[802]. Plato, Tim. 31 b 5.
[803]. Plato, Tim. 54 c 4. It is to be observed that in Tim. 48 b 5 Plato says of the construction of the elements οὐδείς πω γένεσιν αὐτῶν μεμήνυκεν, which implies that there is some novelty in the theory as he makes Timaios state it. If we read the passage in the light of what has been said in § 141, we shall be inclined to believe that Plato is working out the Pythagorean doctrine on the lines of the discovery of Theaitetos. There is another indication of the same thing in Arist. Gen. Corr. Β, 3. 330 b 16, where we are told that, in the Διαιρέσεις, Plato assumed three elements, but made the middle one a mixture. This is stated in close connexion with the ascription of Fire and Earth to Parmenides.
[804]. See above, Chap. IV. p. 213, [n. 462].
[805]. Aet. ii. 6, 5 (R. P. 80); “Philolaos,” fr. 12 (= 20 M.; R. P. 79). On the ὁλκάς, see Gundermann in Rhein. Mus. 1904, pp. 145 sqq. I agree with him in holding that the reading is sound, and that the word means “ship,” but I think that it is the structure, not the motion, of a ship which is the point of comparison.
[806]. Aet. ii. 4, 15, ὅπερ τρόπεως δίκην προϋπεβάλετο τῇ τοῦ παντὸς <σφαίρᾳ> ὁ δημιουργὸς θεός.
[807]. Cf. the ὑποζώματα of Plato, Rep. 616 c 3. As ὕλη generally means “timber” for shipbuilding (when it does not mean firewood), I suggest that we should look in this direction for an explanation of the technical use of the word in later philosophy. Cf. Plato, Phileb. 54 c 1, γενέσεως ... ἕνεκα ... πᾶσαν ὕλην παρατίθεσθαι πᾶσιν, which is part of the answer to the question πότερα πλοίων ναυπηγίαν ἕνεκα φῂς γίγνεσθαι μᾶλλον ἢ πλοῖα ἕνεκα ναυπηγίας; (ib. b 2); Tim. 69 a 6, οἷα τέκτοσιν ἡμῖν ὕλη παράκειται.
[808]. Plato, Phd. 110 b 6, ὥσπερ οἱ δωδεκάσκυτοι σφαῖραι with Wyttenbach’s note.
[809]. Plato, Tim. 55 c 4. Neither this passage nor the last can refer to the Zodiac, which would be described by a dodecagon, not a dodecahedron. What is implied is the division of the heavens into twelve pentagonal fields.
[810]. Gow, Short History of Greek Mathematics, pp. 164 sqq.
[811]. This is pointed out by Kinkel, Gesch. der Phil. vol. i. p. 121.