Études géométriques sur la théorie des parallèles. Traduit de l'allemand par J. Hoüel ...; suivi d'un extrait de la correspondence de Gauss et de Schumacher.

Paris/Bordeaux: Gauthier-Villars/Gounouilhou, 1866.

First edition of the French translation of Lobachevsky’s Geometrische Untersuchungen zur Theorie der Parallellinien (1840), which was principally responsible for the acceptance and dissemination of non-Euclidean geometry in Western Europe.


A fine copy, in wrappers, of the rare separate printing of the first translation of Lobachewsky’s ‘Geometrische Untersuchungen zur Theorie der Parallellinien’ (Dibner 115) which was originally published in Berlin 1840 (see Grattan-Guinness: Landmark Writings in Western Mathematics, p.520 - were the later journal printing is sited; Mémoires de la Société des Sciences Physiques et Naturelles de Bordeaux, vol. 4 ,1867, pp.83-128 and Sommerville: Bibliography of Non-Euclidean Geometry, p.29). This translation by Guillaume-Jules Hoüel (1823-1886) played an important role in the acceptance of Lobachewsky’s non-Euclidean geometry; “Hoüel’s reputation rests primarily on the quality and quantity of his activities in mathematical exposition. His gift for languages was used to evaluate and frequently to expound or translate important foreign mathematical writings. ... Of great importance were his successful efforts to overcome the long-standing failure of mathematicians to appreciate the significance of non-Euclidean geometry. Led by his own research to doubt the necessity of the parallel postulate and by Richard Baltzer to the writings of Lobachevski, Hoüel published in 1866 a translation of one of the latter’s essays along with excerpts from the Gauss-Schumacher correspondence. By 1870 he had published translations of the classic writings in this area of János Bolyai, Beltrami, Helmholtz, and Riemann as well as his own proof of the impossibility of proving the parallel postulate” (D.S.B. VI: 522). “The cause of Lobachevskian geometry was, however, furthered by Hoüel, one of its earliest proponents, who in 1866 brought out a French translation of Geometrische Untersuchungen, with appended extracts from the Gauss-Schumacher correspondence. The following year he also published Bolyai’s appendix on non-Euclidean geometry, which was translated into Italian by Battaglini in 1867. Hoüel’s own Notices sur la vie et les travaux de N. I Lobachevsky appeared in 1870. In the meantime, Lobachevsky’s Geometrische Untersuchungen had been translated into Russian by A. V. Letnikov; it was published in 1868 in the newly founded Moscow magazine Matematichesky sbornik” (D.S.B. VIII: 433). In Sotheran’s catalogue no. 770 from 1918 this separate printing is noted to be “scarce”.

8vo: 252 x 165 mm. Original printed wrappers, spine strip professionally repaired, some light smudging to wrappers, small corner missing, with the signature of "Ch. Pérez" to the front wrapper [French naturalist Prof. Charles Pérez, 1873 Bordeaux -1952 Paris?]. pp. (2:blank), (2:title), IV, 42, (2:blank). Illustrated with numerous white-in-black woodcuts throughout the text. Pages 35-42 constitute the correspondence of six letters between Gauss and Schumacher dated 1831-1846.

Item #2319

Price: $4,850.00