LEADER 02885nam 22005415a 450 001 9910153614903321 005 2010-12-01 010 $a3-03719-587-8 024 7 $a10.4171/087 035 $a(CKB)3710000000962492 035 $a(CH-001817-3)123-101201 035 $a(PPN)178155853 035 $a(DE-4084)10.4171/087 035 $a(EXLCZ)993710000000962492 100 $a20101201j20101201 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNikolai I. Lobachevsky, Pangeometry 210 3 $aEMS Press$d2010 215 $a1 online resource (322 pages) 225 1 $aHeritage of European Mathematics (hem)$v4$x2523-5222 330 $aLobachevsky 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, Lobachevskys _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. 606 $aHistory of mathematics$2bicssc 606 $aHistory and biography$2msc 606 $aGeometry$2msc 606 $aDifferential geometry$2msc 615 07$aHistory of mathematics 615 07$aHistory and biography 615 07$aGeometry 615 07$aDifferential geometry 686 $a01-02$2msc 686 $a51-02$2msc 686 $a01A55$2msc 686 $a51-01$2msc 686 $a51-03$2msc 686 $a53-02$2msc 686 $a53-01$2msc 686 $a53-03$2msc 686 $a53A35$2msc 700 $aPapadopoulos$4edt$02012174 801 0$bDE-4084 906 $aBOOK 912 $a9910153614903321 996 $aNikolai I. Lobachevsky, Pangeometry$94806227 997 $aUNINA