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| Greenhill A.G. — The applications of elliptic functions |
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| Предметный указатель |
Abel 4 18 145 223 277
Abel's theorem 166 249
Abel's theorem, pseudo-elliptic integrals 228
Abelian functions 175
Addition theorem for elliptic functions 113 117
Addition theorem for elliptic functions, of second kind 178 180 193 226
Addition theorem for elliptic functions, of third kind 193 224
Addition theorem of circular and hyperbolic functions 112
Addition theorem, algebraical form of 142
Addition theorem, Theta function 192
Allegret 147
Amplitude 278 289
Amplitude of elliptic integral 4
Amplitude, hyperbolic 15
Anharmonic ratio, of four points 53 57
Anomaly, mean, of a planet 14
Apsidal angle 260 340
Argand 46
Argument 191
Ballistic pendulum, Navez 3 12
Bartholomew Price 3
Basset 288
Basset's Hydrodynamics 219 342
Bertrand 9
Biermann 77 151
Binet 213
Bjerknes 22
Boys 97
Bravais 340
Brioschi 275
Burnside and Panton 148 150
Burnside, W. 38 107 172 209
Capacity, coefficients of electric 287
Capillary attraction 89
Cartesian ovals 257 262
Cartesian ovals, confocal orthogonal 255
Cassinian oval, area of 189
Cassinian oval, rectification of 164
Catenaries 76 92
Catenaries of uniform strength 92
Catenoid 95 98
Cauchy's residue 206
Cayley 56 62 139 142 160 280 311 327
Central orbits 76
Chain, revolving 67 210
Chasles 178
Chevallier 335
Chrystal 66 277
Circular functions, trigonometrical 6
Clifford 17 30 284 295
Complementary modulus 9
Conductivity, thermometric 285
Confocal, ellipses and hyperbolas 184 255
Confocal, paraboloids 273
Confocal, quadric surfaces 271
Cotes's spirals 75 190
Cotes's spirals, theorems 289 325
Cubic substitution 41
Cubicovariant 158
Cubinvariant 62
Cycloidal oscillation 7
Cycloids 190
Darboux 221 236 255
De Moivre's theorem 288
De Sparre 233
Delambre 137
Descriminant 44 48 158
Despeyrous 236
Discriminating cubic 154
Doubly periodic function 208 254 299
Duplication formulas 120
Durege 117 227
Dynamical problem 74
Elastica 87 190
Elastica, tortuous 213
Electrification of two insulated spheres 287
Electrode 278
Ellipse, rolling 71
Ellipse, rolling, first negative pedal of 73
Elliptic functions, addition theorem 142
Elliptic functions, complex multiplication of 12 203 330
Elliptic functions, double periodicity of 254
Elliptic functions, geometrical applications to spherical trigonometry 131
Elliptic functions, multiplication of 329
Elliptic functions, reciprocal modulus 24
Elliptic functions, resolution of, into factors and series 277
Elliptic integral of first kind 4 22 30
Elliptic integral of second kind 64 175 209
Elliptic integral of third kind 108 175 191 206 302
Elliptic integral, complete 8
Elliptic integral, definition of 5
Elliptic integral, degenerate 41 57
Elliptic integral, factor of third kind 226
Elliptic integral, general 200
Elliptic integral, graphs of 66
Elliptic integral, half period of 13
Elliptic integral, inversion of 30
Elliptic integral, modulus complementary 9
Elliptic integral, normalised 203
Elliptic integral, quarter period of 8 321
Elliptic integral, quarter period, complementary 9
Elliptic integral, Tables of 10 11 16 177
Elliptic integral, Weierstrass's defined 42
Enneper 61 326
Epitrochoid 190
Eta function 194 282
Euler 142 251
Euler's addition equation 144 166
Euler's addition equation, constant 281
Euler's addition equation, equations of motion 18 101
Euler's addition equation, pendulum 198
Fagnano's theorems 182
Forsyth 298
FOURIER 66
Fourier, series 285 287
Fricke 155
Fundamenta Nova 310
Fuss 121
Gauss 137 322
Gebbia 220
Genocchi's theorem 264
Geodesics 95
Glaisher 17 33 62 116 133 194
Governor, Watt's 78
Graphs of elliptic integrals 66
Graves 178
Gudermann 5 32 90
Gudermannian 14
Half period, imaginary 44 50
Half period, imaginary, real 43 50
Halphen 128 130 206 217 276 342
Hammond 256 294
Harmonic motion 13
Heat, conduction of 284
Helicoid 95
Helix 20
hermite 150 158 208 215 276 335
Herpolhode 101 107 207 231
Herpolhode, algebraical 228
Herpolhode, points of inflexion 233
hess 233
hessian 62 149 156
