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 The Method which I shall follow is this: (1.) I shall enquire into the State of Ancient and Modern Mathematicks, without any particular Application of the Properties of the several Lines and Numbers, Surfaces and Solids, to Physical Things. (2.) I shall enquire what new Instruments have been invented, or old ones improved, by which the Knowledge of Nature of any sort has been, or may be, further enlarged. (3.) I shall enquire whether any Improvements have been actually made of Natural History, and of any Physico-Mathematical or Physical Sciences, such as Astronomy, Musick, Opticks, Medicks, and the like. (4.) From all this, I shall endeavour to pass a Judgment upon the Ancient and Modern Ways of Philosophizing concerning Nature in general, and its principal Phænomena, or Appearances.

I begin with Geometry and Arithmetick, because they are general Instruments whereby we come to the Knowledge of many of the abstrusest Things in Nature; since, as Plato said of old, God always Geometrizes in all his Works. That this Comparison might be the more exact, I desired my learned and worthy Friend, Mr. John Craige, to give me his Thoughts upon this Matter: His own learned Wri-