[Footnote 72: 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 [Greek: kath' o(/son ê)=n dunato/n]. 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 [Greek: katemathêmatikeu/sato tê\n phu/sin], 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 Coelo, iii. 8, 306-307, and elsewhere.] [Footnote 73: Plato, Timæus, p. 56 C. [Greek: o(/pêper ê( tê=s A)na/gkês e(kou=sa peisthei=sa te phu/sis u(pei=ke.]] [Footnote 74: Plato, Timæus, pp. 55-56.] Such was the mode of formation of the four so-called elemental bodies.[75] Of each of the four, there are diverse species or varieties: and that which distinguishes one variety of the same element from another variety is, that the constituent triangles, though all similar, are of different magnitudes. The diversity of these combinations, though the primary triangles are similar, is infinite: the student of Nature must follow it out, to obtain any probable result.[76] [Footnote 75: Plato, Timæus, p. 57 C. [Greek: o(/sa a)/krata kai\ prô=ta sô/mata.]