Page:The Algebra of Mohammed Ben Musa (1831).djvu/180

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On return of the Dowry.

“A man, in the illness before his death, makes to some one a present of a slave girl, besides whom he has no property. Then he dies. The slave girl is worth three hundred dirhems, and her dowry is one hundred dirhems. The man to whom she has been presented, cohabits with her.” Computation:^[1] Call the legacy of the person to whom the girl is presented, thing. Subtract this from the donation: there remain three hundred less thing. One-third of this difference returns to the donor on account of dowry (since the dowry is one-third of the price): this is one hundred dirhems less one-third of thing. The donor’s heirs obtain, therefore, four hundred less one and one-third of thing, which is equal to twice the legacy, which is thing, or to two things. Transpose the one and one-third thing from the four hundred, and add it to the two things; then you have four hundred, equal to three things and one-third. One thing is, therefore, equal to three-tenths of it, or to one hundred and twenty dirhems, and this is the legacy.

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1. Let a be the slave-girl’s price $-\alpha$her dowry. Then, according to the author, we are to make
   $a-x+\alpha -{\tfrac {\alpha }{a}}x=2x$
   Therefore $x={\tfrac {a}{3a+\alpha }}[a+\alpha ]={\tfrac {3}{10}}\times 400=120$
   The donee is to receive the girl’s dowry, worth $400$, for $280$.