in the Philolaic fragment, with the "hull of the sphere."[1] Whatever we may think of the authenticity of the fragments there is no reason to doubt that this is a genuine Pythagorean expression, and it must be taken in close connexion with the word "keel" applied to the central fire.[2] The structure of the world was compared to the building of a ship, an idea of which there are other traces.[3] The key to what we are told of the dodecahedron is also given by Plato. In the Phaedo, which must have been written before the doctrine of the regular solids was fully established, we read that the "true earth," if looked at from above, is "many-coloured like the balls that are made of twelve pieces of leather."[4] In the Timaeus the same thing is referred to in those words: "Further, as there is still one construction left, the fifth, God made use of it for the universe when he painted it."[5] The point is that the dodecahedron approaches more nearly to the sphere than any other of the regular solids. The twelve pieces of leather used to make a ball would all be regular pentagons; and, if the material were not flexible
- ↑ 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. In the Pythagorean myth of Plato's Politicus, the world is regarded as a ship, of which God is the κυβερνήτης (272 a sqq.). The πόντος τῆς ἀνομοιότητος (273 d) is just the ἄπειρον.
- ↑ Aet. ii. 4, 15, ὅπερ τρόπεως δίκην προϋπεβάλετο τῇ τοῦ παντὸς <σφαίρᾳ> ὁ δημιουργὸς θεός.
- ↑ 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.
- ↑ Plato, Phaed. 110 b 6, ὥσπερ οἱ δωδεκάσκυτοι σφαῖραι, the meaning of which phrase is quite correctly explained by Plutarch, Plat. q. 1003 b καὶ γὰρ μάλιστα τῷ πλήθει τῶν στοιχείων ἀμβλύτητι δὲ τῶν γωνιῶν τὴν εὐθύτητα διαφυγὸν εὐκαμπές ἐστι [τὸ δωδεκάεδρον], καὶ τῇ περιτάσει ὥσπερ αἱ δωδεκάσκυτοι σφαῖρα κυκλοτερὲς γίγνεται καὶ περιληπτικόν.
- ↑ 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, in which the constellations were placed. For the history of such methods see Newbold in Arch. xix. pp. 198 sqq.
