"We are informed by Pappus, that the difficulty of describing the Conic Sections with mechanical accuracy led some of the ancient geometers to employ those higher curves, the description of which was found to be more easy. The conchoid in particular was used for finding between two given straight lines two mean proportionals, from which the doubling the cube was an obvious inference; and the trisection of an arch of the circle was accomplished also by the same curve, and likewise by the spiral and quadratrix. From Pappus it appears, however, that the early Mathematicians had at first some reluctance in admitting either the Conic Sections or superior curves in the solution of problems, considering them as not strictly geometrical; but afterwards these lines became objects of much curious investigation, even among the ancients; and in modern times ultimately were of the most extensive utility, both in abstract and in physical science."
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William Trail, Account of the Mathematical Collections of Pappus, ibid.
https://en.wikiquote.org/wiki/History_of_mathematics
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History of mathematics
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