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(40) In the same manner, if the question be: “A square, multiply its root by four of its roots, and the product will be three times the square, with a surplus of fifty dirhems.”[1] Computation: You multiply the root by four roots, it is four squares, which are equal to three squares and fifty dirhems. Remove three squares from the four; there remains one square, equal to fifty dirhems. One root of fifty, multiplied by four roots of the same, gives two hundred, which is equal to three times the square, and a residue of fifty dirhems.
If the instance be: “A square, which when added to twenty dirhems, is equal to twelve of its roots,”[2] then the solution is this: You say, one square and twenty dirhems are equal to twelve roots. Halve the roots and multiply them by themselves; this gives thirty-six. Subtract from this the twenty dirhems, extract the root from the remainder, and subtract it from the moiety of the roots, which is six. The remainder is the root of the square: it is two dirhems, and the square is four.
If the instance be: “To find a square, of which if one-third be added to three dirhems, and the sum be subtracted from the square, the remainder multiplied by
