 Having now made a general classification of curves, it is easy for me to demonstrate the solution which I have already given of the problem of Pappus. For, first, I have shown [in Book One] that when there are only three or four lines the equation which serves to determine the required points is of the second degree. It follows that the curve containing these points [i.e., the Pappus curve] must belong to the first class, since such an equation expresses the relation between all points of curves of Class I and all points of a fixed straight line. When there are not more than eight given lines the equation is at most a biquadratic, and therefore the resulting [Pappus] curve belongs to Class II or Class I. When there are not more than twelve given lines, the equation is of the sixth degree or lower, and therefore the required curve belongs to Class III or a lower class, and so on for other cases (G, 59).