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Book Categories |
Book I | Elementary Theory | |
Chapter I | The Fundamental Properties of Polynomials | |
1. | Polynomials in one variable | |
2. | Polynomials in N variables | |
Chapter II | Elementary Properties of Curves | |
1. | Ordinary and singular points | |
2. | Determination of curves by points | |
3. | Residuation theorems | |
Chapter III | Real Curves | |
1. | Asymptotes | |
2. | Real singular points | |
Chapter IV | Real Circuits of Curves | |
1. | Topological properties of even and odd circuits | |
2. | Generation of curves by small variation | |
3. | Nesting circuits | |
4. | Apparent order and index of circuits | |
Chapter V | Elementary Invariant Theory | |
1. | Trilinear coordinates | |
2. | Invariants and covariants, first principles | |
3. | Symbolic notation | |
4. | Binary domain | |
5. | Ternary forms | |
Chapter VI | Projective Theory of Singular Points | |
1. | Polar curves and singular points | |
2. | The effect of singular points | |
Chapter VII | Plucker's Equations, and Klein's Equation | |
1. | Forms of Plucker's equations | |
2. | Existence conditions | |
3. | Klein's equation | |
Chapter VIII | The Genus | |
1. | Definition of genus | |
2. | Chasles-Cayley-Brill correspondence formula | |
3. | Correspondences on different curves | |
Chapter IX | Covariant Curves | |
1. | Polar curves | |
2. | Simplest linear systems | |
3. | Fundamental covariant curves | |
4. | Covariants of two curves or envelopes | |
Chapter X | Metrical Properties of Curves | |
1. | Centres of gravity | |
2. | Foci | |
3. | Products of distances | |
4. | Sums of angles | |
5. | Polars | |
6. | Transversals | |
7. | Evolutes | |
Book II | The Singular Points | |
Chapter I | The Reduction of Singularities | |
1. | Quadratic transformations | |
2. | The effect on singularities | |
Chapter II | Development in Series | |
1. | Development of the branches at a point | |
2. | Invariant numbers for branches | |
3. | Intersections of two branches | |
4. | Effect of a quadratic transformation on a branch | |
Chapter III | Clustering Singularities | |
1. | General idea of clustering singularities | |
2. | Singularities of a single branch | |
Chapter IV | Adjoint Curves and Plucker's Equations | |
1. | Adjoint curves in general | |
2. | Residuation | |
3. | Genus | |
4. | Plucker's equations | |
Book III | Systems of Points on a Curve | |
Chapter I | General Theory of Linear Series | |
1. | Linear systems of curves and linear series | |
2. | Sums and differences of series | |
3. | Representation in hyperspace | |
4. | The Riemann-Roch theorem | |
5. | Simple series and composite series | |
Chapter II | Abelian Integrals | |
1. | Integrals of the first sort | |
2. | Integrals of other sorts | |
3. | Abel's theorem | |
Chapter III | Singular Points of Correspondences | |
1. | The Chasles-Cayley-Brill correspondence formula | |
2. | The Jacobian series | |
3. | The De Jonquieres formula | |
Chapter IV | Moduli and Limiting Values | |
1. | The Gap Theorem of Weierstrass | |
2. | Moduli | |
3. | Limiting values | |
Chapter V | Curves of Special Type | |
1. | Curves containing series of given sort | |
2. | Elliptic curves | |
3. | Hyperelliptic curves | |
4. | Polygonal curves | |
5. | [phi]-curves | |
6. | Reducible curves | |
Chapter VI | Non-Linear Series of Groups of Points on a Curve | |
1. | General theorems about series | |
2. | Series of index 1 | |
3. | Groups common to a g[superscript r subscript N] and a [gamma superscript rho subscript M] | |
4. | The defect of equivalence | |
Chapter VII | Higher Theory of Correspondences | |
1. | General theorems | |
2. | Application of Abelian Integrals | |
3. | Representation in hyperspace | |
4. | Generalized values | |
5. | (p, p) correspondences | |
6. | Birational correspondences | |
7. | Halphen's transformation | |
8. | Rational determination of characteristics of a curve | |
Chapter VIII | Parametric Representation of the General Curve. A Sketch | |
1. | Riemann surface for the general curve | |
2. | Uniformization | |
3. | Applications of uniformization | |
4. | Curves of genus 1 | |
Chapter IX | Rational Curves | |
1. | Binary apolar forms | |
2. | Determination of the equation of a rational curve | |
3. | Groups of intersections | |
4. | Equations and conditions for singularities | |
Book IV | Systems of Curves | |
Chapter I | Postulation of Linear Systems By Points | |
1. | Fundamental properties of linear systems | |
2. | Systems defined by simple points | |
3. | Postulation by means of singular points | |
4. | Fundamental curves and special adjoints | |
5. | Situation of singular points | |
Chapter II | The Transformation of Linear Systems | |
1. | Invariants of linear systems | |
2. | Curves transformable into straight lines | |
3. | Reduction of singularities | |
4. | Reduction to linear systems of minimum order | |
5. | Reduction of curves of low genus | |
Chapter III | Ternary Apolarity | |
1. | Linear systems and hyperspace | |
2. | Apolarity | |
3. | Apolarity between forms of different orders | |
4. | Expression of forms in terms of perfect nth powers | |
Chapter IV | Special Curves in Linear Systems | |
1. | The pencil | |
2. | Two-parameter nets | |
3. | The Laguerre net | |
Chapter V | Non-Linear Systems of Curves | |
1. | General formulation | |
2. | Singular points and the envelope | |
3. | The inflexions | |
4. | Projective theorems | |
5. | Systems depending on more than one parameter | |
Chapter VI | The General Cremona Transformation | |
1. | Fundamental properties | |
2. | Nother's factorization theorem | |
3. | Applications of the factorization theorem | |
4. | The identities of Clebsch | |
5. | Transformations in one plane | |
Chapter VII | Types of Cremona Transformations | |
1. | Types of lowest order | |
2. | Numerical relations | |
3. | Transformations with curves of fixed points | |
4. | Involutory transformations | |
5. | Cremona transformations and integral collineations in hyperspace | |
Chapter VIII | Groups of Cremona Transformations | |
1. | Continuous groups | |
2. | Infinite discontinuous groups | |
3. | Finite groups | |
Index of Authors Quoted | 499 | |
Subject Index | 511 |
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Add A Treatise on Algebraic Plane Curves, A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are, A Treatise on Algebraic Plane Curves to the inventory that you are selling on WonderClubX
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Add A Treatise on Algebraic Plane Curves, A thorough introduction to the theory of algebraic plane curves and their relations to various fields of geometry and analysis. Almost entirely confined to the properties of the general curve, and chiefly employs algebraic procedure. Geometric methods are, A Treatise on Algebraic Plane Curves to your collection on WonderClub |