Werke: Volume 3

Werke: Volume 3

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Description

The genius of Carl Friedrich Gauss (1777-1855) and the novelty of his work (published in Latin, German, and occasionally French) in areas as diverse as number theory, probability and astronomy were already widely acknowledged during his lifetime. But it took another three generations of mathematicians to reveal the true extent of his output as they studied Gauss' extensive unpublished papers and his voluminous correspondence. This posthumous twelve-volume collection of Gauss' complete works, published between 1863 and 1933, marks the culmination of their efforts and provides a fascinating account of one of the great scientific minds of the nineteenth century. Volume 3, which appeared in 1866, focuses on analysis. It includes Gauss' work on elliptic functions and on power series, for which he gave the first convergence criteria, as well as his first (1799) proof of the fundamental theorem of algebra, and reviews of works by contemporaries including Fourier.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • German
  • 113905824X
  • 9781139058247

Table of contents

Algebraische Functionen: Abhandlungen: Demonstratio nova theorematis omnen functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse; Demonstratio nova altera theorematis omnen functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse; Theorematis de resolubilitate functionum algebraicarum integrarum in factores reales demonstratio teria; Beweis eines algebraischen Lehrsatzes; Beitrage zur Theorie der algebraischen Gleichungen; Anzeigen eigner Abhandlungen: Demonstratio nova altera theorematis omnen functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse; Theorematis de resolubilitate functionum algebraicarum integrarum in factores reales demonstratio tertia; Beitrage zur Theorie der algebraischen Gleichungen; Anzeigen nicht eigner Schriften: Coytier. Recherches mathematiques; Fourier. Analyse des equationes determinees; Gauss' Reihe: Abhandlungen: Disquisitiones generales circa seriem infinitum; Methodus nova integralium valores per approximationem inveniendi; Anzeigen eigner Abhandlungen: Disquisitiones generales circa seriem infinitam etc. Pars prior; Methodus nova integralium valores per approximationem inveniendi; Nachlass: Determinatio seriei nostrae per aequationem differentialem secundi ordinis; Bemerkungen zu dieser Abhandlang; Mittheilungen UEber Verschiedene Schriften: Peaff. Methodus generalis, aequationes differentiarum partialium, nec non aequationes differentiales vulgares, utrasque primi ordinis, inter quotcunque variabiles, complete integrandi; Callet. Tables logarithmiques; Prasse. Logarithmische Tafeln fur die Zahlen, Sinus und Tangenten; Prasse. Tables logarithmiques pour les nombres, les sinus et les tangentes; Gauss. Tafeln zur bequemern Berechnung des Logarithmen der Summe oder Differenz zweier Grossen, welche selbst nur durch ihre Logarithmen gegeben sind; Pasquich. Abgekurzte Logarithmisch-Trigonometrische Tafeln; [Matthiessen]. Tafel zur Bequemern Berechnung des Logarithmen der Summe oder Differenz zweier Grossen, welche selbst nur durch ihre Logarithmen gegeben sind; Logarithmentafeln mit sechs Ziffern; Babbage. Table of logarithms of the natural numbers; Hassler. Tabulae logarithmicae et trigonometricae; Vega und Hulsse. Sammlung mathematischer Tafeln; Vega. Thesaurus Logarithmorum; Interpolation: Theoria interpolationis methodo nova tractata; Bemerkungen zu dieser Abhandlung; Elliptische Functionen: Abhandlung: Determinatio attractionis, quam in punctum quodvis positionis datae exerceret planeta, si eius massa per totam orbitam ratione temporis, quo singulae partes describuntur, uniformiter esset dispertita; Anzeige der vorhergehendedn Abhandlung; Nachlass: De origine proprietatibusque generalibus numerorum mediorum arithmetico-geometricorum; De functionibus transcendentibus quae ex differentatione mediorum arithmetico-geometricorum oriuntur. Art. 9-11; Fortsetzung der Untersuchungen uber das arithmetisch-geometrische Mittel. Art 12-26; Tabula. Media arithemetico-geometrica inter unitatem et sinus singulorum semigradum; Lemniscatische Functionen (I) dargestellt durch Potenz-Reihen; Lemniscatische Functionen (II) dargestellt durch unendliche Producte und durch trigonometrische Reihen; Zur Theorie der neuen Transscendenten: 1. Anfange der der Untersuchungen uber die neuen Transscendenten; 2. Zur Theorie der transcendenten Functionen gehorig; 3. Neue Anordnung der Theoreme in Bezug auf diejenigen Reihen und unendlichen Producte, welche zu der Theorie der arithmetisch-geometrischen Mittel gehoren; 4. Hundert Theoreme uber die neuen Transscendenten; 5. Allgemeine Theoreme; Pentagramma mirificum; Bemerkungen.show more