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Coolidge J.L. — The Elements of Non-Euclidean Geometry
Coolidge J.L. — The Elements of Non-Euclidean Geometry



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Название: The Elements of Non-Euclidean Geometry

Автор: Coolidge J.L.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1909

Количество страниц: 291

Добавлена в каталог: 25.03.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\frac{1}{k^2}$ 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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