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| Audin M. — Geometry |
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| Предметный указатель |
action 145 190
Aerial 263
Affine conic 185
Affine frame 12
Affine group 19 35 40
Affine independence 12 33
Affine isometry 44 59
Affine line 10
Affine mapping 14
Affine plane 10
Affine projection 33
Affine property 260
Affine quadric 185
Affine space 7
Affine subspace 10
Affine vs projective 147 159 200 210
Affinity 36
Alternated 117
Alternated bilinear form 244
Alternating group 106 130 133 140
Anallagmatic invariant 108 241
Angle at the circumference 74
Angle of a plane rotation 55 78
Angle of a rotation 115
Angle of a similarity 81
Angle of two curves 85
Angle of two planes 121
Angle, geometric 71
Angle, oriented 1
Angle, oriented (of lines) 68
Angle, oriented (of vectors) 66
Antarctic 135
Anti-rotation 114 116
Apex 271
Apollonius 2 236 238
Apparent contour 299
Arc length 261
Archimedian 137
Area of a spherical triangle 121
Area of a time zone 120
Area, signed 119 286
Astroid 254 266
Asymptote 191 260
Axiom, parallel 2 13 122 181
Axis of a proper conic 193
Axis of a rotation 113 115
Axis of revolution 269
Axis of the Earth 135
Axis, focal 194
Axis, major 193
Axis, minor 193
Axis, radical 92 107 217 224
Ball see "Football"
Banach 136
Barycenter 26
Barycenter, preservation of 17
Barycentric coordinates 36 119 178
Base, locus 206
Base, point 94
Basis, direct 60
Basis, orthogonal 226
Basis, orthonormal 52
Bathroom 136
Beethoven 126
Belgian story 238
bernoulli 262
bezout 207
Bifocal property 195
Bilinear form 43 225
Bilinear form, alternated 244
Bilinear form, symmetric 225
Biruled surface 239
bisector 196
Bisector, external 72
Bisector, internal 71
Bisector, perpendicular 47
Bisectors 70 199 219
black 135
Bonnet 294
Bowl 263 see
Brianchon 243
Canonical see "Natural"
Cardioid 254 263
Cartan 242
Cartan, decomposition of 242
Cartesian coordinates 12 30
Cartesian equations 31
Cartesian parametrization 274
Catenary 299
Cauchy 44 58
Caustic 249 258 263 264
Center of a conic 188
Center of a quadric 188 214
Center of a rotation 78
Center of a similarity 80
Center of an excircle see "Excenter"
Center of curvature 256
Center of gravity 27 see
Center of the circumcircle see "Circumcenter"
Center of the incircle see "Incenter"
Central, conic 188
Central, dilatation 16
Central, quadric 188
Centroid 27
Ceva 38
Chasles 8 68 208 244
Chessboard 174
Cicumradius 110
circle 193 216
Circle of Euler 1 61 111 267
Circle, great 120
Circle, inversion 84
Circle, nine point 62 see
Circle, osculating 256 266
Circle, small 120
Circular group 167 224
Circular helix 265
Circular points 216
Circumcenter 61
circumcircle 61
Circumradius 98
Classification 189 193 204 226
Common perpendicular 131
Compactness of the ellipse 191 193
Compactness of the group O(n) 52
Compactness of the projective space 144
Compactness of the sphere 140
Complement of a conic 244
Complement of a hyperplane 40
Complement of a line 36 40 170
Complete quadrilateral 38 61
Completion, projective 149 164 200
Complex exponential 54
Complex numbers, use in plane geometry 79 82 99 164
Cone 243 271 289
Cone of revolution 238 270
Cone, isotropy 200
Confocal, conies 243
Confocal, family 244
Confocal, quadrics 244
Conic, affine 185 189
Conic, central 188
Conic, confocal 243
Conic, degenerate in a pencil 207
Conic, projective 200
Conic, proper 190
Conic, real 244
Conic, section 238
Conic, tangential 243
Conjugacy 100
| Conjugated diameters 236
Conjugation 21 35
Conjugation, principle of 21
Connectedness of  63
