Page:The Algebra of Mohammed Ben Musa (1831).djvu/147

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twentieth, and you have two parts and a half less five one hundred and twentieths of capital. Add hereto two-thirds of the capital, and you have seventy-five one hundred and twentieths of the capital and two parts and a half, equal to seven parts. Subtract, now, two parts and a half from seven, and you retain seventy-five one hundred and twentieths, or five-eighths, equal to four parts and a half. Complete your capital, by (97) adding to the parts as much as three-fifths of the same, and you find the capital equal to seven parts and one-fifth part. Let each part be five; the capital is then thirty-six, each portion five, and the legacy one.

If he leaves his mother, his wife, and four sisters, and bequeaths to a person as much as must be added to the shares of the wife and a sister, in order to make them equal to the moiety of the capital, less two-sevenths of the sum which remains from one-third after the deduction of that complement; the Computation is this:^[1] If

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1. From the context it appears, that when the heirs of the residue are a mother, a wife, and 4 sisters, the residue is to be divided into 13 parts, of which the wife and one sister, together, take 5: therefore the mother and 3 sisters, together, take 8 parts. Each sister, therefore, must take not less than ${\tfrac {1}{13}}$, nor more than ${\tfrac {2}{13}}$. In the case stated at page 102, a sister was made to inherit as much as a wife; in the present case that is not possible; but the widow must take not less than ${\tfrac {3}{13}}$; and each sister not more than ${\tfrac {2}{13}}$. Probably, in this case, the mother is supposed to inherit ${\tfrac {2}{13}}$; the wife ${\tfrac {3}{13}}$; each sister ${\tfrac {2}{13}}$.