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| Sylvester J.J. — The Collected Mathematical Papers, Volume II |
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| Предметный указатель |
1’Entrelacement d’une fonction par rapport a une autre iii 449
Actions mutuelles des formes invariantives derivees, sur les iii 218
Algebra, universal iv 146 208
Alliance, or Ueberschiebung iii 132 217
Allineation, theory of iii 390
Allotrious factori i 438 580
Alternants iv 416
Amphigenous surface ii 436 478
Anakolouthic sum ii 40
Annihilator iv 288 451
Apocopated i 580
Approximation, Poncelet’s, to a linear function of two irrationalities iii 635 644
Approximation, Poncelet’s, to a square root ii 181 200
Arborescent functions ii 49
Arithmetic see “Numbers”
Arithmetic, addition to the vocabulary of iv 588
Arithmetic, theorems in ii 40 484 485
Arithmetical progression containing an infinite number of primes ii 712 iv
Arithmetical series, On iv 687
Arrangement, compound ii 325
Arrangements, a theorem of Cauchy for ii 245 290
Associated algebraical forms i 198
Astronomical prolusions ii 519 546
Asymptotic limits for number of primes iii 530 iv
Asyzygetic invariants, extension of theorem iv 515
Atomic theory and theory of concomitants iii 148
Axis of rotation of a rigid body i 157
Barycentric perspective ii 342 358
Bernoulli’s numbers ii 254
Bezoutians i 430 444 548 557 580
Bezoutic square i 430 444
Bezoutoid i 555
Bicorn ii 469 478 iii
Binariants iii 571 iv
Binary system of cubics compared with ternary system of quadratics ii 15
Binomial extractor iii 14
Biorthogonal reduction of lineo-linear form iv 638 650 654
Bipartition iv 34
Bipotential iii 38
Biquadratic see “Quartic”
Bismarck iii 32
Bisyntheme i 92
Boole-Mongian iv 283 380
Bring, Jerrard and Hamilton on quintic equation iv 531 553
Brioschi’s equation for symmetric functions iv 166
Buffon’s problem of the needle iv 663
Burman’s law for inversion of independent variable ii 44 50 65
Caesura ii 146
Calculus of forms, On the i 284 328 402 411 ii
Canonic roots ii 331
Canonical forms i 184 190 202 208
Canonical forms for binary forms i 190 202
Canonical forms for even degrees i 216 271 279 293
Canonical forms for odd degrees i 208 265
Canonical forms for several variables iv 527
Canonical forms of binary sextic ii 18
Canonical forms of cubic surface i 195
Canonical forms of quartic and octavic ii 18
Canonical forms of ternary cubic i 201
Canonical forms, a discovery in i 265
Canonical forms, a memoir on elimination, transformation, and canonical forms i 184
Canonical forms, Essay on i 203
Cartesian ovals ii 527 550
Catalectic i 211
Catalecticant i 293
Cayley’s theorem for number of invariants iii 55 iv 519
Central force ii 547
Centre of gravity of figures in homography ii 323
Centre of gravity of figures in homography, of a quadrilateral ii 338
Centre of gravity of figures in homography, of a truncated pyramid ii 342
Characteristic i 580
Chemistry and algebra iii 103 150
Circle of convergence ii 301
Circle, successive involutes to ii 629 630 641 663
Cissoid iii 16
Clausen and von Staudt’s law for factors of denominators of Bernoulli’s numbers ii 254
Clebsch, a theorem for curves of the fourth order iv 527
Coexistence, rational derivation from equations of i 40 47 54
Cogredience and contragredience i 285
Cogredience and contragredience, compound i 287
Cogredient and Contragredient i 581
Cogredient and Contragredient, systems i 290
Colligation iii 23
Combinant i 402 411 554 580
Combinatorial aggregation i 91
Commemoration-day address at Baltimore iii 72
Commutants i 201 255 305
Compound cogredience i 287
Compound partitions ii 113
Computing products without logarithms ii 34
Concomitance, complex i 291
Concomitant i 200 286 581
Concomitant of given order and degree for any system of forms iii 67 113 241
Concomitant, plexus i 291
Concomitants, derivation of one from another i 287 290
Cone projecting intersection of two surfaces i 169
Congruences, the resultant of two iii 475
Conies, differential equation of iv 282 380
Conies, having contact of third order i 155
Conies, intersections and contacts i 119
Conies, intersections of two i 162
Conies, meeting cubic curve in six consecutive points ii 59
