Page:Reflections upon ancient and modern learning (IA b3032449x).pdf/202

 ctions, in the Reflexion and Refraction of Light, are the undoubted Discoveries of these later Times. It were easie to give more Instances of this Nature, but these are sufficient to shew how far the Modern Mathematicians have out-done the Ancients, in discovering the noblest and usefullest Theorems, even of those few Figures which they chiefly considered.'

'But all this is nothing, in Comparison of that boundless Extent which the Modern Mathematicians have carried Geometry on to: Which consists in their receiving into it all the Curve Lines in Nature, together with the Area's and Solids that result from them; by distinguishing them into certain Kinds, and Orders; by giving general Methods of describing them, of determining their Tangents, their Lengths, their Area's, and the Solids made by the Rotation of them about their Axes. Add to all this, the general Methods that have been invented of late for finding the Properties of a great Number of these Curves, for the Advancement of Opticks, Mechanicks, and other Parts of Philosophy: And let any Man of Sense give the Preference to the Ancient Geometry if he can.'