 The same point is made later in Book Two, where Descartes emphasizes that “no matter how we conceive a curve to be described, provided it be one of those which I have called geometric,” it will always be possible to find an equation determining all of the curve’s points (G, 56). He reiterates that geometric curves can be classified according to their equations but also points out that within a specific class, a curves’ simplicity should be ranked according to the motions required for construction. For instance, although the circle belongs to the same class as the ellipse, hyperbola, and parabola, these latter curves are “equally complex” whereas the circle “is evidently a simpler curve” and will thus be more useful in the construction of problems (G, 56). (See Manders 2008, 77, for discussion of Leibniz’s and Poncelet’s dissatisfaction with the connection between the algebraic form that Descartes uses to represent geometrical curves and the spatial, diagrammatic representation of these curves.)