Page:The Algebra of Mohammed Ben Musa (1831).djvu/106

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to a stranger one-eighth and one-seventh of her (67) capital;” then you constitute the shares of the heirs, by taking them out of twenty.^[1] Take a capital, and subtract from it one-eighth and one-seventh of the same. The remainder is, a capital less one-eighth and one-seventh. Complete your capital by adding to that which you have already, fifteen forty-one parts. Multiply the parts of the capital, which are twenty, by forty-one; the product is eight hundred and twenty. Add to it fifteen forty-one parts of the same, which are three hundred: the sum is one thousand one hundred and twenty parts. The person to whom one-eighth and one-seventh were bequeathed, receives one-eighth and one-seventh of this. One seventh of it is one hundred and sixty, and one-eighth one hundred and forty. Subtracting this, there remain eight hundred and twenty parts for the heirs, proportionably to their legal shares.

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1. A husband is entitled to ${\tfrac {1}{4}}$th of the residue, and the sons and daughters divide the remaining ${\tfrac {3}{4}}$ths of the residue in such proportion, that a son receives twice as much as a daughter. In the present instance, as there are three daughters and one son, each daughter receives ${\tfrac {1}{3}}$ of ${\tfrac {3}{4}},={\tfrac {3}{20}}$ of the residue, and the son ${\tfrac {6}{20}}$. Since the stranger takes ${\tfrac {1}{8}}+{\tfrac {1}{7}}={\tfrac {15}{56}}$ of the capital, the residue $={\tfrac {41}{56}}$ of the capital, and each ${\tfrac {1}{20}}$th share of the residue $={\tfrac {1}{20}}\times {\tfrac {41}{56}}={\tfrac {41}{1120}}$ of the capital, The stranger, therefore, receives ${\tfrac {15}{56}}={\tfrac {15\times 20}{56\times 20}}={\tfrac {300}{1120}}$ of the capital.