The Obsolesence of Oracles (32)

Yes, said I, Theodorus of Soli[*] seems to follow up the subject not ineptly in his explanations of Plato’s mathematical theories. He follows it up in this way: a pyramid, an octahedron, an icosahedron, and a dodecahedron, the primary figures which Plato predicates, are all beautiful because of the symmetries and equalities in their relations, and nothing superior or even like to these[*] has been left for Nature to compose and fit together. It happens, however, that they do not all have one form of construction, nor have they all a similar origin, but the pyramid is the simplest and smallest, while the dodecahedron is the largest and most complicated. Of the remaining two the icosahedron is more than double the octahedron in the number of its triangles. For this reason it is impossible for them all to derive their origin from one and the same matter. For those that are simple and small and more rudimentary in their structure would necessarily be the first to respond to the instigating and formative power, and to be completed and acquire substantiality earlier than those of large parts and many bodies, from which class comes the dodecahedron, which requires

more labour for its construction. Hence it follows that the only primal body is the pyramid, and not one of the others, since by their nature they are outdistanced by it in coming into being. Accordingly, the remedy which exists for this strange state of affairs consists in the division and separation of matter into five worlds, one where the pyramid shall acquire substantiality first, another for the octahedron, and another for the icosahedron; then from the one that first acquires substantiality in each world the rest will have their origin, since a transmutation for everything into everything takes place according to the adaptability of parts to fit together, as Plato[*] himself has indicated, going into the details of nearly all cases. But for us it will suffice to acquire the knowledge in brief form. Since air is formed when fire is extinguished, and when rarefied again gives off fire out of itself, we must observe the behaviour of each of the generative elements and their transmutations. The generative elements of fire are the pyramid,[*] composed of twenty-four primary triangles, and likewise for air the octahedron, composed of forty-eight of the same. Therefore one element of air is produced from two corpuscles of fire combined and united; and that of air again, when divided, is separated into two corpuscles of fire, and again, when compressed and condensed, it goes off into the form of water. The result is that in every case the one which first acquires substantiality always affords the others a ready means of coming into being through transmutation; and it is not one alone that first exists, but another in a different environment is endowed with movement, which takes the lead and forestalls the others in coming into being, and thus the name of being first is kept by all.