Page:The Algebra of Mohammed Ben Musa (1831).djvu/105

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On another Species of Legacy.

“A man dies, leaving his mother, his wife, and two brothers and two sisters by the same father and mother with himself; and he bequeaths to a stranger one-ninth of his capital.”

Computation:^[1] You constitute their shares by taking them out of forty-eight parts. You know that if you take one-ninth from any capital, eight-ninths of it will remain. Add now to the eight-ninths one-eighth of the same, and to the forty-eight also one-eighth of them, namely, six, in order to complete your capital. This gives fifty-four. The person to whom one-ninth is bequeathed receives six out of this, being one-ninth of the whole capital. The remaining forty-eight will be distributed among the heirs, proportionably to their legal shares.

If the instance be: “A woman dies, leaving her husband, a son, and three daughters, and bequeathing

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1. It appears in the sequel (p. 96) that a widow is entitled to ${\tfrac {1}{8}}$th, and a mother to ${\tfrac {1}{8}}$th of the residue; ${\tfrac {1}{8}}+{\tfrac {1}{6}}={\tfrac {14}{48}}$, leaving ${\tfrac {34}{48}}$ of the residue to be distributed between two brothers and two sisters; that is, ${\tfrac {17}{48}}$ between a brother and a sister; but in what proportion these 17 parts are to be divided between the brother and sister does not appear in the course of this treatise.
   

   Let the whole capital of the testator = $1$
   and let each 48th share of the residue = $x$
   ${\tfrac {8}{9}}=48x\;\therefore \;{\tfrac {1}{9}}=6x\;\therefore \;{\tfrac {1}{54}}=x$

   that is, each 48th part of the residue = ${\tfrac {1}{54}}$th of the whole capital.

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