 For instance, to solve the angular section problem, Descartes begins by presenting an instrument that includes four rulers (OA, OB, OC, OD), which are hinged at point O  (figure 1).  We then take four rods (HJ, FJ, GI, EI), which are of equal length \(a\), and attach them to the arms of the instrument such that they are a distance \(a\) from O and are pair-wise hinged at points J and I. Leaving OA stationary, we now move OD so as to vary the measure of angle DOA, and following the path of point J, we generate the curve KLM  (figure 2).  As Descartes has it, we can construct the curve KLM on any given angle by means of the instrument described above, because the angle we are trisecting plays no role in the construction of KLM. And once the curve KLM is constructed, the given angle can be trisected by means of some basic constructions with straight lines and circles. In this respect, the curve KLM is, for Descartes, the means for solving the angle trisection problem, and moreover, his treatment suggests that the construction can be generalized further so that, by means of his “new compass,” an angle can also be divided into 4, 5, or more equal parts. (I borrow my treatment of this construction from Domski 2009, 121, which is itself indebted to the presentation in Bos 2001, 237–239.)