Addition-theorems, 35, 115
Admittance of dielectric, 171
Algebraic identity, 120
Alternating currents, 111, 129, 169
Ambiguity of value, 23, 32, 132
Amplitude
    hyperbolic, 90
    of complex number, 137
Anti-gudermanian, 78, 88, 140, 156, 160
Anti-hyperbolic functions, 32, 53, 67, 81, 103, 132
Applications, 137–187
Arch, 142, 155
Areas, 4, 6, 25, 105, 107, 185
Argand diagram, 128, 174

Bassett’s Hydrodynamics, 187
Beams, flexure of, 163
Bedel and Crehore’s alternating currents, 111, 169
Byerly’s Fourier Series, etc., 187, 192

Callet’s Tables, 192
Capacity of conductor, 169
Catenary, 139
    Elastic, 151
    of uniform strength, 144
Cayley’s Elliptic Functions, 84, 90
Center of gravity, 186
Characteristic ratios, 11
Chart
    Mercator’s, 161
    of hyperbolic functions, 129, 174
Circular functions, 3, 16, 37, 51, 64, 81, 103, 113, 123
    of complex numbers, 123
    of gudermanian, 80
Complementary triangles, 13
Complex numbers, 111–137
    Applications of, 169–183
    Tables, 189, 196
Conductor resistance and impedance, 174
Construction
    for gudermanian, 84
    of charts, 128
    of graphs, 96
Convergence, 60, 68
Conversion-formulas, 41
Corresponding points
    on conics, 3, 78
    on sectors and triangles, 6, 78
Cotes, reference to, 202
Currents, alternating, 169
Curvature, 151, 159, 185

Deflection of beams, 166
Derived functions, 47, 53, 87
Difference formula, 35
Differential equation, 51, 65, 140, 147, 156, 160, 173
Dirksen’s Organon, 202
Distributed load, 167

Electromotive force, 169, 174
Elimination of constants, 51
Ellipses, chart of confocal, 129
Elliptic
    functions, 3
    integrals, 3
    sectors, 3
Elliptic functions, 90
Elliptic integrals, 90
Elliptic sectors, 90
Equations
    Differential, see Differential Equation
    Numerical, 103, 142, 149
Evolute of tractory, 157
Expansion in series, 59, 68, 93
Exponential expressions, 62, 65, 203

Ferroni, reference to, 202
Flexure of Beams, 163
Foncenex, reference to, 202
Forti’s Tavoli e teoria, 192, 202
Fourier series, 169, 187
Function
    anti-gudermanian, see Anti-gudermanian
    anti-hyperbolic, see Anti-hyperbolic functions
    circular, see Circular functions
    elliptic, see Elliptic functions
    gudermanian, see Gudermanian function
    hyperbolic, defined, 18
    of complex numbers, 111
    periodic, 130
Functions
    of pure imaginaries, 120
    of sum and difference, 35

Geipel and Kilgour’s Electrical Handbook, 191
Generalization, 118
Geometrical interpretation, 107
Geometrical treatment of hyperbolic functions, 3–13, 35
Glaisher’s exponential tables, 191
Graphs, 96
Greenhill’s
    Calculus, 203
    Elliptic Functions, 3
Gronau’s
    Tafeln, 192, 202
    Theor. und Anwend., 202
Gudermanian
    angle, 84
    function, 92, 101, 140, 161, 191, 202
Gudermann’s notation, 84
Gunther’s Die Lehre, etc., 187, 202

Haskell on fundamental notions, 203
Hoüel’s notation, etc., 84, 90, 202
Hyperbola, 3–4, 84, 107, 129, 185
Hyperbolic funcitons
    addition-theorems for, 35
Hyperbolic functions
    applictions of, 136–187
    defined, 18
    derivatives of, 47
    expansions of, 57
    exponential functions for, 62
    graphs of, 96
    integrals involving, 103
    of complex numbers, 111–137
    relations among, 18
    relations to circular functions, 80, 123
    relations to gudermanian, 84
    tables of, 193–200
    variation of, 47

Imaginary, see Complex
Impedance, 171
Integrals, 103
Interchange of hyperbolic and circular functions, 123
Interpolation, 105, 142, 148, 177, 179, 189, 191
Intrinsic equation, 108, 140, 146, 153, 157
Involute
    of catenary, 142
    of tractory, 157

Jones’ Trigonometry, 159

Kennelly on alternating currents, 111, 172
Kennelly’s chart, 129, 171

Laisant’s Essai, etc., 187, 202
Lambert’s
    notation, 84
    place in the history, 202
Limiting ratios, 44, 57, 94
Logarithmic
    curve, 185
    expressions, 73, 94
Love’s elasticity, 187
Loxodrome, 159

Macfarlane on definitions, 203
Maxwell’s Electricity, 187
Measure
    defined, 4
    of sector, 4–16
Mercator’s Chart, 161
Modulus, 84, 137, 212
Moment of inertia, 186
Multiple values, 23, 32, 132

Newton, reference to, 202
Numbers, complex, 111–137

Ohm, reference to, 202
Operators, generalized, 113, 171

Parabola, 108, 185
Periodicity, 130, 191
Permanence of equivalence, 113
Phase angle, 169, 178
Physical problems, 139–187
Potential theory, 187
Product-series, 124
Pure imaginary, 120

Ratios
    characteristic, 11
    limiting, 44
Rayleigh’s Theory of Sound, 169
Reactance of conductor, 175
Reduction formula, 107, 109
Relations among functions, 18, 81, 123
Resistance of conductor, 169
Rhumb line, 161
Riccati’s place in the history, 202

Schellback, reference to, 202
Sectors of conics, 8, 78
Self-induction of conductor, 169
Series, 57, 92
Spheroid, area of oblate, 185
Spiral of Archimedes, 185
Steinmetz on alternating currents, 111, 171
Suceptance of dielectric, 175

Tables, 121, 189
Terminal conditions, 165, 175, 182
Tractory, 142, 155

Variation of hyperbolic functions, 28
Vassal’s Tables, 192
Vectors, 111, 170
Vibrations of bars, 187

Wheeler’s Trigonometry, 192