Lobachevsky N.I. Pangeometry

Edited and translated by Athanase Papadopoulos. — European Mathematical Society Publishing House, 2010. — 323 p. — (Heritage of European Mathematics). — ISBN: 978-3-03719-087-6Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The 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. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.Foreword
On the present edition
Pangeometry
English translation
French original from 1856
Russian original from 1855
Lobachevsky's biography
Preface to Lobachevsky’s 1886 biography
Lobachevsky’s biography (1886)
A commentary on Lobachevsky’'s PangeometryOn the content of Lobachevsky’s Pangeometry
On hyperbolic geometry and its reception
On models, and on model-free hyperbolic geometry
A short list of references
Some milestones for Lobachevsky’s works on geometry