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In speaking of the number 729 as proper to human life, he

probably 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.