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Hamilton W.R. — The collected mathematical papers. Volume 3: algebra
Hamilton W.R. — The collected mathematical papers. Volume 3: algebra

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Название: The collected mathematical papers. Volume 3: algebra

Автор: Hamilton W.R.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 672

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $n^4$ 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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