master, so that one hundred dirhems and thing remain in the hands of the slave’s heirs. Herefrom are(first) subtracted the debts, namely, ten dirhems; there remain then ninety dirhems and thing. Of this he has bequeathed one-third, that is, thirty dirhems and one-third of thing; so that there remain for the heirs sixty dirhems and two-thirds of thing. Of this the two daughters receive two-thirds, namely, forty dirhems and four-ninths of thing, and the master (104) receives twenty dirhems and two-ninths of thing, so that the heirs of the master obtain three hundred and twenty dirhems less seven-ninths of thing. Of this the debts of the master must be deducted, namely, twenty dirhems; there remain then three hundred dirhems less
are to be taken for 
given, ought to be made equal to 
.
But the author directs that the equation for determining 
be
![{\displaystyle {\begin{aligned}&{\tfrac {7}{9}}[a-x]+{\tfrac {2}{9}}[\alpha -\epsilon ]-\mu =2x\\&\therefore \;x={\tfrac {1}{25}}[7a+2[\alpha -\epsilon ]-9\mu ]&=108\\&{\text{Hence the slave receives, the debts which he owes,}}\;\epsilon &=10\\&{\text{+the legacy to the stranger}}={\tfrac {1}{25}}[9[\alpha -\epsilon ]-6a-3\mu ]&=66\\&{\text{+the inheritance of 1st daughter}}={\tfrac {1}{25}}[6[\alpha -\epsilon ]-4a-2\mu ]&=44\\&{\text{+the inheritance of 2d daughter}}={\tfrac {1}{25}}[6[\alpha -\epsilon ]-4a-2\mu ]&=44\\&{\text{Total}}\;={\tfrac {1}{25}}[21\alpha -4\epsilon -14a-7\mu ]&=164\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e495da4ce3ecbe3c9a03e119b0ba6feeb085adfc)
And the master takes ![{\displaystyle \mu +2x={\tfrac {1}{25}}[4\alpha -4\epsilon +14a-7\mu ]=236}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9db3b662d79c51941c1335f4694d0e8285d236b9)
Had the slave died possessed of no property whatever, his
ransom would have been 
.
His ransom, here stated, exclusive of the sum which the master inherits from him, or 
.
