Timaeus
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
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 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 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
one, they will form one large mass of another kind. So much for
their passage into one another. I have now to speak of their
several kinds, and show out of what combinations of numbers each
of them was formed. The first will be the simplest and smallest
construction, and its element is that triangle which has its
hypotenuse twice the lesser side. When two such triangles are
joined at the diagonal, and this is repeated three times, and the
triangles rest their diagonals and shorter sides on the same
point as a centre, a single equilateral triangle is formed out of
six triangles; and four equilateral triangles, if put together,
make out of every three plane angles one solid angle, being that
which is nearest to the most obtuse of plane angles; and out of
the combination of these four angles arises the first solid form
which distributes into equal and similar parts the whole circle
in which it is inscribed. The second species of solid is formed
out of the same triangles, which unite as eight equilateral
triangles and form one solid angle out of four plane angles, and
out of six such angles the second body is completed. And the
third body is made up of 120 triangular elements, forming twelve
solid angles, each of them included in five plane equilateral
triangles, having altogether twenty bases, each of which is an
equilateral triangle. The one element (that is, the triangle
which has its hypotenuse twice the lesser side) having generated
these figures, generated no more; but the isosceles triangle
produced the fourth elementary figure, which is compounded of
four such triangles, joining their right angles in a centre, and
forming one equilateral quadrangle. Six of these united form
eight solid angles, each of which is made by the combination of
three plane right angles; the figure of the body thus composed is
a cube, having six plane quadrangular equilateral bases. There
was yet a fifth combination which God used in the delineation of
the universe.
Now, he who, duly reflecting on all this, enquires whether the
worlds are to be regarded as indefinite or definite in number,
will be of opinion that the notion of their indefiniteness is
characteristic of a sadly indefinite and ignorant mind. He,
however, who raises the question whether they are to be truly
regarded as one or five, takes up a more reasonable position.
Arguing from probabilities, I am of opinion that they are one;
another, regarding the question from another point of view, will
be of another mind. But, leaving this enquiry, let us proceed to
distribute the elementary forms, which have now been created in
idea, among the four elements.
To earth, then, let us assign the cubical form; for earth is the
most immoveable of the four and the most plastic of all bodies,
and that which has the most stable bases must of necessity be of
such a nature. Now, of the triangles which we assumed at first,
that which has two equal sides is by nature more firmly based
than that which has unequal sides; and of the compound figures
which are formed out of either, the plane equilateral quadrangle
has necessarily a more stable basis than the equilateral
triangle, both in the whole and in the parts. Wherefore, in
assigning this figure to earth, we adhere to probability; and to
water we assign that one of the remaining forms which is the
least moveable; and the most moveable of them to fire; and to air
that which is intermediate. Also we assign the smallest body to
fire, and the greatest to water, and the intermediate in size to
air; and, again, the acutest body to fire, and the next in
acuteness to air, and the third to water. Of all these elements,
that which has the fewest bases must necessarily be the most
moveable, for it must be the acutest and most penetrating in
every way, and also the lightest as being composed of the
smallest number of similar particles: and the second body has
similar properties in a second degree, and the third body in the
third degree. Let it be agreed, then, both according to strict
reason and according to probability, that the pyramid is the
solid which is the original element and seed of fire; and let us
assign the element which was next in the order of generation to
air, and the third to water. We must imagine all these to be so
small that no single particle of any of the four kinds is seen by
us on account of their smallness: but when many of them are
collected together their aggregates are seen. And the ratios of
their numbers, motions, and other properties, everywhere God, as
far as necessity allowed or gave consent, has exactly perfected,
and harmonized in due proportion.
From all that we have just been saying about the elements or
kinds, the most probable conclusion is as follows:—earth, when
meeting with fire and dissolved by its sharpness, whether the
dissolution take place in the fire itself or perhaps in some mass
of air or water, is borne hither and thither, until its parts,
meeting together and mutually harmonising, again become earth;
for they can never take any other form. But water, when divided
by fire or by air, on re-forming, may become one part fire and
two parts air; and a single volume of air divided becomes two of
fire. Again, when a small body of fire is contained in a larger
body of air or water or earth, and both are moving, and the fire
struggling is overcome and broken up, then two volumes of fire
form one volume of air; and when air is overcome and cut up into
small pieces, two and a half parts of air are condensed into one
part of water. Let us consider the matter in another way. When
one of the other elements is fastened upon by fire, and is cut by
the sharpness of its angles and sides, it coalesces with the
fire, and then ceases to be cut by them any longer. For no
element which is one and the same with itself can be changed by
or change another of the same kind and in the same state. But so
long as in the process of transition the weaker is fighting
against the stronger, the dissolution continues. Again, when a
few small particles, enclosed in many larger ones, are in process
of decomposition and extinction, they only cease from their
tendency to extinction when they consent to pass into the
conquering nature, and fire becomes air and air water. But if
bodies of another kind go and attack them (i.e. the small
particles), the latter continue to be dissolved until, being
completely forced back and dispersed, they make their escape to
their own kindred, or else, being overcome and assimilated to the
conquering power, they remain where they are and dwell with their
victors, and from being many become one. And owing to these
affections, all things are changing their place, for by the
motion of the receiving vessel the bulk of each class is
distributed into its proper place; but those things which become
unlike themselves and like other things, are hurried by the
shaking into the place of the things to which they grow like.
Now all unmixed and primary bodies are produced by such causes as
these. As to the subordinate species which are included in the
greater kinds, they are to be attributed to the varieties in the
structure of the two original triangles. For either structure did
not originally produce the triangle of one size only, but some
larger and some smaller, and there are as many sizes as there are
species of the four elements. Hence when they are mingled with
themselves and with one another there is an endless variety of
them, which those who would arrive at the probable truth of
nature ought duly to consider.
Unless a person comes to an understanding about the nature and
conditions of rest and motion, he will meet with many
difficulties in the discussion which follows. Something has been
said of this matter already, and something more remains to be
said, which is, that motion never exists in what is uniform. For
to conceive that anything can be moved without a mover is hard or
indeed impossible, and equally impossible to conceive that there
can be a mover unless there be something which can be
moved—motion cannot exist where either of these are wanting, and
for these to be uniform is impossible; wherefore we must assign
rest to uniformity and motion to the want of uniformity. Now