Page:The Algebra of Mohammed Ben Musa (1831).djvu/152

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tion is as follows:^[1] Give to the wife the ten dirhems of her dowry, so that there remain ninety dirhems, out of which she bequeaths a legacy. Call the gift to her thing; there remain ninety less thing. At the disposal of the woman is therefore ten plus thing. From this her debts must be subtracted, which are ten dirhems. She retains then only thing. Of this she bequeaths one-third, namely, one-third of thing: there remains two-thirds of thing. Of this the husband receives by inheritance the moiety, namely, one-third of thing. The heirs of the husband obtain, therefore, ninety dirhems, less two-thirds of thing; and this is twice as much as the gift to her, which was thing; that is, two things. Reduce this, by removing the two-thirds of thing from ninety, and adding them to two things. Then you have ninety dirhems, equal to two things and two-thirds. One thing is three-eighths of this; that is to say, thirty-three dirhems and three-fourths, which is the gift (to the wife).

If he has married her, paying (a marriage settle-

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1. The same things being assumed as in the last example $s-[d+x]$ remains with the husband; $d$ goes to pay the debts of the wife; and ${\tfrac {x}{3}}$ reverts from the wife to the husband.
   $\therefore \;s-d-{\tfrac {2}{3}}x=2x\;\therefore \;{\tfrac {3}{8}}[s-d]=x$
   $\therefore \;$ if $s=100$, and $d=10$, $x=33{\tfrac {3}{4}}$; she bequeaths $11{\tfrac {1}{4}};11{\tfrac {1}{4}}$ reverts to her husband; and her other heirs receive $11{\tfrac {1}{4}}$. The husband’s heirs receive $2x=67{\tfrac {1}{2}}$.