cy (the government of
honour) arises out of aristocracy (the government of the best). Clearly,
all political changes originate in divisions of the actual governing
power; a government which is united, however small, cannot be moved.

Very true, he said.

In what way, then, will our city be moved, and in what manner will the
two classes of auxiliaries and rulers disagree among themselves or with
one another? Shall we, after the manner of Homer, pray the Muses to tell
us 'how discord first arose'? Shall we imagine them in solemn mockery,
to play and jest with us as if we were children, and to address us in a
lofty tragic vein, making believe to be in earnest?

How would they address us?

After this manner:--A city which is thus constituted can hardly be
shaken; but, seeing that everything which has a beginning has also an
end, even a constitution such as yours will not last for ever, but will
in time be dissolved. And this is the dissolution:--In plants that grow
in the earth, as well as in animals that move on the earth's surface,
fertility and sterility of soul and body occur when the circumferences
of the circles of each are completed, which in short-lived existences
pass over a short space, and in long-lived ones over a long space. But
to the knowledge of human fecundity and sterility all the wisdom and
education of your rulers will not attain; the laws which regulate them
will not be discovered by an intelligence which is alloyed with sense,
but will escape them, and they will bring children into the world when
they ought not. Now that which is of divine birth has a period which is
contained in a perfect number (i.e. a cyclical number, such as 6, which
is equal to the sum of its divisors 1, 2, 3, so that when the circle
or time represented by 6 is completed, the lesser times or rotations
represented by 1, 2, 3 are also completed.), but the period of
human birth is comprehended in a number in which first increments
by involution and evolution (or squared and cubed) obtaining three
intervals and four terms of like and unlike, waxing and waning numbers,
make all the terms commensurable and agreeable to one another. (Probably
the numbers 3, 4, 5, 6 of which the three first = the sides of the
Pythagorean triangle. The terms will then be 3 cubed, 4 cubed, 5 cubed,
which together = 6 cubed = 216.) The base of these (3) with a third
added (4) when combined with five (20) and raised to the third power
furnishes two harmon