 In the Collection, Pappus presents a solution to the three and four line versions of the problem (i.e., the versions of the problem in which we begin with three or four given lines and angles) as well as Apollonius’s solution to the six-line case, which relies on his theory of conics and the transformation of areas to construct the locus of points (Pappus, 118–123). However, Pappus does not treat the general \((n\)-line) case, and this is the advance of the solution Descartes achieves in 1632, a solution published in La Géométrie, where he claims that, unlike the ancients, he has found a method to successfully “determine, describe, [and] explain the nature of the line required when the question [of the Pappus Problem] involves a greater number of lines” (G, 22). And as Descartes reports to Mersenne in 1632, he could not have found his general solution without the help of algebra: