Respecting such proportions, the theory which Plato here lays out is admitted by himself to be a novel one; but it is doubtless borrowed, with more or less modification, from the Pythagoreans. Every solid body is circumscribed by plane surfaces: every plane surface is composed of triangles: all triangles are generated out of two--the right-angled isoskeles triangle--and the right-angled scalene or oblong triangle. Of this oblong there are infinite varieties: but the most beautiful is a right-angled triangle, having the hypotenuse twice as long as the lesser of the two other sides.[71] From this sort of oblong triangle are generated the tetrahedron or pyramid--the octahedron--and the eikosihedron: from the equilateral triangle is generated the cube. The cube, as the most stable and solid, was assigned by the Demiurgus for the fundamental structure of earth: the pyramid for that of fire: the octahedron for that of air: the eikosihedron for that of water. The purpose was that the four should be in continuous geometrical proportion: as Fire to Air, so Air to Water: as Air to Water, so Water to Earth. Lastly, the Dodekahedron was assigned as the basis of structure for the spherical Kosmos itself or universe.[72] Upon this arrangement each of the three elements--fire, water, air--passes into the other; being generated from the same radical triangle. But earth does not pass into either of the three (nor either of these into earth), being generated from a different radical triangle. The pyramid, as thin, sharp, and cutting, was assigned to fire as the quickest and most piercing of the four elements: the cube as most solid and difficult to move, was allotted to earth, the stationary element. Fire was composed of pyramids of different size, yet each too small to be visible by itself, and becoming visible only when grouped together in masses: the earth was composed of cubes of different size, each invisible from smallness: the other elements in like manner, each from its respective solid,[73] in exact proportion and harmony, as far as Necessity could be persuaded to tolerate. All the five regular solids were thus employed in the configuration and structure of the Kosmos.[74] [Footnote 71: Plato, Timæus, pp. 53-54. 53 C: [Greek: a)êthei= lo/gô| dêlou=n].]