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| Coxeter H.S.M., Greitzer S.L. — Geometry revisited |
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| Предметный указатель |
 123
Affine collineation 101
altitudes 9
Ammonium radical  127
Angle bisectors, external 16
Angle bisectors, internal 9
Angle of incidence 87
Angle of reflection 87
Antipodal points 152 183
Antisimilitude, circle of 121 186
Archimedes of Syracuse 6 59
Area 3
Area, negative 52
Area, positive 52
Artificial satellite 149
Artobolevski , I.I. 109
Asymptotes of a hyperbola 139 141 146
Ball, W. W. R. 181
Bell, E. 1 31 46 59 181
Bevan, B. 22
Bolyai, J. 126
Bottema's triangle 156
Bottema, O. 16
Brahmagupta 57
Brahmagupta, formula 56ff
Braikenridge, W. 76
Brianchon, C. J. 77
Brianchon, C. J., theorem 77 79 144
Brunelleschi, F. 70
Butterfly Theorem 45 162
Cartesian coordinates 32
Casey, J. 24 112
Catenary 129
Center of a conic 147
Center of gravity 7
Centroid 7
Ceva, Giovanni 4
Ceva, Giovanni, theorem 4 53 67
Cevian 4
circle 27 107
Circle, auxiliary 150
Circle, coaxal 35 120 137 183
Circle, Euler 22
Circle, great 152 185
Circle, nine-point 20 21 117 131
Circle, of antisimilitude 121 186
Circle, of Apollonius 114
Circle, of inversion 108
Circle, orthogonal 115
Circle, reciprocating 136
Circle, Soddy's 114 130 176
Circumcenter 7 29 111
circumcircle 7 131 137
Coaxal circles 35 120 137 183
Coaxal circles, pencil of 35
Cohn - Vossen, S. 182
Collinearity 51
comet 140 178
Concurrence 51
Configuration 125 133
Configuration, dual 133
Congruence 80
conic 132 138 179 183
Conic, central 147
Conjugate lines 135
Conjugate points 135
Contrapositive 15
Coolidge, J. L. 129
Coprime 93
Courant, R. 88 181
Court, N. A. 181
Coxeter, H. S. 75 181
Cross ratio 107 112 153 184
Deltoid 44
Desargues, G. 70
Desargues, theorem 70 146
Descartes, R. 31
Diagonal 52 73
Dilatation 80 94 184
Dilatation, central 94 101
Direct similarity 184
Directed distances 141
Directed line segments 30
Directrix 141 146
Dodgson, C. L. 51 154 183
Dual configuration 133
Duality 132
Durell, N. V. 181
Eccentricity  139
ellipse 139
Enneagon (9-gon) 50
Envelope 134
Equilateral triangle 25 63 162
Escribed circles 13
Euclid of Alexandria 1 27 141
Euler, L. 19 29 130
Euler, L., circle 22
Euler, L., line 19 137 157 162 184
Excenters 13
Excircles 13
Exradii 13
Fagnano problem 88
Fagnano, J. F. 88
Fejes T th, L. 181
Fermat point 83
Fermat, P. 31 65
Feuerbach theorem 22 117
Feuerbach, K. 22
Flaubert, G. 132
Focal distance 141
Focus 132 141
Forder, H. G. 74 99 181
Functions, exponential 126
Functions, hyperbolic 126
Gardner, Martin 15
Gauss, C. F. 126
Geometry, hyperbolic 126
Geometry, inversive 88 132
Geometry, non-Euclidean 126
Geometry, projective 51 136
Gergonne point 13
Gnomonic projection 151 185
Greitzer, S. L. 75
Half-tum 21 80 85 95 147
Hardy, G. H. 182
Henderson, A. 16
Heron of Alexandria 59
Heron of Alexandria, formula 58
Hexagon 73 179
Hilbert, D. 182
Hobson, E. W. 109
Homeomorphism 101
Homothetic 5 72
Horner, W. G. 46
Hudson, H. P. 111
Hyperbola 139
Hyperbola, rectangular 141
Hyperbolic functions 126
Hyperbolic geometry 126
Hypocycloid 44
Ideal line 150
Ideal point 150
Identity 81
Incenter 10 29 111
incidence 133
incircle 10
Inradius 10
Invariant point 99
Inverse, locus 108
Inverse, of a circle through  109
| Inverse, of a line 109
