Page:The Algebra of Mohammed Ben Musa (1831).djvu/76

 thing; it is two squares and two things, equal to one dirhem and a half. Reduce them to one square: that is, take the moiety of all you have. You say, therefore, one square and one thing are equal to three-fourths of a dirhem. Reduce this, according to what I have taught you in the beginning of this work.

If the instance be: “A number, you remove one-third of it, and one-fourth of it, and four dirhems: then you multiply the remainder by itself, and the number, is restored, with a surplus of twelve dirhems:” then the computation is this: You take thing, and subtract from it one-third and one-fourth; there remain five- twelfths of thing. Subtract from this four dirhems: the remainder is five-twelfths of thing less four dirhems. Multiply this by itself. Thus the five parts become five-and-twenty parts; and if you multiply twelve by itself, it is a hundred and forty-four. This makes, therefore, five and twenty hundred and forty-fourths of a square. Multiply then the four dirhems twice by the five-twelfths; this gives forty parts, every twelve of which make one root (forty-twelfths); finally, the four