Stephanus 55

55a angle, one that arises next in succession to the bluntest of the plane angles. When four such have been completed, the first solid kind is constructed—one that distributes the whole circumference into equal and like parts. The second comes from the same triangles, put together as eight equilateral triangles, each set of four planes producing one solid angle; and when six such had come to be, the second body in its turn thus found its end. The third came to be from twice sixty of the elements compacted together, 55b with twelve solid angles, each enclosed by five equilateral triangular planes, and twenty bases of equilateral triangles. And the other of the two elements was dismissed, having begotten these; but the isosceles triangle begat the nature of the fourth, constructed in fours, gathering its right angles to the center and making one equilateral square; and six such, 55c compacted together, produced eight solid angles, each fitted together from three right plane angles; and the shape of the body constructed came out cubic, having six square plane bases with equal sides. There being still one fifth construction, the god used it for the whole, working it over with figures.

Someone reckoning all this in due measure might here be at a loss whether one must say there are unlimited worlds or a limited number: the 55d unlimited ones he would judge, in truth, to be the doctrine of some science of the unlimited, in which one must be expert; but whether it is ever right to say that they are in truth by nature one or five—standing at that question he would more fittingly be in perplexity. Our account, then, declares it to be by nature one—a god—in accordance with the likely account; another man, having looked elsewhere toward other things, will judge otherwise. But let this be set aside, and let us now distribute in the account the kinds that have come to be into fire and earth and water and air. To earth, then, let us give the cubic kind: 55e for earth is the most immobile of the four kinds and the most plastic of bodies, and the thing that has the safest bases must of all things have come to be such; and the base that is safer by nature, of the triangles posited at the start, is that of the equal-sided over that of the unequal-sided, and the plane composed from each—the equilateral from the equilateral triangle, the square from the right-angled one—stands more firmly of necessity, both in its parts and as a whole.

Timaeus: for this reason

55a angle, it makes one that comes right after the most obtuse of the plane angles. When four of these are completed, the first solid form is put together, one that divides a whole sphere into equal and similar parts. The second comes from the same triangles, but from eight equilateral triangles put together, which make one solid angle out of four plane angles. And when six of these are produced, the second body is completed in this way. The third is formed from twice sixty of the elements fitted together, 55b with twelve solid angles, each of them enclosed by five equilateral plane triangles, and it has twenty bases, which are equilateral triangles. So one of the two triangles was done with generating these, and the isosceles triangle went on to generate the nature of the fourth: it is put together in groups of four, bringing the right angles together at the center and producing one equilateral square. Six of these 55c fitted together produced eight solid angles, each made of three right plane angles joined together. The shape of the body that was formed is a cube, with six square equilateral faces as its bases. There was still one fifth kind of construction left, and the god used it up on the whole, filling in the picture of the universe.

So if someone, thinking all this through properly, were at a loss over whether we should say that there are infinitely many worlds or a limited number, on the 'infinitely many' side 55d he would think it the view of someone truly without limit, in a matter where one needs to be experienced. But whether it is right ever to say that in truth they are one or five, on this ground he would reasonably be at a loss. So the god reveals to us that the universe is naturally one, in line with the likely account; but someone else, looking at other things, will hold a different opinion. Let us set this question aside, and let us now distribute the kinds our account has produced among fire and earth and water and air. Let us give the cube shape to earth. 55e Of the four kinds, earth is the least able to move, and of bodies it is the most easily molded. And the body with the most stable bases must of necessity have come to be like this. Of the two triangles we laid down at the start, the one with equal sides is by nature a more stable base than the one with unequal sides. And of the flat figures put together out of each of them, the equilateral square necessarily stands more firmly than the equilateral triangle, both in its parts and as a whole.

Timaeus: So

55a 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 is constructed, which divides the whole of the circumscribed sphere into equal and similar parts. And the second solid 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. 55b And the third solid 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 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, 55c 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, 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 55d 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 55e 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.