Einfurung in die Grundlagen der Geometrie. Erster (und Zweiter) Band.
1893·Munster, Osnabruck & Mainz:
by KILLING, Wilhelm Karl Joseph (1847-1923).
Munster, Osnabruck & Mainz:: Ferdinand Schoningh, 1893, 1898., 1893. Two works in one volume. 8vo. x, 357, ; vi, 361,  pp. 48 figures, bibliographies. Offsetting to title, German bookseller’s ticket inside front cover. Contemporary quarter dark green pebbled cloth over green marbled boards, gilt-ruled and stamped spine, cloth tips. Fine. RARE. First edition of the author's monumental work in geometry and non-Euclidean geometry of n-dimensions. In 1900 Killing was the second recipient of the Lobachevsky prize, awarded by the Kazan Physical and Mathematical Society. / "On Weierstrass's recommendation Killing was appointed to a chair of mathematics at the Lyceum Hosianum in Braunsberg in 1882. Killing spent ten years in Braunsberg, isolated mathematically, but during this period he produced some of the most original mathematics ever produced. Lie algebras were introduced by Lie in about 1870 in his work on differential equations. Killing introduced them independently with quite a different purpose since his interest was in non-euclidean geometry. The classification of the semisimple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research. The main tools in the classification of the semisimple Lie algebras are Cartan subalgebras and the Cartan matrix both first introduced by Killing. He also introduced the idea of a root system which appears throughout much of the algebra of today. Let us now examine in more detail how Killing's ideas on the classification developed." – J. J. O'Connor and E. F. Robertson. / Wilhelm Killing introduced Lie algebras independently of Lie in his study of non-Euclidean geometry. The classification of the simple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research. He received his doctorate and had been trained to become a Gymnasium teacher of mathematics and physics, teaching at schools in Berlin. Killing’s first publication was in 1879, and was followed by several others on the topic of non-Euclidean geometry in n-dimensions. He was appointed the chair of mathematics at the Lyceum Hosianum in Braunsberg in 1882, spending ten years there during which he produced some of the most original mathematics ever done. Killing was awarded the Lobachevsky Prize in 1900; his award was the second ever made, the first having been presented to Lie. [GAP] / GAP-System.org website; St. Andrews University, School of Mathematics; Duncan M'Laren Young Sommerville, An introduction to the geometry of n dimensions, 1929. See also: Sommerville, The Elements of Non-Euclidean Geometry. Chicago, 1919.
(Inventory #: S13403)
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