mind, though in enunciating it he does not declare the restriction under which alone it is true. M. Boeckh (Untersuchungen über das Kosmische System des Platon, p. 17) approves of Martin's explanation. At the same time M. Martin has given no proof that Plato had in his mind the distinction between prime numbers and other numbers, for his references in p. 338 do not prove this point; moreover, the explanation assumes such very loose expression, that the phrase of M. Cousin in his note (p. 334) is, after all, perfectly just: "Platon n'a pas songé à donner à sa phrase une rigueur mathématique": and the more simple explanation of M. Cousin (though Martin rejects it as unworthy) may perhaps include all that is really intended. "Si deux surfaces peuvent être unies par un seul terme intermédiaire, il faudra deux termes intermédiaires pour unir deux solides: et l'union sera encore plus parfaite si la raison des deux proportions est la même."] [Footnote 26: Plat. Timæus, p. 32 E.] [Side-note: Body of the Kosmos, perfectly spherical--its rotations.] The Kosmos was constructed as a perfect sphere, rounded, because that figure both comprehends all other figures, and is, at the same time, the most perfect, and most like to itself.[27] The Demiurgus made it perfectly smooth on the outside, for various reasons.[28] First, it stood in no need of either eyes or ears, because there was nothing outside to be seen or heard. Next, it did not want organs of respiration, inasmuch as there was no outside air to be breathed:--nor nutritive and excrementary organs, because its own decay supplied it with nourishment, so that it was self-sufficing, being constructed as its own agent and its own patient.[29] Moreover the Demiurgus did not furnish it with hands, because there was nothing for it either to grasp or repel--nor with legs, feet, or means of standing, because he assigned to it only one of the seven possible varieties of movement.[30] He gave to it no other movement except that of rotation in a circle, in one and the same place: which is the sort of movement that belongs most to reason and intelligence, while it is impracticable to all other figures except the spherical.[31] [Footnote 27: Plato, Timæus, p. 33 B. [Greek: kuklotere\s au)to\ e)torneu/sato], &c.] [Footnote 28: Plato, Timæus, p. 33 C. [Greek: lei=on de\ dê\ ku/klô| pa=n e)/xôthen au)to\ a)pêkribou=to, pollô=n cha/rin], &c. Aristotle also maintains that the sphericity of the Kosmos is so exact that no piece of workmanship can make approach to it. (De Coelo, ii. p. 287, b. 15.)] [Footnote 29: Plato, Timæus, p. 33 E. On this point the Platonic Timæus is not Pythagorean, but the reverse. The Pythagoreans recognised extraneous to the Kosmos, [Greek: to\ a)/peiron pneu=ma] or [Greek: to\ keno/n]. The Kosmos was supposed to inhale this vacuum, which penetrating into the interior, formed the separating interstices between its constituent parts (Aristot. Physic. iv. p. 213, b. 22).]