Page:The Algebra of Mohammed Ben Musa (1831).djvu/173

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the legacy itself, namely, two hundred and twenty-five dirhems less one-eighth thing are equal to thing. Reduce this by means of one-eighth of thing, which you add to thing; then you have two hundred and twenty-five dirhems, equal to one thing and one-eighth. Make the equation: one thing is as much as eight-ninths of two hundred and twenty-five, namely, two hundred dirhems.

“Suppose that some one in his illness emancipates a slave, of the price of three hundred dirhems; the slave dies, leaving five hundred dirhems and a daughter, and bequeathing one-third of his property; then the daughter dies, leaving her mother, and bequeathing one-third of her property, and leaving three hundred dirhems.” Computation:^[1] Subtract from the property left

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1. A. is emancipated, and dies, leaving a daughter, and bequeathing one-third of his property to a stranger.
   The daughter dies, leaving a mother, and bequeathing one-third of her property to a stranger.
   A.’s price is $a$; his property is $\alpha$
   The daughter’s property is $d$.
   A.’s ransom is $a-x$; $\alpha -a+x$ is his property, clear of ransom.
   ${\tfrac {1}{3}}[\alpha -a+x]$ goes to the stranger; and the like amount to A.’s daughter, and to the master.
   ${\tfrac {1}{3}}[3d+\alpha -a+x]$ is the property left by the daughter.
   ${\tfrac {1}{9}}[3d+\alpha -a+x]$ is the bequest of the daughter to a stranger.
   ${\tfrac {2}{9}}[3d+\alpha -a+x]$ is the residue, of which ${\tfrac {1}{3}}d$,
   viz. ${\tfrac {2}{27}}[3d+\alpha -a+x]$ is the mother’s,
   and ${\tfrac {4}{27}}[3d+\alpha -a+x]$ is the master’s;