Page:The method of fluxions and infinite series.djvu/25

THE METHOD of FLUXIONS, AND INFINITE SERIES. INTRODUCTION : Or, the Refolution of Equations by Infinite Series. IAVING obferved that moft of our modern Geome-- tricians, neglecting the Synthetical Method of the Ancients; have apply'd themfelves chiefly to the cultivating of the Analytical Art ; by the affiftance of which they have been able to overcome fo many and fo great difficulties, that they feem to have exhaufted all the Speculations of Geometry, excepting the Quadrature of Curves, and Ibme other matters of a like nature, not yet intirely difcufs'd : I thought it not amifs, for the fake of young Students in this Science, to compofe the following Treatife, in which I have endeavour'd to enlarge the Boundaries of Analyticks, and to improve the Doctrine of Curve-lines. 2. Since there is a great conformity before the Operations in Species, and the fame Operations in common Numbers; nor do they feem to differ, except in the Characters by which they are re- B prefented,.