early in 1658 a similar discovery, independent of that of neile, was made by van heuraët, and this was published by van schooten in his edition of descartes's "geometria" in 1659. van heuraët's method is as follows. he supposes the curve to be referred to rectangular axes; if this be so, and if ("x", "y") be the coordinates of any point on it, and "n" be the length of the normal, and if another point whose coordinates are ("x", η) be taken such that η : "h" = "n" : "y", where "h" is a constant; then, if "ds" be the element of the length of the required curve, we have by similar triangles "ds" : "dx" = "n" : "y". therefore, "h ds" = η "dx". hence, if the area of the locus of the point ("x", η) can be found, the first curve can be rectified. in this way van heuraët effected the rectification of the curve "y" = "ax" but added that the rectification of the parabola "y" = "ax" is impossible. since it requires the quadrature of the hyperbola. the solutions given by neile and wallis are somewhat similar to that given by van heuraët, though no general rule is enunciated, and the analysis is clumsy. a third method was suggested by fermat in 1660, but it is inelegant and laborious.