| INTrODUCTION GENERAL CONSIDERATIONS ONMATHEMATICAL SCIENCE THE OBECT OF MATHEMATICS Measuring Magnitudes Difficulties General Method Illustrations 1. Falling Bodies 2. Inaccessible Distances 3. Astronomical Facts TILUE DEFINITION OF MATHEMATICS A Science, not an Art ITS TWO FUNDAMENTAL DIVISIONS Their different Objects Their different Natures Conch'ere Mathematies Geometry and Mechanics Abstract Mathematics The Calculus, or Analysis EXTENT OF ITS FIELD Its Universality Its Limitations BOOK Ⅰ ANALYSIS CHAPPTER Ⅰ.GENERAL VIEW OF MATHEMANTICAI ANALYSIS CHAPPTER Ⅱ.ORDINARY ANALYSIS; OR,ALGEBRA CHAPPTER Ⅲ.TRANSCENDENTAL ANALYSIS:ITS DEFFERENT CONCEPTIONS CHAPPTER Ⅳ.THE DIFFERENTIAL AND INTEGRAL CALCULUS CHAPPTER Ⅴ.THE CALCULUS OF VARIATIONS CHAPPTER Ⅵ.THE CALCULUS OF FINITE DIFFERENCES BOOK Ⅱ.CEOMETRY CHAPPTER Ⅰ.A GENERAL VIEW OF GEOMETRY CHAPPTER Ⅱ.ANCIENT OR SYNTHETIC GEOMETRY CHAPPTER Ⅲ.MODERN OR ANALYTICAI GEOMETRY |
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