 In Book One, Descartes applies his geometrical analysis to the four-line case of the Pappus problem. He begins by designating two given line segments (of unknown length) AB and BC as oblique coordinates \(x\) and \(y\), respectively, such that all other lines needed to solve the problem will be expressed in terms of \(x\) and  \(y\).[6]  Then, by considering the angles given in the problem and the properties of similar triangles, he generates an algebraic expression of the sought after points C in terms of the two unknowns \(x\) and \(y\) and the known quantity \(z\) (where \(z\) designates the ratio given in the problem) (G, 29–30).