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Coxeter H.S.M. — Non-Euclidean Geometry |
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Предметный указатель |
Abscissa 74 104 107 206
Absolute ix 126 153—157 195 199 224 252
Absolute geometry 11 17 26 179—185
Absolute involution 96 104 198
Absolute points 106
Absolute polarity 95 110 128 157 181 185 193 211 212 224 252 296
Acute segment 103
Acute-angle hypothesis 5
Addition of points 71
Affine geometry 18 24 31 35 77 96 159 178
Altitudes of a triangle 220 223 231 233 289
Analytical geometry 71—94 121—127 132 148—153 156 209—212 224—231 253—265 281—285
Angle descriptive 163 180
Angle metrical 6 14 107 112 127 129 132 207—211 225 260
Angle of parallelism 9 189 208 239 277 295—296 300 305 312
Angle-bisector 200 220
Angle-sum of a triangle 2 7 191 243 263
Apollonius of Perga 48
Appendix 299 316
ARC 249 303 307
Area 6 18 241 253
Area of a circle 8 250
Area of a horocyclic sector 243 250 258
Area of a triangle 7 9 243—247 257
Area of the elliptic plane 242 250
Areal coordinates 237
Aristaeus 48
Associated reguli 63 69 272
Associative law 72
Astral geometry 7
Astronomy 9
Asymptotic approach of parallel lines 6 210 257 301
Axial pencil 21; see also Pencil generalized
Axiom 16
Axiom Pasch's 20 (2.115) 162
Axiom Playfair's 3 186
Axioms of congruence 180
Axioms of continuity 23 36 162 174 194
Axioms of descriptive geometry 161
Axioms of incidence 20
Axioms of parallelism 186 187 197
Axioms of plane hyperbolic geometry 199
Axioms of plane inversive geometry 297
Axioms of plane projective geometry 28
Axioms of separation 22 174
Axis of a circle 116 213
Axis of a pencil of planes 21
Axis of a projectivity 60
Axis of a rotation 130
Axis of a translation 136 202
Axis of an equidistant curve 213
Baker, H.E. 18 28 166—171 232—233
Baldus, Richard 204 213 252
Bellavitis, Giusto 59
Beltrami, Eugenio 252 255—258 260 262 264
Bernays, Paul 24
BETWEEN 18 23 159
Bibliography 317—325
Bilinear relation 75
Binary expansion 101
Birectangle, isosceles 5 190 241 308—309
Bisection 100 200 268 297
Bolyai's parallel construction 204
Bolyai, Farkas 2 10 301
Bolyai, Janos 10 17 157 179 204 215 220 250 277 298 300
Bonola, Roberto 3 134 171 199 210 211 215 252 302 315
Boole, George 122
Brianchon, C.J. 59 62 200
Bundle (of lines and planes) 14 21
Bundle generalized 166—171 184 197 213 218
Bundle of parallels 24 177 184 187 195
Bundles, correlated 219
Canonical form for a conic 87 209
Canonical form for a polarity 86 91 249
Canonical form for a quadric 92
Canonical form for an involution 76
Carroll, Lewis 301
Carslaw, H.S. 176 188 199 206 210 215 241 244 249 250 259 267
Cartan, Elie 89 94 137
Cartesian coordinates 24 211 253—256 258—260 262 312
Categorical 160 186 196
Cayley, Arthur 13 109 122 125 126 149 157 182 196 226 266
Central projection 256
Centre of a (flat) pencil 20
Centre of a bundle 21
Centre of a circle 1 213
Centre of a projectivity 60 203
Centre of a rotation 111 202
Centroid 31 221 230 236 239
Chasles, Michel 53 106 217
circle 1 2 14 115—117 122 181 213—218 221—222 226—231 237 252 259—264; Area Circumference Coaxal
Circular points at infinity 106
Circum-centres 221 223 230
Circum-radius R 230 236 239
Circumferences 8 11 250
