Lobachevsky (27 results)

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Taschenbuch. Condition: Neu. Neuware - Neither general relativity (which revealed that gravity is merely manifestation of the non-Euclidean geometry of spacetime) nor modern cosmology would have been possible without the almost simultaneous and independent discovery of non-Euclidean geometry in the 19th century by three great mathematicians - Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss (whose ideas were later further developed by Georg Friedrich Bernhard Riemann).This volume contains three works by Lobachevsky on the foundations of geometry and non-Euclidean geometry: 'Geometry', 'Geometrical investigations on the theory of parallel lines' and 'Pangeometry'. It will be of interest not only to experts and students in mathematics, physics, history and philosophy of science, but also to anyone who is not intimidated by the magnitude of one of the greatest discoveries of our civilization and would attempt to follow (and learn from) Lobachevsky's line of thought, helpfully illustrated by over 130 figures, that led him to the discovery.

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(25 x 16,5 cm). (2) 25 S. Original-Broschur, unbeschnitten. Seltener Rechenschaftsbericht mit einem Mitgliederverzeichnis. - Stempel auf Einband.

Volume one of the Neomonic Series. Small 8vo. viii, 40, 17 pp. Original printed wrappers, paper folder; cover lightly soiled. Burndy bookplate. Very good. Rare. Halsted was a member of the University of Texas at Austin Department of Pure and Applied Mathematics (1884-1903) where he taught noted mathematicians R. L. Moore and L. E. Dickson among other students. He explored the foundations of geometry and introduced Non-Euclidean geometry into the United States through his own work and his many important translations. "In a period when American mathematics had few distinguished names, the eccentric and sometimes spectacular Halsted established himself as an internationally known scholar, creative teacher, and promoter and popularize of mathematics. He was a member of and an active participant in the major mathematical societies of the United States, England, Italy, Spain, France, Germany, and Russia. His activities penetrated deeply in three main fields: translations and commentaries on the works of Nicolai Lobachevski, Janos Bolyai, Girolamo Saccheri, and Henri Poincare; studies in the foundations of geometry; and criticisms of the slipshod presentations of the mathematical textbooks of his day." [DSB]. DSB Vol. VI, pp. 76-77.

