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| Coolidge J.L. — The Elements of Non-Euclidean Geometry |
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| Предметный указатель |
 measure of curvature of space 53 176 189 204 275 281
Absolute 88 94 95 97 98 99 101 102 103 106 107 110 111 113 116 117 118 119 124 127 129 132 134 138 142 143 146 152 154 155 157 161 162 187 205 226 231 232 233 234 244 246
Actual elements 85
Amaldi 177
Amplitude of tetrahedron 179 180 181
Amplitude of triangle 170 171 172 173
Angle, interior and exterior 30 87 88 279
Angle, interior and exterior, dihedral 39
Angle, interior and exterior, measure of 38 87
Angle, interior and exterior, null 30
Angle, interior and exterior, of skew lines 113
Angle, interior and exterior, of two planes, cosine 70
Angle, interior and exterior, parallel 106 107
Angle, interior and exterior, plane, of dihedral 39
Angle, interior and exterior, re-entrant 31
Angle, interior and exterior, right 32
Angle, interior and exterior, straight 31
Angles of a triangle 31
Angles of a triangle, Clifford 126
Angles of a triangle, exterior of a triangle 31
Archimedes 24
Area 170 175 178 211
Area of a circle 178
Area of a plane 178
Area of a polygon 178
Area of a triangle 175 176 177
Aronhold 159
Asymptotes 152
Asymptotic lines 196 202 203 212 213
Author 116 127 130 154 156 158 167 226 230 232 234
Axes, co-ordinate 64 67
Axial plane of sphere 138
Axis of a chain 119
Axis of a chain of a pencil of complexes 116
Axis of a circle 131 134 135 150
Axis of a circle of a conic 143
Axis of a circle, radical of two circles 134 135 136
Barbarin 154
Battaglini 131
Beck 116
Beltrami 67 210
Bianchi 6 187 188 204 206 210 226 280 281
Birectangular quadrilateral 43 44 49
Bisector of an angle 102 103 109 133 135 136 143 146 153 157 159 220 222
Bolza 209
Borel 34
Bound of half-line 28
Bound of half-plane 30
Bromwich 154
Canal surface 156
Cayley 88 97 157
Central conic 143—153
Central quadric 157—160
Centre of a circle 135 136 137
Centre of a circle, of a conic 143 148 149 150
Centre of a circle, of gravity of points 102 103 109 133 135 136 143 146 153 159 220 222
Centre of quadric 157
Centre of quadric of similitude 134 135 136
Ceva 105
Chain congruence 121 129
Chain congruence of crosses 119 120 128
circle 131—137 143 151 178 188
Circle, auxiliary to conic 152
Clebsch 159 176
Clifford 99 126 129 156 157 205 212 240
Co-ordinates of a line 110 264
Co-ordinates of a line of a plane 264
Co-ordinates of a line, of a point 64 68 176 187 188 194 236 237 263 264 275
Coaxal pencil of complexes 116 124
Coaxality 20
Collinearity 18 102 103 104 105 134 136 251
Collineations 29 38 69 70 94 119 127 239 265 266 268
Comparableness of angles 34 35
Complex of lines 116
Concurrence 18 102 103 105 134 136 251
Cone of revolution 185
Confocal conies 153
Confocal quadrics 160 164
Conformal transformations 198
Congruence of distances 14 15 16 17 28 36 79
Congruence of distances of angles 31 33 34 36 38 39
Congruence of distances of lines, analytic 215—235
Congruence of distances of lines, general 218
Congruence of distances of normals 162 208 210 222 223 224 225 226 227 229 235
Congruence of distances of normals, to surfaces of Gaussian curvature zero 123 208 226 227 235
Congruence of distances of segments 28
Congruence of distances of triangles 31 32
Congruence of distances, chain 121 129
Congruence of distances, isotropic 164 226 227 230 232 234 235
