Page:The Algebra of Mohammed Ben Musa (1831).djvu/165

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Computation:^[1] Call the legacy to each of them thing; the ransom of each will be three hundred less thing; then take the inheritance of the deceased slave, which is five hundred dirhems, and subtract his ransom, which is three hundred less thing; the remainder of his inheritance will be two hundred plus thing. Of this, one hundred dirhems and half a thing return to the master by the law of succession, so that now altogether four hundred dirhems less a half thing are in the hands of the master’s heirs. Take also the ransom of the other slave, namely, three hundred dirhems less thing; then the heirs of the master obtain seven hundred dir-

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1. The first slave is A.; his cost $a$; his property $\alpha$; he leaves a daughter.
   The second slave is B.; his cost $b$.
   Then (as in page 147) ${\tfrac {1}{2}}[\alpha -a+x]$ goes to the daughter ; and $x=a{\tfrac {\alpha +a+2b}{5a+6b}}$
   The daughter receives $[a+b]{\tfrac {3\alpha -2a}{5a+6b}}$
   The master receives from A.${\tfrac {2a[a+\alpha +b]+3\alpha b}{5a+6b}}$
   and the master receives from A. and B. together $2[a+b]{\tfrac {\alpha +a+2b}{5a+6b}}$
   

   But if $b=a$	$x={\tfrac {1}{11}}[\alpha +3a]=127{\tfrac {3}{11}}$
   The daughter receives	${\tfrac {2}{11}}[3\alpha -2a]=163{\tfrac {7}{11}}$
   The master receives from A.	${\tfrac {1}{11}}[5\alpha +4a]=336{\tfrac {4}{11}}$
   The master receives from B.	${\tfrac {1}{11}}[8a-\alpha ]=172{\tfrac {8}{11}}$
   The master receives from A and B.	${\tfrac {4}{11}}[\alpha +3a]=509{\tfrac {1}{11}}$

   If $b=0$,
   The daughter receives ${\tfrac {1}{5}}[3\alpha -2a]$
   The master ${\tfrac {2}{5}}[\alpha +a]$, as in page 142.