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| Audin M. — Geometry |
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| Предметный указатель |
Poincare 181 293
Point at infinity 91 148 164 167 186 221
Point of Fermat 105
Point of Gergonne 134
Point of inflexion 259
Point, base 94
Point, circular 216
Point, cusp 258
Point, elliptic 283 290
Point, hyperbolic 283 290
Point, limiting 94
Point, parabolic 284 298
Point, planar 284 298
Point, regular 258 273
Point, singular 258 273 274 277 298
Point, weighted 26
Polar decomposition 242
Polar of a point with respect to a conic 203 240
Polar, form 225
Polar, hyperplane 203
Polar, ocean 135
Polarity with respect to a quadric 203
Pole of a hyperplane with respect to a quadric 203
Pole of a line with respect to a conic 203
Pole of an inversion 84
Pole, north 134
Polyhedron 122
Polyhedron, dual 125
Polyhedron, Platonic 2 128
Polyhedron, regular 126
Porism of Steiner 109
Position of a curve with respect to its tangent 259
Position of a parabola with respect to its tangent 236
Position of a surface with respect to its tangent plane 282
Position of an ellipse with respect to its tangent 191
Position, general 280
Positive definite quadratic form 43
Power of a point with respect to a circle 89
Power of an inversion 84
Preservation of alignment 156
Preservation of angles 70 71 81 83 86 111 165
Preservation of barycenter 17
Preservation of circles 91 166
Preservation of collinearity 16 41 179
Preservation of orientation 50 60
Preservation of orthogonality 44 86
Preservation of the cross-ratio 161
Preservation of the norm 44
Preservation of the scalar product 44
Principal curvature 290
Principle of conjugation 21
Principle of Huygens 257 274
Problem of Fagnano 101
Product, scalar 43 215 225
Product, vector 117
Projection in projective geometry see "Perspectivity"
Projection, affine 33
Projection, stereographic 134 140 164
Projective completion 149 159 164 200 210
Projective conic 200
Projective duality 153 172 242
Projective frame 157 178
Projective group 156 165 204
Projective hyperplane 145 146
Projective line 143 147 164
Projective plane 143 148
Projective quadric 200
Projective reader 185
Projective space 143
Projective subspace 145
Projective transformation 155 204
Projective transformation (of the line) 159 165
Proper, affine quadric 185
Proper, projective quadric 200
Property, affine (of a curve) 248 260
Property, bifocal 195
Property, global 248 293
Property, local 248 293
Property, metric 215 248 293
Property, monofocal 194
Property, tangential (of conies) 196 199 243 249
Pseudosphere 299
Ptolemy 108
Punctual masses 26
Pyramid 126 132
Pythagoras 98
Quadratic form 43 225 283
Quadric 184 269
Quadric at infinity 238
Quadric in dimension 3 234
Quadric, affine 185 234
Quadric, central 188
Quadric, confocal 244
Quadric, degenerate in a pencil 207
Quadric, projective 200
Quadric, proper affine 185
Quadric, proper projective 200
Quadric, real 234 239
Quadrilateral, complete 38 61
Quaternions 141
Radical axis 92 107 217 224
Radius of the circumcircle 110 see
Radius of the incircle 110
Radius, curvature 256
Rain 2 264
Rainbow 2 249 264
Range, harmonic 164
Rank of a quadratic form 227 234
Rank of a skew-symmetric matrix 245
Ratio of a dilatation 16
Ratio of a similarity 79
Real conic 244
Real cubic 244
Real quadric 234 239
Rectangular hyperbola 193
Reduced equation 193
Reflection 46 59 222
Reflection, glide 77 116
Regular point 258 273
Regular polygon 126
Regular polyhedron 126
Regular surface 273
Relation of Euler 110
Relation, metric (in the triangle) 98
Revolution 269
Riemann 164 293
Rigid motion 50 58
Rotation in space 113
Rotation, plane 55 78
Rotatory reflection 114 116
Rule, parallelogram 9
Rule, slide 1
Ruled surface 234 239 270 296 297
Ruler 176
Saddle 234 298
Saddle, horse 271 283
Saddle, monkey 298
