## A Treatise on Algebraic Plane CurvesStudents and teachers will welcome the return of this unabridged reprint of one of the first English-language texts to offer full coverage of algebraic plane curves. It offers advanced students a detailed, thorough introduction and background to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. |

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### Contents

BOOK I | 1 |

Representation in hyper space | 3 |

Resultant of two polynomials | 7 |

CHAPTER II | 14 |

Tangential equations | 20 |

Nothers Fundamental Theorem | 29 |

Studys theorem and its consequences | 36 |

Contacts with asymptotes | 42 |

The RiemannRoch theorem | 260 |

Canonical series and canonical curves | 267 |

Sufficiency of these conditions | 273 |

Integrals of other sorts | 275 |

Groups common to a g and a gj | 281 |

CHAPTER IV | 289 |

Limiting values | 295 |

CHAPTER V | 301 |

Real singular points | 47 |

Generation of curves by small variation | 57 |

Nesting circuits | 62 |

Cross ratios | 69 |

Polar operator | 75 |

Discriminant of general quadratic form | 81 |

Ternary forms | 86 |

The effect of singular points | 92 |

Determination of the number of inflexions and cusps | 98 |

Singularities of a rational curve | 104 |

Genus | 108 |

Projection of a real curve on an imaginary plane | 111 |

CHAPTER VIII | 119 |

Correspondences of value 0 | 126 |

Deduction of the general formula Riemanns theorem | 128 |

Correspondences on different curves | 135 |

Line polars | 142 |

Pencils of curves | 148 |

Pliicker characteristics of Hessian Steinerian and Cayleyan | 154 |

Satellite curve | 160 |

Warings theorem | 166 |

Products of distances | 174 |

Sums of angles determined by tangents and foci | 180 |

Metrical covariants associated with polars | 188 |

Conditions for an algebraic involute Humberts theorem | 194 |

Reduction of singularities | 196 |

Limiting cases | 200 |

Nothers transformation theorem | 207 |

DEVELOPMENT IN SERIES | 213 |

Order and class of a branch | 219 |

Number of intersections in general case | 225 |

CHAPTER III | 232 |

Satellite points | 239 |

Definition of genus of a general curve | 245 |

Adjunction theorem | 254 |

Transformation of hyperelliptic curve to canonical form | 305 |

Transformation to canonical form | 311 |

Residuation theorems 245 | 313 |

Series of index 1 | 317 |

Extension of RiemannRoch theorem | 323 |

CHAPTER VII | 329 |

Linear dependence of correspondences | 335 |

Relation of circuits to rational points in hyperspace | 336 |

p p correspondences | 342 |

Curves with only simple branches Clebschs transformation | 348 |

PARAMETRIC REPRESENTATION OF THE GENERAL | 354 |

Applications of uniformizalion | 360 |

CHAPTER IX | 368 |

Determination of the equation of a rational curve | 370 |

Cuspidal and undulational conditions | 376 |

Postulation bymeans of singular points | 383 |

Situation of singular points | 392 |

Necessary and sufficient conditions for the reduction to a curve | 399 |

Reduction of curves lacking adjoint systems of high index | 406 |

Apolarity | 412 |

The inflexional locus | 421 |

NONLINEAR SYSTEMS OF CURVES | 425 |

The inflexions | 433 |

Number of curves in a fcparameter system which touch k curves | 439 |

Properties of the Jacobian 424 | 446 |

Montesanos theorem | 453 |

Transformations in one plane | 459 |

Fixed points of two sorts | 466 |

Transformations with curves of fixed points | 474 |

Involutory transformations of lowest class | 482 |

CHAPTER VIII | 489 |

Finite groups | 496 |

511 | |