Hicks 288 351
Hill 291
Hobson 277 280 330
Holzmueller 257
Homogeneity 203 247 270
Homogeneous variables 155
Hooke's law 94
Hoyer 237
| Huygens 6
Hyperbolic amplitude 15
Hyperbolic amplitude, functions 15
Hyperelliptic function 175
Hyperelliptic function, integral 168 309
Hypotrochoid 190
Icosahedron form 156
Imaginary period 254
Induction, electric coefficient 287
Inflexion, points of, on herpolhodes 233
Integrals, circular and hyperbolic 30
Integrals, hyperelliptic 160
Integrals, poles of 45 53
Invariants 43 62 143
Invariants, absolute 45 49 143
jacobi 5 139 160 284
Jacobi's notation 18 50
Jenkins 84 131
Jochmann 278
Kaleidoscope 293
Kepler's problem 14
Kiepert 331
Kirchoff 87 344
Kirchoff's kinetic analogue 214
Kleiber 190
Klein 35 151 271
kronecker 146
Kummell 136
Lagrange 131 340
Lambert's series 287
Lame's differential equations 210 216 275
Lame's differential equations, parameters 272 274
Landen's point 23 117
Landen's point, second transformation 120 320
Landen's point, transformation 55 60 186 322
Lecornu 212
legendre 4 18 64 131 323
Legendre's relation 164 178
Lemniscate 199
Lemniscate, rectification of 33
Limacon 190
Linear substitution 143
Linear substitution, transformations 163 316
Lintearia 87
Lodge 15 278 293
Love 293
MacCullogh 179 220
MacMahon 147 295
Mannheim 221
Maxwell 79 89 272 287
Mean anomaly 14
Mercator's chart 17
Mercator's chart, Sumner lines 89
Meridional part 17
Michell 292
Minding 121
Modular angle 4
Modular angle, equation of third order 323
Modular angle, equations 323 327
Modulus of elliptic integral 4
Modulus of elliptic integral, change from, and its reciprocal 24
Modulus of elliptic integral, complementary 9
Modulus of elliptic integral, singular 331
Morgan Jenkins 84 131
Motion of a body in infinite liquid under no forces 219 342
Motion of a projectile, resisting medium 65
Motion of electricity or fluid 266
Motion, mean, of a planet 14
Motion, Poinsot's geometrical representation 101
Motion, solutions of Euler's equations of 28 101
Mueller 314
Napier 137
Nodoid 95 98
Norm 278
Octahedron form 157
Octahedron form, irrationality 317
Orbits, central 76
Oscillations of pendulums, bell, etc. 3
Oscillations, cycloidal 7
Oscillations, quadrantal 103
Oscillations, rectilinear 25
Oscillations, vertical, of a carriage or ship 82
PARAMETER 191 207
Pendulum 1
Pendulum, Euler's 198
Pendulum, Navez, ballistic 3 12
Pendulum, performing complete revolutions 18
Pendulum, period of 8
Pendulum, reaction of axis of suspension 82
Pendulum, simple equivalent 3
Pendulum, speed of 3
Pendulum, spherical 214
Period, parallelogram 46
Period, rectangle 270
Poinsot 233
Poinsot's geometrical representation of motion 101
Poles of integral 255
Polhode 101
Polhode, separating 230
Poristic polygons, Poncelet's 121
Poristic polygons, Poncelet's, heptagons 130
Poristic polygons, Poncelet's, pentagons 128
Poristic polygons, Poncelet's, quadrilaterals 126
Poristic polygons, Poncelet's, triangles 124
Poundal 1
Price 3 79
Pringsheim 160
Projectile, trajectory of, for cubic law of resistance 244
Pseudo-elliptic 242 347
Pseudo-elliptic, integrals, Abel's 228 300
Quadrantal oscillations 103
Quadri-quadric function 148
Quadric surfaces, confocal 271
Quadric surfaces, transformations 35 321
Quadrinvariant 62
Radian 1
Real half period 43
Reciprocant 294
Reduction, formula of 63
Reversion of series 202
Revolving chain 67 210
Richelot 121 164
Riemann 312
Riemann, differential relation 316
Roberts 162 165 199
Robertson Smith 291
Rocking stone 198
Rolling and sliding cone 108
Routh 3 28 101 217 238
Russel 62 149 151 158 327
Salmon 149 157 162 178 222
Schwarz 26 46 157 298
Sextic covariant 150 157 163 321
Siacci 220
Sigma function 201
simple harmonic motion 13
Simpson 9
Slade 233
smith 27 222
Spherical pendulum 214
Spherical trigonometry 169
Spherical trigonometry, geometrical application of elliptic functions to 131
Spinning top 214
Spiral, Cotes's 75
Steiner 121
Substitution, linear 143
Sumner lines on Mercator's chart 89
Surface, special minimum 26
Swinging body, internal stresses of 84
Sylvester 221 294
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