Article ID: CBB000932085

Grasping the Conceptual Difference between János Bolyai and Lobachevskii's Notions of Non-Euclidean Parallelism (2009)

unapi

Abstract The paper examines the difference between János Bolyai's and Lobachevskii's notion of non-Euclidean parallelism. The examination starts with the summary of a widespread view of historians of mathematics on János Bolyai's notion of non-Euclidean parallelism used in the first paragraph of his Appendix. After this a novel position of the location and meaning of Bolyai's term parallela in his Appendix is put forward. After that János Bolyai's Hungarian manuscript, the Commentary on Lobachevskii's Geometrische Untersuchungen is elaborated in order to see how Bolyai and Lobachevskii's notions of parallelism differ. The careful examination of the Commentary reveals a seeming incoherence of Bolyai's translation, and finally the explanation of this incoherence offered by the Received View and that of the novel position will be compared and assessed.

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https://data.isiscb.org/isis/citation/CBB000932085/

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Authors & Contributors
Abardia, Judit
Boskoffb, Wladimir G.
Braver, Seth Philip
Carter, Jessica
Cerroni, Cinzia
Christiansen, Andreas
Journals
Historia Mathematica
Osmanli Bilimi Arastirmalari: Studies in Ottoman Science
VIET: Voprosy Istorii Estestvoznaniia i Tekhniki
British Society for the History of Mathematics Bulletin
Cultura e Scuola
Historia Scientiarum: International Journal of the History of Science Society of Japan
Publishers
Carocci Editore
Guaraldi
Lang
The MIT Press
University of Montana
Concepts
Non-euclidean geometry
Mathematics
Geometry
Textbooks
Physics
Philosophy of mathematics
People
Lobachevskii, Nikolai Ivanovich
Poincaré, Jules Henri
Ekinci, Salih Zeki
Gauss, Carl Friedrich
Bolyai, Janos (Johann) von
Abel, Niels Henrik
Time Periods
19th century
20th century, early
20th century
Places
Europe
Italy
Norway
Turkey
United States
Romania
Institutions
Istanbul Darülfünunu
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