Paris: Gauthier-Villars, 1866.
1st Edition. Soft cover. Very Good. Item #003395
8vo (246 x 165 mm). , iv, 42 pp. White-on-black-ground woodcut diagrams in text. Original printed wrappers (dog-earing of outer corners, spine reinforced with paper, upper spine chipped, light spotting. Text little age-toned, but generally bright and clean internally. Provenance: Giancarlo Beltrame Library. ----
DSB VIII, p.429-34; Dibner 115 (first edition). RARE FIRST SEPARATE EDITION IN FRENCH of Lobachevsky's "Geometrische Untersuchungen zur Theorie der Parallellinien", first published in Berlin in 1840. Lobachevsky's epoch-making discovery of non-Euclidean geometry was published first in Russian in a series of papers in the Kazan University Courier 1829-30. "Lobachevsky's work was little heralded during his lifetime. M. V. Ostrogradsky, the most famous mathematician of the St. Petersburg Academy, for one, did not understand Lobachevsky's achievement, and published an uncomplimentary review of 'O nachalakh geometrii'; the magazine Syn otechestva soon followed his lead, and in 1834 issued a pamphlet ridiculing Lobachevsky's paper. Although Gauss, who had received a copy of the Geometrische Untersuchungen from Lobachevsky, spoke to him flatteringly of the book, studied Russian especially to read his works in their original language, and supported his election to the Göttingen Gesellschaft der Wissenschaften, he never publicly commented on Lobachevsky's discovery. His views on the new geometry became clear only after the publication, in 1860-1865, of his correspondence with H. C. Schumacher. Following this, in 1865, the English algebraist Cayley ... brought out his 'A Note Upon Lobachevsky's Imaginary Geometry' from which it is evident that he also failed to understand Lobachevsky's work. 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." (DSB VIII, p.433). "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. In the theory of complex numbers Hoüel introduced many of his countrymen to the researches of William R. Hamilton, Hermann Grassmann, Giusto Bellavitis, and Bernhard Riemann through his Théorie élémentaire des quantités complexes and other writings. Of greater 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. Hoüel also compiled logarithmic tables, worked on planetary perturbation theory, was an editor of the Bulletin des sciences mathématiques et astronomiques, and wrote a major text in analysis, Cours de calcul infinitéstimal." (DSB VI, p.522). - Visit our website to see more images!
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