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| Hamilton W.R. — The collected mathematical papers. Volume 3: algebra |
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| Предметный указатель |
Abel, N.H., equation of fifth degree xx 478 517 561 563—70
Aconic function of six vectors 368 418 422
Adeuteric function 154 249 422
Adeuteric function and a determinant 423
Albert, A. xvii 656
Algebra, alternative division xvii 3 5 117
Algebra, associative division xvi
Algebra, geometrical conception of 118
Algebra, linear associative xix
Algebra, normed xvii
Algebra, science of pure time 3 5 117
Algebra, triple 141. See also Triplets
Algebraic couples 3 7 76 159
Algebraic equation xiii xx 471
Algebraic keys 155
Algebraic operations 33 44 120
Algebraic ratios of steps in time 121
Algorithms of spherical trigonometry 230
Analogies as series of proportional steps 60
Analogies of time, continued 13 15
Apollonius 5
Application of quaternions to dynamical questions 441
Argand, J.R. 135 137 150 177
Association, equations of 114 148 195 213 233 318 337 346
Associative polynomes and quines 339
Automorphism of quaternions 643
Auxiliary sphere 249
Badano and the twenty-four values of Lagrange's function 571
Badano inadequacy for fifth degree equations 582 602
Badano, P.G. 570 581—602
Barycentric calculus 435
Base, multiple of a given 8 24
Biaxial wave, conical and circular ridges in 467
Binary system, equation for motion of 451
Binomial coefficients, theorem relating to 603
Biquaternions 125 305 313 406 424 430 656
Birkoff, G. xix
Bivectors 424
Bivectors with null square 424
Blij, F. van der 656
Bodies, attracted according to Newton's Law 441 449
Bodies, hodographic theory of motion of a system of 457
Brauer, R. xxi
Bring, E.S. xx
Brownin, B. xvii
Buee, Abbe 135 136 137 150
Calculus for spherical trigonometry 230
Calculus of polarities 111
Calculus of quaternions 117 152 281 298 356
Calculus of variations, dynamical use 450
Calculus, Icosian 609
Calculus, Icosian, and a new system of roots of unity 610
Calculus, Icosian, and quaternions 609
Carmichael 155 433
Carnot, L. 135
Cauchy — Riemann equations 97 155
Cauchy — Riemann equations, extension of 664
Cauchy, A.L. 7 123 233 237
Cayley — Hamilton theorem xviii 350
Cayley, A. xvii 108 153 155 236 237 330 361 391 423 436 650
Cayley, characteristics of quaternion derivation 168
Cayley, characteristics of transposition 161
Cayley, numbers 650
Central ellipsoid (Poinsot) 385
Central orbit 443
Chasles, M. 154 246 267 368 430 435
Circle touching three circles on a sphere 394
Circular hodograph, law of 457
Circular sections of ellipsoid See under Ellipsoid
Coaxality, equation of 239
Cockle, J. 149 155
Coincidence, quadruple momental 163
Comet, distance of 464
complex numbers See imaginary quantities and couples
Composition and the comparison of step couples 8 16 76
Composition of forces 381
Cone and osculating cone 380
Cone of second degree 367
Cone, common centres of curvature of two reciprocal 393
Cone, containing six vectors 214
Cone, generation of reciprocal 393
Congruence 657
Conjugate functions 3 7 76 97
Conjugate quaternion 235
Conjugation, equations of 97
Conjugation, law of 320
Continued analogies (as series of proportional steps) 13 14 15.
