The founding text of non-Euclidian geometry
Rare first edition of this founding text of non-Euclidian geometry.
PMM, 293.
LOBACHEVSKI, Nicolai Ivanovitch. Geometrische Untersuchungen zur Theorie der Parallellinien.
Berlin, G. Fincke, 1840.
8vo [188 x 113 mm], (1) title-page, 61 pp., (1) p., 2 folding plates. Some foxing. Preserved in its original green printed wrappers, lower cover renewed.
Very scarce first edition of this founding text of non-Euclidian geometry.
PMM 293; Poggendorff I, 1482; Engel 13; DSB VIII, 432 f.; Norman I, 1379.
« 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 work in their original language, and supported his election to the Göttingen Gesellschaft der Wissenschaften” (DSB).
« The revolution in our conception of the nature of mathematics can be traced back to the explicit formulation of the first non-Euclidian geometries early in the nineteenth century.
The researches that culminated in the discovery of non-Euclidean geometry arose from unsuccessful attempts to prove the axiom of parallels in Euclidean geometry. This postulate asserts that through any point there can be drawn one and only one straight line parallel to a given straight line. Although this statement was not regarded as self-evident and its derivation from the other axioms of geometry was repeatedly sought, no one openly challenged it as an accepted truth of the universe until Lobatchewsky published the first non-Euclidean geometry […]. In Lobatchewsky’s geometry an infinity of parallels can be drawn through a given point that never intersect a given straight line.
Nicolai Ivanovitch Lobatchewsky was born in Nizhni-Novgorod, Russia, and studied at the University of Kazan, where in 1827 he was appointed professor. His fundamental paper was read to his colleagues in Kazan in 1826 but he did not publish the results until 1829-30 when a series of five papers appeared in the Kazan University Courier, the first of which bore the title cited above, ‘The Origins of Geometry’. He amplified his findings (still in Russian) in 1836-8 under the title ‘New Elements of Geometry, with a Complete Theory of Parallels’. In 1840 he published a brief summary in Berlin under the title Geometrische Untersuchungen zur Theorie der Parallellinien”. (PMM).
The present work is the earliest obtainable book-edition presenting the new geometry.
It is illustrated with 2 folding plates of geometrical figures.
The present copy is preserved in its original green printed wrappers.
ABPC doesn’t list any copy of this work.
Part of Lobachevski’s memoir printed in 1829-1830 by the Kazan University was sold by Christie’s New York on the 29th of October 1998 for 405 000 $ (about 2 200 000 F at the time).
Price: € 35 000
