पृष्ठ 377 / 1391

the two first irrationals, or 2 and 3: and (gamma) by the cube of

3, or 27. Thus we have (48 + 5 + 27) 100 = 1000 x 2 cubed. This

second harmony is to be the cube of the number of which the

former harmony is the square, and therefore must be divided by

the cube of 3. In other words, the whole expression will be: (1),

for the first harmony, 400/9: (2), for the second harmony,

8000/27.'

The reasons which have inclined me to agree with Dr. Donaldson

and also with Schleiermacher in supposing that 216 is the

Platonic number of births are: (1) that it coincides with the

description of the number given in the first part of the passage

(Greek...): (2) that the number 216 with its permutations would

have been familiar to a Greek mathematician, though unfamiliar to

us: (3) that 216 is the cube of 6, and also the sum of 3 cubed, 4

cubed, 5 cubed, the numbers 3, 4, 5 representing the Pythagorean

triangle, of which the sides when squared equal the square of the

hypotenuse (9 + 16 = 25): (4) that it is also the period of the

Pythagorean Metempsychosis: (5) the three ultimate terms or bases

(3, 4, 5) of which 216 is composed answer to the third, fourth,

fifth in the musical scale: (6) that the number 216 is the

product of the cubes of 2 and 3, which are the two last terms in

the Platonic Tetractys: (7) that the Pythagorean triangle is said

by Plutarch (de Is.