The terms will then be 3 cubed, 4 cubed, 5 cubed, which together = 6 cubed = 216.) The base of these (3) with a third added (4) when combined with five (20) and raised to the third power furnishes two harmonies; the first a square which is a hundred times as great (400 = 4 x 100) (Or the first a square which is 100 x 100 = 10,000.

The whole number will then be 17,500 = a square of 100, and an oblong of 100 by 75.), and the other a figure having one side equal to the former, but oblong, consisting of a hundred numbers squared upon rational diameters of a square (i.e.omitting fractions), the side of which is five (7 x 7 = 49 x 100 = 4900), each of them being less by one (than the perfect square which includes the fractions, sc.

50) or less by (Or, 'consisting of two numbers squared upon irrational diameters,' etc.

= 100.

For other explanations of the passage see Introduction.) two perfect squares of irrational diameters (of a square the side of which is five = 50 + 50 = 100); and a hundred cubes of three (27 x 100 = 2700 + 4900 + 400 = 8000).