 In the Collection, Pappus does not offer a firm verdict on whether the conics and “more complicated” curves meet the rigorous standards of geometrical construction and hence, on whether they are admissible in the domain of geometry. In the case of the conics, he relies on Apollonius’s commentary and reports the usefulness of these curves for the synthesis (or proofs) of some problems (Pappus, 116). However, to claim a curve useful is quite different from claiming it can be constructed by properly geometrical methods (as we’ll see more clearly below). Moreover, in the case of the quadratrix, Pappus sets out the description of the curve in Book IV of the Collection, and then immediately proceeds to identify the common objections to the curve’s description, e.g., that there is a petitio principii in the very definition of the curve, without commenting on whether these objections can be overcome. Thus, although it was known by the ancients that conics and other complicated curves could be used to solve outstanding problems, it was not clear to early modern mathematicians whether the ancients considered these solutions genuinely geometrical. In other words, it was not clear from Pappus’s Collection whether these curves were admissible in geometrical problem-solving and therefore, whether solid problems (such as identifying the mean proportionals between given line segments) or line-like problems (such as trisecting an angle and squaring the circle) had genuine geometrical solutions.