Congruence of distances, synectic 120 122
Congruent figures 28
Congruent transformations 29 37 38 69 70 73 74 80 82 92—100 239 268 269 270 271 278 279 280
conic 142—153 272
Conic, eleven-point or line 147
Conjugate diameters of a conic 148
Conjugate diameters of a conic, directions on a surface 195 196
Conjugate diameters of a conic, harmonic 252 253 254 257 259 261
Connectivity of space 238
Consistent region 78 79 80 83 236 237 238
Continuity, axiom of 23 24 75 249
Continuity, axiom of, in change of angles and sides of a triangle 40 41 42
Coplanarity 109 138
Cosine of angle 54 70 279
Cosine of angle of distance 52 285
Cosines, direction 67 69 278
Cosines, direction, law of 57
cross 117 118 119 124 125 231
Cross ratios 73 86 88 89 90 91 247 259 260 261 262 264 265
Cross space 118
Curvature of a curve 133 188 189 200 201
Curvature of a curve of space 53 176 189 204 275 281
Curvature of a curve, Gaussian 67 123 130 204 205 206 207 208 275 281 282 283
Curvature of a curve, geodesic 208 209
Curvature of a curve, lines of 198 199
Curvature of a curve, mean relative 200 212
Curvature of a curve, surfaces of zero 123 204 205 206 207 208 226 227 235
Curvature of a curve, total relative 200 203 204 205
Dannmeyer 170
Darboux 141 212 278
Dehn 46 181
Density of segment 16
Desargues 75 146 251
Desmie configuration 108 109 110 138
Diagonal points of quadrangle 252
Diagonals of quadrilateral 252
Diameters of conic 148 149 150 151
Diameters of conic, of quadric 159 160
Difference of distances 17 35
Director points and directrices 144 145 146
Discrepancy of a triangle 46 174
Distance 13 72 73 74 76 78 87 89 90 91 272 273 285
Distance of two points, cosine 52 69 78 285
Distance of two points, cosine, element 66 67 187 194 276—284
Distance of two points, cosine, from point to plane 70
Distance of two points, cosine, of skew lines 111 112 114
Distance, directed 62 66 90
Division of segment 24 25 26 27
Dunkel 60
Dupin 141 197 201 205
d’Ovidio 112 142 170
Edge of tetrahedron 20
ellipse 142 143 146 153 167 168 169
Ellipsoid 154 156 167 168 169
Elliptic co-ordinates 153 161
Elliptic co-ordinates surfaces 156
Elliptic co-ordinates, hypothesis 46 73 74 274 285
Elliptic co-ordinates, space 82 83 245
Engel 43
Enlargement of congruent transformation 29
Enriques 33 177 247
| Equidistant curves 132 143
Equivalent points 81 82 236
Euclid 47 72
Euclidean hypothesis 46 72 73 274 285
Euclidean hypothesis, space 77 91 239 240 241 242
Evolutes 192 193 194
Excess of a triangle 174 175 176 177
Extension of segment 15 79
Extension of segment of space 77 78 79 80
Extremity of segment 15
Face of tetrahedron 20
Fibbi 215 221
Focal cones 158 159
Focal cones conies 158 159 167 168 169
Focal cones lines 144 145 146 147 151
Focal cones points and planes 221 222 223 224
Focal cones surfaces 210 226 232
foci 144 145 146 147 151
Forms, fundamental one-dimensional 259 260 261 267
frenet 190
Fricke 244
Frischauf 176 186
Fubini 227 229
Fundamental region 239-46
Fundamental region one-dimensional forms 259 260 261 267
Geodesic curvature 208 209
Geodesic curvature lines 163 209 210 274—281 284 285
Geodesic curvature lines, surfaces 279 280 281
Gerard 48 53
Graves 153
Greater than 15 16 17 34 35 37 92
Half-line 28-33 38 64 67
Half-plane 30 37 38 39
Halsted 24 75 177
Hamilton 98 120 221
Harmonic conjugate 252 253 255 261
Harmonic conjugate separation 252 253 254 257
Harmonic conjugate set 252 253
hilbert 13 24 36 75 177 265
Homothetic conies 152 153
