Krol, Z. (Author)
The article is treating of a new interpretation of ancient geometry (part I) and is willing to explain several mathematical and historical conceptions that were presented in Pappus' 'Comment on the Xth Book of 'Elements' of Euclid' (part II). Euclid's 'Elements' were a kind of 'intuitive model', quite different from the contemporary one, divested of the 'infinite space' notion. Reconstruction of the hermeneutic horizon of the ancient mathematics allows us to explain the structure and mathematics presented in the columns of the Xth book of 'Elements'. The following subjects were handled: (1) reasons for elimination of the Euclid's 'infinite space' notion and substituting it for Plato's Diad in ancient times, (2) basing geometry and searches over the incommensurable magnitudes on one distinguished line together with mathematical consequences, (3) differences in the way of thinking of ancient and contemporary mathematician. Scientific studies allow to qualify from the historical point of view the share in development of the incommensurable magnitudes theories presented by Theaetetus of Athens, Apollonius of Perga, Euclid and Eudoxus. In the article a reconstruction of the mathematical contents of the lost Apollonius' treatise on incommensurable magnitudes is also presented A traditionally established pattern of the development of geometry, according to which Euclidean geometry used to extend as theory basing on relatively unalterable outfit of the fundamental intuition as, for instance, Euclid's infinite space, continuum intuitions and metric intuitions (what is important, the first revolutionary change was a discovery of non Euclidean geometry in the 19th century) cannot be sustained.
...More
Book
Sefrin-Weis, Heike;
(2010)
Pappus of Alexandria: Book 4 of the Collection
(/isis/citation/CBB001024842/)
Thesis
Stevens, Paul Anthony;
(2008)
Mathematics and Dialectic in Plato's “Theaetetus”
(/isis/citation/CBB001560568/)
Book
Jaap Mansfeld;
(1998)
Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism with an Appendix on Pappus and the History of Platonism
(/isis/citation/CBB015172971/)
Article
Geymonat, Mario;
(2009)
Arithmetic and Geometry in Ancient Rome: Surveyors, Intellectuals, and Poets
(/isis/citation/CBB000933728/)
Article
Solere, Jean-Luc;
(2003)
L'ordre axiomatique comme modèle d'écriture philosophique dans l'Antiquité et au Moyen Age
(/isis/citation/CBB000770963/)
Article
Nathan Sidoli;
(2018)
The Concept of Given in Greek Mathematics
(/isis/citation/CBB871621734/)
Book
Fried, Michael N.;
(2011)
Edmond Halley's Reconstruction of the Lost Book of Apollonius's Conics: Translation and Commentary
(/isis/citation/CBB001024500/)
Book
Apollonius of Perga, ;
Rashed, Roshdi;
Bellosta, Hélène;
(2010)
La section des droites selon de rapports
(/isis/citation/CBB001220540/)
Article
Fried, Michael;
(2003)
The Use of Analogy in Book VII of Apollonius' Conica
(/isis/citation/CBB000740736/)
Thesis
McKinney, Colin Bryan Powell;
(2010)
Conjugate Diameters: Apollonius of Perga and Eutocius of Ascalon
(/isis/citation/CBB001560832/)
Article
Nikolantonakis, Konstantinos;
(2007)
The Treatise “On the Section of a Cylinder” of Serenus of Antinoeia and the Apollonian Tradition
(/isis/citation/CBB000933151/)
Book
Apollonius, ;
(2002)
Apollonius's Conics Book IV
(/isis/citation/CBB000203100/)
Book
Giuseppe Cambiano;
(2006)
Figure, macchine, sogni. Saggi sulla scienza antica
(/isis/citation/CBB013124835/)
Article
Fabio Bellissima;
(2011)
L'antanairesi e la teoria armonica greca
(/isis/citation/CBB718056038/)
Article
Siebert, Harald;
(2014)
Transformation of Euclid's Optics in Late Antiquity
(/isis/citation/CBB001450115/)
Article
Vitrac, Bernard;
(2003)
Les scholies grecques aux Éléments d'Euclide
(/isis/citation/CBB000770961/)
Thesis
Lacey, Duane J.;
(2007)
Euclid's Taxonomy of Irrationals
(/isis/citation/CBB001560851/)
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/)
Be the first to comment!