Page:The Algebra of Mohammed Ben Musa (1831).djvu/182

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is this:^[1] Call the legacy thing; the deduction is three hundred dirhems less thing. The donor has ceded the dowry to the donee by (the donee’s) having cohabited with her: this amounts to one-third of thing: and the donee cedes one-third of the deduction, which is one hundred less one-third of thing. Thus, the donor’s heirs obtain four hundred less one and two-thirds of thing, which is twice as much as the legacy. Reduce this, by separating the one and two-thirds of thing from four hundred, and add them to the two things. Then you have four hundred things, equal to three things and two-thirds. One thing of these is three-elevenths of four hundred; namely, one hundred and

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1. If the donor has previously cohabited with the slave-girl, it appears from the last example, that the donee is entitled to ransom her for $a-x-{\tfrac {\alpha }{a}}x$.
   If the donee cohabits with the slave-girl, it appears from the last example but one, that he is entitled to redeem the dowry, $\alpha$, for $\alpha -{\tfrac {\alpha }{a}}x$
   The redemption of the girl and dowry is
   $a-x-{\tfrac {\alpha }{a}}x+\alpha -{\tfrac {\alpha }{a}}x$,
   which, according to the author, is to be made equal to $2x$.
   That $a+\alpha -{\tfrac {a+2\alpha }{a}}x=2x$
   Whence $x={\tfrac {a}{3a+2\alpha }}\times [a+\alpha ]=109{\tfrac {1}{11}}$
   The donee is to receive the girl and dowry, worth $400$, for $290{\tfrac {10}{11}}$.