Page:The Algebra of Mohammed Ben Musa (1831).djvu/116

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of which the mother receives. Now you perceive that the (74) legacies amount to two parts plus one-ninth of the entire capital. Subtracting this, there remains eight-ninths of the capital less two parts, for distribution among the heirs. Complete the capital, by making the eight-ninths less two parts to be thirteen parts, and adding two parts to it, so that you have fifteen parts, equal to eight-ninths of capital; then add to this one-eighth of the same, and to the fifteen parts add likewise one-eighth of the same, namely, one part and. seven-eighths; then you have sixteen parts and seven-eighths. The person to whom one-ninth is bequeathed, receives one-ninth of this, namely, one part and seven-eighths; the other, to whom as much as the share of the mother is bequeathed, receives two parts. The remaining thirteen parts are divided among the heirs, according to their legal shares. You best determine the respective shares by dividing the whole heritage into one hundred and thirty-five parts.

If she has bequeathed as much as the share of the husband and one-eighth and one-tenth of the capital,^[1]

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Let of ${\tfrac {1}{13}}$ the residue $=v$
$1-{\tfrac {1}{9}}=13v\;\therefore \;{\tfrac {8}{9}}=15v$
$\therefore \;v={\tfrac {8}{135}}$ of the capital
A mother’s share= ${\tfrac {16}{135}}$


1. ${\tfrac {1}{8}}+{\tfrac {1}{10}}={\tfrac {9}{40}}$
   A husband’s share of the residue is ${\tfrac {3}{13}}$
   $\therefore 1-{\tfrac {9}{40}}-3v=13v\;\therefore \;{\tfrac {31}{40}}=16v$
   $\therefore v={\tfrac {31}{640}}$; a husband’s share = ${\tfrac {93}{640}}$
   The stranger’s legacy = ${\tfrac {237}{640}}$