( 163 )
one-fourth. Computation:[1] The price of the girl is five hundred dirhems. The legacy out of this is thing; there remain five hundred dirhems less thing. The dowry is one hundred dirhems less one-fifth of thing; thus the heirs obtain six hundred dirhems less one and one-fifth of thing. Subtract now the legacy of the person to whom one-fourth has been bequeathed, namely, three-fourths of thing; for if one-third is thing then one-fourth is as much as three-fourths of the same. There remain then six hundred dirhems less one thing and thirty-eight fortieths. This is equal to the legacy taken twice. The moiety of it is equal to the legacies by themselves, namely, three hundred dirhems less thirty-nine fortieths of thing. Reduce this by means of the latter fraction. Then you have three hundred (116) dirhems, equal to one hundred dirhems and two things and twenty-nine fortieths. Remove one hundred on account of the other one hundred. There remain two hundred dirhems, equal to two things and twenty-nine-fortieths. Make the equation. You will then find one thing to be equal to seventy-three dirhems and forty-three one-hundred-and-ninths dirhems.
- ↑ The same notation being used as in the two former examples, the equation for determining , according to the author, is
Whence
![{\displaystyle a-x+b-{\tfrac {b}{a}}x-{\tfrac {3}{4}}x=2[\alpha +1{\tfrac {3}{4}}x]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5cdf67b2c28abb044609064496257ab7507c8e0a)
![{\displaystyle x={\tfrac {4a}{21a+4b}}[a+b-2\alpha ]=73{\tfrac {43}{100}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec2e405ac96db3ce2a27e3ac6d293942313e6f27)
