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

This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at Gutenberg.

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 |

Contents2

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

40Appendix.202

Index206

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

40Appendix.202

Index206