Bair, Jacques (Author)
Błaszczyk, Piotr (Author)
Guillén, Elías Fuentes (Author)
Heinig, Peter (Author)
Kanovei, Vladimir (Author)
Katz, Mikhail G. (Author)
In a paper published in 1970, Grattan-Guinness argued that Cauchy, in his 1821 Cours d'Analyse, may have plagiarized Bolzano's Rein analytischer Beweis (RB), first published in 1817. That paper was subsequently discredited in several works, but some of its assumptions still prevail today. In particular, it is usually considered that Cauchy did not develop his notion of the continuity of a function before Bolzano developed his in RB and that both notions are essentially the same. We argue that both assumptions are incorrect, and that it is implausible that Cauchy's initial insight into that notion, which eventually evolved to an approach using infinitesimals, could have been borrowed from Bolzano's work. Furthermore, we account for Bolzano's interest in that notion and focus on his discussion of a definition by Kästner (in Section 183 of his 1766 book), which the former seems to have misrepresented at least partially.
...More
Chapter
Grabiner, Judith;
(1984)
Cauchy and Bolzano: Tradition and transformation in the history of mathematics
(/isis/citation/CBB000009330/)
Article
Moore, Matthew E.;
(2002)
A Cantorian Argument Against Infinitesimals
(/isis/citation/CBB000300363/)
Thesis
Keele, Lisa;
(2008)
Theories of Continuity and Infinitesimals: Four Philosophers of the Nineteenth Century
(/isis/citation/CBB001560801/)
Article
Błaszczyk, Piotr;
Katz, Mikhail G.;
Sherry, David;
(2013)
Ten Misconceptions from the History of Analysis and Their Debunking
(/isis/citation/CBB001252715/)
Article
Bråting, Kajsa;
(2007)
A New Look at E.G. Björling and the Cauchy Sum Theorem
(/isis/citation/CBB000720350/)
Article
José Ángel Roldán Casas;
(2021)
El reconocimiento del mérito científico a través de la historia de algunos de los epónimos estadísticos más relevantes: ¿Se verifica la ley de Stigler?
(/isis/citation/CBB844603043/)
Chapter
Elena Ausejo Martínez;
F. Javier Medrano Sánchez;
(2015)
Jorge Juan y la consolidación del cálculo infinitesimal en España (1750-1814)
(/isis/citation/CBB198901217/)
Article
Spalt, Detlef D.;
(2002)
Cauchys Kontinuum: Eine historiografische Annäherung via Cauchys Summensatz
(/isis/citation/CBB000200224/)
Article
Petrova, Svetlana S.;
(2008)
Cauchy et le calcul symbolique
(/isis/citation/CBB001021145/)
Article
Delcourt, Jean;
(2011)
Analyse et géométrie, histoire des courbes gauches De Clairaut à Darboux
(/isis/citation/CBB001034291/)
Article
Barany, Michael J.;
(2011)
God, King, and Geometry: Revisiting the Introduction to Cauchy's Cours d'analyse
(/isis/citation/CBB001036223/)
Article
Lubet, Jean-Pierre;
(2010)
Calcul symbolique et calcul intégral de Lagrange à Cauchy
(/isis/citation/CBB001033635/)
Article
Novy, Luboš;
(2008)
Les relations entre la logique et la mathématique dans l'oeuvre de Bernard Bolzano
(/isis/citation/CBB001021148/)
Article
Elías Fuentes Guillén;
Davide Crippa;
(2021)
The 1804 examination for the chair of Elementary Mathematics at the University of Prague
(/isis/citation/CBB710675257/)
Book
Boniface, Jacqueline;
(2002)
Les constructions des nombres réels dans le mouvement d'arithmétisation de l'analyse
(/isis/citation/CBB000771381/)
Article
Rusnock, Paul;
(2013)
On Bolzano's Concept of a Sum
(/isis/citation/CBB001212145/)
Article
Peter Simons;
(2015)
Bolzano's Monadology
(/isis/citation/CBB137993666/)
Article
Grattan-Guinness, Ivor;
(2008)
Differential Equations and Linearity in the 19th and Early 20th Centuries
(/isis/citation/CBB001021149/)
Book
Cauchy, Augustin-Louis;
Pérez Fernández, F. Javier;
Díaz Moreno, José M.;
(1998)
Cours d'analyse de l'Ecole Royale Polytechnique
(/isis/citation/CBB000530050/)
Article
Frisch, Uriel;
Villone, Barbara;
(2014)
Cauchy's Almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow
(/isis/citation/CBB001451853/)
Be the first to comment!