Conies, porismatic property of i 155
Conjugate equations ii 399
Conjugate system of regular substitutions ii 623
Conjunctive i 581
Connumerant ii 133
Conoid i 228
Consecutive points, four upon a tangent line of a surface i 177
Constructive Theory of Partitions iv 1
Contacts of conies i 119 223
Contacts of conies, of lines and surfaces of the second order i 219 227 ii
Contents of polygons, von Staudt’s theorems for i 382
Continuants iii 249
Continued fractions i 641
Continued fractions for the quadrature of the circle ii 691
Continued fractions, arithmetic theorem iv 659
Continued fractions, expressing the roots of a quadratic iv 641 645 647
Continued fractions, improper i 583
Contrary, reciprocal or complementary substitutions i 200
Contravariant i 200 581
Contravariant, changing to a covariant i 200
Contravector ii 19
Convergence, circle of ii 301
Convergence, corona of ii 301
Coreciprocants iv 419
Corpus of matrices iv 222
Correlations, of two conies i 119
Correspondence between arrangements of complex numbers iv 59
Correspondence of partitions iv 24 38
Covariant i 200 581
Crocchi’s theorem iii 653
Cross-gratings used to prove formulae in elliptic functions iii 667
Crystals, Fresnel’s theory of i 1
Cube root extracting machine iii 18
Cubes, sum and difference, numbers so resoluble iii 347
Cubic and linear form, concomitants of iii 97 393
Cubic and quadratic, concomitants of iii 97 394
Cubic and quadratic, concomitants of syzygies iii 505
Cubic and quartic, concomitants of iii 127 39
Cubic and quartic, concomitants, reconciliation of two enumerations of concomitants iii 132 136
Cubic curve and conic of sextactic contact ii 59
Cubic curve, law of squares iii 359
Cubic curve, polygons inscribed and circumscribed iii 341
Cubic curve, rational derivation of points ii 107 iii
Cubic curvetriangles inscribed and circumscribed iii 474
Cubic Form, in integers i 107 110 114 ii 107 iii
Cubic residues, 2 and 3 as iii 345
Cubic surface, expressed by five cubes i 195
Cubic surface, expressed by five cubes, polar reciprocal i 302
| Cubic surface, expressed by five cubes, twenty-seven lines of ii 242 451
Cubic, binary, concomitants of iii 283 579
Cubic, binary, concomitants of, generating function for covariants iii 113
Cubic, quadratic and quartic iii 625
Cubic, ternary, degeneracies of i 335
Cubic, ternary, degeneracies of, concomitants of i 192 308 327 331 599 ii 387
Cubics, two binary, concomitants of iii 97 395
Cubics, two binary, concomitants of, reconciliation of two enumerations of concomitants iii 258
Cumulant i 504 580
Cursality or genus of a plane curve iii 14
Curve of any order, differential equation of iv 495 524 529
Curves in space analogous to Cartesian ovals ii 555 559
Cyclodes ii 629 641 663
Cyclotheme i 93
Cyclotomy iii 317 326 381 428 437 446 477 479 iv 626
Decimic, binary, concomitants of iii 256 302
Definite integrals, two new ii 208 298
Degree of a symmetrical function in the coefficients i 595
Denumerant ii 120 iii 614
Denumerant for invariants of octavic iii 52
Denumerant of a diptych ii 668
Derivation, rational, from equations of coexistence i 40 47 54
Derivative, of two equations, of specified degree i 41
Derivative, of two equations, of specified degree, points of curves of third order ii 107 iii
Determinants and duadic disynthemes iii 264
Determinants and polar umbrae ii 327
Determinants and quadratic forms i 129 147
Determinants of parallel motion iii 35
Determinants of two quadratic forms, summary of possibilities i 236
Determinants, a fundamental theorem i 252
Determinants, combination of i 399
Determinants, compound i 126
Determinants, comprising the secular determinant iii 453
Determinants, definition i 581
Determinants, determinants composes, sur les iii 456
Determinants, diminished i 126 136
Determinants, double ii 326 331 336
Determinants, minor, condition of all vanishing i 147 221
Determinants, relation of minor determinants of equivalent quadratics i 241 647
Determinants, relative i 183 188
Determinants, Sylvester’s theorems in the First Volume i 647
Dialytic elimination i 133 256 581
Dialytic elimination for ternary forms i 62 76
Dialytic elimination, extensions of i 256
Dialytic elimination, origin of iii 77
