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| Hamilton W.R. — The collected mathematical papers. Volume 3: algebra |
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| Предметный указатель |
Linear function of a quaternion xviii 348 350
Lipschitz, R. xviii
Lloyd, H. 145
Logarithmic and exponential function-couples xiv 8 9 86 95 100
Logarithmic couples 124
Logometers 150
Lorentz transformation 643
Lubbock 567
Lunar regression of node 462
Lunar theory 455
Lunar variations 461
Lunar variations, laws of 462
MacCullagh, J. 142 376 379 385 386 387 391 465
Matrices xviii
Matrices and quaternions 643
McConnell, A.J. xvi
Mobius, A.F. 154
Modular theory of quaternions 657
Modulus, barycentric calculus 435
Modulus, law of xvii 190 218
Momental quaternion 160
Momental separation, characteristics of 160
Momental set See Sets
Moments, comparison of pairs 162
Moments, couples of 8 16 76 121
Moments, ordinal relations between 119 162
Moments, sets of 159 162 163 173
Moments, sets of, composition and decomposition of original relations between 176
Moon See Lunar theory
Mourey 150 277
Multiplication coefficients of derivation and 186
Multiplication of a real by a quaternion 222
Multiplication of step couple by a couple 8 9 80 122
Multiplication of step couple by a number 8 9 78 121
Multiplication of two pare imaginaries 222
Multiplication, constants of 122
Murnaghan, F.D., quaternions as four by four real matrices 643
Murphy analysis of roots of equations 567
Murphy, R. 100 567 569
Napier, J. 6 225
Negative quantities, square root of (geometrical representation) 106
Newton's Law of attraction 441 449
Newton, I. 5
Non-distributive operator 268
Norm xvii 657—65
Number couple 167
Number couple, addition, subtraction, multiplication and division of 8 78 80 83
Number couple, pair, quotient of two step-pairs 122
Number couple, power of 8 84 92
Numbers, algebraic, operation in positive or contra-positive 120 121
Numeral separation, characteristics of 184
Numeral sets, addition and subtraction of 196
Numeral sets, conception of 178
Numeral sets, division of 197
Numeral sets, multiplication of 184 193
Numeral sets, powers of 201
Numeral sets, pre-multiplying one by another 199
Numeral sets, submultiplying and reciprocal of 201
Numerical quaternions, product and quotient of 190
O'Brien 155
Octadic transposition 168 171
octahedron 609 623 646
Octaves xvii 648 650
Octaves, law of moduli 651
Octaves, multiplication table 648
Octaves, non-associative 650
Octonians See Octaves
Octonomials 406
Ohm, M. 100 124 125 126 153
Oldham, W. 154
Order See Progression
Ordinal couple 167
Ordinal couple, derivation, characteristics of 167
Ordinal couple, sets See Sets
Osculating surface of second order 395
Osculating twisted cubic to a curve of double curvature 435
Pair numbers, quotient of two step pairs 122
Pascal's theorem, generalization of 417 431
Pascal, B., theorem of 246 367 417
Peacock, G. xiv 125 126 135 150 153 279 356 359
Peacock, treatise on algebra 359
Pentagon, continued product of sides 368 369
Pentagon, spherical 214
Perturbation theory 459
Pierce, B. xix
Planetary distance 464
Plato 609
Pluquaternions 155 294 406 656
Poinsot's theory of mechanical couples 452
Poinsot, L. 368 381 385 387 406
Polars, reciprocal 239 polygenic syngraphy 431
Polygons (Gauche), inscription of, in surfaces of second degree 291 293 295 297 316 398 403 407.
