( 152 )
“Suppose that a man in his illness emancipates a slave, whose price is three hundred dirhems, but who has already advanced to the master five hundred dirhems; then the slave dies before the death of his master, and leaves one thousand dirhems and a daughter. The master has two hundred dirhems debts.”[1] Computation: Take the inheritance of the slave, which is one thousand dirhems, and the five hundred, which the master has spent. The ransom from this is three hundred less thing. There remain therefore twelve hundred plus thing. The moiety of this belongs to the daughter: it is six hundred dirhems plus half a thing. Subtract it from the property left by the slave, which was one
- ↑ A.’s price is ; he has advanced to his master ; he leaves property . He dies before his master, and leaves a daughter.
The master’s debts are ; is what A. receives, in being emancipated; ; is the ransom; is what the daughter receives.
Then is what remains to the master; and is what remains to him, after paying his debts; and this is to be made equal to .
Whence
If the mode given in page had been followed, it would have given
and the daughter’s portion .
![{\displaystyle {\tfrac {1}{2}}[\alpha +a^{\prime }-a+x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd3a00a706a3bdfb008e47ddb9a38447f855da95)
![{\displaystyle \alpha -{\tfrac {1}{2}}[\alpha +a^{\prime }-a+x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5084f1264d152a9eb34e3b93a69f6e7385317e1d)
![{\displaystyle \alpha -{\tfrac {1}{2}}[\alpha +a^{\prime }-a+x]-\mu }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4285c062804cfa899ab845bcd55e0a8847c9bbf7)
![{\displaystyle x={\tfrac {1}{5}}[\alpha +a-a^{\prime }-2\mu ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4f3b162f14020504f8c5765f799a3905ae63119)
![{\displaystyle ={\tfrac {1}{5}}[3\alpha -2a+2a^{\prime }-\mu ]=640}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a81182b994b4d5e05e9010db6a4daa238706a853)
![{\displaystyle ={\tfrac {1}{5}}[2\alpha +2a-2a^{\prime }+\mu ]=360}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f470d2789e747f65cfb71551ef54e147bcaa6377)
![{\displaystyle ={\tfrac {1}{5}}[2\alpha +2a-2a^{\prime }-4\mu ]=160}](https://wikimedia.org/api/rest_v1/media/math/render/svg/638b06f3e62268cbb24fa75cd47fd9d27efbd689)
![{\displaystyle x={\tfrac {1}{5}}[\alpha +a+a^{\prime }-2\mu ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc7700d688738a67e6d4fa199d05a706a89e515e)
![{\displaystyle ={\tfrac {1}{5}}[3\alpha =2a+3a^{\prime }-\mu ]=740}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae617a4ced7a8c2e7c59a6cecf4915890774f672)
