C.G.J. Jacobi's gesammelte Werke : herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften

Author(s)

• Jacobi, C. G. J. (Carl Gustav Jakob)
• Borchardt, Carl Wilhelm

Bibliographic Information

C.G.J. Jacobi's gesammelte Werke : herausgegeben auf Veranlassung der königlich preussischen Akademie der Wissenschaften

edited by C.W. Borchardt

（Cambridge library collection, . Mathematics）

Cambridge University Press, 2013

• v. 1
• v. 2
• v. 3
• v. 4
• v. 5
• v. 6
• v. 7
• suppl.

Note

Reprint. Originally published: Berlin : Verlag von G. Reimer, 1881-1891

Vol. 1 / edited by G. W. Borchardt; v. 2-7 / edited by K. Weierstrass; suppl. / edited by E. Lottner

Description and Table of Contents

Volume

v. 1 ISBN 9781108059244

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Carl Wilhelm Borchardt (1817-80), Volume 1 appeared in 1881.

Table of Contents

• Vorrede
• 1. Gedachtnissrede auf Carl Gustav Jacob Jacobi von Lejeune Dirichlet
• 2. Extrait de deux lettres de M. Jacobi de l'universite de Koenigsberg a M. Schumacher
• 3. Demonstratio theorematis ad theoriam functionum ellipticarum spectantis
• 4. Fundamenta nova theoriae functionum ellipticarum
• 5. Addition au memoire de M. Abel sur les fonctions elliptiques
• 6. Note sur la decomposition d'un nombre donne en quatre carres
• 7. Notice sure les fonctions elliptiques
• 8. Ueber die Anwendung der elliptischen Transcendenten auf ein bekanntes Problem der Elementar-Geometrie
• 9. De functionibus ellipticis commentatio prima et altera
• 10. Note sur une nouvelle application de l'analyse des fonctions elliptiques a l'algebre
• 11. Formulae novae in theoria transcendentium ellipticarum fundamentales
• 12. Ueber die zur numerischen Berechnung der elliptischen Functionen zweckmassigsten Formeln
• 13. Ueber einige die elliptischen Functionen betreffenden Formeln
• 14. Anzeige von legendre
• Nachlass.

Volume

v. 2 ISBN 9781108059251

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 2 appeared in 1882.

Table of Contents

• 1. De theoremate Abeliano observatio
• 2. Considerationes generales de transcendentibus Abelianis
• 3. Ueber die Figur des Gleichgewichts
• 4. De functionibus duarum variabilium quadrupliciter periodicis
• 5. De usu theoriae integralium ellipticorum et integralium Abelianorum in analysi Diophantea
• 6. Note von der geodatischen Linie auf einem Ellipsoid
• 7. Demonstratio nova theorematis Abeliani
• 8. Ueber die Additions theoreme der Abelschen Integrale zweiter und dritter Gattung
• 9. Note sur les fonctions Abeliennes
• 10. Extrait de deux lettres de Ch. Hermite a C. G. J. Jacobi
• 11. Extrait d'une lettre de Jacobi adresse a Hermite
• 12. Ueber die Vertauschung von Parameter und Argument bei der dritten Gattung der Abelschen und hoeheren Transcendenten
• 13. Ueber eine neue Methode zur Integration
• 14. Notiz uber A. Goepel
• 15. Ueber die unmittelbare Verification einer Fundamentalformel der Theorie der elliptischen Functionen
• 16. Ueber die partielle Differentialgleichung
• 17. Ueber die Differentialgleichung
• 18. Ueber eine particulare Loesung der partiellen Differentialgleichung
• 19. Ueber unendliche Reihen
• 20. Sur la rotation d'un corps
• 21. Auszug eines Schreibens von C. G. J. Jacobi an E. Heine
• Nachlass.

Volume

v. 3 ISBN 9781108059268

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 3 appeared in 1884.

Table of Contents

• Vorwort
• 1. Disquisitiones analyticae de fractionibus simplicibus
• 2. Ueber die Haptaxen der Flachen der zweiten Ordnung
• 3. De singulari quadam duplicis integralis transformatione
• 4. Exercitatio algebraica circa discerptionem singularem fractionum
• 5. De transformatione integralis duplicis indefiniti
• 6. De transformatione et determinatione integralium duplicium commentatio tertia
• 7. De binis quibuslibet functionibus homogeneis secundi ordinis
• 8. Observatiunculae ad theoriam aequationum algebraicarum pertinentes
• 9. Theoremata nova algebraica circa systema duarum aequationum inter duas variabiles propositarum
• 10. De eliminatione variabilis e duabus aequationibus algebraicis
• 11. De integralibus quibusdam duplicibus
• 12. De relationibus, quae locum habere debent inter puncta
• 13. De formatione et proprietatibus determinantium
• 14. De determinantibus functionalibus
• 15. De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum
• 16. Zur combinatorischen Analysis
• 17. Sulla condizione di uguaglianza di due radici dell' equazione cubica
• 18. Ueber eine neue Aufloesungsart der bei der Methode der kleinsten Quadrate vorkommenden linearen Gleichungen
• 19. Ueber die Darstellung einer Reihe gegebener Werthe durch eine gebrochene rationale Function
• 20. Extrait d'une lettre adressee a M. Liouville
• 21. Ueber die Anzahl der Doppeltangenten ebener algebraischer Curven
• 22. Auszug dreier Schreiben von Herrn Prof. Hesse und eines Schreibens an Herrn Prof. Hesse
• Nachlass.

