Page:The Algebra of Mohammed Ben Musa (1831).djvu/150

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ten dirhems. Then the wife dies, bequeathing one-third of her property. After this the husband dies.”^[1] Computation: You take from the one hundred that which belongs entirely to her, on account of the dowry, namely, ten dirhems; there remain ninety dirhems, out of which she has bequeathed a legacy. Call the sum given to her (by her husband, exclusive of her dowry) thing; subtracting it, there remain ninety dirhems less thing. Ten dirhems and thing are already in her hands; she has disposed of one-third of her property, which is three dirhems and one-third, and one-third of thing; there remain six dirhems and

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1. Lets $s$ be the sum, including the dowry, paid by the man, as a marriage settlement; $d$ the dowry; $x$ the gift to the wife, which she is empowered to bequeath if she pleases.
   She may bequeath, if she pleases, $d+x$; she actually does bequath ${\tfrac {1}{3}}[d+x]$; the residue is ${\tfrac {2}{3}}[d+x]$, of which one half, viz. ${\tfrac {1}{3}}[d+x]$ goes to her heirs, and the other half reverts to the husband
   $\therefore$ the husband’s heirs have $s-[d+x]+{\tfrac {1}{3}}[d+x]\;{\text{or}}\;s-{\tfrac {2}{3}}[d+x]$; and since what the wife has disposed of, exclusive of the dowry, is $x$, twice which sum the husband is to receive, $s-{\tfrac {2}{3}}[d+x]=2x\;\therefore \;{\tfrac {1}{8}}[3s-2d]=x$. But $s=100\;;d=10\;\therefore \;x=35\;;d+x=45\;;{\tfrac {1}{3}}[d+x]=15$. Therefore the legacy which she bequeaths is $15$, her husband receives $15$, and her other heirs, $15$. The husband’s heirs receive $2x=70$.
   But had the husband also bequeathed a legacy, then, as we shall see presently, the law would have defeated, in part, the woman’s intentions.