‎"LOBATSCHEVSKY (LOBACHEVSKY, LOBACHEVSKII, LOBACEVSKIJ, LOBATSCHEWSKIJ), (NIKOLAI IVANOVITSCH).‎
‎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.‎

Reference : 40401

‎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 The last two chapters of the unpublished work is offered here, and the chapters deals with the solution of triangles, on given measurements, and on probable errors in calculation, deaply connected to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Principles of Geometry with a Complete Theory of Parallels), which incorporated a version of his first work,the still unpublished ""Geometriya"".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).‎