ies; the first a square which is a hundred times
as great (400 = 4 x 100) (Or the first a square which is 100 x 100 =
10,000. The whole number will then be 17,500 = a square of 100, and an
oblong of 100 by 75.), and the other a figure having one side equal to
the former, but oblong, consisting of a hundred numbers squared upon
rational diameters of a square (i.e. omitting fractions), the side of
which is five (7 x 7 = 49 x 100 = 4900), each of them being less by one
(than the perfect square which includes the fractions, sc. 50) or less
by (Or, 'consisting of two numbers squared upon irrational diameters,'
etc. = 100. For other explanations of the passage see Introduction.) two
perfect squares of irrational diameters (of a square the side of which
is five = 50 + 50 = 100); and a hundred cubes of three (27 x 100 = 2700
+ 4900 + 400 = 8000). Now this number represents a geometrical figure
which has control over the good and evil of births. For when your
guardians are ignorant of the law of births, and unite bride and
bridegroom out of season, the children will not be goodly or
fortunate. And though only the best of them will be appointed by their
predecessors, still they will be unworthy to hold their fathers' places,
and when they come into power as guardians, they will soon be found
to fail in taking care of us, the Muses, first by under-valuing music;
which neglect will soon extend to gymnastic; and hence the young men of
your State will be less cultivated. In the succeeding generation rulers
will be appointed who have lost the guardian power of testing the metal
of your different races, which, like Hesiod's, are of gold and silver
and brass and iron. And so iron will be mingled with silver, and brass
with gold, and hence there will arise dissimilarity and inequality and
irregularity, which always and in all places are causes of hatred
and war. This the Muses affirm to be the stock from which discord has
sprung, wherever arising; and this is their answer to us.

Yes, and we may assume that they answer truly.

Why, yes, I said, of course they answer truly; how can the Muses speak
falsely?

And what do the Muses say next?

When discord arose, then the two races were drawn different ways: the
iron and brass fell to acquiring money and land and houses and gold and
silver; but the gold and silver races, not wanting money but having the
true riches in their own nature, inclined towards virtue and the ancient
order of thin