Page:The Algebra of Mohammed Ben Musa (1831).djvu/108

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law).”^[1] Computation: You constitute the shares of the (69) heritage, by taking them out of twelve parts: the son receives seven of them, the husband three, and the mother two parts. You know that the husband must give up one-third of his share; accordingly he retains twice as much as that which is detracted from his share for the legacy. As he has three parts in hand, one of these falls to the legacy, and the remaining two parts he retains for himself. The two legacies together are imposed upon the son. It is therefore necessary to subtract from his share two-fifths and one-fourth of the same. He thus retains seven twentieths of his entire original share, dividing the whole of it into twenty equal parts. The mother retains as much as she contributes to the legacy; this is one (twelfth part), the entire amount of what she had received being two parts.

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1. If the bequests stated in the present example were charged on the heirs collectively, the husband would be entitled to $\scriptstyle {\frac {1}{4}}$, the mother to $\scriptstyle {\frac {1}{6}}$ of the residue $\scriptstyle {\frac {1}{4}}$+$\scriptstyle {\frac {1}{6}}$ = $\scriptstyle {\frac {5}{12}}$; the remainder $\scriptstyle {\frac {7}{12}}$, would be the son’s share of the residue; but since the bequests, ${\tfrac {2}{5}}+{\tfrac {1}{4}}={\tfrac {13}{20}}$ of the capital, are charged upon the son and mother, the law throws a portion of the charge on the husband.

   The Husband contributes	${\tfrac {1}{4}}\times {\tfrac {1}{3}}=20\times {\tfrac {1}{240}}$,	and retains	${\tfrac {1}{4}}\times {\tfrac {2}{3}}=40\times {\tfrac {1}{240}}$
   The Mother contributes	${\tfrac {1}{6}}\times {\tfrac {1}{2}}=20\times {\tfrac {1}{240}}$,	and retains	${\tfrac {1}{6}}\times {\tfrac {1}{2}}=20\times {\tfrac {1}{240}}$
   The Son contributes	${\tfrac {7}{12}}\times {\tfrac {13}{20}}=91\times {\tfrac {1}{240}}$,	and retains	${\tfrac {7}{12}}\times {\tfrac {7}{20}}=49\times {\tfrac {1}{240}}$
   Total contributed = ${\tfrac {131}{240}}$		Total retained = ${\tfrac {109}{240}}$

   ${\tfrac {2}{5}}+{\tfrac {1}{4}}={\tfrac {8}{20}}+{\tfrac {5}{20}}={\tfrac {13}{20}}$
   The Legatee, to whom the ${\tfrac {2}{5}}$ are bequeathed, receives ${\tfrac {8}{13}}\times {\tfrac {131}{240}}={\tfrac {8\times 11}{3120}}$
   The Legatee, to whom ${\tfrac {1}{4}}$ is bequeathed, receives ${\tfrac {5}{13}}\times {\tfrac {131}{240}}={\tfrac {5\times 131}{3120}}$