 As indicated above, Descartes attempts to establish via his synthesis that the curves that solve the Pappus Problem are “geometric” by his own stated standard, that is, that the Pappus curves are constructible by the “precise and exact” motions needed to construct genuinely geometric curves. However, it is not at all clear that Descartes has proven this point. Even when addressing the basic four-line Pappus Problem in Book Two, Descartes does not appeal to motions that are evidently clear and distinct as he constructs the Pappus curves that solve the problem (in this case, the circle, parabola, hyperbola, and ellipse). Rather, he relies on Apollonius’s theory of conics, which requires that a cone be cut at a designated point in the plane, and as Bos remarks, this Apollonian technique for constructing conics “is not a method of construction that immediately presents itself to the mind as clear and distinct” (Bos 2001, 325). Specifically, since it was not evident to mathematicians at the time whether constructions that required locating a cone in the plane met the exact and rigorous standards of geometrical reasoning, Descartes’ treatment of the Pappus curves in this four-line case does not convincingly demonstrate their “geometric” status. Later in Book Two, when he treats the five-line Pappus Problem, matters get more complicated.