Pagina 376 di 1391

Now if we remember that the number 216 = 8 x 27 = 3 cubed + 4

cubed + 5 cubed, and 3 squared + 4 squared = 5 squared, we must

admit that this number implies the numbers 3, 4, 5, to which

musicians attach so much importance. And if we combine the ratio

4/3 with the number 5, or multiply the ratios of the sides by the

hypotenuse, we shall by first squaring and then cubing obtain two

expressions, which denote the ratio of the two last pairs of

terms in the Platonic Tetractys, the former multiplied by the

square, the latter by the cube of the number 10, the sum of the

first four digits which constitute the Platonic Tetractys.' The

two (Greek) he elsewhere explains as follows: 'The first (Greek)

is (Greek), in other words (4/3 x 5) all squared = 100 x 2

squared over 3 squared. The second (Greek), a cube of the same

root, is described as 100 multiplied (alpha) by the rational

diameter of 5 diminished by unity, i.e., as shown above, 48:

(beta) by two incommensurable diameters, i.e.