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The conclusions which he draws from these data are summed up by

him as follows. Having assumed that the number of the perfect or

divine cycle is the number of the world, and the number of the

imperfect cycle the number of the state, he proceeds: 'The period

of the world is defined by the perfect number 6, that of the

state by the cube of that number or 216, which is the product of

the last pair of terms in the Platonic Tetractys (a series of

seven terms, 1, 2, 3, 4, 9, 8, 27); and if we take this as the

basis of our computation, we shall have two cube numbers (Greek),

viz. 8 and 27; and the mean proportionals between these, viz. 12

and 18, will furnish three intervals and four terms, and these

terms and intervals stand related to one another in the

sesqui-altera ratio, i.e. each term is to the preceding as 3/2.