( 158 )
by the slave his ransom, which is three hundred dirhems less thing; there remain two hundred dirhems plus thing. He has bequeathed one-third of his property, that is, sixty-six dirhems and two-thirds plus one-third of thing. According to the law of succession, (112) sixty-six dirhems and two-thirds and one-third of thing belong to the master, and as much to the daughter. Add this to the property left by her, which is three hundred dirhems: the sum is three hundred and sixty-six dirhems and two-thirds and one-third of thing. She has bequeathed one-third of her property, that is, one hundred and twenty-two dirhems and two-ninths and one-ninth of thing; and there remain two hundred and forty-four dirhems and four-ninths and two-ninths of thing. The mother receives one-third of this, namely, eighty-one dirhems and four-ninths and one-third of one-ninth of a dirhem plus two-thirds of one-ninth of thing. The remainder returns to the master; it is a hundred and sixty-two dirhems and eight-ninths and two-thirds of one-ninth of a dirhem plus one-ninth and one-third of one-ninth of thing, as his share of the heritage.
Hence, according to the author, we are to make
![{\displaystyle a-x+{\tfrac {1}{3}}[\alpha -a+x]+{\tfrac {4}{27}}[3d+\alpha -a+x]=2x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a20749bf1a1c43e9eb8a783f10c8e1014be47155)
| Therefore | |
| The daughter’s share | |
| The daughter’s bequest | |
| The mother’s share | |
| The master’s |
![{\displaystyle x={\tfrac {1}{68}}[13\alpha +14a+12d]=210{\tfrac {5}{17}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee99b805874c9926b6d090bc2abc38844a5b16a3)
![{\displaystyle ={\tfrac {1}{68}}[27\alpha -18a+4d]=136{\tfrac {13}{17}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/055a1b8cd76d14af9cc4692d04754c54f1475412)
![{\displaystyle ={\tfrac {1}{68}}[9\alpha -6a+24d]=145{\tfrac {10}{17}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9aeeb4c76771dbd5a481c4ecc41e36c42f611110)
![{\displaystyle ={\tfrac {2}{68}}[3\alpha -2a+8d]=97{\tfrac {1}{17}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52cc52d33083f5f4e69e16f554329ea95af75a54)
![{\displaystyle ={\tfrac {2}{68}}[13\alpha +14a+12d]=420{\tfrac {10}{17}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bc76306b49746b78c578eda52d18d8515dff203e)
