Book 1 — CHAPTER III.
W. M. (William Mitchell) Gillespie translation
TRANSCENDENTAL ANALYSIS: its different conceptions 88
Preliminary Remarks 88 Its early History 89
Method of Leibnitz 91
Infinitely small Elements 91 Examples: 1. Tangents 93 2. Rectification of an Arc 94 3. Quadrature of a Curve 95 4. Velocity in variable Motion 95 5. Distribution of Heat 96 Generality of the Formulas 97 Demonstration of the Method 98 Illustration by Tangents 102
Method of Newton 103
Method of Limits 103 Examples: 1. Tangents 104 2. Rectifications 105 Fluxions and Fluents 106
Method of Lagrange 108
Derived Functions 108 An extension of ordinary Analysis 108 Example: Tangents 109 Fundamental Identity of the three Methods 110 Their comparative Value 113 That of Leibnitz 113 That of Newton 115 That of Lagrange 117