Book contents
- Frontmatter
- PREFACE
- Contents
- CLASSIFICATION
- 1 On a Theorem in the Geometry of Position
- 2 On the Properties of a certain Symbolical Expression
- 3 On certain Definite Integrals
- 4 On certain Expansions, in series of Multiple Sines and Cosines
- 5 On the Intersection of Curves
- 6 On the Motion of Rotation of a Solid Body
- 7 On a class of Differential Equations, and on the Lines of Curvature of an Ellipsoid
- 8 On Lagrange's Theorem
- 9 Demonstration of Pascal's Theorem
- 10 On the Theory of Algebraical Curves
- 11 Chapters in the Analytical Geometry of (n) Dimensions
- 12 On the Theory of Determinants
- 13 On the Theory of Linear Transformations
- 14 On Linear Transformations
- 15 Note sur deux Formules données par MM. Eisenstein et Hesse
- 16 Mémoire sur les Hyperdéterminants
- 17 Note on Mr Bronwin's paper on Elliptic Integrals
- 18 Remarks on the Rev. B. Bronwin's paper on Jacobi's Theory of Elliptic Functions
- 19 Investigation of the Transformation of certain Elliptic Functions
- 20 On certain results relating to Quaternions
- 21 On Jacobi's Elliptic Functions, in reply to the Rev. B. Bronwin: and on Quaternions
- 22 On Algebraical Couples
- 23 On the Transformation of Elliptic Functions
- 24 On the Inverse Elliptic Functions
- 25 Mémoire sur les Fonctions doublement périodiques
- 26 Mémoire sur les Courbes du Troisième Ordre
- 27 Nouvelles remarques sur les Courbes du Troisième Ordre
- 28 Sur quelques Intégrales Multiples
- 29 Addition à la Note sur quelques Intégrales Multiples
- 30 Mémoire sur les Courbes à double Courbure et les Surfaces développables
- 31 Démonstration d'un Théorème de M. Chasles
- 32 On some Analytical Formulae and their application to the Theory of Spherical Coordinates
- 33 On the Reduction of du ÷ √U, when U is a Function of the Fourth Order
- 34 Note on the Maxima and Minima of Functions of Three Variables
- 35 On Homogeneous Functions of the Third Order with Three Variables
- 36 On the Geometrical Representation of the Motion of a Solid Body
- 37 On the Rotation of a Solid Body round a Fixed Point
- 38 Note on a Geometrical Theorem contained in a Paper by Sir W. Thomson
- 39 On the Diametral Planes of a Surface of the Second Order
- 40 On the Theory of Involution in Geometry
- 41 On certain Formulas for Differentiation, with applications to the evaluation of Definite Integrals
- 42 On the Caustic by Reflection at a Circle
- 43 On the Differential Equations which occur in Dynamical Problems
- 44 On a Multiple Integral connected with the Theory of Attractions
- 45 On the Theory of Elliptic Functions
- 46 Note on a System of Imaginaries
- 47 Sur la Surface des Ondes
- 48 Note sur les Fonctions de M. Sturm
- 49 Sur quelques Formules du Calcul Intégral
- 50 Sur quelques Théorémes de la Géométrie de Position
- 51 Problème de Géométrie Analytique
- 52 Sur quelques Propriétés des Déterminants Gauches
- 53 Recherches sur l&Élimination, et sur la Théorie des Courbes
- 54 Note sur les Hyperdéterminants
- 55 Sur quelques Théorèmes de la Géométrie de Position
- 56 Demonstration of a Geometrical Theorem of Jacobi's
- 57 On the Theory of Elliptic Functions
- 58 Notes on the Abelian Integrals—Jacobi's System of Differential Equations
- 59 On the Theory of Elimination
- 60 On the Expansion of Integral Functions in a series of Laplace's Coefficients
- 61 On Geometrical Reciprocity
- 62 On an Integral Transformation
- 63 Démonstration d'un Théorème de M. Boole concernant des Intégrales Multiples
- 64 Sur la généralisation d'un Théoréme de M. Jellett qui se rapporte aux Attractions
- 65 Nouvelles Recherches sur les Fonctions de M. Sturm
- 66 Sur les Fonctions de Laplace
- 67 Note sur les Fonctions Elliptiques
- 68 On the application of Quaternions to the Theory of Rotation
- 69 Sur les Déterminants Gauches
- 70 Sur quelques Théorèmes de la Géométrie de Position
- 71 Note sur les Fonctions du Second Ordre
- 72 Note on the Theory of Permutations
- 73 Abstract of a Memoir by Dr Hesse on the construction of the Surface of the Second Order which passes through nine given points
- 74 On the Simultaneous Transformation of Two Homogeneous Functions of the Second Order
- 75 On the Attraction of an Ellipsoid
- 76 On the Triple Tangent Planes of Surfaces of the Third Order
- 77 On the order of certain Systems of Algebraical Equations
- 78 Note on the Motion of Rotation of a Solid of Revolution
- 79 On a System of Equations connected with Malfatti's Problem, and on another Algebraical System
