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| Sylvester J.J. — The Collected Mathematical Papers, Volume II |
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| Предметный указатель |
Independent variable, change of ii 44 50 65 iv
Indicatrix ii 398
Induction and verification in Mathematics ii 714
Inertia, law of, for quadratic forms i 381 511 583 iv
Infinitesimal variation i 33 326 ii
Integers, successions that cannot be indefinitely continued iii 656
Integration, double i 36
Interaction of covariants and invariants iii 207
Intercalations, theory of i 511 545 583
Intercalations, theory of, effective scale of i 582
Intermutants i 201 317
Interpolation, Lagrange’s rule i 645
Interpositions, theory of i 614
Intuitional exegesis of generalised Farey series iv 78
Invariant factors of a determinant [unnamed] i 221
Invariants i 583
Invariants of a function of even degree i 273
Invariants, general theorem for number of iii 93 117 232 iv 515
Invariants, limits to the order and degree of iii 101
Invariants, number of, theorem of reciprocity i 606
Involutants iv 133 134
Involutes to a circle ii 629 630 641 663
Involution of lines ii 236 240 304 iii 651 iv
Irrationality of  iv 680 682
Irrationality, value of linear function of ii 250 305 iii 644
Ivory’s theorem for potential iii 45
Jacobi, at Trinity College, Cambridge iii 77
Jacobi, at Trinity College, Cambridge, theorem of, proved by partitions iv 60 97
Jacobian i 583
Jerrard’s form for a quintic is singular i 211
Kant’s Doctrine of Space and Time ii 719
Kenotheme i 175 583
Lady’s fan iii 35
Lagrange’s theorem for linear function of an irrationality ii 250 305
Lagrange’s theorem for linear function of an irrationality, theorem of interpolation i 645
Lambert’s theorem for elhptic motion ii 496 519
Latent integer ii 100
Latent roots of a matrix iv 110
Law of succession i 287
Law of synthesis i 292 348
Laws of verse iii 123
Limits for the real roots of an equation i 423 424 620 627 630
Limits for the real roots of an equation for number of concomitants of binary forms iii 110
Limits for the real roots of an equation for prime numbers iii 530 IV
Limits for the real roots of an equation to the order and degree of concomitants iii 113
Linear and cubic forms, concomitants of iii 97
Linear and cubic forms, concomitants of and quadratic forms, concomitants of iii 392
Linear and cubic forms, concomitants of, functions, two, concomitants of iii 392
Linear and cubic forms, concomitants of, substitutions, powers and roots of iii 562
Linear complex, construction from five lines ii 237
Lineo-linear form reduced to canonical shape iv 638 650 654
Lines in space, involution of ii 236 240 304 iii 651 iv
Lines on a cubic surface ii 242 451
Linkwork and linkage iii 9
Logarithmic waves, rectifiable compound ii 694
Lomniscate iii 14
l’Equation qui sert a determiner les inegalites seculaires des planetes i 366
MacMahon’s transformation of subinvariants iv 164 236
Malfatti’s problem of inscribed circles i 153
Mathematical questions in the Educational Times iv 743
Mathematics and Observation ii 655 714
Mathematics, philosophy not calculation iv 329
Matrices i 247 583
Matrices, and the law of Harriot iv 169
Matrices, biorthogonally reduced to canonical form iv 638 650 654
Matrices, equations in iv 152 176 181 199 206 231 272
Matrices, inversely orthogonal ii 615
Matrices, involution of iv 115 219
Matrices, latent roots and vacuity of iv 215
Matrices, latent roots of iv 110
Matrices, multiplicity of iv 210
Matrices, orthogonal ii 615
Matrices, powers and roots of iii 562 565
Matrices, properties of split iii 645
Matrices, systems iv 133
Matrices, vacuity, nullity and latency iv 133
Matrices, zero, nullity and content of iv 211
Mean value of coefficients in an infinite determinant iii 253 257 277
Mechanical conversion of motion iii 7
Meicatalecticizant i 293
Minor determinants i 147 584
Minor determinants and linearly equivalent quadratic functions i 241 647
Minor determinants, conditions for all to vanish i 147 221
Mixed reciprocants iv 289 312
Monadelphic iii 153
Mongian iv 283 380
Monotheme i 175 584
Monothetic equations iv 169 173
Motion, mechanical conversion of iii 7
Multipartite system of equations, resultant of ii 329
Multiple quantity iv 133
Multiple roots i 66 69 370
Multiple roots and evectant of discriminant i 367 370
Mutual action of concomitants iii 218
Napier and Briggs, anecdote of iv 279
Newton’s rule for imaginary roots ii 376 489 491 493 495 498 514 615 623 704 iii iv
Nomes ii 272 288