Inverse, of a point 108 150 185
Inverse, of a triangle 110
inversion 108ff
Inversion, antiinversion 180
Inversion, circle of 108
Inversion, in a sphere 150
Inversion, inversive definition of 116
Inversive distance 123 185
Inversive geometry 88 132
Inversive plane 112 113 150 151
Isogonal conjugates 93
Isometry 81 185
Jacobian 175
Johnson, R. A. 46 182
Jupiter 178
Kazarinoff, N. D. 88 182
Kempe, A. B. 109
Kepler, J. 27 140
Klein, F. 27 80
Lagrange, J. 63
Lamb, H. 56 182
Laplace, P. 63
Law of Cosines 58
Lehmus, C. L. 14
Leibniz, G. W. 74
Limiting points 120
Line at infinity 144
Linkage 109
Lipkin, L. 109
Lobachevsky, N. 126
Lockwood, E. H. 109 182
Logarithm (natural) 123 124
Maclaurin, C. 76
Magnus, L. J. 108
Mapping 80
Medial triangle 18
Medians 7
Menelaus of Alexandria 66
Menelaus of Alexandria, theorem 66
Mid-circle 121 137 174 186
Miquel, A. 62
Mirror 86
Morley theorem 47
Morley, F. 47 88
Napoleon Bonaparte 63
Napoleon triangles 61 63ff 186
Napoleon triangles, inner 63 64 100
Napoleon triangles, outer 63
Naraniengar 47
Neuberg, J. 23
Newton, I. 30 74 140
Nine-point center 21
Nine-point circle 20 21 117 131
Non-Euclidean geometry 126
O'Beirne, O. H. 89 182
Oppenheim, A. 25
Orbit 140
Ore, O. 182
Orthic triangle 9 16 88
orthocenter 9 38 111
Orthocentric quadrangle 39 119
Orthogonality 114
Palindrome 63
Pappus Of Alexandria 67 141 146
Pappus of Alexandria theorem 67
parabola 139 146 179
Parade of angles 25
Parallelogram 56
Parallelogram, degenerate 81
Pascal line 75 186
Pascal theorem 74 166
Pascal, B. 74 144
Peaucellier cell 109
Peaucellier, A. 109
Pedal point 22
Pedal triangle 22 40 186
Pedoe, D. 182
Pencil of circles 35 186
Pentagon 50 52 79
Perel'man, A. I. 89
Perfect, H. 182
Perspective 49
Perspective triangles 70
Perspectivity from a line 70
Perspectivity from a point 70
Petard, H. 103
Petersen - Schoute theorem 100
Petersen, J. 99 182
Pivot theorem 62
Planets 27 140
Planets, perturbation by 178
Point at infinity 113 144
polar 133 150
Polar circle of a triangle 137 187
Polarity 145
Pole 133
Polygon 51
Poncelet, J. V. 22
Power of a point 27 30
Preservation of angles 114
Principle of duality 133
Procrustean stretch 101 102
Projection, gnomonic 151
Projection, stereographic 151 180 188
Projective geometry 51 136
Projective plane 132 144 150 152
Ptolemy's theorem 42 106 165
Quadrangle, complete 134
Quadrangle, convex 52
Quadrangle, crossed 52
Quadrangle, cyclic 57
Quadrangle, orthocentric 39 119
Quadrangle, re-entrant 52
Quadrilateral, complete 134
Radical axis 34 78 122 160 187
Radical center 35 38
Ratio of magnification 94
Reciprocating circle 136
Reciprocation 132 187
Reductio ad absurdum 16
Reflection 86
Regular polygon 187
Robbins, H. 88 181
Rotation 80 82 96
Satterly, J. 9
Schoute, P. H. 99
Schwarz, H. A. 88
Self-conjugate line 135
Self-conjugate point 135
Self-inverse point 108
Self-polar triangle 136 146
Separation 103 188
Shervatov, V. G. 182
Similar triangles 34 62
Similarity 80 94 188
Similarity, direct 95
Simson line 40 41 43 62
Simson line, oblique 62
Simson, R. 6 41
Smogorzhevskil, A. S. 77 182
Soddy's circles 114 130 176
Spieker 75
Spiral similarity 95 188
squares 65 96
Steiner - Lehmus theorem 14
Steiner porism 124 175 180
Steiner, J. 14 30
Stereographic projection 151 180 188
Stewart 6
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