- 80 Sur quelques Transmutations des Lignes Courbes
- 81 Addition au Mémoire sur quelques Transmutations des Lignes Courbes
- 82 On the Triadic Arrangements of Seven and Fifteen Things
- 83 On Curves of Double Curvature and Developable Surfaces
- 84 On the Developable Surfaces which arise from two Surfaces of the Second Order
- 85 Note on a Family of Curves of the Fourth Order
- 86 On the Developable derived from an Equation of the Fifth Order
- 87 Notes on Elliptic Functions (from Jacobi)
- 88 On the Transformation of an Elliptic Integral
- 89 On the Attraction of Ellipsoids (Jacobi's Method)
- 90 Note sur quelques Formules relatives aux Coniques
- 91 Sur le Problème des Contacts
- 92 Note sur un Système de certaines Formules
- 93 Note sur quelques Formules qui se rapportent à la Multiplication des Fonctions Elliptiques
- 94 Note sur l'Addition des Fonctions Elliptiques
- 95 Note sur quelques Théorèmes de la Géométrie de Position
- 96 Mémoire sur les Coniques inscrites dans une même Surface du Second Ordre
- 97 Note sur la Solution de l'Équation x57 − 1 = 0
- 98 Note relative à la sixième section du Mémoire sur quelques Théorèmes de la Géométrie de Position
- 99 Note sur quelques Formules qui se rapportent à la Multiplication des Fonctions Elliptiques
- 100 Note sur la Théorie des Hyperdéterminants
- Notes and References
- Frontmatter
- PREFACE
- Contents
- CLASSIFICATION
- 1 On a Theorem in the Geometry of Position
- 2 On the Properties of a certain Symbolical Expression
- 3 On certain Definite Integrals
- 4 On certain Expansions, in series of Multiple Sines and Cosines
- 5 On the Intersection of Curves
- 6 On the Motion of Rotation of a Solid Body
- 7 On a class of Differential Equations, and on the Lines of Curvature of an Ellipsoid
- 8 On Lagrange's Theorem
- 9 Demonstration of Pascal's Theorem
- 10 On the Theory of Algebraical Curves
- 11 Chapters in the Analytical Geometry of (n) Dimensions
- 12 On the Theory of Determinants
- 13 On the Theory of Linear Transformations
- 14 On Linear Transformations
- 15 Note sur deux Formules données par MM. Eisenstein et Hesse
- 16 Mémoire sur les Hyperdéterminants
- 17 Note on Mr Bronwin's paper on Elliptic Integrals
- 18 Remarks on the Rev. B. Bronwin's paper on Jacobi's Theory of Elliptic Functions
- 19 Investigation of the Transformation of certain Elliptic Functions
- 20 On certain results relating to Quaternions
- 21 On Jacobi's Elliptic Functions, in reply to the Rev. B. Bronwin: and on Quaternions
- 22 On Algebraical Couples
- 23 On the Transformation of Elliptic Functions
- 24 On the Inverse Elliptic Functions
- 25 Mémoire sur les Fonctions doublement périodiques
- 26 Mémoire sur les Courbes du Troisième Ordre
- 27 Nouvelles remarques sur les Courbes du Troisième Ordre
- 28 Sur quelques Intégrales Multiples
- 29 Addition à la Note sur quelques Intégrales Multiples
- 30 Mémoire sur les Courbes à double Courbure et les Surfaces développables
- 31 Démonstration d'un Théorème de M. Chasles
- 32 On some Analytical Formulae and their application to the Theory of Spherical Coordinates
- 33 On the Reduction of du ÷ √U, when U is a Function of the Fourth Order
- 34 Note on the Maxima and Minima of Functions of Three Variables
- 35 On Homogeneous Functions of the Third Order with Three Variables
- 36 On the Geometrical Representation of the Motion of a Solid Body
- 37 On the Rotation of a Solid Body round a Fixed Point
- 38 Note on a Geometrical Theorem contained in a Paper by Sir W. Thomson
- 39 On the Diametral Planes of a Surface of the Second Order
- 40 On the Theory of Involution in Geometry
- 41 On certain Formulas for Differentiation, with applications to the evaluation of Definite Integrals
- 42 On the Caustic by Reflection at a Circle
- 43 On the Differential Equations which occur in Dynamical Problems
- 44 On a Multiple Integral connected with the Theory of Attractions
- 45 On the Theory of Elliptic Functions
- 46 Note on a System of Imaginaries
- 47 Sur la Surface des Ondes
- 48 Note sur les Fonctions de M. Sturm
- 49 Sur quelques Formules du Calcul Intégral
- 50 Sur quelques Théorémes de la Géométrie de Position
- 51 Problème de Géométrie Analytique
- 52 Sur quelques Propriétés des Déterminants Gauches
- 53 Recherches sur l&Élimination, et sur la Théorie des Courbes
- 54 Note sur les Hyperdéterminants
- 55 Sur quelques Théorèmes de la Géométrie de Position
