Page:The Algebra of Mohammed Ben Musa (1831).djvu/124

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sevenths of the capital, which is one thousand one hundred and forty-five. The sum is one thousand three (80) hundred and sixteen parts. This may be divided into seven shares, each of one hundred and eighty-eight parts; then this is the share of the daughter, whilst every son receives twice as much.

If the heirs are the same, and he bequeaths to some person as much as the share of the daughter, and to another person one-fourth and one-fifth out of what remains from two-fifths of his capital after the deduction of the share; this is the computation:^[1] You must observe that the legacy is determined by the two-fifths. Take two-fifths of the capital and subtract the shares: the remainder is, two-fifths of the capital less the share. Subtract from this remainder one-fourth and one-fifth of the same, namely, nine-twentieths of two-fifths, less as much of the share. The remainder is one-fifth and one-tenth of one-fifth of the capital less eleven-twentieths of the share. Add thereto three-fifths of the

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1. ${\tfrac {1}{4}}+{\tfrac {1}{5}}={\tfrac {9}{20}}$
   Let the 1st legacy $=v=$ a daughter’s share
   Let the 2d legacy $=y$
   ${\begin{aligned}1-v-y=7v\\\therefore {\tfrac {3}{5}}+{\tfrac {2}{5}}-v-{\tfrac {9}{20}}\left[{\tfrac {2}{5}}-v\right]=7v\\\therefore {\tfrac {3}{5}}+{\tfrac {11}{20}}\left[{\tfrac {2}{5}}-v\right]=7v\\\therefore {\tfrac {3}{5}}+{\tfrac {11}{10\times 5}}=\left[7+{\tfrac {11}{20}}\right]v\\\therefore {\tfrac {41}{5}}={\tfrac {151}{2}}v\;\;\therefore v={\tfrac {82}{755}}\\\end{aligned}}$
   and the 2d legacy, $y,={\tfrac {99}{155}}$