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| Postnikov M. — Lectures in Geometry. Semester I. Analytic Geometry. |
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| Предметный указатель |
Angle of rotation 301
Angle of rotation between two planes 161
Anticommutativity of external multiplication 74
Anticommutativity of external product 74
Area of a bivector 151
Associativity of vector addition 17
Asymptote 201
Bases of opposite signs 102
Bases of the same sign 102
Bases, deformation of 112
Bases, equivalent 115
Basis deformable into a basis 40
Basis of vector space 40
Basis, orthonormal 140
Basis, standard 45
Bessel inequality 139
Bivector 64 65
Bundle of planes 282
Cauchy — Buniakowski inequality 130
Centre of a curve 194
Centre of symmetry 195
circle 226
Cone, directrix of 240
Cone, vertex of 239
Configuration theorems 307
Coordinates of a vector 41
Coordinates, affine 49
Coordinates, polar 178
Coordinates, projective 272
Cross ratios of four points 327
Curve, algebraic of order n 183
Curve, real algebraic 191
Curve, second-degree central 196
Curve, second-degree elliptic-type 202
Curve, second-degree hyperbolic-type 202
Curve, second-degree noncentral 196
Curve, second-degree parabolic-type 202
Cylinder 248
Cylinder, axis of 248
Cylinder, Elliptical 248
Cylinder, hyperbolic 251
Cylinder, imaginary 250
Cylinder, parabolic 252
Desargues theorem 302
Diameters, conjugate 207
Dimension of a vector space 40
Direction, asymptotic 200
Direction, chordwise 206
Direction, nonasymptotic 200
Direction, nonsingular 203
Direction, principal 222
Direction, singular 203
Distance between points 129
Distance from a point to a plane 161
Distance from a point to a straight line 157
ellipse 168
Ellipse, affine 182
Ellipse, centre of 170
Ellipse, directrices of 170
Ellipse, eccentricity of 170
Ellipse, focal distance of 170
Ellipse, focal property of 171
Ellipse, focal radii of 171
Ellipse, foci of 170
Ellipse, major and minor axes of 170
Ellipse, major and minor semiaxes of 170
Ellipse, striction 233
Ellipse, vertices of 170
Ellipsoid 228
Ellipsoid, imaginary 231
Equation of a plane, parametric vector 84
Equation of a straight line, parametric vector 54
Equations of second-degree curves, canonica'affine 185
Expansion of a vector with respect to a basis 41
Families of vectors, linearly equivalent 118
Family of vectors, complete 39
Family of vectors, orthonormal 139
Fixed points of linear fractional transformation 323
Form of a given basis, metric 137
Form, bilinear 135
Form, positive definite 136
Form, quadratic 136
Form, symmetrical 135
Fourier coefficients 138
Geometry, affine 47
Geometry, Euclidean 129
Geometry, projective-affine 260
Gram — Schmidt orthogonalization process 142
Group of automorphisms of an affine space 276
Group of linear fractional transformations 316
Group of projective transformations 316
Group, general linear 275
Half-planes determined by a straight line 62
Hyperbola 172
Hyperbola, affine 182
Hyperbola, asymptotes of 173
Hyperbola, branches of 173
Hyperbola, centre of 174
Hyperbola, directorial property of 175
Hyperbola, directrices of 174
Hyperbola, focal distance of 174
Hyperbola, focal parameter of 174
Hyperbola, foci of 174
Hyperbola, linear eccentricity of 174
Hyperbola, real and imaginary axes of 174
Hyperbola, semiaxes of 174
Hyperbola, vertices of 174
Hyperboloid of one sheet 233
Hyperboloid of two sheets 231
inversion 318
Isometries of a cube 338
| Isometries of a regular dodecahedron 340
Isometries of a regular icosahedron 340
Isometries of a regular octahedron 346
Isometries of a tetrahedron 339
Isomorphism of affine spaces 48
Isomorphism of Euclidean vector spaces 143
Isomorphism of vector spaces 43
Isomorphism, coordinate 44 45
Isomorphism, established from the equality of coordinates 45
Line, parallel to a plane 92
Matrix of transition from a basis to a basis 97
Matrix, equivalent 115
Matrix, orthogonal 144
Matrix, proper orthogonal 145 146
Model of affine geometry 262
Motion of Euclidean space 286
Multiplication in a vector space, scalar 128
Multiplier of linear fractional transformation 328
Orientation of a half-plane 107 108
Orientation of a half-space 110
Orientations of vector space 103
Oval 216
parabola 166
Parabola, affine 182
Parabola, axis of 167
Parabola, focal distance of 168
Parabola, focal parameter of 168
Parabola, focus of 168
Parabola, vertex of 167
Paraboloids, elliptical 242
Paraboloids, hyperbolic 243
Parseval's formula 140
Pencil of planes 280
Pencil of straight lines 256
Pencil, ideal 259
Pencil, ordinary 258
Plane, extended 260
Plane, given by a point and a bivector 82
Plane, projective 269
Plane, projective-affine 260
Points of a plane, nonseparated by a straight line 85 86
Points of a space, nonseparated by a plane 87
Poles of rotation of a sphere 334
Product of a bivector by a number 121
Product of a trivector by a number 121
Product of bivectors, external 121
Product, scalar 125
Product, vector 152
Properties of external multiplication, algebraic 73
Radius vector of a point 49
Rotation 295
Sections, conic 242
Set of vectors, linearly dependent 29
Side of a straight line 105
Space, affine 46
Space, arithmetic projective 277
Space, Euclidean point 128
Space, projective 279
Space, projective-affine 278
Space, real-complex 189
Space, vector (affine) oriented 103
Spaces, affine isomorphic 48
Spaces, Euclidean vector 128
Sphere 228
Stereographic projection 314
Straight line, in space 51 52
Subset, linearly (in)dependent 29
Subspace, real 187
Sum of bivectors 70
Sum of trivectors 124
Surface, l-fold ruled 234
Symmetry in a centre O 195
Symmetry with respect to a circle 317
Symmetry with respect to a straight line 319
System of opposite signs 103
System of the same sign 103
System, affine coordinate 49
System, canonical affine coordinate 182
System, rectangular coordinate 141
Tangent 200
Theorem, configuration 307
Theorem, Desargues 302
Theorem, Fano 308
Theorem, Pappus — Brianchon 310
Theorem, Pappus — Pascal 305
Transformations, affine 286
Transformations, elliptical 324
Transformations, hyperbolic 324
Transformations, linear fractional 315
Transformations, loxodromic 325
Transformations, orthogonal 286
Transformations, parabolic 323
Transformations, projective 286
Translation, (parallel) 95
Triangle inequality 131
Unit vector 141
Vector 15
Vector space, associated with an affine space 48
Vector spaces, isomorphic 43
Vector spaces, real-complex isomorphic 188
Vector, complementary to bivector 152
Vector, Euclidean 128
Vector, finite-dimensional 39
Vector, length of 129
Vector, parallel to a bivector 69
Vector, proportional to a vector 35
Vectors, a linear combination of 28
Vectors, a trivial linear combination of 28
Vectors, collinear 35 68
Vectors, coplanar 36
Volume of a parallelepiped, oriented 125
Volume of a trivector 149
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