De Defectu Oraculorum

Manfully and zealously, said Ammonius, have these matters been worked out by Theodorus; but I should be surprised if it should not appear that he has made use of assumptions which nullify each other. For he insists that all the five shall not undergo construction at the same time, but the simplest always, which requires the least trouble to construct, shall first issue forth into being. Then, as a corollary to this, and not conflicting with it, he lays down the principle that not all matter brings forth the simplest and most rudimentary form first, but that sometimes the ponderous and complex forms, in the time of their coming into being, are earlier in arising out of matter. But apart from this, five bodies having been postulated as primary, and on the strength of this the number of worlds being put as the same, he adduces probability with reference to four only; the cube he has taken off the board, as if he were playing a game with counters, since, because of its nature, it cannot transmute itself into them nor confer upon them the power of transmutation into itself, inasmuch as the triangles are not homologous triangles. For in the others the common triangle which underlies them all is the half-triangle; but in this, and peculiar to it alone, is the isosceles triangle, which makes no convergence towards the other nor any conjunction that would unify the two. If, therefore, there are five bodies and five worlds, and in each one body only has precedence in coming into being, then where the cube has been the first to come

into being, there will be none of the others, since, because of its nature, it cannot transmute itself into any one of them. I leave out of account the fact that they make the element of the dodecahedron, as it is called, something else and not that scalene from which Plato constructs the pyramid and the octahedron and the icosahedron. So, added Ammonius, laughing,either you must solve these problems or else contribute something of your own concerning this difficulty in which we all find ourselves involved.