- 56 Demonstration of a Geometrical Theorem of Jacobi's
- 57 On the Theory of Elliptic Functions
- 58 Notes on the Abelian Integrals—Jacobi's System of Differential Equations
- 59 On the Theory of Elimination
- 60 On the Expansion of Integral Functions in a series of Laplace's Coefficients
- 61 On Geometrical Reciprocity
- 62 On an Integral Transformation
- 63 Démonstration d'un Théorème de M. Boole concernant des Intégrales Multiples
- 64 Sur la généralisation d'un Théoréme de M. Jellett qui se rapporte aux Attractions
- 65 Nouvelles Recherches sur les Fonctions de M. Sturm
- 66 Sur les Fonctions de Laplace
- 67 Note sur les Fonctions Elliptiques
- 68 On the application of Quaternions to the Theory of Rotation
- 69 Sur les Déterminants Gauches
- 70 Sur quelques Théorèmes de la Géométrie de Position
- 71 Note sur les Fonctions du Second Ordre
- 72 Note on the Theory of Permutations
- 73 Abstract of a Memoir by Dr Hesse on the construction of the Surface of the Second Order which passes through nine given points
- 74 On the Simultaneous Transformation of Two Homogeneous Functions of the Second Order
- 75 On the Attraction of an Ellipsoid
- 76 On the Triple Tangent Planes of Surfaces of the Third Order
- 77 On the order of certain Systems of Algebraical Equations
- 78 Note on the Motion of Rotation of a Solid of Revolution
- 79 On a System of Equations connected with Malfatti's Problem, and on another Algebraical System
- 80 Sur quelques Transmutations des Lignes Courbes
- 81 Addition au Mémoire sur quelques Transmutations des Lignes Courbes
- 82 On the Triadic Arrangements of Seven and Fifteen Things
- 83 On Curves of Double Curvature and Developable Surfaces
- 84 On the Developable Surfaces which arise from two Surfaces of the Second Order
- 85 Note on a Family of Curves of the Fourth Order
- 86 On the Developable derived from an Equation of the Fifth Order
- 87 Notes on Elliptic Functions (from Jacobi)
- 88 On the Transformation of an Elliptic Integral
- 89 On the Attraction of Ellipsoids (Jacobi's Method)
- 90 Note sur quelques Formules relatives aux Coniques
- 91 Sur le Problème des Contacts
- 92 Note sur un Système de certaines Formules
- 93 Note sur quelques Formules qui se rapportent à la Multiplication des Fonctions Elliptiques
- 94 Note sur l'Addition des Fonctions Elliptiques
- 95 Note sur quelques Théorèmes de la Géométrie de Position
- 96 Mémoire sur les Coniques inscrites dans une même Surface du Second Ordre
- 97 Note sur la Solution de l'Équation x57 − 1 = 0
- 98 Note relative à la sixième section du Mémoire sur quelques Théorèmes de la Géométrie de Position
- 99 Note sur quelques Formules qui se rapportent à la Multiplication des Fonctions Elliptiques
- 100 Note sur la Théorie des Hyperdéterminants
- Notes and References
Summary
RATHER more than a year ago I was requested by the Syndics of the University Press to allow my mathematical papers to be reprinted in a collected form: I had great pleasure in acceding to a request so complimentary to myself, and I willingly undertook the work of superintending the impression of them, and of adding such notes and references as might appear to me desirable.
The present volume contains one hundred papers (numbered 1, 2, 3,…,100) originally published in the years 1841 to 1853. They are here reproduced nearly, but not exactly, in chronological order: and as nearly as may be in their original forms; but in a few cases where the paper is controversial, or where it is a translation (into French or English) of an English or French paper, only the title is given: there are in some few cases omissions which are indicated where they occur. The number is printed in the upper inside corner of the page; it is intended that the numbers shall run consecutively through all the volumes; and thus a paper can be referred to simply by its number.
I have of course corrected obvious typographical errors, and in particular have freely altered punctuation, but I have not attempted to verify formulae. Additions are made in square brackets []; to avoid confusion with these, square brackets occurring in the original papers have in general been changed into twisted ones {}, but where they occur in a formula it was not always possible to make the alteration.
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- Information
- The Collected Mathematical Papers , pp. v - viPublisher: Cambridge University PressPrint publication year: 2009First published in: 1889