Connectedness of  57
Connectedness of the ellipse 191
Connectedness of the parabola 193
Connectedness of the projective space 144
Conoid of Pluecker 296
Constrained extrema 298
Convex 28 122
Convex, hull 29 122
coordinates 12
Coordinates, barycentric 36 119 178
Coordinates, Cartesian 12 30
Coordinates, homogeneous 157 179
Cosine 55
Criteria for congruence 103
Criteria for similarity 106
Cross product see "Vector product"
Cross-ratio and orthogonality 216
Cross-ratio and permutations 164
Cross-ratio of four collineal points 161
Cross-ratio of four lines 172
Cross-ratio of four points on a conic 209
Cross-ratio, computation 162
Cross-ratio, preservation of the 161
Cross-ratio, real 166
cube 128
Cubic, cuspidal 251 258 261
Cubic, nodal 261
Cubic, real 244
Cup of coffee 249 see
Curvature of a cone 289
Curvature of a cylinder 289
Curvature of a plane 289
Curvature of a plane curve 255
Curvature of a space curve 265
Curvature of a torus of revolution 299
Curvature of Gauss 287
Curvature of surfaces of revolution 299
Curvature of the sphere 122 124 289
Curvature, algebraic 255
Curvature, center 256
Curvature, direction of 290
Curvature, principal 290
Curvature, radius 256
Curve 258
Curve, cycloidal 252
Curve, parallel 257
Curve, parametrized 247
Curve, regular 258
Cusp 299
Cusp, point 258
Cuspidal, cubic 251 258 261
Cyclic group 130
Cyclic points 76
Cyclicity 75 166
Cycloid 265
Cycloidal curve 252
Cylinder 271 289
Cylinder of revolution 270
Decomposition of Cartan 242
Decomposition, polar 242
Desargues 26 39 151 154 176
Descartes 264
Diagonalization of real symmetric matrices 233
Diagonalization, simultaneous 189 230 234 285
Diameters of a circle 223
Diameters, conjuated 236
Diffeomorphism 85
Differential of a mapping 85 111 280
Dihedral group 130 132 141
Dilatation 16 35
Dimension of a projective space 143
Dimension of an affine space 8
Direct basis 60
Direct similarity 80 165
Direction of an affine space 8
Direction of curvature 290
Directrix 194 219
Discriminant 263 274 299
Discriminant of a quadratic form 241
Distance on the sphere 138
Distance, Euclidean 44
Distance, hyperbolic 181
Distance, intrinsic 138
dodecahedron 128 139
Dot product see "Scalar product"
Double line 185 192 207
Double vector product 131
Dual of a conic 243
Dual of a convex 136
Dual of a polyhedron 125 136
Dual of a quadric 243
Duality and polarity 203
Duality between convex subsets 136
Duality between polyhedra 125
Duality, projective 153 172 242
Duerer 2 128 143 249
Earth 2 122 135 176
Easter Island 126
Eccentricity 194
EDGE 123
ellipse 190 211 266
Ellipsoid 214 269
Elliptic integral 339
Elliptic paraboloid 214
Elliptic point 283 290
Envelope 199 248 299
Envelope of normals 257
Envelope of the Simson lines 266
Epicycloid 253 264
Equation of a quadric 184
Equation, Cartesian 31
Equation, parametric 30
Equation, reduced 193
Equibarycenter 26
Erdoes 102
Euclid 2 7
Euclidean affine space 44
Euclidean vector space 44
Euler 61 110 111 123 284 293
Evolute 257
Evolute of a catenary 299
Evolute of a cycloid 265
Evolute of a parabola 266
Evolute of an ellipse 266
Excenter 98
Excircle 98
Exponential, complex 54
External bisector 72
extrema 295
Face 123
Fagnano 101
Family of lines 249
Family, confocal 244
Fermat 105
Feuerbach 110
Finite subgroup 130
Finite subgroup of  130 140
First criterion for congruence 103
First criterion for similarity 106
First fundamental form 287
First theorem of Apollonius 236
Flex 259
Focal axis 194
Focus 194 218
Football see "Soccer"
Form, bilinear alternated 244
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