The Swedish mathematician Torsten Brodén (1857--1931) wrote two articles on the foundations of Euclidean geometry. The first was published in 1890, almost a decade before Hilbert's first attempt, and the second was published in 1912. Brodén's philosophical view of the nature of geometry is discussed and his thoughts on axiomatic systems are described. His axiomatic system for Euclidean geometry from 1890 is considered in detail and compared with his later work on the foundations of geometry. The two continuity axioms given are compared to and proved to imply Hilbert's two continuity axioms of 1903.
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Reich, Karin;
(2008)
Der Desarguessche und der Pascalsche Satz: Hessenbergs Beitrag zu Hilberts Grundlagen der Geometrie
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Stillwell, John;
(2014)
Ideal Elements in Hilbert's Geometry
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Corry, Leo;
(2006)
Axiomatics, Empiricism, and Anschauung in Hilbert's Conception of Geometry: Between Arithmetic and General Relativity
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Chapter
Contro, Walter S.;
(1985)
Eine schwedische Axiomatik der Geometrie vor Hilbert: Torsten Brodéns Om geometriens principer von 1890
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Book
Gabriele Lolli;
(2016)
Tavoli, sedie, boccali di birra: David Hilbert e la matematica del Novecento
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Sieg, Wilfried;
(2014)
The Ways of Hilbert's Axiomatics: Structural and Formal
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Article
Cerroni, Cinzia;
(2007)
The Contributions of Hilbert and Dehn to Non-Archimedean Geometries and Their Impact on the Italian School
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Toepell, M.-M.;
(1985)
Zur Schlüsselrolle Friedrich Schurs bei der Entstehung von David Hilberts Grundlagen der Geometrie
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Eduardo N. Giovannini;
(2021)
David Hilbert and the foundations of the theory of plane area
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Chapter
Hallett, Michael;
(2010)
Frege and Hilbert
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Book
Hilbert, David;
Hallett, Michael;
Majer, Ulrich;
(2004)
David Hilbert's Lectures on the Foundations of Geometry, 1891-1902
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Article
Michael Friedman;
(2021)
On Mascheroni's La geometria del compasso at the beginning of the 19th century
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Book
Emanuele Gambetta;
(2020)
Philosophy of the Infinite
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Corry, Leo;
(2004)
David Hilbert and the Axiomatization of Physics (1898-1918): From Grundlagen der Geometrie to Grundlagen der Physik
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Thesis
Ogawa, Yoshinori;
(2002)
The Pursuit of Rigor: David Hilbert's Early Philosophy of Mathematics
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Article
Ausejo Martínez, Elena;
Ausejo Lifante, Elena;
(2017)
Correspondencia de Zoel García de Galdeano con matemáticos alemanes: Georg Cantor
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Book
Cantor, Georg;
Ferreirós, José;
(2006)
Fundamentos para una teoría general de conjuntos: Escritos y correspondencia selecta
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June Barrow-Green;
Reinhard Siegmund-Schultze;
(2016)
“The First Man on the Street” — Tracing a Famous Hilbert Quote (1900) Back to Gergonne (1825)
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Article
Willea, Matthias;
(2011)
“Metamathematics” in Transition
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Book
Gauthier, Yvon;
(2002)
Internal Logic: Foundations of Mathematics from Kronecker to Hilbert
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