a few years later, in 1659, wallis published a tract containing the solution of the problems on the cycloid which had been proposed by blaise pascal. in this he incidentally explained how the principles laid down in his "arithmetica infinitorum" could be used for the rectification of algebraic curves and gave a solution of the problem to rectify (i.e., find the length of) the semicubical parabola "x" = "ay", which had been discovered in 1657 by his pupil william neile. since all attempts to rectify the ellipse and hyperbola had been (necessarily) ineffectual, it had been supposed that no curves could be rectified, as indeed descartes had definitely asserted to be the case. the logarithmic spiral had been rectified by evangelista torricelli and was the first curved line (other than the circle) whose length was determined, but the extension by neile and wallis to an algebraic curve was novel. the cycloid was the next curve rectified; this was done by christopher wren in 1658.