"It may be proper... to mention the distinctions of geometrical propositions (especially of problems) assumed by the ancients, as they are stated by Pappus in two passages of his work... It appears that it was the difficulty, or rather the impossibility, of resolving some problems by the circle and straight line, which suggested the investigation of other curve lines, by the description of which the solution of such problems might be accomplished. The doubling of the cube, and the trisection of an arch of a circle, were two celebrated problems which exercised the ingenuity of the more ancient geometers, but which were found not to be resolvable by plane geometry. From the very brief accounts which remain of these speculations, it appears that the first attempt of producing new curves, which might be employed in geometrical science, was from the section of a solid by a plane; and the only solids considered in the early state of the science, which by such a section could produce curves different from the circle, were the cylinder and cone. But as the sections of the latter comprehended the curves resulting from the sections of the former, the three new curves, arising from the different possible sections of the cone by a plane, obtained the name of Conic Sections. By these curves the two before-mentioned problems were easily resolved; and from this origin, all problems requiring for their solution the description of one or more of them, were called solid, though they had no other relation to solid figures. Some other curves were also invented by ingenious men of those times for the fame purpose; but the Ancients did not pursue this branch of geometry, and considered only a small number of such lines, without having had any notion of the unbounded number which modern speculations have brought into notice; and therefore, without proposing any principle of systematic arrangement."