Having said this, I paused. And Philippus immediately cried out: Whether this be certain or not, I will not be too positive; but if we carry God beyond one world, it would more gratify me to know why we should make him the Creator only of five worlds and no more, and what proportion this number bears to that of the worlds, than to know why the word E I was inscribed upon this temple. For this is neither a triangular, a quadrate, a perfect, nor a cubic number, neither does it yield any elegancy to such as are delighted in this kind of sciences. As to what concerns the argument dawn from the number of elements, which Plato seems to have touched upon, it is obscure and improbable, and will not afford this consequence,—that, as there are formed from matter five sorts of regular bodies, which have equal angles and equal sides, and are environed with equal superficies, so there were from the beginning five worlds, made and formed of these five bodies. Yet Theodorus the Solian, said I, when he reads Plato’s mathematics to his scholars, both keeps to the text and clearly expounds it, when he saith, the pyramid, octahedron, dodecahedron. icosahedron (which Plato lays down as the first bodies) are all beautiful both in their proportions and equalities; Nature cannot contrive and make better than these, nor perhaps so good. Yet they have not all the same constitution and origin; for the least and slightest of the five is the pyramid; the greatest, which has most parts, is the dodecahedron; and of the other two, the icosahedron is greater than the octahedron by more than twofold, if you compare their number of triangles. And therefore it is impossible they should be all made at once, of one and the same matter; for the smallest and most subtile have been certainly more pliable to the hand of the workman who moved and fashioned the matter, and consequently were sooner made and shaped, than those which have stronger parts and a greater mass of bodies, and whose composition was more laborious and difficult, like the dodecahedron. Whence it follows that the pyramid was the first body, and not one of the others, which were by nature last produced. Now the way also to avoid this absurdity is to separate and divide matter into five worlds; here the pyramid (for she is the first and most simple), there the octahedron, and there the icosahedron; and out of that which exists first in every one of these the rest draw their original by the concretion of parts, by which every thing is changed into every thing, as Plato himself shows us by examples throughout. But it will suffice us briefly to learn thus much. Air is engendered by the extinction of fire, and the same being subtilized and rarefied produceth fire. Now by the seeds of these two we may find out the passions and transmutations of all. The seminary or beginning of fire is the pyramid, consisting of twenty-four first triangles; and the octahedron is the seminary of the air, consisting of forty-eight triangles of the same kind. So that the one element of air stands upon two of fire, joined together and condensed. And again, one body or element of air is divided into two of fire, which again, becoming thick and hard, is changed into water; so that, throughout, that which comes first into light gives easily birth unto the rest by transmutation. And so it comes to pass, that there is not merely one first principle of all things; but one thing is so mixed with the origin of another, in the several changes and alterations of nature by motion, that the same name and denomination belong equally to all. But here Ammonius interrupted him, and said: Notwithstanding that those things are so peremptorily and so pompously asserted by Theodorus, yet I shall wonder if he be not forced to make use of such suppositions as are destructive of themselves and one of another. For he will have it, that the five worlds he speaks of were not composed all at one time, but that that which was subtilest, and which gave least trouble in the making, came out first into being. And as if it were a consequent, and not a repugnant thing, he supposes that the matter does not always drive out into existence that which is most subtile and simple, but that sometimes the thickest, grossest, and heaviest parts do anticipate the more subtile in generation. But besides this, supposing that there be five primitive bodies or elements, and consequently that there be as many worlds, there are but four of those orders which he discourses rationally concerning. For as to the cube, he takes it away and removes it, as it were in a game of counters; for it is naturally unfit either to turn into any thing besides itself, or to yield that any of those other bodies be converted into it, inasmuch as the triangles of which they consist be not of the same sort. For all the rest consist in common of demi-triangles (or halves of equilateral triangles); but the proper subject of which the cube is particularly composed is the right isosceles triangle, which admits no inclination to a demi-triangle, nor can possibly be united and incorporated with it. If there be then five bodies, and consequently five worlds, and in each of these worlds the principle of generation be that body which is first produced, it must happen that, where the cube is the first in generation, none of the rest can possibly be produced, it being contrary to its nature to change into any of them. Not to insist here, that Theodorus and those of his mind make the element or principle of which the dodecahedron is composed to be different from the rest, it not being that triangle which is termed scalene, with three unequal sides, out of which the pyramid, octahedron, and icosahedron, according to Plato, are produced; so that (said Ammonius laughing) you must solve these objections, or offer something new concerning the matter in debate. See Plato’s discussion of triangles and the regular solids, Timaeus, pp. 53 C-56 C, with the commentaries See also Grote’s Plato, Vol. III. p. 269. (G.) And I answered him, that, for my part, I knew not at present how to say any thing which carried more