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Pangeometria, pp. 273-350 in: Giornale di Matematiche, Vol. V
Verlag: Naples: Benedetto Pellerano, 1867
Anbieter: Landmarks of Science Books, Richmond, Vereinigtes Königreich
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Soft cover. Zustand: Very Good. 1st Edition. First edition in Italian, translated by Giuseppe Battaglini, complete journal volume in original printed wrappers, of Lobachevsky's final work on non-Euclidean geometry, first published in Kazan in 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 about 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. "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 all of Euclid's axioms except the fifth postulate hold true is not in itself contradictory. He called such a system imaginary geometry, proceeding from an analogy with imaginary numbers. If imaginary numbers are the most general numbers for which the laws of arithmetic of real numbers prove justifiable, then imaginary geometry is the most general geometrical system. It was Lobachevsky's merit to refute the uniqueness of Euclid's geometry and to consider it a special case of a more general system" (B.A. Rosenfeld in DSB). 4to, pp. [ii], 382 (pp. 381-382, index, misbound at beginning). Original printed wrappers, unopened (spine rubbed with loss at ends).
