iple in all this. Identification of the
different numbers with different things can only be left to the whim
and fancy of the individual. The Pythagoreans disagreed among
themselves as to what number is to be assigned to what thing. For
example, justice, they said, is that which returns equal for equal. If
I do a man an injury, justice ordains that injury should be done to
me, thus giving equal for equal. Justice must, therefore, be a number
which returns equal for equal. Now the only numbers which do this are
square numbers. Four equals two into two, and so returns equal for
equal. Four, then, must be justice. But nine is equally the square of
three. Hence other Pythagoreans identified justice with nine.

According to Philolaus, one of the most prominent Pythagoreans, the
quality of matter depends upon the number of sides of its smallest
particles. Of the five regular solids, three were known to the
Pythagoreans. That matter whose smallest particles are regular
tetrahedra, said Philolaus, is fire. Similarly earth is composed {38}
of cubes, and the universe is identified with the dodecahedron. This
idea was developed further by Plato in the "Timaeus," where we find
all the five regular solids brought into the theory.

The central fire, already mentioned as identified with the unit, is a
characteristic doctrine of the Pythagoreans. Up to this time it had
been believed that the earth is the centre of the universe, and that
everything revolves round it. But with the Pythagoreans the earth
revolves round the central fire. One feels inclined at once to
identify this with the sun. But this is not correct. The sun, like the
earth, revolves round the central fire. We do not see the central fire
because that side of the earth on which we live is perpetually turned
away from it. This involves the theory that the earth revolves round
the central fire in the same period that it takes to rotate upon its
axis. The Pythagoreans were the first to see that the earth is itself
one of the planets, and to shake themselves free from the geocentric
hypothesis. Round the central fire, sometimes mystically called "the
Hearth of the Universe," revolve ten bodies. First is the
"counter-earth," a non-existent body invented by the Pythagoreans,
next comes the earth, then the sun, the moon, the five planets, and
lastly the heaven of the fixed stars. This curious system might have
borne fruit in astronomy. That it did not do so was largely due to t