Page:Reflections upon ancient and modern learning (IA b3032449x).pdf/204

 was one of the most confused, and defective.'

'From comparing the Ancient and Modern Geometry, I proceed to the Comparison of those Arts, to which we owe the Improvements both of the one, and the other. These are chiefly Two, ''viz. Algebra, and the Method of Indivisibles''. As to the latter of these, I shall not stand to enquire whether Cavallerius was the first Inventor, or only the Restorer of it. I know (k) Dr. Wallis is of Opinion that it is nothing but the Ancients Method of Exhaustions, a little disguised. It is enough for your Purpose, that by the help of Cavallerius's Method, Geometry has been more promoted in this last Age, than it was in all the Ages before. It not only affords us neat and short Demonstrations, but shews us how to find out the abstrusest Theorems in Geometry. So that there has hardly been any considerable Improvement of late, which does not owe its Rise to it; as any Man may see, that considers the Works of Cartes, Fermat,, Huygens, Neil, Wallis, Barrow, Mercator, Leibnitz, and ''Newton. Archimedes'''s Propositions of the Properties of a Sphere and a Cylinder, are some of the easiest Examples of this Method. How vastly Errata