Couverture rigide. Condition: Très bon. Edition originale. Pleine toile verte moderne. Un volume in-8 (230x154 mm), (2)-132 pages et 9 planches. Dos légèrement passé. Premier édition en français de cet important ouvrage publié en Russe, entre 1835 et 1838, dans la revue des Mémoires scientifiques de Kazan. Lobachevsky est considéré (avec Bolyai) comme le fondateur de la géométrie non Euclidienne. C'est en 1826, qu'il présente pour la première fois ses concepts sur la géométrie non Euclidienne à l'université de Kazan. Cet article ne sera pas publié et il faudra attendre 1829-1830 pour que sa théorie soit pour la première fois publiée sous le titre "sur les fondations de la géométrie". Entre 1835 et 1838, il publie ses "Nouveaux principes de la géométrie avec une théorie complète des parallèles" en Russe qui est considérée comme étant sa meilleure publication sur la géométrie non Euclidienne. "It is from this memoir that one can draw the most completely information on the global scientific, worldoutlook and philosophical views of this great mathematician" (Popov). Rare première traduction en français de de texte majeur pour l'histoire des mathématiques. References : Popov ['Lobachevsky Geometry and Modern Nonlinear Problems', p.4 : "This is the largest work of N.I. Lobachevsky, which sums up in detail, and in the necessary cases develops, the results of his earlier work. It is from this memoir that one can draw the most completely information on the global scientific, worldoutlook and philosophical views of this great mathematician. In this work the fundamental notions of geometry are discussed in detail: adjacency, cuts and the definition of the notions of the notion of point connected with them, lines, surfaces, and also the basic theorems on perpendicular straight lines and planes, relations in triangles, linear and angular measures, measuring of areas, an others. Starting from more general fundamental premises (compared with earlier works), a theory of parallel straight lines is constructed in detail. The fundamental equations of the imaginary geometry are introduced. As a whole, in this work Lobachecsky establishes the precise axiomatic foundations of geometry and defines the principles of its logical development, accompanying them with the corresponding foundational results in each of the fields he considered"], Kline [p. 873 : "He presented his views on the foundations of geometry in a paper before the department of mathematics and physics of the University in 1826. However, the paper was never printed and was lost. He gave his approach to non-Euclidean geometry in a series of papers, the first two of which were published in Kazan journals. The first was entitled " On the Foundations of Geometry" and appeared in 1829-30. The second, entitled "New Foundations of Geometry with a Complete Theory ol Parallels" (1835-37), is a better presentation of Lobatchevsky's ideas"]. _________________________________________________________________________ __________ ______________________________ENGLISH_DESCRIPTION : Modern full green cloth. 8vo (230x154 mm), (2)-132 pages and 8 plates. Spine a little faded. First edition in french of this the "New Foundations of Geometry with a Complete Theory ol Parallels". References : Popov ['Lobachevsky Geometry and Modern Nonlinear Problems', p.4 : "This is the largest work of N.I. Lobachevsky, which sums up in detail, and in the necessary cases develops, the results of his earlier work. It is from this memoir that one can draw the most completely information on the global scientific, worldoutlook and philosophical views of this great mathematician. In this work the fundamental notions of geometry are discussed in detail: adjacency, cuts and the definition of the notions of the notion of point connected with them, lines, surfaces, and also the basic theorems on perpendicular straight lines and planes, relations in triangles, linear and angular measures, measuring of areas, an others. Starting from more general fundamental premises (compared with earlier works), a theory of parallel straight lines is constructed in detail. The fundamental equations of the imaginary geometry are introduced. As a whole, in this work Lobachecsky establishes the precise axiomatic foundations of geometry and defines the principles of its logical development, accompanying them with the corresponding foundational results in each of the fields he considered"], Kline [p. 873 : "He presented his views on the foundations of geometry in a paper before the department of mathematics and physics of the University in 1826. However, the paper was never printed and was lost. He gave his approach to non-Euclidean geometry in a series of papers, the first two of which were published in Kazan journals. The first was entitled " On the Foundations of Geometry" and appeared in 1829-30. The second, entitled "New Foundations of Geometry with a Complete Theory ol Parallels" (1835-37), is a better presentation of Lobatchevsky's ideas"]. 450g.

8vo. 134 pp., final blank leaf. Original printed wrappers with printed title enclosed in decorative border. First separate printing: exceptionally rare offprint of this important essay on the foundations of calculus and real analysis by the first inventor of non-Euclidean geometry. "As early as 1835, Lobachevsky showed in [this] memoir the necessity of distinguishing between continuity and differentiability" (Cajori). - Lobachevsky's works in other areas of mathematics were either directly relevant to his geometry (as his calculations on definite integrals and probable errors of observation) or results of his studies of foundations of mathematics (as his works on the theory of finites and the theory of trigonometric series). "The mathematicians of the 18th century did not touch the question of the relation between continuity and differentiability, presuming silently that every continuous function is eo ipso a function having a derivative. Ampère tried to prove this position, but his proof lacked cogency. The question about the relation between continuity and differentiability awoke general attention between 1870 and 1880, when Weierstrass gave an example of a function continuous within a certain interval and at the same time having no definite derivative within this interval (non-differentiable). Meanwhile, Lobachevski already in the thirties showed the necessity of distinguishing the 'changing gradually' (in our terminology: continuity) of a function and its 'unbrokenness' (now: differentiability). With especial precision did he formulate this difference in his Russian Memoir of 1835: 'A method for ascertaining the convergence, etc.'. A function changes gradually when its increment diminishes to zero together with the increment of the independent variable. A function is unbroken if the ratio of these two increments, as they diminish, goes over insensibly into a new function, which consequently will be a differential-coefficient. Integrals must always be so divided into intervals that the elements under each integral sign always change gradually and remain unbroken" (Halsted, p. 242). This work includes an extensive discussion of infinite series, including a new convergence criterion, now known as "Lobachevsky's test". Much space is also devoted in this memoir to definite integrals, prompted by the computation of areas and volumes in Lobachevskian geometry. One year later, Lobachevsky devoted a whole memoir to this subject. - Wrappers wrinkled; some damage to border on lower cover; spine and corners professionally restored with like paper. Chipped corners of title-page remargined; interior shows creasing with occasional light waterstains to margins. Exceptionally rare, as are all of Lobachevsky's Kazan publications, even in Russian collections: OCLC lists the Harvard copy only. - Cajori, History of Mathematics, S. 421. Halsted, "Biology and Mathematics", 12th Annual Report of the Ohio State Academy of Science (1903), S. 239-247. OCLC 84296869.

