The twenty triangular faces of an icosahedron form the faces or
sides of two regular octahedrons and of a regular pyramid (20 = 8
x 2 + 4); and therefore, according to Plato, a particle of water
when decomposed is supposed to give two particles of air and one
of fire. So because an octahedron gives the sides of two pyramids
(8 = 4 x 2), a particle of air is resolved into two particles of
fire.
The transformation is effected by the superior power or number of
the conquering elements. The manner of the change is (1) a
separation of portions of the elements from the masses in which
they are collected; (2) a resolution of them into their original
triangles; and (3) a reunion of them in new forms. Plato himself
proposes the question, Why does motion continue at all when the
elements are settled in their places? He answers that although
the force of attraction is continually drawing similar elements
to the same spot, still the revolution of the universe exercises
a condensing power, and thrusts them again out of their natural
places. Thus want of uniformity, the condition of motion, is
produced. In all such disturbances of matter there is an
alternative for the weaker element: it may escape to its kindred,
or take the form of the stronger—becoming denser, if it be
denser, or rarer if rarer. This is true of fire, air, and water,
which, being composed of similar triangles, are interchangeable;
earth, however, which has triangles peculiar to itself, is
capable of dissolution, but not of change. Of the interchangeable
elements, fire, the rarest, can only become a denser, and water,
the densest, only a rarer: but air may become a denser or a
rarer. No single particle of the elements is visible, but only
the aggregates of them are seen. The subordinate species depend,
not upon differences of form in the original triangles, but upon
differences of size. The obvious physical phenomena from which
Plato has gathered his views of the relations of the elements
seem to be the effect of fire upon air, water, and earth, and the
effect of water upon earth. The particles are supposed by him to
be in a perpetual process of circulation caused by inequality.
This process of circulation does not admit of a vacuum, as he
tells us in his strange account of respiration.