Page:The Algebra of Mohammed Ben Musa (1831).djvu/102

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ON LEGACIES.

 

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On Capital, and Money lent.

(65) “A man dies, leaving two sons behind him, and bequeathing one-third of his capital to a stranger. He leaves ten dirhems of property and a claim of ten dirhems upon one of the sons.”

Computation: You call the sum which is taken out of the debt thing. Add this to the capital, which is ten dirhems. The sum is ten and thing. Subtract one-third of this, since he has bequeathed one-third of his property, that is, three dirhems and one-third of thing. The remainder is six dirhems and two-thirds of thing. Divide this between the two sons. The portion of each of them is three dirhems and one-third plus one-third of thing. This is equal to the thing which was sought for.^[1] Reduce it, by removing one-third from

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1. If a father dies, leaving $n$ sons, one of whom owes the father a sum exceeding an $n$th part of the residue of the father’s estate, after paying legacies, then such son retains the whole sum which he owes the father: part, as a set-off against his share of the residue, the surplus as a gift from the father.
   In the present example, let each son’s share of the residue be equal to $x$.
   ${\tfrac {2}{3}}[10+x]=2x\;\therefore \;1+x-3x\;\therefore \;10=2x\;\therefore \;x=5.$
   The stranger receives $5$; and the son, who is not indebted to the father, receives $5$.