paternal uncle five, subtract one share, and multiply them by ten, then by four, which results in one hundred and sixty. Divide it, and it results in eight and eight parts [of nineteen], which is the maternal uncle's bequest. Another method: take from the ten its fourth, multiply the remainder by twenty, then divide it by nineteen, and subtract from it its fifth, multiply the remainder by twenty, and divide it. By algebra, let the maternal uncle's bequest be a thing (shay'), and the paternal uncle's bequest be ten minus a fourth of a thing. Take its fifth and add it to the thing; this is two shares minus half of a tenth of a thing, equaling ten. Drop the common terms from both sides; it becomes eight and eight parts out of nineteen. If you subtract its fourth from the ten, seven and seventeen parts remain. If he bequeaths to his paternal uncle ten minus half of his maternal uncle's bequest, and to his maternal uncle ten minus a third of his grandfather's bequest, and to his grandfather ten minus a fourth of his paternal uncle's bequest, then his paternal uncle's bequest is six and two-fifths, his maternal uncle's bequest is seven and one-fifth, and his grandfather's bequest is eight and two-fifths. Its procedure is to multiply the denominators one by another; multiply two by three by four, which is twenty-four, and add one to it, which becomes twenty-five; this is the divisor. Then subtract one from the two, and multiply one by three, then add one to it, and multiply it by four, which becomes sixteen; then multiply it by ten, which becomes one hundred and sixty. Divide it by twenty-five, and there results from the division six and two-fifths, which is the paternal uncle's bequest. Subtract one from the three, two remain; multiply them by four, which is eight; add one to it, and multiply it by two, then by ten, which becomes one hundred and eighty; divide it by twenty-five. Then subtract one from the four, and multiply three by two, then add one to it, which becomes seven; multiply it by three, then by ten, which becomes two hundred and ten, divided by twenty-five. Another method: place with the paternal uncle four things, with the maternal uncle two dinars, and with the grandfather three dirhams. Then add to what is with the paternal uncle a dinar, and to what is with the maternal uncle a dirham, and balance what is with one of them with what is with the other, and drop the common terms. It results in four things, equaling a dinar and a dirham. Drop the term 'things', and put in its place a dinar and a dirham, then balance what is with the maternal uncle with what is with the grandfather after the addition, which is two dinars and a dirham with the maternal uncle, versus three dirhams and a quarter of a dirham, and a quarter of a dinar with the grandfather. When you drop the common terms, two dirhams and a quarter remain, equivalent to a dinar and three quarters. Expand the whole into quarters; they become seven quarters of a dinar, equaling nine of the dirhams. Swap, and make the dirham seven, and the dinar nine. Then return to what you assumed, and you will find with the paternal uncle a dirham and a dinar, which is sixteen, with the maternal uncle eighteen, and with the grandfather twenty-one. The complete ten is twenty-five, and the sixteen of it is six and two-fifths, the eighteen is seven and one-fifth, and the twenty-one is eight and two-fifths. If there is with them a brother, and the grandfather's bequest is ten minus a fourth of what is with the brother, and the brother's bequest is ten minus a fifth of what is with the paternal uncle, then by this method you place with the paternal uncle five things, with the maternal uncle two dinars, with the grandfather three dirhams, and with the brother four fulus. Then you balance what is with the paternal uncle with what is with the maternal uncle as we mentioned, and you make the things a dinar and a dirham. Then you balance what is with the maternal uncle with what is with the grandfather, and you make the two dinars two dirhams and a fals. Then you balance what is with the grandfather with what is with the brother, and you extract the fals as twenty-six, the dirham as thirty-one, and the dinar as forty-four. It becomes clear that what is with the paternal uncle is seventy-five, with the maternal uncle eighty-eight, with the grandfather ninety-three, and with the brother one hundred and four. When you add to what is with each person what you excluded from it, it becomes with him...