Circumscribed circles (or Circum-circles) 221 230 237
class 16
Clifford parallel 134 151 154
Clifford parallelogram 142
Clifford surface 143—145 148 153 155 251
Clifford translation 135—142 149 155
Clifford, W.K. 128 270
Coaxal circles 261
Coaxal circles, Clifford surfaces 145
Coaxial planes 21
Collinear 20 80
Collineation 49 60—63 82 90
Colours ix
Colunar triangles 220 233
Common parallel 205
Common perpendicular 133 147 158 191 204 272
Complex geometry Euclidean 106 261
Complex geometry non-Euclidean 207 212 217
Complex geometry projective 94 106 126 153 207
Complex number 94 107 258 262
Complex, linear 69 92
Composition of rotations 118—120 125
Cone, quadric 26 62 178
Cone, right circular 14 48
Conformal mapping 258—265 295
Congruence (relation) 18 95 100 103 106 115 132 179 201 241
Congruence, linear 92 151 155
Congruent transformation 95 113 126 130—132 139—141 150 154 179 201—203 245; Opposite
conic 26 48 56—62 87 199 215
Conjugate lines 52 65 86 252
Conjugate planes 65
Conjugate points 52 65 86 95 96 106
Conjugate quaternions 123
Consistency of axioms 4 10 23 97 197 255
Construction for a common parallel 205
Construction for a common perpendicular 191
Construction for parallels to a given line 204 289—291
Contact see Double Quadruple Ring Third
Continuity 23 74 101 162 174 187 194 201
Convex region 159 162
Coolidge, J.L. 117 134 151 229 248
Coordinate transformation 76 83
coordinates see Areal Cartesian Homogeneous Non-homogeneous Pliicker Study Trilinear
Coplanar 20
Correlation 51 65 85 91 219
Correspondence 16 52 215; Ordered
cosh 206
Coxeter, H.S.M. 9 201 275 288 293—295
Craats, Jan van de 314
Cremona, Luigi 59
Cross (angle) 112
Cross ratio 76 84 90 105 107 120 126—132 259 262 299
Curvature of space 11 212
Curvature, Gaussian (or Specific) 12 144 211 257
Curve 248
| CYCLE 213 309
Cyclic order on a line 18
de la Hire, Philippe 29
de Sitter, Willem 209
Dedekind, Richard 19 74 101 162
Defect, angular 6 246 301
Degenerate involution 71
Degenerate polarity 186 212
Dehn, Max 166—173 179 187 194
Desargues, Girard 14 28 172
Descriptive geometry 159—178
Developable surfaces 144 220 251
Diagonal triangle 27 56
Diameter 213 252
DICTIONARY 14 24—26 97 266
Differential geometry 12 15 247—251 255—257 260 265 283
Dihedral angle 129 163
dimensions 21
Direct collineation 64
Direct congruent transformation 132 140 141 146 154 202
Direct correspondence 36
Direct projectivity 43
Directed angle 112
Directrices of a congruence 93 155
Distance 225; see also Elliptic Hyperbolic
Distributive law 72
Dodgson, C.L. 301
Donkin, W.E. 109 119 122 136—138
Donnay, J.D.H. 304
Double contact 127 217 260
Double perspectivity 34
Double point 36
Double rotation 131 141 150
Doubly oriented line 34 137
Doubly-asymptotic triangle 188 210 245 301
Duality 19 26 51 62 165
Dummy suffix convention 83
Duplication of the cube 48
Elements of Euclid 1 115 181—184 188 191
ellipse 18 48 252—254
Elliptic (linear) congruence 93 151 155
Elliptic distance 14 103 117 120—122 126 132 254—255
Elliptic geometry 4 13—15 95—156 207 220—223 242 252—255 260 264—266
Elliptic involution 45—47 96 104 252
Elliptic line 55 96—108 112 253
Elliptic point 55
Elliptic polarity 54 66 86 96 110 157 252
Elliptic projectivity 43 75 203
Elliptic trigonometry 232—238 272
