Timaeus — Plato

evenly hither and thither, was shaken by them, and by its motion again shook them ; and the elements when moved were separated and carried continually, some one way, some another ; as, when grain is shaken and winnowed by fans and other instruments used in the threshing of corn, the 53 close and heavy particles are borne away and settle in one direction, and the loose and light particles in another.

In this manner, the four kinds or elements were then shaken by the receiving vessel, which, moving like a winnowing machine, scattered far away from one another the elements most unlike, and forced the most similar elements into close contact. Wherefore also the various elements had different places before they were arranged so as to form the universe. At first, they were all without reason and measure.

But when the world began to get into order, fire and water and earth and air had only certain faint traces of themselves, and were altogether such as everything might be expected to be in the absence of God ; this, I say, was their nature at that time, and God fashioned them by form and number.

Let it be consistently maintained by us in all that we say that God made them as far as possible the fairest and best, out of things which were not fair and good. And now I will endeavour to show you the disposition and generation of them by an unaccustomed argument, which I am compelled to use ; but I believe that you will be able to follow me, for your education has made you familiar with the methods of science.

In the first place, then, as is evident to all, fire and earth and water and air are bodies.

And every sort of body possesses solidity, and every solid must necessarily be contained in planes ; and every plane rectilinear figure is composed of triangles ; and all triangles are originally of two kinds, both of which are made up of one right and two acute angles ; one of them has at either end of the base the half of a divided right angle, having equal sides, while in the other the right angle is divided into unequal parts, having ! unequal sides.

These, then, proceeding by a combination of probability with demonstration, we assume to be the original elements of fire and the other bodies ; but the principles which are prior to these God only knows, and he of men

Tiviaeus. TlMAEUS. forces, which swayed her to .-xnd fro. Thus earth, air, fire and water, were sifted into their proper places, while they were yet in a rudimentary state, before Clod perfected them by form and number.

The manner of their generation was as follows: — The four elements are solid bodies, and all solids are made up of plane surfaces, and all plane surfaces of triangles. All triangles

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The two component elements of space.

Timaeus. \ TiMAEUS. are ultimately of two kinds, — i. e. the rectangular isosceles, and the rectangular scalene.

The rectangular isosceles, which has but one form, and that one of the many forms of scalene which is half of an equilateral triangle were chosen for making the elements.

Three of them are generated out of the latter: the fourth alone from the former. Therefore only three can pass into each other.

who is the friend of God. And next we have to determine what are the four most beautiful bodies which are unlike one another, and of which some are capable of resolution into one another ; for having discovered thus much, we shall know the true origin of earth and fire and of the proportionate and intermediate elements. And then we shall not be willing to allow that there are any distinct kinds of visible bodies fairer than these.

Wherefore we must endeavour to construct the four forms of bodies which excel in beauty, and then we shall be able to say that we have sufficiently apprehended their nature. Now of the two triangles, the isosceles 54 has one form only ; the scalene or unequal-sided has an infinite number.

Of the infinite forms we must select the most beautiful, if we are to proceed in due order, and any \ one who can point out a more beautiful form than ours for I the construction of these bodies, shall carry off the palm, not • as an enemy, but as a friend.

Now, the one which we maintain to be the most beautiful of all the many triangles (and we need not speak of the others) is that of which the double forms a third triangle which is equilateral ; the reason of this would be long to tell ; he who disproves what we are saying, and shows that we are mistaken, may claim a friendly victory.

Then let us choose two triangles, out of which fire and the other elements have been constructed, one isosceles, the other having the square of the longer side equal to three times the square of the lesser side.

Now is the time to explain what was before obscurely said : there was an error in imagining that all the four elements might be generated by and into one another ; this, I say, was an erroneous supposition, for there are generated from the triangles which we have selected four kinds — three from the one which has the sides unequal ; the fourth alone is framed out of the isosceles triangle.

Hence they cannot all be resolved into one another, a great number of small bodies being combined into a few large ones, or the converse. But three of them can be thus resolved and compounded, for they all spring from one, and when the greater bodies are broken up, many small bodies will spring up out of them and take their own proper figures ; or, again, when many small bodies are dissolved into their triangles, if they become