Hyperbolic Functions

James McMahon
Professor of Mathematics in Cornell University.


The Project Gutenberg EBook of Hyperbolic Functions, by James McMahon.

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Title: Hyperbolic Functions
Author: James McMahon
Release Date: Oct 10, 2004 [EBook #13692]
Language: English
Character set encoding:UTF-8
Markup: HTML5 + MathML
Source Markup: LATEX
Editors’ Preface.3
Author’s Preface.5
1Correspondence of Points on Conics.3
2Areas of Corresponding Triangles.6
3Areas of Corresponding Sectors.8
4Charactersitic Ratios of Sectorial Measures.11
5Ratios Expressed as Triangle-measures.13
6Functional Relations for Ellipse.15
7Functional Relations for Hyperbola.18
8Relations Among Hyperbolic Functions.21
9Variations of the Hyperbolic Functions.28
10Anti-hyperbolic Functions.32
11Functions of Sums and Differences.35
12Conversion Formulas.41
13Limiting Ratios.44
14Derivatives of Hyperbolic Functions.47
15Derivatives of Anti-hyperbolic Functions.53
16Expansion of Hyperbolic Functions.57
17Exponential Expressions.62
18Expansion of Anti-functions.67
19Logarithmic Expression of Anti-Functions.73
20The Gudermanian Function.77
21Circular Functions of Gudermanian.80
22Gudermanian Angle84
23Derivatives of Gudermanian and Inverse.87
24Series for Gudermanian and its Inverse.92
25Graphs of Hyperbolic Functions.96
26Elementary Integrals.103
27Functions of Complex Numbers.111
28Addition-Theorems for Complexes.115
29Functions of Pure Imaginaries.120
30Functions of x + iy in the Form X + iY .126
31The Catenary139
32Catenary of Uniform Strength.144
33The Elastic Catenary.151
34The Tractory.155
35The Loxodrome.159
36Combined Flexure and Tension.163
37Alternating Currents.169
38Miscellaneous Applications.185
39Explanation of Tables.189