertion of the fact. Furthermore, there are many known cases where the study of geometry does not give pleasure to the student.” Adam seems to think it may refer to the personality of Eudoxus.
12 An obvious allusion to the proverb found in many forms in many languages. Cf. also Polit. 277 A-B, 264 B, Soph.Antig. 231σχολῇ ταχύς, Theognis 335, 401μηδὲν ἄγαν σπεύδειν, Suetonius, Augustus 25, Aulus Gellius x. 11. 4, Macrob.Sat. vi. 8. 9, “festina lente,” “hâtez-vous lentement” (Boileau, Art poétique, i. 171), “Chi va piano va sano e va lontano” (Goldoni, I volponi,I. ii.), “Eile mit Weile” and similar expressions; Franklin's “Great haste makes great waste,” etc.
14 This is the meaning. Neither Stallbaum's explanation, “quia ita est comparata, ut de ea quaerere ridiculum sit,” nor that accepted by Adam, “quia ridicule tractatur,” is correct, and 529 E and 521 A are not in point. Cf. 528 B p. 176, note a.
15 Cf. Laws 822 A ff.
16 i.e. “assuming this to exist,” “vorhanden sein,” which is the usual meaning of ὑπάρχειν in classical Greek. The science, of course, is solid geometry, which is still undeveloped, but in Plato's state will be constituted as a regular science through endowed research.
17 Cf. Vol. I. p. 410, note c, on 442 E, Gorg. 482 E, Rep. 581 D, Cratyl. 400 A, Apol. 32 A, Aristot.Pol. 1333 b 9.
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