Homothetic conies quadrics 160
Horocycle 132 143 243
Horocyclic surface 156 205
Hyperbola 142 146 167 168 169
Hyperbolic hypothesis 46 72 73 78 274 285
Hyperbolic hypothesis, space 78 236
Hyperboloid 155 167 168 169
Ideal elements 84 85
Imaginary elements 86 87 266 267
Improper cross 117 118 127 231
Improper cross, ray 231 232
Indicatrix of Dupin 201 205
Infinitely distant elements 84 85
Infinitesimal domain 42 47 68 174 175
Initial point 62
Intersection of lines 17 249
Intersection of lines of planes 22 251
Involution 86 87 266 267
Isosceles quadrilateral 43 50
Isosceles quadrilateral, triangle 32 34
Isotropic curves 203 209
Isotropic curves, congruence 164 226 227 230 232 234 235
Joachimsthal 197
JORDAN 277
Killing 142 237 245
Klein 97 129 161 244
Kummer 215
Layer of cross space 118 119 125
Left and right generators of Absolute 99 124 125 234
Left and right parataxy 99 208 225
Left and right translations 99 100 245
Length of arc 276
Less than 15 16 17 34 35 37 92
Levy 13 75
Lie 268 270 271
Liebmann 142
Limiting points and planes 219 220 222
Lindemann 139 176
Line 17 78 248 249
Lobatchewskian hypothesis 46
Lobatchewsky 46 106
Lueroth 87 89 267
Manning 107 176 205
Marie, Ste— 7
Measnre of distance 27 28 87
Measnre of distance of curvature of space 33 176 189 204 207 275 281
Menelaus 105
Meunier 201 208
Middle point of segment 24
Minimal surfaces 129 210-14
Moment, relative of two lines 112
Moment, relative of two lines, relative of two rays 115 192
Moore 13 46 75
Motions 97 98 99
Muenich 139
Multiply connected space 238—246
Normals to curve 192 193 194
Normals to curve to surface 162 197 208 210 222 223 224 225 226 227 229 235
Null angle 30
Null angle, distance 14
Opposite edges of tetrahedon 20
Opposite edges of tetrahedon, half-lines 31
Opposite edges of tetrahedon, senses 63 86 266
Opposite edges of tetrahedon, sides of plane 22
Origin 64
Orthogonal points 101 103 118 132 135 136 137 138 139 143 189 205 215 217 219 224
Orthogonal substitutions 69 70 73 97 98
Orthogonal substitutions, system of surfaces 197 198
Padoa 13 254
parabola 142 143
Parabolic hypothesis 46
Paraboloid 155 157
Parallel angle 106 107 110
Parallelism 85 99 106 113 234 235
Parataxy 99 114 125 129 206 207 208 225 233 234 235
Pasch 13 29 86 265
Peano 13
Pencil of complexes 116
Pencil of complexes of geodesies 279
Perpendicularity 34 36 37 39 101 103 118 132 135 136 137 138 139 143 182 183 193 197 217 219 220 224 279
Phi function 50 51 52
Picard 175 210
Pieri 13 74 86 247
Plane 20 21 22 38 67 70 81 82 95 109 110 118 224 242 243 249 250 251 253 259 264 265 268 269
Poincare 139
Point 13 78 84 86 247 266 275
Polygon 178
Principal points and planes 220
Products connected with a conic 145 149 150
Projection 253 260
Projectivity 259 260 262 267
Pseudo-isotropic congruence 229 230 234 235
Pseudo-normal congruence 224 229
Pseudo-parallelism of lines 113 234 235
Pythagorean Theorem 55 57
Quadrangle, complete 252
Quadrilateral 43 44 49 174
Quadrilateral complete 252 253 266
Quaternions 98 245
Ratio of opposite sides of quadrilateral 49 50 51 52 53
Ratios, constant connected with conies 144 151
Ray 114 115 191 192 227 228 234 235
rectangle 43 44 45 46
Reflection in plane 39 82
Reflection in plane in point 62
Region consistent 78 79 80 81 83 236 237 238
Region, fundamental 239—246
Region, fundamental, restricted 269 276 277 278
Revolution, surfaces of 155 156
Riccordi 131
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