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Plato begins by speaking of a perfect or cyclical number (Tim.),

i.e. a number in which the sum of the divisors equals the whole;

this is the divine or perfect number in which all lesser cycles

or revolutions are complete. He also speaks of a human or

imperfect number, having four terms and three intervals of

numbers which are related to one another in certain proportions;

these he converts into figures, and finds in them when they have

been raised to the third power certain elements of number, which

give two 'harmonies,' the one square, the other oblong; but he

does not say that the square number answers to the divine, or the

oblong number to the human cycle; nor is any intimation given

that the first or divine number represents the period of the

world, the second the period of the state, or of the human race

as Zeller supposes; nor is the divine number afterwards mentioned

(Arist.).