 We notice in the above remarks that Pappus bases his classification of geometrical problems on the construction of the curves necessary for the solution of a problem: If a problem is solved by a curve constructible by straightedge and compass, it is planar; if a problem is solved by a curve constructible by conic section, it is solid; and if a problem is solved by a curve that requires a more complicated construction—that has an “inconstant and changeable origin”—, it is line-like. Though a seemingly straightforward directive for how to classify geometrical problems, there remained an ambiguity in Pappus’s text about whether the so-called solid and line-like problems—problems that required the construction of conics and more complicated curves, such as the spiral—were in fact solvable by genuinely geometrical methods. That is, there was an ambiguity, and thus, an open question for early modern mathematicians, about whether problems that could not be solved by straightedge and compass construction met the rigorous standards of geometry. (For the special status of constructions by straightedge and compass in Greek mathematics, see Heath (1921) and Knorr (1986). For helpful overviews of the historical development of Greek mathematics, see classics such as Merzbach and Boyer (2011) and volume 1 of Kline (1972).)