KHAYYAM main contribution to that subject is a serious attack on cubic equations, such as finding x given that 2x3 – 2x2 + 2x – 1 = 0. This particular problem has a geometric origin:
Given that for the right-angled triangle shown, the sum of the height and the shortest side is equal to the hypotenuse, find the ratio of the length of the shortest side to that of the other side.
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