Paris: Bachelier, 1852. First edition, author’s presentation copy, of “his treatise on higher geometry ... [which] gave him a world-wide reputation” (Smith). Chasles “developed the theory and showed that the use of sensed magnitudes and imaginary elements gives to geometry the freedom and power of analysis” (DSB).
Author’s presentation copy, of “his treatise on higher geometry...[which] gave him a world-wide reputation” (Smith, History, Vol. 1, p. 498).
“In 1846 a chair of higher geometry was created for Chasles at the Sorbonne and he remained there until his death... He published highly original work... His work was marked by its unity of purpose and method. The purpose was to show not only that geometry, by which he meant synthetic geometry, had methods as powerful and fertile for the discovery and demonstration of mathematical truths as those of algebraic analysis, but that these methods had an important advantage, in that they showed more clearly the origin and connections of these truths. The methods were those introduced by L. Carnot, G. Monge and V. Poncelet and included a systematic use of sensed magnitudes, imaginary elements, the principle of duality and transformations of figures... Chales wrote two textbooks for his course at the Sorbonne. The first of these, the Traité de géométrie supérieure is based on the elementary theories of the cross ratio, homographic ranges and pencils and involution... In the case of the cross ratio, which Chasles called the anharmonic ratio, he was anticipated by A. Moebius. However, it was Chasles who developed the theory and showed that the use of sensed magnitudes and imaginary elements gives to geometry the freedom and power of analysis” (DSB III, pp. 212-4).
Chasles (1793-1880) studied under Poisson at the Ecole Polytechnique. On the basis of his Aperçu historique sur l'origine et le développement des méthodes en géométrie (1837) he was made a professor at the Ecole Polytechnique, and was awarded a chair at the Sorbonne in 1846. The present work enjoyed considerable success, a second edition appearing in 1880.
Provenance: Signed presentation inscription from the author to R.G. Latham to head of portion of original wrappers on front pastedown. Robert Gordon Latham FRS (1812-88) was a philologist, ethnologist, and curator of the ethnological department at The Crystal Palace.
8vo (213 x 135 mm), pp  lxxxiii [1:blank] 603 [1:blank] and 12 lithographed folding plates, contemporary half morocco, some very light foxing to first gathering and plates.