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[528a] Or are you speaking to neither, but chiefly carrying on the discussion for your own sake,1 without however judging any other who may be able to profit by it?” “This is the alternative I choose,” he said, “that it is for my own sake chiefly that I speak and ask questions and reply.” “Fall back2 a little, then,” said I; “for we just now did not rightly select the study that comes next3 after geometry.” “What was our mistake?” he said. “After plane surfaces,” said I, “we went on to solids in revolution before studying them in themselves. [528b] The right way is next in order after the second dimension4 to take the third. This, I suppose, is the dimension of cubes and of everything that has depth.” “Why, yes, it is,” he said; “but this subject, Socrates, does not appear to have been investigated yet.5” “There are two causes of that,” said I: “first, inasmuch as no city holds them in honor, these inquiries are languidly pursued owing to their difficulty. And secondly, the investigators need a director,6 who is indispensable for success and who, to begin with, is not easy to find, and then, if he could be found, as things are now, seekers in this field would be too arrogant7 [528c] to submit to his guidance. But if the state as a whole should join in superintending these studies and honor them, these specialists would accept advice, and continuous and strenuous investigation would bring out the truth. Since even now, lightly esteemed as they are by the multitude and hampered by the ignorance of their students8 as to the true reasons for pursuing them,9 they nevertheless in the face of all these obstacles force their way by their inherent charm10 [528d] and it would not surprise us if the truth about them were made apparent.” “It is true,” he said, “that they do possess an extraordinary attractiveness and charm. But explain more clearly what you were just speaking of. The investigation11 of plane surfaces, I presume, you took to be geometry?” “Yes,” said I. “And then,” he said, “at first you took astronomy next and then you drew back.” “Yes,” I said, “for in my haste to be done I was making less speed.12 For, while the next thing in order is the study13 of the third dimension or solids, I passed it over because of our absurd neglect14 to investigate it, and mentioned next after geometry astronomy,15 [528e] which deals with the movements of solids.” “That is right,” he said. “Then, as our fourth study,” said I, “let us set down astronomy, assuming that this science, the discussion of which has been passed over, is available,16 provided, that is, that the state pursues it.” “That is likely,” said he; “and instead of the vulgar utilitarian17 commendation of astronomy, for which you just now rebuked me, Socrates, I now will praise it on your principles.

1 Cf. Charm. 166 D, Phaedo 64 C, Soph. 265 A, Apol. 33 A.

2 ἄναγε is a military term. Cf. Aristoph.Birds 383, Xen.Cyr. vii. 1.45, iii. 3. 69.

3 ἑξῆς Cf. Laches 182 B.

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.

9 Lit. “in what respect they are useful.” Plato is fond of the half legal καθ᾽ τι. Cf. Lysis 210 C, Polit. 298 C.

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.

11 πραγματείαν: interesting is the development of this word from its use in Phaedo 63 A (“interest,” “zeal,” “inquiring spirit.” Cf. Aristot.Top. 100 a 18, Eth. Nic. 1103 b 26, Polyb. i. 1. 4, etc.

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.

13 μέθοδον: this word, like πραγματεία came to mean “treatise.”

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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