class="pginternal" tag="{http://www.w3.org/1999/xhtml}a">18
- Difficulties 19
- General Method 20
- Illustrations 21
-
- 1. Falling Bodies 21
- 2. Inaccessible Distances 23
- 3. Astronomical Facts 24
True Definition of Mathematics 25
- A Science, not an Art 25
Its Two Fundamental Divisions 26
- Their different Objects 27
- Their different Natures 29
- Concrete Mathematics 31
- Geometry and Mechanics 32
- Abstract Mathematics 33
- The Calculus, or Analysis 33
Extent of Its Field 35
- Its Universality 36
- Its Limitations 37
BOOK I.
ANALYSIS.
CHAPTER I.
- Page
- GENERAL VIEW OF MATHEMATICAL ANALYSIS 45
- The True Idea of an Equation 46
-
- Division of Functions into Abstract and Concrete 47
- Enumeration of Abstract Functions 50
- Divisions of the Calculus 53
-
- The Calculus of Values, or Arithmetic 57
- Its Extent 57
- Its true Nature 59
- The Calculus of Functions 61
- Two Modes of obtaining Equations 61
-
- 1. By the Relations between the given Quantities 61
- 2. By the Relations between auxiliary Quantities 64
- Corresponding Divisions of the Calculus of Functions 67
CHAPTER II.
- ORDINARY ANALYSIS; OR, ALGEBRA. 69
-
- Its Object 69
- Classification of Equations