Polygons (Gauche), inscription of, with sides through fixed points 404 408
Polynomes, addition law 317
Polynomes, as linear algebra 318
Polynomes, associative law 318 322 339
Polynomes, conjugate 319 321
Polynomes, constants of multiplication 322 331
Polynomes, distributive law 329
Polynomes, equality of 317
Polynomes, scalar of 319
Polynomes, vector of 322
Polynomes, versor of 322
Polynomes, with S, V, K as operators 320
Positive square root of general existence 8 54
Powering of a number couple by a whole number 8 9
Precedence, non-analogy of 164
Principal function of the motional system of bodies 451
Progression 5 117 118
Pyramid See Tetrahedron
Pyramidal function 419 422
Quadratic equation and quaternions 206
Quadric, cone 436
Quadric, surfaces 214
Quadrilateral inscribed in a circle 370
Quadrilateral plane 370
Quadrilateral spherical 213 292 369
Quaternion calculus xiii 117 152 232 241 349 415
Quaternion derivation 161 166 189
Quaternion equation, of ellipsoid 259; of index surface 465
Quaternion factors 233
Quaternion integers 657
Quaternion units xv 103 108 111 113 142 170 217 227 231 355
Quaternion units, inverses of 171
Quaternions xv 103 106 111
Quaternions and astronomy 452
Quaternions and continued fractions 304 307
Quaternions and couples 206
Quaternions and Pascal's theorem 246 367 417
Quaternions and quadratic equations 206
Quaternions and reciprocity of curves in space 434
Quaternions and surfaces of the second order 378
Quaternions as quotient of two directed lines 153 366
Quaternions as sets 186
Quaternions, addition and subtraction 111 174 227
Quaternions, amplitude of 111 174 208 218 227 364
Quaternions, arithmetic of 648
Quaternions, associative law 114 148 153 195 213 233
Quaternions, coaxial (multiplication of) 364 366
Quaternions, codirectional 225 234
Quaternions, coefficients of multiplication 186 192
Quaternions, colatitude of See Latitude
Quaternions, conjugate 235 238
Quaternions, constituents of 227
Quaternions, cubes and cube roots of 204
Quaternions, discovery of xiii xv 103 106 111 142
Quaternions, distance of comet or planet 464
Quaternions, distributive law of 142 233
Quaternions, division 109 197 200 232
Quaternions, division algorithm for 658
| Quaternions, exercises 298
Quaternions, exponential function of 207 223 225
Quaternions, extension of 316 317
Quaternions, fourth roots of unity 172
Quaternions, Fresnel's wave surface 463 467
Quaternions, geometrical basis of 125
Quaternions, grammarithm 144
Quaternions, Icosian calculus and 609
Quaternions, imaginary See Biquaternions
Quaternions, inverse of See Division and reciprocal set
Quaternions, latitude and longitude of 112 218 229 364
Quaternions, law of moduli 191 218 229 365
Quaternions, linear function of, inversion of 348 356
Quaternions, logarithm of 116 211
Quaternions, logarithm of, involves two indeterinates 212
Quaternions, matrix representation 643
Quaternions, modulus of 104 112 144 190 209 218 228 364
Quaternions, moment 159
Quaternions, multiplication (non-commutative) 105 108 111 147 153
Quaternions, multiplication, geometrical interpretation 144
Quaternions, powers of 202 223
Quaternions, product of two lines in space 144 146 220
Quaternions, proportional fourth 152 356
Quaternions, quantum mechanics xix
Quaternions, reciprocal of 238
Quaternions, roots of 223 230
Quaternions, rotation, in hyperbolic space 645
Quaternions, rotations 151 215 226 229 643
Quaternions, scalar part of 236 366 372
Quaternions, spherical geometry 112 212 220 230 236 365
Quaternions, squares and square roots of 202 222
Quaternions, tensor of 237 249 372
Quaternions, theorem of Dupin 432
Quaternions, theorem of Joachimsthal 416
Quaternions, theory of relativity 643
Quaternions, transformations of 644
Quaternions, vector part 208 236 356 366 372
Quaternions, versor of 237 249 372
Quines 336
Quines, constants of multiplication 339
Quines, equations of association 337 346
Quines, multiplication of 337
Radical as function of roots 529
