And when four equilateral triangles are combined so that three plane angles meet in a point, they form one solid angle, which comes next in order to the most obtuse of the plane angles. And when four such angles are produced, the first solid figure Footnote 1i.e., the tetrahedron or pyramid (molecule of fire). is constructed, which divides the whole of the circumscribed sphere into equal and similar parts. And the second solid Footnote 2i.e., the octahedron (molecule of air). is formed from the same triangles, but constructed out of eight equilateral triangles, which produce one solid angle out of four planes; and when six such solid angles have been formed, the second body in turn is completed. And the third solid Footnote 3i.e., the icosahedron (molecule of water). is composed of twice sixty of the elemental triangles conjoined, and of twelve solid angles, each contained by five plane equilateral triangles, and it has, by its production, twenty equilateral triangular bases.
Now the first of the elemental triangles ceased acting when it had generated these three solids, the substance of the fourth Kind Footnote 4i.e., the cube, composed of 6x4 rectangular isosceles triangles (molecule of earth). being generated by the isosceles triangle. Four of these combined, with their right angles drawn together to the center, produced one equilateral quadrangle; and six such quadrangles, when joined together, formed eight solid angles, each composed of three plane right angles; and the shape of the body thus constructed was cubic, having six plane equilateral quadrangular bases. And seeing that there still remained one other compound figure, the fifth, Footnote 5i.e., the dodecahedron. How God used it up
is obscure: the reference may be to the 12 signs of the Zodiac. God used it up for the Universe in his decoration thereof.
Now in reasoning about all these things, a man might question whether he ought to affirm the existence of an infinite diversity of Universes or a limited number; and if he questioned aright he would conclude that the doctrine of an infinite diversity is that of a man unversed Footnote 6There is a play here on the two senses of ἄπειρος, unlimited and unskilled; Cf. Phileb. 17 E. The doctrine of an infinite number of worlds was held by the Atomists. in matters wherein he ought to be versed; but the question whether they ought really to be described as one Universe or five is one which might with more reason give us pause. Now our view declares the Universe to be essentially one, in accordance with the probable account; but another man, considering other facts, will hold a different opinion. Him, however, we must let pass. But as for the Kinds which have now been generated by our argument, let us assign them severally to fire and earth and water and air. To earth let us give the cubic form; for of the four Kinds earth is the most immobile and the most plastic body, and of necessity the body which has the most stable bases must be pre-eminently of this character. Now of the triangles we originally assumed, the basis formed by equal sides is of its nature more stable than that formed by unequal sides; and of the plane surfaces which are compounded of these several triangles, the equilateral quadrangle, both in its parts and as a whole, has a more stable base than the equilateral triangle.