The “common notions” prefacing the Elements of Euclid are a very peculiar set of axioms, and their authenticity, as well as their actual role in the demonstrations, have been object of debate. In the first part of this essay, I offer a survey of the evidence for the authenticity of the common notions, and conclude that only three of them are likely to have been in place at the times of Euclid, whereas others were added in Late Antiquity. In the second part of the essay, I consider the meaning and uses of the common notions in Greek mathematics, and argue that they were originally conceived in order to axiomatize a theory of equivalence in geometry. I also claim that two interpolated common notions responded to different epistemic needs and regulated diagrammatic inferences.
...More
Book
Berlinski, David;
(2013)
The King of Infinite Space: Euclid and His Elements
(/isis/citation/CBB001213232/)
Book
Suppes, Patrick;
Moravcsik, Julius M.;
Mendell, Henry;
(2000)
Ancient & Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr
(/isis/citation/CBB000101823/)
Article
Vitrac, Bernard;
Djebbar, Ahmed;
(2012)
Le Livre XIV des Éléments d'Euclide: versions grecques et arabes (seconde partie)
(/isis/citation/CBB001252980/)
Thesis
Welsh, Whitney Elizabeth;
(2011)
Unthinkable: Mathematics and the Rise of the West
(/isis/citation/CBB001560636/)
Article
Raymond, Dwayne;
(2011)
From a Particular Diagram to a Universal Result: Euclid's Elements, Book I
(/isis/citation/CBB001250013/)
Article
Edelheit, Amos;
(2009)
Francesco Patrizi's Two Books on Space: Geometry, Mathematics, and Dialectic beyond Aristotelian Science
(/isis/citation/CBB000932499/)
Article
Michalis Sialaros;
Jean Christianidis;
(2016)
Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra
(/isis/citation/CBB721594429/)
Thesis
Lacey, Duane J.;
(2007)
Euclid's Taxonomy of Irrationals
(/isis/citation/CBB001560851/)
Book
David S. Richeson;
(2019)
Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity
(/isis/citation/CBB243851906/)
Article
Harari, Orna;
(2003)
The Concept of Existence and the Role of Constructions in Euclid's Elements
(/isis/citation/CBB000300433/)
Article
Ladislav Kvasz;
(2020)
Cognitive Unity of Thales’ Mathematics
(/isis/citation/CBB542780608/)
Article
Wagner, Roy;
(2009)
For Some Histories of Greek Mathematics
(/isis/citation/CBB000932767/)
Article
Marcella Giulia Lorenzi;
Mauro Francaviglia;
(2010)
Dal cosmo al numero e alla geometria euclidea
(/isis/citation/CBB384645759/)
Article
Fabio Bellissima;
(2011)
L'antanairesi e la teoria armonica greca
(/isis/citation/CBB718056038/)
Article
Webster, Colin;
(2014)
Euclid's Optics and Geometrical Astronomy
(/isis/citation/CBB001451440/)
Book
Euclid, ;
Taisbak, Christian Marinus;
(2003)
Dedomena---Euclid's Data, or, The Importance of Being Given
(/isis/citation/CBB000301663/)
Book
Tóth, Imre;
(2010)
Fragmente und Spuren nichteuklidischer Geometrie bei Aristoteles
(/isis/citation/CBB001420976/)
Article
Krol, Z.;
(2007)
Introduction to Ancient Theories of Proportion
(/isis/citation/CBB000931652/)
Article
Vincenzo De Risi;
(2022)
Euclid’s Fourth Postulate: Its authenticity and significance for the foundations of Greek mathematics
(/isis/citation/CBB852153445/)
Article
Siebert, Harald;
(2014)
Transformation of Euclid's Optics in Late Antiquity
(/isis/citation/CBB001450115/)
Be the first to comment!