"He next considered curves of the form y = x^\frac{1}{m} and established the theorem that the area bounded by the curve, the axis of x, and the ordinate x = 1 is to the area of the rectangle on the same base and of the same altitude as m:m + 1. This is equivalent to finding the value of \int_{0}^{1}x^\frac{1}{m}dx. He illustrated this by the parabola in which m = 2. He stated but did not prove the corresponding result for a curve of the form y = x^\frac{p}{q}."