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Contents
2
Editors’ Preface.
3
Author’s Preface.
5
1
Correspondence of Points on Conics.
3
2
Areas of Corresponding Triangles.
6
3
Areas of Corresponding Sectors.
8
4
Charactersitic Ratios of Sectorial Measures.
11
5
Ratios Expressed as Triangle-measures.
13
6
Functional Relations for Ellipse.
15
7
Functional Relations for Hyperbola.
18
8
Relations Among Hyperbolic Functions.
21
9
Variations of the Hyperbolic Functions.
28
10
Anti-hyperbolic Functions.
32
11
Functions of Sums and Differences.
35
12
Conversion Formulas.
41
13
Limiting Ratios.
44
14
Derivatives of Hyperbolic Functions.
47
15
Derivatives of Anti-hyperbolic Functions.
53
16
Expansion of Hyperbolic Functions.
57
17
Exponential Expressions.
62
18
Expansion of Anti-functions.
67
19
Logarithmic Expression of Anti-Functions.
73
20
The Gudermanian Function.
77
21
Circular Functions of Gudermanian.
80
22
Gudermanian Angle
84
23
Derivatives of Gudermanian and Inverse.
87
24
Series for Gudermanian and its Inverse.
92
25
Graphs of Hyperbolic Functions.
96
26
Elementary Integrals.
103
27
Functions of Complex Numbers.
111
28
Addition-Theorems for Complexes.
115
29
Functions of Pure Imaginaries.
120
30
Functions of
x
+
i
y
in the Form
X
+
i
Y
.
126
31
The Catenary
139
32
Catenary of Uniform Strength.
144
33
The Elastic Catenary.
151
34
The Tractory.
155
35
The Loxodrome.
159
36
Combined Flexure and Tension.
163
37
Alternating Currents.
169
38
Miscellaneous Applications.
185
39
Explanation of Tables.
189
40
Appendix.
202
Index
206
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