Page:The Algebra of Mohammed Ben Musa (1831).djvu/75

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hems. Remove now two dirhems from thirteen, on account of the other two dirhems, the remainder is eleven dirhems. Remove then the eleven-twelfths of a root from the one (root on the opposite side), there remains one-twelfth of a root and eleven dirhems, equal to one-twelfth of a square. Complete the square: that is, multiply it by twelve, and do the same with all you have. The product is a square, which is equal to a hundred and thirty-two dirhems and one root. Reduce this, according to what I have taught you, it will be right.

If the instance be: “A dirhem and a half to be divided among one person and certain persons, so that the share of the one person be twice as many dirhems as there are other persons;”^[1] then the Computation is this:^[2] You say, the one person and some persons are one and thing: it is the same as if the question had been one dirhem and a half to be divided by one and thing, and the share of one person to be equal to two things. Multiply, therefore, two things by one and

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1. The enunciation in the original is faulty, and I have altered it to correspond with the computation. But in the computation, $x$, the number of persons, is fractional! I am unable to correct the passage satisfactorily.
2. ${\begin{aligned}{\tfrac {1{\tfrac {1}{2}}}{1+x}}=2x\\x2+x={\tfrac {3}{4}}\\x=1-{\tfrac {1}{2}}\\x={\tfrac {1}{2}}\end{aligned}}$