Page:The Algebra of Mohammed Ben Musa (1831).djvu/117

( 101 )

then you begin by dividing the heritage into thirteen parts. Add to this as much as the share of the husband, namely, three; thus you have sixteen. This is what remains of the capital after the deduction of one- eighth and one-tenth, that is to say, of nine-fortieths. The remainder of the capital, after the deduction of one-eighth and one-tenth, is thirty-one fortieths of the same, which must be equal to sixteen parts. Complete your capital by adding to it nine thirty-one parts of the same, and multiply sixteen by thirty-one, which gives four hundred and ninety-six; add to this nine thirty-one parts of the same, which is one hundred and forty-four (75). The sum is six hundred and forty. Subtract one-eighth and one-tenth from it, which is one hundred and forty-four, and as much as the share of the husband, which is ninety-three. There remains four hundred and three, of which the husband receives ninety-three, the mother sixty-two, and every daughter one hundred and twenty-four.

If the heirs are the same,^[1] but that she bequeaths to a person as much as the share of the husband, less one-ninth and one-tenth of what remains of the capital,

---

1. ${\tfrac {1}{9}}+{\tfrac {1}{10}}={\tfrac {19}{90}}$
   $1-3v+{\tfrac {19}{90}}[1-3v]=13v$
   $\therefore {\tfrac {109}{90}}[1-3]=13v$
   $\therefore {\tfrac {109}{90}}=[13+{\tfrac {109}{30}}]v$
   $\therefore v={\tfrac {109}{1497}}$
   The husband’s share $={\tfrac {327}{1497}}$
   The stranger’s legacy $={\tfrac {80}{1497}}$