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

( 66 )

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.^[1] 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.”^[2] Then, this is the root of a

---

1. ${\begin{aligned}{\tfrac {x^{2}-4x}{3}}&=4x\\x^{2}-4x&=12x\\x^{2}&=16x\\x=16&\;\therefore \;x^{2}=256\end{aligned}}$
2. ${\begin{aligned}{\sqrt {x^{2}-x}}+x&=2\\{\sqrt {x^{2}-x}}&=2-x\\x^{2}-x&=4+x^{2}-4x\\x^{2}+3x&=4+x^{2}\\3x&=4\\x&=1{\tfrac {1}{3}}\end{aligned}}$