Engel, Friedrich 6 277
Enriques, Federigo 29 36—45 54—56 61—63 101
Equidistant curve 213—217 222 227 260 309 312
Equidistant surface 218
Equivalent regions 241
Erlanger Programm 17 115
Escribed circles (or Ex-circles) 221 231 239
Euclid 1 18 48 175 181 197; Postulates
Euclidean geometry 6 9 17 96 99 106 117 144 178 186—187 197 202 220 251—266 297—298
Euclidean geometry as a limiting case 8 212 235 237 242
Euler, Leonhard 109
Ewald, Gunther 297
Factor of proportionality 82
Fibonacci numbers 293
Finite but unbounded space 11 301
Fixed points of a collineation 61
Flat pencil (of lines) 6 20 158 175
Flat pencil generalized 199 213 261
Forder, H.G. 112 186 187 195 272 299
Forms, primitive 21
Four-dimensional space 12 26
Fractional linear transformation 75
Fundamental theorem of projective geometry 42 76
Gauss, C.F. 2 7 8 144 157 175 176 190 215 234 247 257 275
Genealogy of geometries 19
Generators of a quadric 62 68 94
Generators of the Absolute 153—156
Geodesies 144 256—257
Geographical sphere 298
Glide-reflection 201—203 267
Gnomonic projection 256
Goursat, Edouard 150
Greuzer, S.L. 292
Group 16 103 115 138 140 145
H(AB, CD) 28
Half-plane 163 263 299
Half-space 163 178 302
Halsted G.B. 267
Hamilton, Sir W.R. 109 119 122
Hamlet ix
Harmonic conjugate 28 39 42 45 76 81 107
Harmonic homology 50 64 65 81 116 203 228
Harmonic set of lines 30 51
Harmonic set of points 28 40 51
Heffter, Lothar 18 84 90
Hesse, L.O. 53 223
Hessenberg, Gerhard 71
Hexagon 59 201
Hilbert, David 24 179 180 191 194 195 205 241 301
Hippocrates of Chios 1 48
Hire, Philippe de la 29
history 1—15 48 226 277 289—291
Hobson, E.W. 254
Holgate, T.F. 39
Homogeneous coordinates 25 76—94 121 124—127 132 148—153 156 209—212 224—233 236 240 253
Homogeneous space 15 256
Homography 265 266
Homology see Harmonic
Horocycle 9 213 214 217—222 227 239 244 250 257 290 303 308
Horosphere 7 9 218—220 251 280 311
Hyper-space 12 14 26 94 160 265
Hyper-sphere 12 264
Hyperbola 18 48 252—254
Hyperbolic ix
Hyperbolic cosine 206
Hyperbolic distance 157 201 206—211 254—255 294—295
Hyperbolic functions 206 254 292—296
Hyperbolic geometry 4—11 157 178 187—210 213—223 243—247 252—258 260—266 300
Hyperbolic involution 45 76 252
Hyperbolic line 55 201 253
Hyperbolic point 55
Hyperbolic polarity 54 56 86 110 157 252
Hyperbolic projectivity 43 75 203
Hyperbolic trigonometry 220 237—240 277—282
Hypercycle see Equidistant curve
Hyperosculation 218
Ideal line 171 185 199 209
Ideal plane 173 185
Ideal point 158 171—178 185 199 209 300; Ultra-infinite
Imaginary geometry 10 158
Improper bundle 166 174 184
In-centre 200 221 231 236
In-radius r 221 231 235 237 239
incidence 18 20 80 171 203
Infinitesimal 9 212 235 238 298
infinity ix see line Plane
Inscribed circle (or In-circle) 221 231
Interior of a conic 56 87
Interior of an interval 23 36—38 41
Intermediacy 159
Intersection condition for lines 89 152 271
interval 23 36—38 41 161
Invariant 17 77;
Inverse correspondence 17
inversion 259 263 276 297
Inversive distance 265 292 296 299 313
Involution 44 61 76 203 252; Degenerate Elliptic Hyperbolic
Involutory collineation 50
Isosceles birectangle 5 190 241 308—309
Isotropic space 15
Johnson, R.A. 112 221
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