Page:The Algebra of Mohammed Ben Musa (1831).djvu/184

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two-thirds-equal to twice the two legacies, which are two things and two-thirds. The moiety of this, namely, one hundred and fifty less one and one-third of thing, must, therefore, be equal to the two legacies. Reduce it, by removing one and one-third of thing, and adding the same to the two legacies (things). Then you find one hundred and fifty, equal to four things. One thing is one-fourth of this, namely, thirty-seven and a half.

If the case be, that both the receiver and the donor have cohabited with her, and the latter has disposed of one-third of his capital by way of legacy; then the computation,^[1] according to Abu Hanifah, is, that you call the legacy thing. After the deduction of it, there remain three hundred less thing. Then the dowry is taken, which is one hundred less one-third of thing; so that there are four hundred dirhems less one and one-third of thing. The sum returned from the dowry is one-third of thing; and the legatee, who is to receive one-third, obtains as much as the legacy of the first, namely, thing and one-third of thing. Thus there

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1. According to the author’s rule, which is purely arbitrary,
   $a-2x+\alpha -{\tfrac {3\alpha }{a}}x=4[1+{\tfrac {\alpha }{a}}]x$
   Whence $x=a{\tfrac {a+\alpha }{6a+7\alpha }}=48$
   The donee will have to redeem the girl and dowry, worth $400$, for $352$.