Chapter III
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