Page:The Algebra of Mohammed Ben Musa (1831).djvu/82

 roots give one square; and, consequently, the whole of it multiplied by three roots of it gives one square and a half. This entire square, when multiplied by one root, gives half a square; the root of the square must therefore be a half, the square one-fourth, two-thirds of the square one-sixth, and three roots of the square one and a half. If you multiply one-sixth by one and a half, the product is one-fourth, which is the square.

Instance: “A square; you subtract four roots of the same, then take one-third of the remainder; this is equal to the four roots.” The square is two hundred and fifty-six. Computation: You know that one-third of the remainder is equal to four roots; consequently, the whole remainder must be twelve roots; add to this the four roots; the sum is sixteen, which is the root of the square.

Instance: “A square; you remove one root from it; and if you add to this root a root of the remainder, the sum is two dirhems.” Then, this is the root of a