Note 72 — Chapter XXXVIII · TIMÆUS AND KRITIAS.
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That Plato intended, by this elaborate geometrical construction, to arrive at a continuous geometrical proportion between the four elements, he tells us (p. 32 A-B), adding the qualifying words καθ’ ὅσον ἦν δυνατόν. M. Boeckh, however (De Platonicâ Corporis Mundani Fabricâ, pp. viii.-xxvi.), has shown that the geometrical proportion cannot be properly concluded from the premisses assumed by Plato:— “Platonis elementorum doctrinam et parum sibi constare, neque omnibus numeris absolutam esse, immo multis incommodis laborare, et divini ingenii lusui magis quam disciplinæ severitati originem debere fatebimur; nec profundiorem et abstrusiorem naturæ cognitionem in eâ sitam esse suspicabimur — in quem errorem etiam Joh. Keplerus, summi ingenii homo, incidit”.
Respecting the Dodekahedron, see Zeller, Gesch. der Philos. ii. p. 513, ed. 2nd. There is some obscurity about it. In the Epinomis (p. 981 C) Plato gives the Æther as a fifth element, besides the four commonly known and recited in the Timæus. It appears that Philolaus, as well as Xenokrates, conceived the Dodekahedron as the structural form of Æther (Schol. ad Aristot. Physic. p. 427, a. 16, Brandis): and Xenokrates expressly says, that Plato himself recognised it as such. Zeller dissents from this view, and thinks that nothing more is meant than the implication, that the Dodekahedron can have a sphere described round it more readily than any of the other figures named.
Opponents of Plato remarked that he κατεμαθηματικεύσατο τὴν φύσιν, Schol. ad Aristot. Metaph. A. 985, b. 23, p. 539, Brandis. Aristotle devotes himself in many places to the refutation of the Platonic doctrine on this point; see De Cœlo, iii. 8, 306-307, and elsewhere.