and hence that, if the ordinate "y" of a curve can be expanded in powers of "x", its area can be determined: thus he says that if the equation of the curve is "y" = "x" + "x" + "x" + ..., its area would be "x" + x/2 + "x"/3 + ... he then applied this to the quadrature of the curves "y" = ("x" − "x"), "y" = ("x" − "x"), "y" = ("x" − "x"), etc., taken between the limits "x" = 0 and "x" = 1. he shows that the areas are, respectively, 1, 1/6, 1/30, 1/140, etc. he next considered curves of the form "y" = "x" and established the theorem that the area bounded by this curve and the lines "x" = 0 and "x" = 1 is equal to the area of the rectangle on the same base and of the same altitude as "m" : "m" + 1. this is equivalent to computing