Nonic, binary, table of concomitants iii 281 293
Nonions iii 647 iv 122 154
Notation for loci in space i 175
Null system [unnamed] ii 237
Nullity of a matrix iv 133
Number, Space and Order, cardinal notions of Mathematics ii 5
Numbers, Partition of see “Partitions”
Numbers, theory of i 107 110 114 ii 178 225 iii 438 440 446 iv
Numbers, theory of as sums of cubes iii 347
Numbers, theory of, arithmetical series iv 687
Numbers, theory of, cubic ternary form i 107 110 114 ii 107 iii
Numbers, theory of, dividing the sum of a geometrical series iv 607 625
Numbers, theory of, Ely’s proof of a theorem for residues iv 50
Numbers, theory of, expressed as four squares ii 101
Numbers, theory of, fractions with limited iii 672 687 iv
Numbers, theory of, geometrical proof of a theorem in iii 635 644
Numbers, theory of, Hamilton’s iv 550 553 585
Numbers, theory of, irrationality of iv 680 682
Numbers, theory of, law of reciprocity iii 433
Numbers, theory of, of Bernoulli and Euler ii 254
Numbers, theory of, of primes ii 225 iii iv 696
Numbers, theory of, perfect iv 611 615 626
Numbers, theory of, resultant of two congruences iii 475
Numbers, theory of, successions of integers not indefinitely continuable iii 580 656
Numbers, theory of, vocabulary for iv 588
Numbers, theory of, Wilson’s theorem i 39 ii 249 293
Octavic, canonical form ii 18
Octavic, invariants of iii 52
Octavic, irreducible covariants iii 480
Octavic, reconciliation of two enumerations of concomitants iii 509
Octavic, table of concomitants iii 115 290
Octopus iii 34
Operations, calculus of ii 567 608
Optical theory of crystals i 2
Orbit, under attraction of a circular plate ii 539 550
Orders, loss of, deduced from discriminant i 139
Orders, theory of i 145 170 221 549 584 587
Orthogonal invariants i 351
Orthogonal reeiprocants iv 249 338
Osculants ii 364 368
Oyster, twin-soul to the mathematician iii 73
Pantigraph iii 12 26
Parados iii 20 36
Partial differential operators ii 567 608
Partitions and rational fractions iii 605
Partitions, a Constructive Theory of- iv 1
Partitions, a theorem of Cauchy for ii 245 290
Partitions, compound ii 113
Partitions, Durfee’s theorem iii 659
Partitions, Euler’s theorem for pentagonal numbers iii 685 iv 95
Partitions, Euler’s theorem of reciprocity for i 597 iv
Partitions, expression of a certain product as a series iii 677
Partitions, Franklin’s proof of Euler’s theorem iii 664
| Partitions, fundamental theorem of the new method iii 658
Partitions, of an even number into two primes ii 709
Partitions, of numbers ii 86 90 176 701 iii 680 683 iv
Partitions, proof of a formula of elliptic functions iv 34
Partitions, Seven Lectures on ii 119
Partitions, symmetrical functions of ii 110
Partitions, table of iv 391
Pascal’s theorem i 138 145 151
Peaucellier’s bar motion iii 7
Perfect numbers iv 589 604 611 615 626
Permutants i 201 210 214 318
Perpetuant iii 592 iv
Perpetuitant iv 138
Perspective, barycentric ii 342 358
Persymmetrical i 584
Pertactile point on a cubic curve iii 367
Plagiogonal invariants i 351
Plagiograph iii 26
Plexus of forms i 291 346
Poinsot’s representation of the motion of a rigid body ii 517 577 602
Polar reciprocal i 303 363 377
Polar reciprocal of a cubic surface i 302
Polar umbrae ii 327
Poles, in the theory of potential iii 49
Polhods iii 4
Polynomial functions, expressed by fewer linear functions of variables i 587
Poncelet’s approximation for radicals ii 181
Post-Schwarzian iv 321
Potential, theory of iii 49
Presidential Address to British Association ii 650
Pressure of earth on revetment walls ii 215
Prime numbers between given limits iii 530 iv 711
Prime numbers between given limits, Goldbach — Euler theorem iv 734
Prime numbers between given limits, inequalities for iv 592
Prime radical circulator ii 97
Principiant iv 382
Principiant, expressed as an invariant iv 465
Probabilities, a class of questions ii 480
Probability, Buffon’s problem iv 663
Probationary Lecture on Geometry ii 2
Problem of least circle enclosing given points ii 190
Product, a continued, expressed as a series iii 677
Projectiles, a trifle on ii 55
Projectiles, a trifle on, construction for ii 61
Projective Eeciprocants iv 382
Protomorphs iv 250 289
Pure Eeciprocants iv 257 289 312 341 391 403 514
Quadratic (and quadric and cubic, concomitants of iii 97
Quadratic (and quadric and cubic, concomitants of, syzygies iii 505
Quadratic (and quadric) and two quartics iii 627
Quadratic (and quadric) concomitants of iii 283
Quadratic (and quadric) cubic and quartic, concomitants of iii 625