Soft cover. Condition: Very Good. 8vo. [26 x 16 cm), (51-) 83 pp., (the issue paginated 216 [2]). Bound in original printed wrappers, leaves uncut. Very rare first edition of a treatise on a total solar eclipse by Nicolai Lobachevsky, one of the Russian mathematicianżs few works to treat a subject other than non-Euclidean geometry. Lobachevsky observed the eclipse of 8 July 1842 (recorded in the volume as 26 June, using the Old Style calendar) and made minute records of its contact, path and duration. More importantly, he also attempted to explain the presence of the visible solar corona, an extremely rare phenomenon that remained a mystery to astronomers until the late 19th C. Nicolai Lobachevsky (1792-1856) studied under the German mathematician Martin Bartels at Kazan University, where, by age 28, he was appointed chair of the Department of Mathematics and Physics. He wrote his first major work, Geometriya, in 1823; by 1826 he had formulated the principle theorems of the groundbreaking non-Euclidean geometry, which paved the way for advancements in relativity theory and quantum physics. *Kagan 11. Not in DSB.

Soft cover. Condition: Very Good. 2 parts in one vol. 4to. [30.4 x 23 cm], 1-26 pp.; 27-34 pp., (the whole issue paginated [ii] 96 [2]); title with old stamp in Russian and shelfmark, crossed-through, some very faint marginal waterstaining, a very good copy in original printed wrappers, żUchenya Zapiski. 1852ż on front wrapper within an ornamental border, wrappers worn. Very rare first edition of Lobachevskyżs last work on analysis, a treatise on the values of certain defined integrals, along with an examination of the Gamma function. *Kagan 13; Engel 18. Not in DSB. For Lobachevskyżs biography, see the previous entry.

Hardcover. Condition: Very Good. 1st Edition. 2°. 61 p. Half leather, rubbed and somewhat worn. Interior partly foxed, last leaf very dusty (not affecting Lobachevsky's paper). Some creases to leaves. A library stamp and shelfmarks to title page. *** Published in a supplement to "Metereologische Beobachtungen aus dem Lehrbezirk der Kaiserlich. Russischen Universitaet Kasan". Here including the second paper published with it, "Allgemeine Bemerkungen ueber den Vortrag der Physik auf Gymnasien" by Ernst Knorr. *** Very rare.

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.

(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.

Kazan, 1834. 8vo. Contemporary blank, blue wrappers (original?). A closed tear and a bit of staining to back wrapper and some tears and scratches to spine. Internally very nice and clean. Presumably not an off-print, as there are stitching-holes to the margins, indicating that it has been removed from a volume, although the wrappers could look original, certainly contemporary. With the original title-page for Book 11 of the "Uchenye zapiski" + pp. (167)-226. Scarce first printing of Lobachavsky's main contribution to his second most important field (after non-Euclidean geometry), namely infinite series, more specifically trigonometric series. This constitutes one of Lobachevsky's earliest papers and the one in which he presents his new results in the theory of trigonometric series. It is here that he gives his definition of a function as a correspondence between two sets of real numbers, the same definition that Dirichlet some three years later discovers independently of Lobachevsky (and is given the general credit for). This important paper was published in the Scientific Memoirs of the Kazan University. "Some of Lobachevsky's early papers, too, were on such nongeometrical subjects as algebra and the theoretical aspects of infinite series. Thus, in 1834 he published his paper "Algebra ili ischislenie konechnykh" ("Algebra, or Calculus of Finites"), of which most had been composed as early as 1825. The first issue of the "Uchenye zapiski" ("Scientific Memoirs") of Kazan University, founded by Lobachevsky, likewise carried his article "Ob ischezanii trigonometricheskikh strok" ("On the Convergence of Trigonometrical Series"). The chief thrust of his scientific endeavor was, however, geometrical, and his later work was devoted exclusively to his new non-Euclidean geometry." (DSB).