Continued fractions xvi 304
Continued fractionsapplied to geometry 310 425
Continuous progression, notion of 5
Converge to root of a quadratic 308
Conway, A.W. 643 644
Coplanarity, equation of 239
Couples 3 76 97 159 180 206
Couples, central, energy of 468
Couples, circular functions of 90
Couples, circular functions of, and contra positives 7
Couples, derivation of ordinal 180
Couples, exponential function 9 88 95 124
Couples, logarithmic function 9 86 95 124
Couples, number See Number
Couples, of moments (and steps in time) 8 16 76 121
Couples, ordinal 167
Couples, statistical 381
Coxeter, H.S.M. xviii xxiv
Crystals, biaxial 465
cube 609 623 646
Cubic, osculating to given curve of double curvature 436
Curtis, C.W. 656
Curvature of normal section (ellipsoid) 396
Curvature, lines of 261 396
Curves, Gauche, third degree 435
Curves, reciprocity of 434
Cycles, Icosian 626—39
d'Alembert, J.-le-R. 97
Davies, T.S. 294
de Moivre, A. 432 482 564
de Moivre, soluble form of equation of fifth degree 483 495
De Morgan, A. 107 135 141 150 155 270
Degen, C.B. 655
Derivation 171 179 186
Desargues' theorem (for surfaces of second degree) 407
Descartes, R. 550
Detachment, conditions of 179 184
Determinant 423
Development surface 295
Dickson, L.E. 517 656
Differences, finite See Finite
Dirac, P.A.M. 644
dodecahedron xxii 609 610 611 646
Donkin 155
Dupin, C., theorem of 432
Dyck, W. xxii
Dynamics 441 449
Dynamics of a rigid system 383
Dyson, F.J. xix
Eccentricity, medial 401
Eight squares, theorem of xvii 648
Elements xiii xviii 435
Elimination, algebraic 471 481
Ellipsoid 401
Ellipsoid, circular sections of 258 270 376
Ellipsoid, curvature of normal section 396
Ellipsoid, directions of lines of curvature 396
Ellipsoid, equation of 248 259 280 283 374 378 397 453
Ellipsoid, focal ellipse and hyperbola 397
Ellipsoid, generated by intersecting diagonals of a quadrilateral on a sphere 250 273 375
Ellipsoid, generated by rhombus of constant perimeter 275
Ellipsoid, generated by two sliding spheres 276 392 399
Ellipsoid, generated by two sliding spheres, confocal 400
| Ellipsoid, radius vector, length of 258
Ellipsoid, reciprocal 267 274 278 379
Ellipsoid, tangent plane 260
Ellipsoid, tangents to lines of curvature 267
Ellipsoid, theorem on foci and quadrilateral 290
Equations of association see association
Equations of elevated degree: validity of Jerrard's method for reaching same 482 564
Equations of fifth degree xx 471 478 561 565 579 582
Equations of fifth degree, numerical example 593
Equations of homoconicism 244 247 368
Equations of homodeuterism 417 421 423
Equations of motion of a binary system 451
Equations of motion of a rigid body 383
Equations, biquadratic 519
Equations, cubic 518 575
Equations, de Moivre's form 495
Equations, nth degree in quaternions have  roots 314
Equations, quadratic 518 574
Equilibrium of forces 381
Euclid 5 149 292
Euclidean algorithm xviii 658
Euler, L. xvii 226 555 655
Excess, spherical 390
Extensions of quaternions 316 317
Ferrari, L. 556
Fictitious moon 452
Fictitious sun 460
Finite differences 304
Fluxion, notion of 5
Focal lines of a cone 214
Foci, medial 401
Forces, central, of attraction 442
Forces, centre of applied 468
Forces, equilibrium of 381
Forces, system of three remultiplication of quaternions 113
Four squares theorem xvii 144 648
Francais 135 150 277
Fresnel, A.J., wave surface 465
Frobenius, F.G. xvi
Function, aconic, of six vectors 368 418
Function, adeuretic 154 249 422
Function, conjugate 3 7
Function, couples, exponential and logarithmic See under Couples
Function, irrational and irreducible 526
Function, Lagrange, of roots of an equation 572
Function, Lagrange, roots of an equation of sixth degree 573
