"The inspiration of Fermat's discussion of the conic sections, and that is practically the whole of his analytic geometry, comes direct from Apollonius. The same had been true of Pappus, fourteen centuries before. His point of departure is the famous four-line problem... This question seems to have stumped both Euclid and Aristaeus, and to have been first solved by Apollonius. In Apollonius's own work we find what is rather the converse of this problem. Almost the first piece of geometrical writing which Fermat did was to prove the three-line case."