"In 1659 Wallis published a tract on s in which incidentally he explained how the principles laid down in his Arithmetica infinitorum could be applied to the rectification of s: and in the following year one of his pupils, by name William Neil, applied the rule to rectify the x^3 = ay^2. This was the first case in which the length of a curved line was determined by mathematics, and as all attempts to rectify the ellipse and hyperbola had (necessarily) been ineffectual, it had previously been generally supposed that no curves could be rectified."