Function, principal 451
Function, rational reduced by quintic 471
Function, rational, irreducible 520 524
Function, six valued of three variables with a two valued cube 545
Function, symmetric 543
Function, syntypical 541 546
Function, twenty-four, etc., valued function of four variables 546 579
Gauche curve of the third degees 435
Gauche polygons 293 398 403 407
Gauche polygons, in reciprocal surface 404
Gauss property of geodetic lines 396
Gauss, K.F. xvii 135
Gaussian integers 657
Generators of point groups xxv 624 626 629
Geodetic lines 396
Gergonne 135 150
Gibbs, J.W. xix
Gompertz, B. 136 150
Gormley, P. 644
Gradient, vector 262 432
Grammarithm 145 147 367
Graph theory xxii
Grassman, H.G. xviii xix 153
Graves, C. 139 140 141 195 225 226 280 361 362 603 609
Graves, J.T. xiv xvii xxi 7 96 97 100 106 108 129 138 140 142 153 217 221 225 226 237 266 279 294 330 365 611 612 648 656 657
Graves, letter to 106 217 612 625
Graves, memorandum to 611
Gregory 141 153
Group generators and Hamiltonian paths xxv 624 631
Hamilton, Archbald xv
Hamilton, William Edwin xiii
Hamilton, William Edwin, numbers xxi 514
Hamiltonian method and the five regular solids 646
Hamiltonian paths xxii 610 611 646 647
Hammond, J. xxi
Herschel, J.F.W. 154 249 2G0 304 441
hexahedron See Cube
Hilbert, D. xxi
Hodograph, circular, law of 457
Hodographic theory of the motion of a system of bodies 457
Homoconicism, equation of 244 247 368
Homodeuterism, equation of 417 421 423
Homography 427
Homospheric 368
Hurwitz, A. xviii xix
Hyperbolic space 644
Hyperboloid of two sheets having double contact with an ellipsoid 294
Hyperboloid, equation of 248
icosahedron 609 610 611 646
Icosian calculus xiii xxi 609 645
Icosian calculus, non-commutative, associative multiplication 613
Icosian calculus, solids 646
Icosian calculus, summary of Hamiltonian method and the five regular solids 646
Icosian complete non-cyclical successions 618
Icosian cycles 626 639
Icosian cycles, applied to Hamiltonian paths 614
Icosian cyclical successions 616
Icosian game xxii
Imaginary quantities xiii 111 117
Imaginary quantities, geometrical representation of 106 117 136
Imaginary quantities, multiplication of 222
Imaginary quaternion 212 214 305 312
Imaginary quaternion as roots of quadratic equation 123
Imponential function See Logarithmic
Inertia, moment of 385
Instantaneous axis of rotation 385 386
Integers, quaternion 657
Inverse square law see Newton's Law
Involution 427
Jacobi, C.G.J., elliptic functions xvii
Jerrard's notation for symmetric functions 484
Jerrard, failure of method for resolving equations of higher degree 481
Jerrard, G. B. xx 478 481 488 489 490 492 493 495 496 499 501 564 566
Jerrard, limitations to method 488
Jerrard, method of reducing equation of fifth degree 479 480
Jerrard, two functions of ten variables 565
Joachimsthal, theorem of 416
Joly, C.J. xiii
Kant, I. 117 118
Kepler's laws 451
Keys, algebraic 155
Kilmister, C. 644
Kirkman on pluquaternions 294 406 656
Kirkman, T.P. 155 294 656
Klein, F.C. xliii
Kleinfeld, E. 656
Knight problem xxii
Lagrange and resolution of, biquadratic 575
Lagrange and resolution of, cubic 575
Lagrange and resolution of, quadratic 574
Lagrange function of roots of an equation 572
Lagrange, J.L. xix 570 572 579 649
Lanczos, C., Dirac's wave equation 644
Lanczos, C., extension of Cauchy — Riemann equations to four dimensions 644
Lanczos, C., Lorentz transformation p(q) 79
Laplace operator 263 376
Law of circular hodograph 457
Law of modulus 104 190
Law of scales 152
Line, condition that three points lie on 371
Line, directed 298
Line, equation of 302
Line, operations on 299 366 368
Line, quotient of 364
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