robably intended to intimate
that one year of the tyrannical = 12 hours of the royal life.

The simple observation that the comparison of two similar solids
is effected by the comparison of the cubes of their sides, is the
mathematical groundwork of this fanciful expression. There is some
difficulty in explaining the steps by which the number 729 is obtained;
the oligarch is removed in the third degree from the royal and
aristocratical, and the tyrant in the third degree from the
oligarchical; but we have to arrange the terms as the sides of a square
and to count the oligarch twice over, thus reckoning them not as = 5 but
as = 9. The square of 9 is passed lightly over as only a step towards
the cube.

3. Towards the close of the Republic, Plato seems to be more and more
convinced of the ideal character of his own speculations. At the end of
the 9th Book the pattern which is in heaven takes the place of the
city of philosophers on earth. The vision which has received form and
substance at his hands, is now discovered to be at a distance. And yet
this distant kingdom is also the rule of man's life. ('Say not lo! here,
or lo! there, for the kingdom of God is within you.') Thus a note
is struck which prepares for the revelation of a future life in the
following Book. But the future life is present still; the ideal of
politics is to be realized in the individual.

BOOK X. Many things pleased me in the order of our State, but there
was nothing which I liked better than the regulation about poetry. The
division of the soul throws a new light on our exclusion of imitation.
I do not mind telling you in confidence that all poetry is an outrage on
the understanding, unless the hearers have that balm of knowledge which
heals error. I have loved Homer ever since I was a boy, and even now
he appears to me to be the great master of tragic poetry. But much as
I love the man, I love truth more, and therefore I must speak out: and
first of all, will you explain what is imitation, for really I do not
understand? 'How likely then that I should understand!' That might very
well be, for the duller often sees better than the keener eye. 'True,
but in your presence I can hardly venture to say what I think.'
Then suppose that we begin in our old fashion, with the doctrine of
universals. Let us assume the existence of beds and tables. There is one
idea of a bed, or of a table, which the maker of each had in his mind
when making them; he did n