Page:The Algebra of Mohammed Ben Musa (1831).djvu/181

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“Or, suppose that he, in his illness, has made a present of the slave girl, her price being three hundred, her dowry one hundred dirhems; and the donor dies, after having cohabited with her.” Computation:^[1] Call the legacy thing: the remainder is three hundred less thing. The donor having cohabited with her, the dowry remains with him, which is one-third of the legacy, since the dowry is one-third of the price, or one-third of thing. Thus the donor’s heirs obtain three (117) hundred less one and one-third of thing, and this is twice as much as the legacy, which is thing, or equal to two things. Remove the one and one-third of thing, and add the same to the two things. Then you have three hundred, equal to three things and one-third. One thing is, therefore, three-tenths of it, namely ninety dirhems. This is the legacy.

If the case be the same, and both the donor and donee have cohabited with her; then the Computation

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1. If the donor has cohabited with the slave-girl, the donor’s heirs are to retain the dowry, but must allow the donee, in addition to the legacy $x$, the further sum of ${\tfrac {\alpha }{a}}x$;
   The ransom is then $a-x-{\tfrac {\alpha }{a}}x$ which according to the author is to be made equal to $2x$.
   Whence $x={\tfrac {a^{2}}{3x+a}}=90$
   The donee is to receive the girl, worth $300$, for $210$.