Page:Reflections upon ancient and modern learning (IA b3032449x).pdf/349

 amongst those numerous Commendations which are given to Archimedes, some would have been spent upon the many noble Theorems which he discovered, and not almost all upon the Engines wherewith he baffled Marcellus at the Siege of Syracuse. The Proposition, That the Superficies of a Sphere is equal to the Area's of Four of its greatest Circles, which is one of the most wonderful Inventions that was ever found in Geometry, shews him to have been a much greater Man, than all that is said of him by the Roman, or Greek Historians. Had experimental Philosophy been anciently brought upon the Stage, had Geometry been solemnly and generally applied to the Mechanism of Nature, and not solely made use of to instruct Men in the Art of Reasoning, and even that too, not very generally neither, the Moderns would not have had so great Reason to boast as now they have: For these are things which come under ocular Demonstration, which do not depend upon the Fancies of Men for their Approbation, as Oratory and Poetry very often do. So that one may not only in general say that the Ancients are out-done by the Moderns in these Matters, but also assign most of the particulars, and determine the Proportion