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| Авторизация |
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| Prasolov V.V., Tikhomirov V.M. — Geometry |
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| Предметный указатель |
Absolute 90 95 193
Absolute value 11
Affine ratio 13
Affine space 20 42
Affine variety 22 34
Alexandroff, P.S. 126
Algebraic curve 161
Almagest 84
Angle of parallelism 100
Apollonius xi 8 61 69 132
Archimedes xi 36 126 132
Area of parallelogram 10
Argument 11
Arnold, V.I. 133
Axis of parabola 63
Ball 27
Banach, S. 126
Basis 18 128
Bell, E.T. 5
Beltrami, E. 3 83 133
Birkhoff, G.D. 199
Blaschke, W. 36
Bolyai, J. 3 14 83 133 200
Bonnet, O.P. 145
Bourbaki, N. 1 126 197
Brianchon hexagon 76
Brianchon, C.J. 166
Brianchon’s theorem 166
Bugaenko, V.O. xi
Butterfly problem 16 70
Canonical basis 18
Canonical equation 63
Cartesian model 7 9
Cauchy formula 154
Cauchy theorem 148
Cauchy, A. 36 126
Cayley, A. 3 47 83 89 133
Ceva 2
circle 9 83
Clairaut, A.-C. 21
Classification of second-order curves 61
Classification of second-order curves, affine 63
Classification of second-order curves, metric 61
Classification of second-order curves, projective 63
Clifford translation 112
Clifford, W. 196
Complex number 11
Complex number, conjugate 11
Complex projective plane 98
Complex projective plane, space 158
Cone 43 73
Cone of rotation 73
Cone, right circular 73
Confocal conics 174
Confocal quadrics 176
Conic sections 68
Conics 61
Conics, hyperbolic 205
Conics, spherical 202
Convex analysis 126
Convex closure 36 128
Convex geometry 126
Convex hull 27 128
Convex linear combination 43
Convex polyhedron 140
Convex set 27
coordinates 7 17
Cotes, R. 160
Cotes’ theorem 160
Cramer’s formulas 34
Crelle's Journal 201
Crelle, A.L. 201
Cross ratio 13 49 182
Cross ratio of planes 51
Dandelin, G. 69
Deduction method 5
Defect 104
Desargues, G. 53 55 56 132 165
Desargues’ theorem 55
Descartes, R. 8 9 16 132 140 145
Determinant 10 26
Determinant, principal 62
DIMENSION 18
Directrix 63
Distance 8 19
Divergent lines 115
Dual configuration 163
Dual curve 164
Dual polyhedra 142
Duality 53 124 128
Duality, projective 163
Eccentricity 63
Einstein, A. 38 137 138
Elizabeth, Princess 16
ellipse 61 79
Ellipsoid 73 82
Ellipsoidal coordinates 177
Elliptic geometry 83
Elliptic motion 114
Elliptic pencil 115 194
Equidistant curve 116
Erlangen program 1 3 8 48 83 133
Euclid xi 5 132 197 199
Euclidean plane 6 8 11
Euclidean space 18
Euclidean space, n-dimensional 20
Euclid’s Elements 5 10 132
Euclid’s fifth postulate 6 133 200
Eudoxus 132
Euler — Poincare formula 141
Euler, L. 12 14 15 132 140 145
Euler’s straight line 14
Fermat, P. 8 9 132
Focus 63
Frechet, R.M. 125
Fredholm, L 132
Fundamental domain 187
Galileo 9 132 135
Gauss — Bonnet theorem 145
Gauss, C.F. 3 14 15 83 133 145 200 201
Gauss’ line 14
Gelfand, I.M. ix x 125
Geodesic 84
Geometry, affine 34 39
Geometry, convex 36 126
Geometry, elliptic 83 88
Geometry, Euclidean 5 10 21
Geometry, hyperbolic 83 100
Geometry, infinite-dimensional 123
Geometry, Lobachevsky 83 99 133 139
Geometry, non-Euclidean 83 185 200
Geometry, projective 48 158
Geometry, Riemannian 83 88
Geometry, spherical 84 88
Gram's formula 143
Gram, J.P. 143
Gramian 26
Great circle 84
Gribkov, I.V. xi
Gruenbaum, B. 143
Hadamard, J. 125
Hahn, H. 125
Hamilton, W.R. 21 196
Harmonic mean 13 160
Harmonic quadruple of points 171
Hausdorff, F. 126
Helly, E. 125 129
Helly’s theorem 44
Hilbert, D. 3 6 125 197 199
Hirzebruch, F. 1
