## The Collected Mathematical Papers of James Joseph Sylvester, Volume 3From the Preface: The longest paper in volume I is 'On the Theory of the Syzygetic Relations of Two Rational Integral Functions, comprising an application to the Theory of Sturm's Functions', and to this many of the shorter papers in the volume are contributory...the volume contains also Sylvester's dialytic method of elimination, his Essay on Canonical Forms, and early investigations in the theory of Invariants. It also contains celebrated theorems as to Determinants and investigations as to the Transformation of Quadratic Forms and the recognition of the Invariant factors of a matrix.Among the Papers contained in Volume 2 are the author's Lecture on Geometry, delivered before the Gresham Committee, the author's seven lectures on the Partition of Numbers, in outline, the long memoir on Newton's Rule, the Presidential Address to the Mathematical and Physical section of the British Association at Exeter, and a set of papers 'Nugae Mathematicae.'Volume 3 deals very largely with the author's enumerative method of obtaining the complete system of concomitants of a system of quantics, with the help of generating functions; the brief but very luminous papers...on the Constructive Theory of Partitions. ..his Commemoration Day Address at Johns Hopkins University (1877)...investigations on chemistry and algebra, the paper on Certain Ternary Cubic-Form Equations, and the paper on Subinvariants and Perpetuants.Volume 4 contains Sylvester's Constructive Theory of Partitions, papers on Binary Matrices, and the Lectures on the Theory of Reciprocants. There is an added Index to the four volumes, and Biographical Notice of Sylvester. |

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### Contents

I | 1 |

II | 7 |

III | 26 |

IV | 35 |

V | 37 |

VI | 52 |

VII | 58 |

VIII | 63 |

XLVI | 438 |

XLVII | 440 |

XLVIII | 446 |

XLIX | 449 |

L | 451 |

LI | 453 |

LII | 456 |

LIII | 474 |

IX | 67 |

X | 72 |

XI | 88 |

XII | 93 |

XIII | 101 |

XIV | 103 |

XV | 105 |

XVI | 108 |

XVII | 110 |

XVIII | 117 |

XIX | 127 |

XX | 132 |

XXI | 136 |

XXII | 140 |

XXIII | 144 |

XXIV | 148 |

XXV | 207 |

XXVI | 210 |

XXVII | 218 |

XXVIII | 241 |

XXIX | 249 |

XXX | 252 |

XXXI | 253 |

XXXII | 256 |

XXXIII | 257 |

XXXIV | 258 |

XXXV | 262 |

XXXVI | 264 |

XXXVII | 281 |

XXXVIII | 283 |

XXXIX | 312 |

XL | 392 |

XLI | 411 |

XLII | 414 |

XLIII | 426 |

XLIV | 428 |

XLV | 433 |

LIV | 475 |

LV | 476 |

LVI | 477 |

LVII | 479 |

LVIII | 481 |

LIX | 489 |

LX | 509 |

LXI | 530 |

LXII | 546 |

LXIII | 551 |

LXIV | 557 |

LXV | 562 |

LXVI | 565 |

LXVII | 568 |

LXVIII | 623 |

LXIX | 633 |

LXX | 634 |

LXXI | 635 |

LXXII | 640 |

LXXIII | 642 |

LXXIV | 644 |

LXXV | 645 |

LXXVI | 647 |

LXXVII | 651 |

LXXVIII | 653 |

LXXIX | 656 |

LXXX | 658 |

LXXXI | 661 |

LXXXII | 664 |

LXXXIII | 667 |

672 | |

LXXXV | 677 |

LXXXVI | 680 |

LXXXVII | 683 |

LXXXVIII | 685 |

LXXXIX | 687 |

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### Common terms and phrases

algebraical atoms aura c'est-à-dire calcul carré co-ordinates coefficients composés consequently contain contraire corresponding covariants cubic cyclotomic d'une deg-order degré degree denominator denote denumerant derivative determinant deux differentiant diviseur divisor donnée égal éléments equal equation équations être expression facteurs factor follows forme binaire fraction général génératrice given Gordan graph groundforms Hence homogeneous function inflexion invariants irreducible irréductibles j'ai l'équation l'on l'ordre limit linéaires linear function linearly independent matrices method méthode modulus multiple nodes nombre obtained ordre pair partitions peut point of inflexion positifs premier prime number puissance qu'on quadric quantic quantities quelconque racines rapport rational rational integer reciprocal regarded represent residue respectively résultat roots roots of unity sera seul sextic somme spherical harmonics subinvariants substitution suppose synthemes syzygy Taylor's theorem theorem théorème theory unity valeur variables zero