Volume

v. 4 ISBN 9781108059275

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 4 appeared in 1886.

Table of Contents

• 1. Ueber die Integration der partiellen Differentialgleichungen erster Ordnung
• 2. Ueber die Pfaff'sche Methode, eine gewoehnliche lineare Differentialgleichungen zwischen 2n Variabeln
• 3. Bemerkung zu der Abhandlung des Herrn Prof. Scherk
• 4. Sur le mouvement d'un point et sur un cas particulier du probleme des trois corps
• 5. Zur Theorie der Variationsrechnung und der Differentialgleichungen
• 6. Ueber die Reduction der Integration der partiellen Differentialgleichungen erster Ordnung
• 7. Note sur l'integration des equations differentielles de la dynamique
• 8. Neues Theorem der analytischen Mechanik
• 9. Sur un theoreme de Poisson
• 10. Dilucidationes de aequationum differentialium vulgarium systematis
• 11. De integratione aequationis differentialis
• 12. De motu puncti singularis
• 13. Sur un nouveau principe de la mechanique analytique
• 14. Sur l'elimination des noeuds dans le probleme des trois corps
• 15. Zusatz zu der vorhergehenden Abhandlung
• 16. Theoria novi multiplicatoris systemati aequationum differentalium vulgarium applicandi
• 17. Sul principio dell'ultimo moltiplicatore e suo uso come nuovo principio generale de meccanica
• 18. Zwei Beispiele zur neuen Methode der Dynamik
• Nachlass.

Volume

v. 5 ISBN 9781108059282

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 5 appeared in 1890.

Table of Contents

• Vorwort
• 1. Nova methodus aequationes differentiales partiales primi ordinis inter numerum variabilium quemcunque propositas integrandi
• 2. De investigando ordine sytematis aequationum differentialium vulgarium cuiuscunque
• 3. Ueber diejenigen Probleme der Mechanik
• 4. Ueber die vollstandigen Loesungen einer partiellen Differentialgleichungen erster Ordnung
• 5. Ueber die Integration der partiellen Differentialgleichungen erster Ordnung zwischen vier Variabeln
• 6. De aequationum differentialium isoperimetricarum transformationibus earumque reductione ad aequationem differentialem primi ordinis non linearem
• 7. De aequationum differentialium systemate non normali ad formam normalem revocando
• 8. Anmerkungen des Herausgebers.

Volume

v. 6 ISBN 9781108059299

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 6 appeared in 1891.

Table of Contents

• Vorwort
• 1. Abhandlung zur Theorie der bestimmten Integrale und der Reihen
• 2. Zahlentheoretische Abhandlungen
• Anmerkungen.

Volume

v. 7 ISBN 9781108059305

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891. Edited by fellow German mathematician Karl Weierstrass (1815-97), Volume 7 appeared in 1891.

Table of Contents

• Vorwort
• 1. Geometrische Abhandlungen
• 2. Astronomische Abhandlungen
• 3. Abhandlungen historischen Inhalts
• Nachlass
• Anmerkungen
• Verzeichniss sammtlicher Abhandlungen C. G. J. Jacobi's.

Volume

suppl. ISBN 9781108059312

Description

One of the greatest mathematicians of the nineteenth century, Carl Gustav Jacob Jacobi (1804-51) burst into the limelight with his redevelopment, together with Niels Henrik Abel (1802-29), of the theory of elliptic functions. His pioneering work was characterised by the variety of problems tackled and the power of the tools used to tackle them. His lasting influence on rational mechanics, number theory, partial differential equations, complex variable theory and computation is marked by the number of fundamental concepts that bear his name (the Jacobian, the Jacobi sum and the Jacobi symbol, among others). His collected works, comprising treatises, letters and papers written in German, Latin and French, were published in eight volumes between 1881 and 1891, edited chiefly by Karl Weierstrass (1815-97). Published in 1884, this supplementary volume contains Jacobi's 1842-3 lectures on dynamics as compiled by Alfred Clebsch (1833-72) in the revised second edition by Eduard Lottner (1826-87).

Table of Contents

• Vorwort
• Vorlesungen uber Dynamik.

by "Nielsen BookData"

Details

• NCID: BB12818055
• ISBN:
  • 9781108059244
  • 9781108059251
  • 9781108059268
  • 9781108059275
  • 9781108059282
  • 9781108059299
  • 9781108059305
  • 9781108059312
• Country Code: uk
• Title Language Code: ger
• Text Language Code: gerlatfre
• Place of Publication: Cambridge
• Pages/Volumes: 8 v.
• Size: 30 cm
• Classification:
  • DC : 510.2
  • LCC : QA3 .J16
• Subject Headings:
  • LCSH : Mathematics
• Parent Bibliography ID:
  • BB00083053