 As indicated in the passage above, Descartes establishes in Book Two that Pappus curves fall into the specified classes of geometric curves he has designated, where the class into which a Pappus curve falls depends on the number of lines given in the problem and thus, on the degree of the equation to which the problem is reduced. For instance, when Descartes treats the four-line Pappus Problem in Book Two, he shows that, by varying the coefficients of the second degree equation to which the problem has been reduced (through the analysis of Book One), we can construct either a circle, parabola, hyperbola, or ellipse (G, 59–80). That is, he shows that the Pappus curve that solves the four-line problem is either a circle or one of the conic sections, the very “geometric” curves that he has grouped into Class I.