By L. Boi, D. Flament, Jean-Michel Salanskis
Within the first 1/2 the nineteenth century geometry replaced extensively, and withina century it helped to revolutionizeboth arithmetic and physics. It additionally placed the epistemologyand the philosophy of technology on a brand new footing. In thisvolume a valid review of this improvement is given byleading mathematicians, physicists, philosophers, andhistorians of technology. This interdisciplinary strategy givesthis assortment a distinct personality. it may be used byscientists and scholars, however it additionally addresses a generalreadership.
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Extra resources for Century of Geometry, 1830-1930: Epistemology, History, and Mathematics
Wangerin, Leipzig 1900. ] Theoria residuorum biquadraticorum, Comment. secund. GJttingische gelehrte Anzeigen. Werke 2 (1863), 169-178. [Gray, Jeremy J. ] 1dens of Space. Euclidean, Non-Euclidean and Relativistic. Oxford: Clarendon. 21989. [Gray, Jeremy J. ] Algebraic geometry in the late nineteeth century. In [Rowe/McCleary 1989, 361-388]. ] 0ber philosophisches Studium. Werke 2, 227-296. ] Psychologie als Wissenschaft, Zweiter analvtischer Theil. Werke 6, 1-339. ] Siimtliche Werke in chronologischer Reihenfolge.
Dans la G~om~trie euclidienne ce troupe se r~duit ~. des rotations et ~t des translations. " This might seem to be the Kleinian view, but I think it is not. There is no mention of projective geometry here, the description is naively metrical. Rather, what is described agrees in spirit with what Beltrami had written, and since that had been published in France in Hou~l's translation it is surely a much more likely source for Poincar~, who was not a well-read mathematician. This impression is supported by the way in which Poincar~, like Beltrami, referred to Lobachevskii but not Bolyai.
The relevant context is the other major change in the 19th century study of geometry, the study of projective geometry. The obvious fact about transformations in projective geometry is that such transformations are obtrusive. That is to say, their use obtrudes or forces itself onto one's awareness in a way that Euclidean ones do not. It is my view that at least in the early work of Poncelet and Chasles the subject was conceived of as the study of projective transformations of Euclidean figures.
Century of Geometry, 1830-1930: Epistemology, History, and Mathematics by L. Boi, D. Flament, Jean-Michel Salanskis