Page:The Algebra of Mohammed Ben Musa (1831).djvu/142

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the capital.”^[1] Computation: Determine the parts of the residue, which in the present instance are thirteen. Take the capital, and subtract from it one-fifth of the same, less one part, as the share of a daughter: this being the first legacy. Then subtract also one-fourth, less two parts, as the share of the mother: this being the second legacy. There remain eleven-twentieths of the capital, which, when increased by three parts, are equal to thirteen parts. Remove now from thirteen parts the three parts on account of the three parts (on the other side), and you retain eleven-twentieths of the capital, equal to ten parts. Complete the capital, by adding to the ten parts as much as nine-elevenths of the same; then you find the capital equal to eighteen parts and two-elevenths. Assume now each part to be eleven; then the whole capital is two hundred, each part is eleven; the first legacy will be twenty-nine, and the second twenty-eight. If the case is the same, and she bequeaths to some person as much as must be added to the share (94) of the husband to make it equal to one-third, and to another person as much as must be added to the share of the mother to make it equal to one-fourth; and to a

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1. In this case, the mother has ${\tfrac {2}{13}}$; and each daughter has ${\tfrac {1}{13}}$ of the residue.
   ${\begin{aligned}&1-x-y=13v\\&{\text{i.e.}}\;1-{\tfrac {1}{5}}+v-{\tfrac {1}{4}}+2v=13v\\&\therefore \;{\tfrac {11}{20}}=10v\;\therefore \;v={\tfrac {11}{200}};x={\tfrac {29}{200}};y={\tfrac {28}{200}}\end{aligned}}$