Leipzig, B.G. Tuebner, 1898-99. Royal8vo. Uncut and unopened in original printed wrappers. Wrappers with some tears. Front wrapper loose. Lithographed portrait of Lobachevsky, XVI,236,(3),237-476 pp. First edition. Contains the first translation of Lobachevsky's seminal 1829 paper 'O Nachalakh Geometrii / On the Principles of Geometry' (see Sommerville Bibliography 1829).

Leather Bound. Condition: New. Language: Russian. {Size: 22.22x 29.21 cms} Presenting an Exquisite Leather-Bound Edition, expertly crafted with Original Natural Leather that gracefully adorns the spine and corners. The allure continues with Golden Leaf Printing that adds a touch of elegance, while Hand Embossing on the rounded spine lends an artistic flair. This masterpiece has been meticulously reprinted in 2024, utilizing the invaluable guidance of the original edition published many years ago in 1883. The contents of this book are presented in classic black and white. Its durability is ensured through a meticulous sewing binding technique, enhancing its longevity. Imprinted on top-tier quality paper. A team of professionals has expertly processed each page, delicately preserving its content without alteration. Due to the vintage nature of these books, every page has been manually restored for legibility. However, in certain instances, occasional blurriness, missing segments, or faint black spots might persist. We sincerely hope for your understanding of the challenges we faced with these books. Recognizing their significance for readers seeking insight into our historical treasure, we've diligently restored and reissued them. Our intention is to offer this valuable resource once again. We eagerly await your feedback, hoping that you'll find it appealing and will generously share your thoughts and recommendations. Lang: - Russian, Pages:- 570, Print on Demand. If it is a multi-volume set, then it is only a single volume. We are specialised in Customisation of books, if you wish to opt different color leather binding, you may contact us. This service is chargeable. Product Disclaimer: Kindly be informed that, owing to the inherent nature of leather as a natural material, minor discolorations or textural variations may be perceptible. Explore the FOLIO EDITION (12x19 Inches): Available Upon Request. [Please Note - Text break , Dust in Text] 570.

Full Leather Bound. Condition: NEW. Language: Russian. {Size: 22.22x 29.21 cms} A Unique Premium Leather-Bound book for elite readers/collectors of old rare books. An Original Leather is being used for binding this book with Golden Leaf Printing and designing on Spine, front and Back of the book with edge gilding. WE HAVE MULTIPLE OPTIONS IN COLOR OF LEATHER RED, GREEN, BLUE, MAGENTA, TAN, PURPLE DEEP BROWN, BLACK AND WITH DIFFERENT COLOR LABELS. YOU MAY CHOOSE ANY COLOR OF YOUR CHOICE AND MAIL US. This service is chargeable. Original edition was published in [1883] and this unique edition is Reprinted in 2024 with the help of original edition. Black & white printing on high quality natural shade paper with sewing binding for longer life, professionally processed without changing its contents. As these are old books, we processed each page manually on computer and make them readable. We give our best to give you the best book but in some cases we have to adjust few pages which are blur or missing or black spots. If it is multi volume set, then it is only single volume. We hope that you understand these issues in these old treasure. This is an important book for the readers who want to know more about our old treasure. Our dedicated team is trying to bring these rare books back to the shelves. We are also giving service of printing the hard-to-find books which are not listed in our store. Hope you will like it and give your comments and suggestions. Lang: - Russian, Pages 570, Print on Demand. Product Disclaimer: Please be aware that because leather is a natural material, slight discoloration or change in texture may be visible. {FOLIO EDITION (Size 12x19 Inches) IS ALSO AVAILABLE ON REQUEST}. [Please Note - Text break , Dust in Text] 570.