 The result of Descartes’ analysis, as indicated by the remarks above, is that the curve that includes the sought after points C can be pointwise constructed by using ruler and compass to solve for the roots of a second-degree equation in two unknowns. He then generalizes this result and claims that the solution points for any problem that can be reduced to a second-degree equation can be constructed by ruler and compass. If instead a problem is reduced to an equation of third or fourth degree, the points are constructed by conics, and if a problem is reduced to an equation of fifth or sixth degree, the points are constructed by a curve that is “just one degree higher than the conic sections” (G, 37). In other words, Descartes’ claim is that if a problem can be reduced to a single equation of degree not higher than six, in which the unknown quantity or quantities are expressed in terms of a known quantity, then the roots of the equation can be constructed by straightedge and circle, or by conic, or by a more complicated curve that does not have degree higher than four. Based on this result, Descartes suggests a way to generalize further and solve the \(n\)-line Pappus Problem, for no matter how many given lines and angles with which a Pappus Problem begins, it will be possible to reduce the problem to an equation and then pointwise construct the roots of the equation, i.e., the sought after points C of the problem (G, 37).