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On the other hand, Plato himself indicates that he is not

altogether serious, and in describing his number as a solemn jest

of the Muses, he appears to imply some degree of satire on the

symbolical use of number. (Compare Cratylus; Protag.)

Our hope of understanding the passage depends principally on an

accurate study of the words themselves; on which a faint light is

thrown by the parallel passage in the ninth book. Another help is

the allusion in Aristotle, who makes the important remark that

the latter part of the passage (Greek) describes a solid figure.

(Pol.-'He only says that nothing is abiding, but that all things

change in a certain cycle; and that the origin of the change is a

base of numbers which are in the ratio of 4:3; and this when

combined with a figure of five gives two harmonies; he means when

the number of this figure becomes solid.') Some further clue may

be gathered from the appearance of the Pythagorean triangle,

which is denoted by the numbers 3, 4, 5, and in which, as in

every right-angled triangle, the squares of the two lesser sides

equal the square of the hypotenuse (9 + 16 = 25).