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 harmonised 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 reforming, 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.
