LEADER 05681nam 22006132 450 001 9910812285603321 005 20151002020706.0 010 $a1-61444-516-8 035 $a(CKB)2560000000141208 035 $a(EBL)3330454 035 $a(SSID)ssj0000577713 035 $a(PQKBManifestationID)11345304 035 $a(PQKBTitleCode)TC0000577713 035 $a(PQKBWorkID)10577244 035 $a(PQKB)11566665 035 $a(UkCbUP)CR9781614445166 035 $a(MiAaPQ)EBC3330454 035 $a(Au-PeEL)EBL3330454 035 $a(CaPaEBR)ebr10861034 035 $a(OCoLC)929120504 035 $a(RPAM)4037177 035 $a(EXLCZ)992560000000141208 100 $a20140430d1998|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNon-Euclidean geometry /$fH.S.M. Coxeter$b[electronic resource] 205 $aSixth edition. 210 1$aWashington :$cMathematical Association of America,$d1998. 215 $a1 online resource (xviii, 336 pages) $cdigital, PDF file(s) 225 1 $aSpectrum series 300 $aTitle from publisher's bibliographic system (viewed on 02 Oct 2015). 311 $a0-88385-522-4 320 $aIncludes bibliographical references and index. 327 $a""Front Cover""; ""NON-EUCLIDEAN GEOMETRY""; ""Copyright Page""; ""PREFACE TO THE SIXTH EDITION""; ""CONTENTS""; ""CHAPTER I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY""; ""1.1 Euclid""; ""1.2 Saccheri and Lambert""; ""1.3 Gauss, Wachter, Schweikart, Taurinus""; ""1.4 Lobatschewsky""; ""1.5 Bolyai""; ""1.6 Riemann""; ""1.7 Klein""; ""CHAPTER II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS""; ""2.1 Definitions and axioms""; ""2.2 Models""; ""2.3 The principle of duality""; ""2.4 Harmonic sets""; ""2.5 Sense""; ""2.6 Triangular and tetrahedral regions""; ""2.7 Ordered correspondences"" 327 $a""2.8 One-dimensional projectivities""""2.9 Involutions""; ""CHAPTER III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS""; ""3.1 Two-dimensional projectivities""; ""3.2 Polarities in the plane""; ""3.3 Conies""; ""3.4 Projectivities on a conic""; ""3.5 The fixed points of a collineation""; ""3.6 Cones and reguli""; ""3.7 Three-dimensional projectivities""; ""3.8 Polarities in space""; ""CHAPTER IV. HOMOGENEOUS COORDINATES""; ""4.1 The von Staudt-Hessenberg calculus of points""; ""4.2 One-dimensional projectivities""; ""4.3 Coordinates in one and two dimensions"" 327 $a""4.4 Collineations and coordinate transformations""""4.5 Polarities""; ""4.6 Coordinates in three dimensions""; ""4.7 Three-dimensional projectivities""; ""4.8 Line coordinates for the generators of a quadric""; ""4.9 Complex projective geometry""; ""CHAPTER V. ELLIPTIC GEOMETRY IN ONE DIMENSION""; ""5.1 Elliptic geometry in general""; ""5.2 Models""; ""5.3 Reflections and translations""; ""5.4 Congruence""; ""5.5 Continuous translation""; ""5.6 The length of a segment""; ""5.7 Distance in terms of cross ratio""; ""5.8 Alternative treatment using the complex line"" 327 $a""CHAPTER VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS""""6.1 Spherical and elliptic geometry""; ""6.2 Reflection""; ""6.3 Rotations and angles""; ""6.4 Congruence""; ""6.5 Circles""; ""6.6 Composition of rotations""; ""6.7 Formulae for distance and angle""; ""6.8 Rotations and quaternions""; ""6.9 Alternative treatment using the complex plane""; ""CHAPTER VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS""; ""7.1 Congruent transformations""; ""7.2 Clifford parallels""; ""7.3 The Stephanos-Cartan representation of rotations by points""; ""7.4 Right translations and left translations"" 327 $a""7.5 Right parallels and left parallels""""7.6 Study's representation of lines by pairs of points""; ""7.7 Clifford translations and quaternions""; ""7.8 Study's coordinates for a line""; ""7.9 Complex space""; ""CHAPTER VIII. DESCRIPTIVE GEOMETRY""; ""8.1 Klein's projective model for hyperbolic geometry""; ""8.2 Geometry in a convex region""; ""8.3 Veblen's axioms of order""; ""8.4 Order in a pencil""; ""8.5 The geometry of lines and planes through a fixed point""; ""8.6 Generalized bundles and pencils""; ""8.7 Ideal points and lines""; ""8.8 Verifying the projective axioms"" 327 $a""8.9 Parallelism"" 330 $aThroughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Tranformations that preserve incidence are called collineations. They lead in a natural way to isometries or 'congruent transformations'. Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. 410 0$aMAA spectrum. 606 $aGeometry, Non-Euclidean 615 0$aGeometry, Non-Euclidean. 676 $a516.9 700 $aCoxeter$b H. S. M$g(Harold Scott Macdonald),$f1907-2003,$0903227 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910812285603321 996 $aNon-Euclidean geometry$93969071 997 $aUNINA