Page:Reflections upon ancient and modern learning (IA b3032449x).pdf/203

 'That the Ancients had general Methods of Constructing all plain Problems by a streight Line and a Circle, as also all Solid Problems by the help of a Conick Section, is most certain. But it is as certain that here they stopped, and could go no further, because they would not receive any Order of Curves beyond the Conick Sections, upon some nice Scrupulosity in multiplying the Number of the Postulata, requisite to the describing of them. Whereas the Modern Geometers, particularly the renowned Des Cartes, have given general Rules for Constructing all Problems of the 5th. or 6th. Degree. Which Method, if rightly understood, is applicable to all Problems of any Superior Order.'

'How deficient the Geometry of the Ancients was in that Part which related to the Loca Geometrica, is manifest from the Account that Pappus gives us of that Question, about which Euclid and Apollonius made so many ineffectual Attempts: The Solution whereof we owe entirely to Mr. Isaac Newton (i). For it is evident that Des Cartes mistook the true Intent of the Ancients in this Matter. So that the Loca Solida is now one of the perfectest Parts of Geometry that we have; which before