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"The first book wholly devoted to projective geometry,"

PONCELET, Jean-Victor. Traité des propriétés projectives des figures. Ouvrage utile à ceux qui s'occupent de la géométrie descriptive et d'opérations géométriques sur le terrain. 

Paris, Gauthier-Villars, 1865-1966.

Deux volumes in quarto (268 x213 mm), xxxii-428 pages et 12 planches / viii-452 pages et 6 planches.  reliure : Demi chagrin vert de l'époque, plats en percaline verte. Médaillon doré au centre des plats du Collège de Cognac. Petite déchirure à une planche. Reliures frottées, coiffes supérieures abîmées/.

Seconde édition largement augmentée d'un volume par Poncelet du premier ouvrage entièrement consacré à la géométrie projective. (DSB).

références: DSB [XI, p. 79/80 : "the 'Traité des propriétés projectives des figures' (...) was the first book wholly devoted to projective geometry, a new discipline that was to experience wide success during the nineteenth century. In this domain Poncelet considered himself the successor to Desargues, Blaise Pascal and Maclaurin and the continuator of the work of Monge and his disciples. (...) . The distinction Poncelet made between projective and metric properties prefigures the appearance of the modern concept of structure. Among the many original results presented in the ' Traité ' are those stating that in complex projective space two non-degenerate conics are of the same nature and have four common points (a finding that led to the discovery of cyclic points, imaginary points at infinity common to all the circles of a plane), and that all quadrics possess (real or imaginary) systems of generatrices. The decisive influence that ' Traité des propriétés projectives des figures ' exercised on the development of projective geometry - an influence underestimated by Chasles, Poncelet's direct rival - is brought to light by most commentators, particularly by E. Kotter, who made the most complete analysis of it, but also by A. Schoenflies and A. Tresse, J.L. Coolidge, C.B. Boyer, N. Bourbaki and others (...). Poncelet's geometric work marks the first major step toward the elaboration of the fundamental theories of modern geometry"].

Prix : 600 €

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