e infinite, and the
union of the two), and out of them has formed the outer circle of the
fixed stars and the inner circle of the planets, divided according to
certain musical intervals; he has also created time, the moving image
of eternity, and space, existing by a sort of necessity and hardly
distinguishable from matter. The matter out of which the world is formed
is not absolutely void, but retains in the chaos certain germs or traces
of the elements. These Plato, like Empedocles, supposed to be four in
number--fire, air, earth, and water. They were at first mixed together;
but already in the chaos, before God fashioned them by form and number,
the greater masses of the elements had an appointed place. Into the
confusion (Greek) which preceded Plato does not attempt further to
penetrate. They are called elements, but they are so far from being
elements (Greek) or letters in the higher sense that they are not even
syllables or first compounds. The real elements are two triangles, the
rectangular isosceles which has but one form, and the most beautiful of
the many forms of scalene, which is half of an equilateral triangle. By
the combination of these triangles which exist in an infinite variety of
sizes, the surfaces of the four elements are constructed.

That there were only five regular solids was already known to the
ancients, and out of the surfaces which he has formed Plato proceeds to
generate the four first of the five. He perhaps forgets that he is only
putting together surfaces and has not provided for their transformation
into solids. The first solid is a regular pyramid, of which the base and
sides are formed by four equilateral or twenty-four scalene triangles.
Each of the four solid angles in this figure is a little larger than
the largest of obtuse angles. The second solid is composed of the same
triangles, which unite as eight equilateral triangles, and make one
solid angle out of four plane angles--six of these angles form a regular
octahedron. The third solid is a regular icosahedron, having twenty
triangular equilateral bases, and therefore 120 rectangular scalene
triangles. The fourth regular solid, or cube, is formed by the
combination of four isosceles triangles into one square and of six
squares into a cube. The fifth regular solid, or dodecahedron, cannot
be formed by a combination of either of these triangles, but each of its
faces may be regarded as composed of thirty triangles of another kind.