Write to the booksellers- Home page
- Search by criteria
- author : lobachevsky lobachevskii lobacevskij lobatschewskij nikolai ivanovitsch
3 books for « lobachevsky lobachevs... »Edit
"LOBACHEVSKY (LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).
Reference : 60473
(1855)
Pangeometriya (i.e. Pangeometry). (In: ""Uchenye zapiski""). - [""THE MOST CONSEQUENTIAL AND REVOLUTIONARY STEP IN MATHEMATICS SINCE GREEK TIMES""]
Kazan, Kazan University Press, 1855-56. 4to (263 x 216 mm). In a nice later half calf binding with four raised bands and marbled paper covered boards. Extracted from ""Uchenye zapiski, Imperatorskago Kazanskago Universiteta"", 1855, vol. 1. Two library-stamps to p. 51 with offsetting to p. 50 and small stamp to last free end-paper. With very light creasing to outer margin, otherwise a fine and clean copy. 56 pp.
Exceedingly rare first appearance of Lobachevsky’s landmark 'Pangeometry', a seminal work that serves as a synthesis of his exploration into non-Euclidean geometry and its practical applications and is widely considered his clearest account of the subject. It is also the conclusion of his life's work and the last and final attempt he made to acquire recognition. Lobachevsky's contributions not only marked a turning point in mathematical thought, but were also a catalyst for profound shifts in physics, and philosophy as they expanded the boundaries of human understanding, challenging 2000 year old conventional wisdom"" consequently, he is often referred to as ""The Copernicus of Geometry"". Lobachevsky wrote his Pangeometry in 1855, the year before his death, at a time when he was completely blind. He dictated two versions, a first one in Russian (the present), and a second in French. Despite his revolutionary work, Lobachevsky’s received little, if any, attention from the scientific community. One reason for this was that his works were published in very small numbers in relatively obscure journals – they seem to have had minimal circulation even within Russia. The present treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. “Lobachevskii’s geometry represents the culmination of two thousand years of criticism of Euclid’s fifth, or parallel, postulate, which states that given a line and a point not on the line, there can be drawn through the point one and only one coplanar line not intersecting the given line. As this postulate had stubbornly resisted all attempts (including Lobachevskii’s) to prove it as a theorem, Lobachevskii came to the realization that it was possible to construct a logically consistent geometry in which the Euclidean postulate represented a special case of a more general system that allowed for the possibility of hyperbolically curved space. Lobachevskii’s system refuted the unique applicability of Euclidean geometry to the real world, and pointed the way to the Einsteinian concept of variably curved space” (Norman 1379.). “At the same time as Lobachevsky, other geometers were making similar discoveries. Gauss had arrived at an idea of non-Euclidean geometry in the last years of the eighteenth century and had for several decades continued to study the problems that such an idea presented. He never published his results, however, and these became known only after his death and the publication of his correspondence. Janos Bolyai, the son of Gauss’s university comrade Farkas Bolyai, hit upon Lobachevskian geometry at a slightly later date than Lobachevsky. Since Gauss did not publish his work on the subject, and since Bolyai published only at a later date, Lobachevsky clearly holds priority.” DSB. Lobachevsky's non-Euclidean geometry paved the way for further advancements in mathematics, including the development of differential geometry and the study of Riemannian manifolds. These areas of mathematics have found applications in fields as diverse as physics, engineering, and computer science. Furthermore, his work laid the groundwork for Albert Einstein's theory of general relativity, which relies on the concept of curved spacetime. It showed that there is no single ""correct"" geometry, but rather multiple valid systems. This led to a broader understanding of the nature of axiomatic systems and their relation to reality - implications that extend well beyond the realm of mathematics, shaping our understanding of space, reality, and the limits of human knowledge.
"LOBATSCHEVSKY (LOBACHEVSKY, LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).
Reference : 60236
(1841)
Ueber die Convergenz der uendlichen Reihen (i.e. English: ""On the Convergence of Infinite Series"").
(Kazan, Universitäts-Buchdruckerei, 1841). 4to. In a contemporary modest half calf over marbled paper boards. Published in a supplement to ""Meteorologische Beobachtungen aus dem Lehrbezirk der Kaiserlich. Russischen Universitaet Kasan"". Heft 1, 1835–1836. 1841. Small stamp to upper outer corner of front free end-paper. A few leaves brownspotted. Book block split between pp. 4 and 5, otherwise a fine copy. 48 pp.
Exceedingly rare first appearance of this work by Lobachevsky in which he returns to convergence of infinite series, on the foundations of calculus and real analysis, which he previous had dealt with in his 1834-textbook Algerbra and his 1834-paper ‘Ob ischezanii trigonometricheskikh strok’. Here, he expands and further develops the modern definition of the idea of a function in the works of Dirichlet, Poisson, and himself, adding and supplying more proofs. Primarily famous for his non-Euclidean geometry, Lobachevsky published a few papers on such nongeometrical subjects as algebra and the theoretical aspects of infinite series. The chief thrust of his scientific endeavor was, however, geometrical, and his later work was devoted exclusively to his new non-Euclidean geometry, the present work being one of his last on algebra and infinite series.
"LOBATSCHEVSKY (LOBACHEVSKY, LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).
Reference : 40401
(1842)
Probabilité des résultats moyens tirés d'observations répétées. - [THE FIRST PRINTING OF ANY PART OF HIS ""GEOMETRIYA""]
Berlin, G. reimer, 1842. 4to. No wrappers. In: Crelle's ""Journal für die reine und angewandte Mathematik."", 24. Band, zweites Heft., Titlepage to Zweites Heft and pp. 93-188 and 3 plates. Lobatschewsky's paper pp. 164-170.
First edition and THE FIRST PRINTING of any part of Lobatschefskij's FIRST MAJOR work on geometry, as it is his own translation of the last to chapters of his ""Geometriya"" from 1823, a work which was never published in his lifetime. In its original form the ""Geometriya"" was published in 1909. - The geometrical studies which it contains, led Lobatschewski to his main discovery, the Non-Euclidean Geometry , published in Russian in Kazan 1829, and in it he developes the idea of geometry independent of the fifth postulate. The last two chapters of the unpublished work is offered here, and the chapters deals with the solution of triangles, on given measurements, and on probable errors in calculation, deaply connected to his attempts to establish experimentally what sort of geometry obtains in the real world. - ""The period 1835 to 1838 saw him concerned with writing ""Novye nachalaa geometrii s polnoi teoriei parallellnykh"" (New Principles of Geometry with a Complete Theory of Parallels), which incorporated a version of his first work,the still unpublished ""Geometriya"". The last two chapters of the book were abbriviated and translated for publication in Crelle's Journal in 1842."" (DSB).""Lobachevsky was interested in the theory of parallels from at least 1815. Lecture notes of the period 1815-17 are ectant, in which Lobachevsky attempts various waus to establish the Euclidean theory. he proves Legendre's two propositions, and employs also the ideas of direction and infinite areas. In 1823 he prepared a treatise on geometry for use at the university, but it obtained so unfavourable a report that it was not printed. The MS. remained buried in the University archives until it was discovered and printed in 1909. In this book he states that ""a rigorous proof of the postulate of Euclid has nit hitherto been discovered"" those which have been given may be called explanations, and do not deserve to be considered as mathematical proofs in the full sense.""(Sommerville: The Elements of Non-Euclidean geometry. 1914).
