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2020-10-06 03:41:02
LOBACHEVSKY, Nikolai Ivanovich
Pangeometrie, oder die auf einer allgemeinen und strengen Theorie der Parallelen gegründeten Hauptsätze der Geometrie,' pp. 397-456 in: 'Archiv für wissenschaftliche Kunde von Russland, Vol. 17, no. 3
Berlin: Georg Reimer, 1858. First German edition of Lobachevsky s last publication on non-Euclidean geometry (first published in Kazan 1856). The work was dictated by Lobachevsky, who was by then blind, in French, the previous year, for the commemoration proceedings planned for February 1855, but publication was delayed by the Tsar over a disagreement over the date of the University s founding. In the meantime, the Russian version was prepared and published, more or less simultaneously with the French. This German edition is little known: it is not mentioned in Friedrich Engel s Zwei geometrische Abhandlungen (1898) and Heinrich Liebmann claims in his own German translation (1902) that it is the first. With the title 'Pangeometrie' Lobachevsky emphasizes the universality of his imaginary geometry and gives his most concise formulation of a geometry free of the parallel postulate. In this work Lobachevsky applies differential and integral calculus to non-Euclidean geometry and develops important refinements of his earlier works. "Numerous deductions, notably that of the fundamental equation of hyperbolic geometry, are given in other forms: until his last days, despite his precarious health, Lobachevsky sought to perfect the geometry he had constructed" (Kagan). The work ends with Lobachevsky discussing the geometry of nature and the necessity of experimentally determining if space is in fact non-Euclidean. "In his early lectures on geometry, Lobachevsky himself attempted to prove the fifth postulate; his own geometry is derived from his later insight that a geometry in which … [Click Below for Full Description]
Bookseller: Landmarks of Science Books [Richmond, United Kingdom]
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