 Importantly, the analytic method that Descartes uses in the four-line case is generalized to apply to the general, \(n\)-line version of the Pappus Problem. That is, Descartes’ claim is that no matter how many lines and angles are given in the problem, it is possible, by means of his analytic method, to express the sought after points C in terms of two unknown quantities (in contemporary terms, to reduce the problem to a polynomial equation in two unknowns) (G, 33). As a result, for any \(n\)-line version of the Pappus Problem, we can generate values for C and construct the sought after Pappus curve in a pointwise manner by assigning different values to \(x\) and \(y\). As Descartes puts it,