| Homogeneous coordinates 57
Horocycle 115
Horosphere 195
Hyperbola 61 81
Hyperbolic circle 103
Hyperbolic conics 205
Hyperbolic cosine 97
Hyperbolic geometry 83 100
Hyperbolic law of cosines 102
Hyperbolic law of sines 102
Hyperbolic motion 114
Hyperbolic pencil 115 194
Hyperbolic Pythagorean theorem 101
Hypercycle 116
Hyperplane 22 58 127 128
Hypersphere 195
Incident faces 142
Induced metric 195
inversion 93
Involution 168
Isomorphic vector spaces 18
Kantorovich, L.V. 38
Kepler, J. 9 132 136
Kirkman’s theorem 72
Klein model 90
Klein, F. 1 3 6 47 83 89 133 199
Kolmogorov, A.N. xi 6 125 197-199
Koopmans, T.C. 38
Laguerre, E.N. 160
Laguerre’s formula 160
Laplace, P.S. 14
Law of cosines, hyperbolic 102
Law of cosines, spherical 87
Law of sines, hyperbolic 102
Law of sines, spherical 87
Leibniz, G. 14
Length of a curve on the sphere 84
Length, element 103
Limit circle 115
linear combination 18
Linear equations 34
Linear inequalities 23 36 38
Linear map 18
Linear programming 23
Linear space 18
Linear subspace 18
Linear-fractional transformation 93
Lobachevsky function 207
Lobachevsky geometry 99 133 139
Lobachevsky line in the Klein model 90
Lobachevsky space 193
Lobachevsky, N.I. 3 8 14 83 133 196 200 201
Lyustemik, L.A. 126
Matrix 23
Matrix, nonsingular 25
Menelaus 2 84
Metric space 8
Minding, F. 201
Minkowski, H. 36 38 126 133 146
Minor 26
Modular group 188
Moebius, A.F. 2
Motions of the Euclidean plane 8
Motions of the Euclidean space 21
Motions of the Lobachevsky plane 90 113
Motions of the Lobachevsky space 193
Newton, I. 13 15 132 135 136 138 160
Newton’s Problem 13
Oriented area 25
Oriented volume 26
Orthocentric simplex 30
Orthogonal matrix 21
Orthogonal transformation 21
Orthonormal vectors 19
Pappus 8 53 54 56 165
Pappus’ theorem 54
parabola 61 78
Parabolic motion 114
Parabolic pencil 115 194
Parallel rays in Lobachevsky geometry 100
Parallel straight line 9
Parallelepiped 24
Pascal line 71
Pascal, B. 15 71 132 166
Pascal’s theorem 15 71 166 182
Pavings 185 190
Peano, G. 125
Pencil of lines 115
Poincare disk model 95 236
Poincare upper half-plane model 96
Poincare upper half-space model 249
Poincare, H. 3 83 95 133 140 199
Poincare’s theorem 191
Points in general position 54 59
polar 86
Polar correspondence 86
Polar line 161
Pole 86
Poncelet, J.-V. 53
Poncelet’s theorem 179
Poncelet’s triangle theorem 184
Pope, A. 138
Princess Elizabeth’s theorem 16
Projective correspondence 50
Projective geometry 158
Projective space 57
Projective space, complex 158
Projective transformation 49 58
Pseudosphere 197
Ptolemy 84
Pythagoras xi 8 132
Pythagorean Theorem 12
Pythagorean theorem, hyperbolic 101
Quadrics 73 81
Quadrics, confocal 176
Quaternion model of the Lobachevsky space 196
Quetelet, A. 69
Radical axis 16
Rank 26
Rational parametrization 178
Rectangular parallelepiped 24
Regular polyhedron 153
Regular simplex 27
Riemann, B. 3 8 88
Riemannian geometry 83
Riesz, F. 125
Sarkisyan, R.A. xi
Scalar product 18
Schlaefli symbol 153
Schlaefli symbol of a regular polyhedron 151
Schmidt, E. 125
Schur, F. 6 199
Self-polar triangle 172
Shnirel’man, L.G- 126
simplex 27
Sommerville, D.M.Y. 143
Sperry, R ix
Sphere 27
Sphere in the Lobachevsky space 195
Spherical circle 111
Spherical conics 202
Spherical digon 86
Spherical geometry 84
Steiner — Minkowski formula 155
Steiner, J. 166
Steiner’s construction 166
Steiner’s theorem 72
Steinhaus, H. 126
Stereographic projection 95
Superparallel lines 115
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