Scalar function of Leibniz 60
Scalar product 43 215
Schmidt 62
Schwarz 44 58 180
Schwarz lemma 180
Screw displacement 116
Second criterion for congruence 103
Second criterion for similarity 106
| Second fundamental form 287
Second theorem of Apollonius 236
Second theorem of Desargues 176
Section, conic 238
Separation 135
Signature of a quadratic form 228
Signed area 119 286
Similarity, criteria for 106
Similarity, direct 80 165
Similarity, linear 79
Similarity, opposite 80
Simple group 137
Simplicity of  137
Simson 104 see
Sine 55
Singular point 258 273 274 277 298
Skew-symmetric bilinear form 244
Skew-symmetric matrix 245
Slide rule 1
Small circle 120
Snell 264
soccer 137
Space, affine 7
Space, projective 143
Space, tangent 201
Spanned affine subspace 11
Spanned projective subspace 147
Sphere 120 164 289
Sphere of Riemann 164
Spherical triangle 120 138
Spherical trigonometry 138
Spilett 135
Steiner 104 109 208 see
Stereographic projection 134 140 164
Strip of Moebius 300
Structure of isometries 46
Structure, transport of 9 67
Subspace, affine 10
Subspace, generated 11 147
Subspace, projective 145
Subspace, spanned 11 147
Subspaces, parallel 12
Sum of the angles of a triangle 73 122 182
Summit 298
Sun 135 248 264
Support of a geometric surface 272
surface 272
Surface of revolution 269 296
Surface, geometric 272
Surface, parametrized 272
Surface, regular 273
Surface, ruled 234 239 270 296 297
Swallow tail 274
Sylvester 228
Symmetric bilinear form 43 225
Symmetric group 130 133
Symmetric matrix 225 233
Symmetry 34
Symmetry, orthogonal 45
Tangent hyperplane 201
Tangent mapping 280
Tangent plane 277
Tangent space 201
Tangent to a central conic 199
Tangent to a conic 188 243
Tangent to a curve 248 258 279
Tangent to a parabola 198
Tangent to a quadric 186
Tangent vector 258
Taylor 259 283
Tetrahedron, regular 128 132
Tetrahedron, scalene 36 133
Thales 1 23 34 173
Theorem of Apollonius 236
Theorem of Bezout 207
Theorem of Brianchon 243
Theorem of Ceva 38
Theorem of Chasles 244
Theorem of Chasles and Steiner 208
Theorem of Desargues 26 39 151 154
Theorem of Desargues (second) 176
Theorem of Erdoes and Mordell 102
Theorem of Euler 285 289
Theorem of Feuerbach 1 110
Theorem of Gauss and Bonnet 294
Theorem of Hahn and Banach 136
Theorem of Jacobi 244
Theorem of Jordan 248
Theorem of Liouville 83 111
Theorem of Menelaues 38 39 108 209
Theorem of Miquel 104 177
Theorem of Pappus 25 39 150 176 240
Theorem of Pascal 103 108 209 240
Theorem of Pythagoras 98
Theorem of Thales 1 23 34 173
Theorem of the four vertices 248
Theorem of the six cross-ratios 176
Theorem of Weierstrass 314
Theorem of Witt 213 231
Theorem of zeroes 238
Theorem, fundamental 41 179
Theorem, implicit function 247 277 281
Theorem, Inverse Function 276
Theorem, remarkable of Gauss 291
Theorema egregium 291
Third criterion for congruence 103
Time Zone 120
Topology of 142 180
Topology of the linear group 63
Topology of the orthogonal group 52
Topology of the projective space 144
Topology of the real projective plane 179
Torsion 265
Torus of revolution 270 299
Tractrix 299
Transformation, projective 155
Translation 16
Transport by conjugation 21
Transport of structure 9 67
TRANSPOSE 52
Triangle, hyperbolic 182
Triangle, inequality 44 58
Triangle, spherical 120 138
Triangle, strict inequality 58
Trigonometry, plane 98
Trigonometry, spherical 138
Type of a conic 193
Umbilic 300
Umbrella of Whitney 298
Underlying vector space 8
Using complex numbers 57 79 82 99 164 215
Vector space, Euclidean 44
Vector, isotropic 225 226
Vector, normal 254 284
Vector, tangent 258
Vectorialization 9
Vertex 123 248
Vertex of a cone 271
Vertex of a parabola 193
Vinci 128 137
Vosges 298
Wave-front 258
Weierstrass 314
Whitney 298
Witt 213 231
Zeugma 4 178
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