 A few examples will help clarify what is at stake here. The problem of bisecting a given angle is counted among planar problems, because, as detailed by Euclid in Elements I.9, to construct the line segment that divides a given angle into two equal parts, we construct (by compass) three circles of equal radius, and then (by straightedge) join the vertex of the angle with the point at which the circles intersect (Euclid 1956, Volume I, 264–265). Notice here that, to generate the solution, curves are used to construct a point that gives the solution to the problem, namely, by constructing the circles, we identify a point that allows us to bisect the curve. (When dealing with locus problems, such as the Pappus problem, the curves that are constructed are themselves the solution to the problem. See  section 3  below.) The problem of trisecting an angle, on the other hand, was considered a line-like problem, because its solution required the construction of curves, such as the spiral, which were not constructible by straightedge and compass. Perhaps most famous among line-like problems is that of squaring the circle; for those who deemed this problem solvable, the solution required the construction of a curve such as the quadratrix, a curve that was proposed by the ancients in order to solve this very problem (which is how the curve received its name). Certainly, the generation of such curves could be described; Archimedes famously describes the generation of the spiral in Definition 1 of his Spirals and Pappus describes the generation of the quadratrix in Book IV of the Collection. However, these descriptions were considered “more complicated” precisely because they go beyond the intersection of curves that are generated by straightedge and compass construction. For instance, according to Archimedes, the spiral is generated by uniformly moving a line segment around a given point while tracing the path of a point that itself moves uniformly along the line segment. And, according to Pappus, the quadratrix is generated by the uniform motions of two line segments, where one segment moves around the center of a given circle and the other moves through a quadrant of the circle. (Cf. Bos 2001, 40–42 for the details of both these constructions.) In a similar vein, the construction of conics was considered more complicated: One of the accepted techniques for constructing a conic required cutting a cone in a specified way, which again, went beyond the consideration of intersecting curves that were constructible by straightedge and compass.