Page:The Algebra of Mohammed Ben Musa (1831).djvu/115

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is two-ninths of the capital less two-sevenths and two-thirds of a seventh of the share of a son. Add this to the two-thirds of the capital; the sum is eight-ninths of the capital less two-sevenths and two thirds of a seventh of the share of a son, or eight twenty-one parts of that share, and this is equal to three shares. Reduce this, you have then eight-ninths of the capital, equal to three shares and eight twenty-one parts of a share. Complete the capital by adding to eight-ninths as much as one-eighth of the same, and add in the same proportion to the shares. Then you find the capital equal to three shares and forty-five fifty-sixth parts of a share. Calculating now each share equal to fifty-six, the whole capital is two hundred and thirteen, the first legacy thirty-two, the second thirteen, and of the remaining one hundred and sixty-eight each son takes fifty-six.

 

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On another Species of Legacies.

“A woman dies, leaving her daughter, her mother, and her husband, and bequeaths to some one as much as the share of her mother, and to another as much as one-ninth of her entire capital.”^[1] Computation: You begin by dividing the heritage into thirteen parts, two

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1. In the former examples (p. 90) when a husband and a mother were among the heirs, a husband was found to be entitled to ${\tfrac {1}{4}}={\tfrac {3}{12}}$ and a mother to ${\tfrac {1}{6}}={\tfrac {2}{12}}$ of the residue. Here a husband is stated to be entitled to ${\tfrac {3}{13}}$, and a mother to ${\tfrac {2}{13}}$ of the residue.