Dialytic elimination, restatement i 86
Difference and differential equations ii 689 iii 551 iv
Differential equation of a curve of any order iv 495 524 529
Differential equation of conies iv 282 380
Differential equations of a concomitant i 352
Differential invariants iv 245 520
Differential transformation ii 50 65
Differentiants iii 113 118 124 151 232 iv
Diploidal contact i 225
Diplotheme i 92
Diptych ii 665
Discriminant i 581
Discriminant of the canonizant ii 418
Discriminatrix ii 395 478
Disjunctive i 582
Ditheme i 175
Divisors of cyclotomic functions iii 428 437 446 479
Divisors of the sum of a geometrical series iv 607 625
Double integration i 36
Double six of lines ii 243 451
Duadic disynthemes and determinants iii 264
Duadic syntheme iii 170
Duodecimic, binary, concomitants of iii 489
Dyadism iii 23
D’Alembert-Carnot, geometrical paradox iv 238
E(x), the function ii 177 178 179
Educational Times, index to occurrence of Author’s name in mathematical questions from iv 743
Eduction ii 147
Elimination, a new theory of i 40
Elimination, between quadratic functions i 139 145
Elimination, by inspection i 54
Elimination, Dialytic method i 61 86
Elimination, Dialytic method, extensions of i 256
Elimination, from ternary forms i 62 76 298
Elimination, linear method of i 75
Elimination, note on i 58
Elimination, Sketch of a Memoir on i 184
Elliptic integral of the first kind 11 203 211
Elliptic motion 11 496
Emanant i 288 431 582
Endoscopic and exoscopic i 431 582
Equal roots and multiple points i 367
Equation, roots of, difference functions in correspondence with power sums iv 163
Equations of which all the roots are real iii 411
Equatrix ii 395 478
Euler’s numbers ii 254
Euler’s theorem for parabolic motion ii 522
Euler’s theorem for perfect numbers iv 589
Euler’s theorem for the partition of pentagonal numbers iii 664 685 iv 95
Euler’s theorem for the partition of pentagonal numbers, Franklin’s proof iv 11
Euler’s theorem of reciprocity in partitions i 597 ii
Evectants i 329 367
Even number, partition into two primes ii 709
Expansion of first negative power of a power series ii 103
Extent and content of a partition iv 2
Eyes, ears, nose, lips and chin as singularities iv 293
Ezekiel’s valley of dry bones iv 282
Facultative point, in theory of quintic i 436
Farey series iii 672 687 iv 78 101 603
Fermatian iv 607 625
Fermat’s theorem ii 229 232 234 241 263 iv
Finite differences ii 307 308 313 318 iii 633
Fluids, on the motion and rest of i 28
Form, definition of i 582
Formes-adjointes i 200
Formes-associees iii 108 199
Forms, Calculus of i 284 328 402 411 ii
Fractions with limited numbers iii 672 689 iv 738
Fractions, vulgar, a point in the theory of iii 440
Functional relations among the roots of a quartic i 192
Fundamental theorem of the theory of invariants iii 117 232 iv
Funicular solution of Bufion’s problem iv 663
Generating function for covariants iii 113
Generating function for invariants of binary forms iii 58
Generating function for invariants of octavic iii 52
Generating function for reciprocants iv 402
Generating function in partitions iv 21
Geometrical notions and determinations iv 259
Geometrical problem, on a simple i 392
Geometry, descriptive and metrical ii 8
Geometry, descriptive and metricalLecture before the Gresham Committee ii 2
Germany, the classical land of learning iii 79
Goldbach — Euler theorem for primes iv 734
Graphical conversion of a continued product into a series iv 26 91
Graphical dissection, H.J.S.Smith on iv 49
groups ii 269
Groups, continuous iv 422
Groups, intransitive ii 275
Halphen, on reciprocants iv 290
Hamilton’s numbers iv 553 585
Hamilton’s numbers, Hammond’s theorem on iv 550 557 586
Hammond, benefit of intercourse with iv 300
Hessian, or Hessean i 583
Hessian, or Hessean of a cubic surface i 195
Homaloid i 175
Homaloid, Homaloidal Law i 129 150 ii
Homogeneous functions, general properties i 165
Homonomial resolubility ii 289
Homonymous ii 122
Huxley, on Mathematics ii 653 654
Hyperdeterminants i 185 583
Hyperdeterminants, a discovery in i 265
Imaginaries, the eight square iii 642
Imaginary roots, Newton’s rule for ii 376
Inaugural lecture at Oxford iv 278
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