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Article ID: CBB000932085

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

Tanács, János (Author)

Archive for History of Exact Sciences
Volume: 63
Pages: 537--552

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Non-euclidean geometry Mathematics 19th century Lobachevskii, Nikolai Ivanovich Bolyai, Janos (Johann) von

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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