probability. But perhaps (said I) it is better for a man to give an account of his own opinion than of another’s. Therefore I say that, there being supposed from the beginning of things two several natures contrary to each other,— the one sensible, mutable, subject to generation, corruption, and change every way, the other spiritual and intelligible, and abiding always in the same state,—it would be very strange, my friends, to say that the spiritual nature admitteth of division and hath diversity and difference in it, and to be angry if a man will not allow the passible and corporeal nature to be wholly united in itself, without dividing it into many parts. For it is most suitable to the permanent and divine natures to be tied and linked to each other, and to avoid, as much as is possible, all division and separation; and yet, amongst incorporeal natures the power of diversity works greater differences in regard to essential forms and reason, than those of distance of place in the corporeal world. And therefore Plato, refuting those who hold this proposition, that all is one, asserts these five grounds and principles of all,—entity, identity, diversity, motion, and rest; which five immaterial principles being admitted, it is no marvel if Nature have made every one of these to be an imitation, though not exact, yet as perfect and agreeable as could be drawn, of a correspondent principle in the corporeal mystery, partaking, as much as can be, of its power and virtue. For it is very plain that the cube is most proper and agreeable to repose and rest, by reason of the stability and firmness of those plain surfaces of which it consists. And as to the pyramid, everybody soon sees and acknowledges the nature of fire in it, by the slenderness of its decreasing sides, and the sharpness of its angles; and the nature of the dodecahedron, apt to comprehend all the other figures, may seem more properly to be the corporeal image of Ens, or Being in the general, indifferent to this or that particular form or shape. And of the other two which remain, the icosahedron resembleth the principle of diversity, and the octahedron principally partakes of the identical nature. And thus from one of these the air is produced, which partakes of and borders upon every substance, under one and the same outward form and appearance; and the other has afforded us the element of water, which by mixture may put on the greatest diversity of qualities. Therefore if Nature requires a certain uniformity and harmony in all things, it must be then that there are neither more nor fewer worlds in the corporeal nature than there are patterns or samples in the incorporeal, to the end that each pattern or sample in the invisible nature may have its own primary position and power, answering to a secondary or derivative in the different constitution or composition of bodies. And this may serve for an answer to those that wonder at our dividing Nature, subject to generation and alteration, into so many kinds. But I entreat you all further, attentively to consider with yourselves that, of the two first and supreme principles of all things,—that is to say, the unity, and the indefinite binary or duality,—this latter, being the element and chief origin of all deformity and disorder, is termed infinity, and on the contrary, the nature of unity, determining and limiting the void infinity, which has no proportion nor termination, reduces it into form, and renders it in some manner capable of receiving a denomination which belongs only to sensible and particular things. Now these two general principles appear first in number; for the multitude is indeed no number, unless a certain form of the matter resulting out of indeterminate infinity is cut off, and bounded within respective limits, either shorter or longer. For then each multitude is made number, when once it is determined and limited by unity; whereas, if we take away unity, then the indeterminate duality brings all into confusion, and renders it without harmony, without number or measure. Now, the form not being the destruction of matter, but rather the order and the beauty of it, both these principles therefore must be within number, from whence ariseth the chief disparity and greatest difference. For the infinite and indeterminate principle is the cause of the even number; and the other better principle, which is the unity, is the father (as it were) of the odd number. So that the first even number is two, and the first odd number is three; of which is composed five by conjunction, which is by its composition common to both, but of power or nature not even but odd. For, since sensible and corporeal nature is divided into several parts, on account of its inborn necessity of diversity, it was necessary that the number of these parts should not be either the first even number, nor yet the first uneven or odd, but a third, consisting of both; to the end that it might be procreated out of both principles, viz. of that which causeth the even number, and of that which produceth the odd; for the one cannot be parted from the other, inasmuch as both have the nature, power, and force of a principle. These two principles being then joined together, the better one being mightier prevails over the indeterminate infinity or duality, which divideth the corporeal nature; and thus the matter being divided, the unity interposing itself between has hindered the universe from being divided and parted into two equal portions. But there has been a multitude of worlds caused by the diversity and disagreement of the infinite Nature; but this multitude was brought into an odd number by the virtue and power of identity, or the finite principle; and it was therefore odd, because the better principle would not suffer Nature to stretch itself further than was fitting. For if there had been nothing but pure and simple unity, the matter would have known no separation; but being mixed with the dividing nature of duality, it has by this means suffered separation and division; yet it has stopped here, by the odd numbers being the superior and master to the even.