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namely, two dirhems and one-third; the sum is five and five-sixths. This is the thing, or the amount which is taken from the debt.
If he leaves three sons, and bequeaths one-fifth of his property less one dirhem, leaving ten dirhems of capital and a demand of ten dirhems against one of the sons, the computation is this: You call the sum which is taken from the debt thing. Add this to the capital; it gives ten and thing. Subtract from this one-fifth of it for the legacy; it is two dirhems and one-fifth of thing. There remain eight dirhems and four-fifths of thing; add to this one dirhem, since he stated “less one dirhem.” Thus you have nine dirhems and four-fifths of thing. Divide this between the three sons. There will be for each son three dirhems, and one-fifth and one-third and one-fifth of thing. This equals one thing.[1] Subtract one-fifth and one-third of one-fifth (67) of thing from thing. There remain eleven-fifteenths of thing, equal to three dirhems. It is now required to complete the thing. For this purpose, add to it four-elevenths, and do the same with the three dirhems, by adding to them one dirhem and one-eleventh. Then you have four dirhems and one-eleventh, which are equal to thing. This is the sum which is taken out of the debt.
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The stranger receives
![{\displaystyle {\tfrac {4}{5}}[10+x]+1=3x\;\therefore \;9=2{\tfrac {1}{5}}x\;\therefore \;{\tfrac {45}{11}}\;{\text{or}}\;4{\tfrac {1}{11}}=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/61caa93416e16038a96d1565119ea58fc6b30dfb)
![{\displaystyle {\tfrac {1}{5}}[10+{\tfrac {45}{11}}]-1=1{\tfrac {9}{11}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1f8f3a18c519eeaacc6ad8fc437e3b7403e34e52)