Radical, coextensive in multiplying with a rational function 534
Rational function of three variables 540
Rational function, reduced by quintic 471
Ratios, power, roots and logarithms of 8 60
Ratios, square roots of impossible, ambiguous and incommensurable 8 50
Ray vector, connection with index surface 466
Reciprocal and fractional numbers 8 33
Reciprocal of a product 201
Reciprocal surfaces 379 393
Reciprocity of curves in space 434
Relativity 643
Rigid body motion 385
Rigid body motion, unaccelerated 384
Robinson, T.R. 145
Root, as function of coefficients of an equation 518
Rotations and quaternions 361 643
Rotations of a solid body 381
Rotations, composition of successive 361
Ruffini, P. xx
Salmon higher plane curves 436
Salmon twisted cubics 435 481
Salmon, G. xix 406 435
Scalars 358 359
Scales, law of 152
Scheffler xvii 657
Segre, B. xxi
Separation, characteristics of momental 160
Separation, characteristics of numeral 184
Servois 135 150
Sets 126 133 135 299
Sets of moments 159 162 163 173
Sets, addition and subtraction of 132 196
Sets, conception of successive 178
Sets, constants of multiplication of 132
Sets, division of 132 175 176 197
Sets, exponential and inponential function of 207
Sets, logarithm of 211
Sets, multiplication of 132 134 194 196 199 201
Sets, multiplication of, and associative law 184 196
Sets, multiplication of, and cummutative law 196
Sets, multiplication of, and distributive law 196
Sets, negative 184
Sets, numeral, conception of 178
Sets, operations on 166 174
Sets, ordinal, division of one by another 175 176
Sets, ordinal, multiplication of by a number 174
Sets, powers of 202
Sets, product and quotient of numerical quaternions 176 190
Sets, quotient of two 133
Sets, reciprocal of 201
Sets, submultiplication and reciprocal of successive 201
Sets, successive multiplication 154
Silberstein, L. 643
Similar and similarly situated ellipses 295
Six valued function of three variables 545
Solid body, rotation of 381
Solid, regular 623 646
Space, order in 7
Space, osculating in a given direction 395
Sphere, condition that five points lie on a 369
Sphere, touching four given spheres 394
Spherical excess 390
Spherical geometry and quaternions 212
Spherical parallelogram 363
Spherical polygon, formula for 212
Spherical polygons and product of quaternions 213 214 236 291
Spherical quadrilaterals and conies 363
Spottiswoode 155
Step, null 119
Step, triplet 127
Step-couple, multiplication of by a number 8 9 78 121
Step-couple, multiplication of by a number-couple 8 9 80 122
Step-couple, ratio of one to another 8 80
Step-triads, addition and subtraction of 126
Step-triads, division of 127
Step-triads, multiplication of 127
Steps, addition and subtraction of numeral 196 197 299
Steps, in the progression of time 8 16
Steps, in the progression of time, subtraction, multiplication, reciprocal and fractional numbers 8 33
Steps, in time 22 117 119 120 126
Steps, mean proportional between two 8 50
Steps, proportional, series of 8 60
Steps, submultiple and fractions of 8 33
Steps, unit, primary, secondary and tertiary 127
Stubbs, J.W. 375
Subsequences, non-analogy of 164
Surfaces of fourth degree, as envelope of side of a polygon inscribed in surface of second degree 404
Surfaces of revolution for central forces and orbits 445
Surfaces of second degree 248 378 393 395 447
Surfaces through nine given points 248. See also Polygon inscribed etc.
Sylvester, L. xxi 489
Symbolic and biquadratic equation satisfied by the symbol of linear operation in quaternions 350
Symmetric functions 543
Syngraphy, geometrical 421
Syngraphy, polygonic 431
Syntypical functions 541 546
Tait on Fresnel's wave 467
Tait, P.G. xix
Tangent to circumscribed circle of a triangle at a vertex 370
Tangent to line of curvature 266
Tangent, plane to sphere and point of contact 373
Tension, total of a system of forces 383
Tensor, factors of 237
Tensor, quaternion 237 249 372
Tetrads 316 327 330
tetrahedron 609 646
Three bodies, system of 451
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