TY  - BOOK
AU  - Papadopoulos,Athanase
AU  - Papadopoulos,Athanase
TI  - Nikolai I. Lobachevsky, Pangeometry
T2  - Heritage of European Mathematics (HEM)
SN  - 9783037195871
PY  - 2010///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - History of mathematics
KW  - bicssc
KW  - History and biography
KW  - msc
KW  - Geometry
KW  - Differential geometry
N1  - Restricted to subscribers
N2  - Lobachevsky wrote his Pangeometry in 1855, the year before his death. This memoir is a résumé of his work on non-Euclidean geometry and its applications, and it can be considered as his clearest account on the subject. It is also the conclusion of his lifework, 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 source book and as a repository of inspiration.  The present edition provides the first complete English translation of the Pangeometry that appears 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
UR  - https://doi.org/10.4171/087
UR  - http://www.ems-ph.org/img/books/lobachevsky_mini.jpg
ER  -