 What Descartes achieves here by means of his geometrical analysis is no doubt significant. He has outlined a way of solving the Pappus Problem for any number of given lines. However, questions about proving the Pappus Problem solved still linger come the end of Book One. As in Viète’s analysis, Descartes has shown that a solution to the general problem exists but the algebraic elaboration of the problem does not unto itself give a clue to how we are to geometrically construct the curve that solves the problem. Notice in particular that in Book One the roots (i.e., the points along the sought after curves) are constructed by straight edge, compass, conics, and higher order curves, such that the Pappus curves that include the roots are constructed pointwise. But this leaves us the question: Are the Pappus curves of Book One legitimately geometrical? That is, can the curves that solve the \(n\)-line version of the Pappus Problem themselves be constructed by legitimately geometrical methods? This is an issue broached in Book Two, the main focus of which is how to enact a synthesis, or construction, of a geometrical problem.