Quadratic (and quadric) elimination i 139
Quadratic (and quadric) form indicating number of real roots of an equation i 402
Quadratic (and quadric) forms, law of inertia i 381 511 512 iv
Quadratic (and quadric) functions, relation between the minor determinants of i 241 647
Quadratic (and quadric) functions, resultant of three i 402 415
Quadratic (and quadric) functions, solution of a system of i 152
Quadratic (and quadric) generating function for covariants iii 113
Quadratic (and quadric) loci, contacts i 119 236 ii
Quadratic (and quadric) polynomial, reducible to squares i 378
Quadratic (and quadric) radicals, linear representation of ii 118
Quadratic (and quadric) residues, fundamental theorem ii 180
Quadratic (and quadric) two quadratics and one quartic, concomitants of iii 622
Quadratic (and quadric) two quadratics, concomitants of iii 394
Quadrinvariant i 584
Quadruplane iii 28
Quantics of unlimited order, seminvariants of iii 568
Quantics to order eight, generating functions for covariants iii 113
Quartic (and Quartics) and cubic, concomitants of iii 127 132 136
Quartic (and Quartics) and linear form iii 393
Quartic (and Quartics) and quadratic iii 395
Quartic (and Quartics) and two quadratics iii 622
Quartic (and Quartics) cubic and quadratic iii 625
Quartic (and Quartics) three binary iii 630
Quartic (and Quartics) two and quadratic iii 627
Quartic (and Quartics), canonical form i 269
Quartic (and Quartics), invariants of i 329 599 iii 579
Quartic (and Quartics), invariants of generating function iii 113
Quartic (and Quartics), ternary i 334
Quartic (and Quartics), two binary, concomitants of iii 402
Quartic (and Quartics), two binary, reconciliation of two enumerations of concomitants iii 61 63 95
Quasi-catalecticant iv 400
Quasi-covariant iv 411
Quaternions iv 112 122 162 183 188 225
Quintic, binary, a syzygy i 362
Quintic, binary, canonical form i 193
Quintic, binary, concomitants i 196 204 207 iii 284 580
Quintic, binary, condition for three equal roots i 348
Quintic, binary, generating function for concomitants iii 59 113
Quintic, binary, germ table for iii 577
Quintic, binary, germ table for table of deduction iii 591
Quintic, binary, reality of roots in terms of invariants ii 371 376 418 482
Quintic, binary, sextic and nonic, skew invariants of iii 195
Quintic, binary, Tschirnhausen transformation iv 531 553
Quot-additant ii 87 92
Quot-undulant ii 87
Quotients, Sturmian i 396 495
Quotity ii 86 90
Radicals, approximate linear evaluation ii 118 181 202
Ramification iii 23
Rational derivation of points of a cubic curve ii 107 iii
Reciprocants iv 242 249 255 281 301
Reciprocants, Lectures on the Theory of iv 301
Reciprocity, law of, for forms ii 403 606 iii 174 189
Reciprocity, law of, in the Theory of Numbers iii 433
Reciprocity, method of i 339
Reciprocity, theorem of, in partitions ii 703
Reduced-resultant i 188
Reducible cyclodes ii 663
Reduction in number of variables i 587 (see also “Orders”)
Relative determinants i 188
Residuation, geometrical theory of iii 317 352
Residues, Sturmian i 438
Respondent, inverse of concomitant of i 340
Resultant of a matrix ii 334
Resultant of a system of equations i 259 584 ii 363 369 694 iii
Resultant of three forces, approximate linear representation ii 188
Revenants iii 593
Reversion of series ii 50 65
Reversor iv 451
Revetment walls, pressure of earth on ii 215
Rhizoristic series i 516 584
Riemann surface iv 241
Rigid bodies, on the motion and rest of i 33
Rigid body, rotation of i 157 217 ii 577 588 602 iii
Roots and Newton’s rule ii 361
Roots of a particular form of equation ii 360 374 378 401
Roots of an equation i 66 69
Roots of matrices iii 565
Roots of numerical equations, rational or not i 103
Roots of the secular equation iii 451
Roots of two polynomials, intercalation i 517
Roots of unity see “Cyclotomy”
Roots, equality of i 367 370
Roots, limits to real i 623 627 630
Roots, multiple i 69
Roots, rule for separating ii 542
Roots, Sturmian functions i 45
Schlafli, double six of lines ii 243 451
School girls, problem for fifteen ii 266 276
School girls, problem for fifteen, for nine iv 732
Schwarzian derivative iv 252 284 304
Secular inequality equation i 634 iii iv
Seminvariants to quantics of unlimited order iii 568
Septimic, binary, covariants of iii 146 286
Septimic, binary, generating function for covariants iii 113 140 144
Series for a certain product iii 677
Series, reversion of ii 50 65
Sextic, binary, canonical form i 280 283 ii
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