**EMS Heritage of European Mathematics**

Volume: 4;
2010;
322 pp;
Hardcover

MSC: Primary 01; 51; 53;
**Print ISBN: 978-3-03719-087-6
Product Code: EMSHEM/4**

List Price: $98.00

Individual Member Price: $78.40

# Nikolai I. Lobachevsky, Pangeometry

Share this page *Edited by *
*Athanase Papadopoulos*

Translated by Athanase Papadopoulos

A publication of the European Mathematical Society

Lobachevsky 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.

#### Table of Contents

# Table of Contents

## Nikolai I. Lobachevsky, Pangeometry

#### Readership

Graduate students and research mathematicians interested in non-Euclidean geometry and its applications.