Article ID: CBB925230600

Continuity Between Cauchy and Bolzano: Issues of Antecedents and Priority (2020)

unapi

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
Citation URI
https://data.isiscb.org/isis/citation/CBB925230600/

Similar Citations

Chapter Grabiner, Judith; (1984)
Cauchy and Bolzano: Tradition and transformation in the history of mathematics (/isis/citation/CBB000009330/)

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 Moore, Matthew E.; (2002)
A Cantorian Argument Against Infinitesimals (/isis/citation/CBB000300363/)

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 Elías Fuentes Guillén; Carmen Martínez Adame; (2020)
The Notion of Variable Quantities ω in Bolzano's Early Works (/isis/citation/CBB432034974/)

Article Centrone, Stefania; (2012)
Strenge Beweise und das Verbot der metábasis eis állo génos (/isis/citation/CBB001210991/)

Article Rusnock, Paul; Kerr-Lawson, Angus; (2005)
Bolzano and Uniform Continuity (/isis/citation/CBB000771353/)

Book Parsons, Charles; (2012)
From Kant to Husserl: Selected Essays (/isis/citation/CBB001253011/)

Article Frisch, Uriel; Villone, Barbara; (2014)
Cauchy's Almost Forgotten Lagrangian Formulation of the Euler Equation for 3D Incompressible Flow (/isis/citation/CBB001451853/)

Article Meo, M.; (2004)
The Mathematical Life of Cauchy's Group Theorem (/isis/citation/CBB000410846/)

Book Cauchy, Augustin Louis; Bradley, Robert E.; Sandifer, Charles Edward; (2009)
Cauchy's Cours D'analyse: An Annotated Translation (/isis/citation/CBB001251208/)

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 Grattan-Guinness, Ivor; (2008)
Differential Equations and Linearity in the 19th and Early 20th Centuries (/isis/citation/CBB001021149/)

Chapter Elena Ausejo Martínez; F. Javier Medrano Sánchez; (2015)
Jorge Juan y la consolidación del cálculo infinitesimal en España (1750-1814) (/isis/citation/CBB198901217/)

Book Boniface, Jacqueline; (2002)
Les constructions des nombres réels dans le mouvement d'arithmétisation de l'analyse (/isis/citation/CBB000771381/)

Article Elías Fuentes Guillén; Davide Crippa; (2021)
The 1804 examination for the chair of Elementary Mathematics at the University of Prague (/isis/citation/CBB710675257/)

Authors & Contributors
Cauchy, Augustin Louis
Guillén, Elías Fuentes
Grabiner, Judith V.
Spalt, Detlef D.
Moore, Matthew E.
Meo, M.
Journals
Historia Mathematica
Archive for History of Exact Sciences
Archives Internationales d'Histoire des Sciences
Synthese
History and Philosophy of Logic
Foundations of Science
Publishers
Sociedad Andaluza de Educación Matemática THALES
Ellipses
Springer
Harvard University Press
Indiana University
Publicaciones de la Universidad de Alicante
Concepts
Mathematics
Infinitesimals
Mathematical analysis
Algebra
Functions (mathematics)
Calculus
People
Cauchy, Augustin Louis
Bolzano, Bernard
Cantor, Georg Ferdinand Ludwig
Dedekind, Richard
Bjorling, Emmanuel Gabriel
Kronecker, Leopold
Time Periods
19th century
20th century
18th century
20th century, early
Places
France
Germany
Spain
Institutions
École Polytechnique, Paris
University of Prague
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment