Page:The Algebra of Mohammed Ben Musa (1831).djvu/24

 whole root is equal to twenty, and the square which is formed of it is four hundred.

I found that these three kinds; namely, roots, squares, and numbers, may be combined together, and thus three compound species arise; that is, “squares and roots equal to numbers;” “squares and numbers equal to roots;” “roots and numbers equal to squares.”

Roots and Squares are equal to Numbers; for instance, “one square, and ten roots of the same, amount to thirty nine dirhems;” that is to say, what must be the square which, when increased by ten of its own roots, amounts to thirty-nine? The solution is this: you halve the number of the roots, which in the present instance yields five. This you multiply by itself; the product is twenty-five. Add this to thirty-nine; the sum is sixty-four. Now take the root of this, which is eight, and subtract from it half the number of the roots, which is five; the remainder is three. This is the root of the square which you sought for; the square itself is nine.