fifth, that we may know which is the happier, and then we
shall be able to determine whether the argument of Thrasymachus or our
own is the more convincing. And as before we began with the State and
went on to the individual, so now, beginning with timocracy, let us
go on to the timocratical man, and then proceed to the other forms of
government, and the individuals who answer to them.

But how did timocracy arise out of the perfect State? Plainly, like
all changes of government, from division in the rulers. But whence came
division? 'Sing, heavenly Muses,' as Homer says;--let them condescend to
answer us, as if we were children, to whom they put on a solemn face
in jest. 'And what will they say?' They will say that human things are
fated to decay, and even the perfect State will not escape from this
law of destiny, when 'the wheel comes full circle' in a period short or
long. Plants or animals have times of fertility and sterility, which the
intelligence of rulers because alloyed by sense will not enable them to
ascertain, and children will be born out of season. For whereas divine
creations are in a perfect cycle or number, the human creation is in
a number which declines from perfection, and has four terms and three
intervals of numbers, increasing, waning, assimilating, dissimilating,
and yet perfectly commensurate with each other. The base of the number
with a fourth added (or which is 3:4), multiplied by five and cubed,
gives two harmonies:--the first a square number, which is a hundred
times the base (or a hundred times a hundred); the second, an oblong,
being a hundred squares of the rational diameter of a figure the side of
which is five, subtracting one from each square or two perfect squares
from all, and adding a hundred cubes of three. This entire number is
geometrical and contains the rule or law of generation. When this law is
neglected marriages will be unpropitious; the inferior offspring who are
then born will in time become the rulers; the State will decline, and
education fall into decay; gymnastic will be preferred to music, and
the gold and silver and brass and iron will form a chaotic mass--thus
division will arise. Such is the Muses' answer to our question. 'And a
true answer, of course:--but what more have they to say?' They say that
the two races, the iron and brass, and the silver and gold, will draw
the State different ways;--the one will take to trade and moneymaking,
and the others, having