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| Ïîèñê ïî óêàçàòåëÿì |
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| Coxeter H.S.M. — The Real Projective Plane |
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| Ïðåäìåòíûé óêàçàòåëü |
Abscissa 30 150 153 181
Absolute involution 117 184—180 188
Addition of points 145—148
Affine coordinates, ISO 181
Affine geometry 1 85 98 145 158—159 180—188
Affinity 112
Altitudes of a triangle 118 128 184
Analytic geometry 30 168—188
angle 8 9 125—129 184
Angle bisector 126 131
Anharmonic ratio (see Cross ratio)
Antiprojectivity 188
Apollonius 69—70 73 111—113 123—124 134 189
Archimedes 137—139
Area 2 10 5 108 115 125 181—182
Areal coordinates 182 183
Artin, Emil 105
Associative laws 14 1—14
Asymptotes of a hyperbola 4 110 113—116 183
Axiom of continuity 31 138
Axioms of incidence 12 14
Axioms of order 22 33
Axis of a conic 122 124
Axis of an elation or homology 54
Axis of conic 90 95
Axis on two lines 41
Biratio (see Cross ratio)
Bisection of a segment 101 140
Bisection of an angle 126 131
Braikenridge, William 69—70 78—79 88
Branches of a hyperbola, S 110
Brianchon, C. J. 70 89 185
Bundle of lines and planes 5
Calculus of extension 169
Canonical form for a conic 175
Canonical form for a hyperbolic involution 153
Canonical form for a polarity 173
Canonical form for an elliptic involution 154
Cantor, Georg 103 138—142
Cartesian coordinates 148 150 183 185
Categoricalness 159—160
Center of a circle 119
Center of a conic 109—112
Center of a pencil 18
Center of an elation or homology 54
Center of an involution, on the affine line 103
Center on a conic 93
Centers of similitude 120—122
Central conics 110 123
Central inversion 105
Central of a triangle 122 182 186
Central projection 2—7
Chain on the complex line 187
Chaslcs, Michel 62 70 77—78 111—112 129 172 189
Chord of a conic 111
circle 3 53 69 92 119—124 183—186 188
Circuincircle of a triangle 119 122 185
Circular points at infinity 188
Circumrenter of a triangle 119 122 186
Classification of conics 109—110
Classification of polarities 70
Classification of projectivities 42 91
Collinear points 7 12 27 160—161
Collineation 36 52—58 67 91 167—170 Perspective
Common pair of two involutions 48 93
Commutative laws 145—148
complex numbers 187—188
Concentric circles 120 184
Concurrent lines 6 12 162
Cone 3 69 122
Configuration of Desargues 13 14 55 62 65—66 73 81
Configuration of inflexions of a cubic 188
Configuration of Pappus 40 42 66 163 174
Confocal conics 184
Congruence by a half-turn 106
Congruence by rotation 124
Congruence by translation 100 105
Congruent angles 126—129
Congruent transformation 129
conic 69—70 72—97 109—116 122—125 132—136 145—150 154 175—184 Center Construction Diameter Directrix Eccentricity Ellipse Focus Hyperbola Parabola Polarity Tangent Vertex
Conic through five points 77—79
Conjugate axis of a hyperbola 123
Conjugate diameters 111
Conjugate hyperbolas 112
Conjugate lines 59 61 73 93 172
Conjugate points 59 61 73 171
Consistency 158—159
Construction for a conic 76 79
Construction for a diameter 111
Construction for a focus 133—134
Construction for a polarity 64
Construction for a projectivity 89 41
Construction for a tangent 74 79
Construction for an involution 50 93
Construction for the invariant points of a projectivity 92
Continuity 22 103 138 165
Coolidge, J. L. 52 95 126 189
Coordinate axes 180
Coordinate transformation 169 176 183
coordinates (see Affine coordinates Areal Barycentric Cartesian Envelope Homogeneous Trilinear
Correlation 52 57—64 170—171
Correspondence 18 159 Opposite Ordered
Coxeter, H. S. M. 5 26 131 189
Cremona, Luigi 2 52 61 92 189
cross (see Angle)
Cross ratio of four points on a line 165
Cross ratio of two points and two lines 166
Cubic curve 188
Cyclic order 22—24
De la Hire (see La Hire)
Dedekind, Richard 22 137 143—144
Degenerate conic 81—82 97 176—177
Degenerate involution 47 49 60 147 148 177
Degenerate polarity 173—174 184—185
Dehn, Max 41 109 189
Dense set 140
Desargues involution theorem 77 81 87 118 178
Desargues two-triangle theorem 6—7 12 17 41 55 62 65 73 80
Desargues, Girard 8 70 103—104 126
Descartes, Ren 6 69
Diagonal triangle 14 73—74
Diameter of a circle 120
Diameter of a conic 110—116
Dietrich, V. E. 121
Dilatation 105
Direct correspondence 28 130
Direct projectivity 42
Directed angle 8—9 127
Directrix 134—136
Dissection of a polygon 106—109
Distance 101 181
Distributive law 149
Divergent sequence 167
Division of a segment 102—103
Double contact 77 87 124
Double point (see Invariant point)
Du Val, Patrick 61
Duality 13—16 66
Duplication of the cube 69
Durell, C. V. 121 180
Eccentric ellipse 120
Eccentricity 119 135—136
Elation 54—56 105 170
Elements of Euclid 1 4 6 120
ellipse 109—110 120 134
Elliptic involution 47 03 111
Elliptic polarity 70
Elliptic projeetivily 42 91
Enriques, Federigo 22 36 44 52 54 50 62 70 72 88 92 137 143—144 189
Enumerable separation set 112
| Envelope 72 77—78 175—177
Envelope coordinates 157 160
Equation for a conic 175
Equation for a line 15 5 1 50
Equation for a point 157 100
Equivalent polygons 107
Erdos, Paul 27
Euclid 4 6 69 101 119 122 131
Euclidean geometry 1 4 52 98 117—13 5 158—159 183—18 5
Eudoxus 138
Euler, Leonhard 2 122 180
Excenter 128
Fermat, Pierre 60
Focal distances 136
Focus 132 13 5 184
Forder 11
Fractional distance 103
Fregier point. 119
Fundamental theorem 38 142—143
Gallai (see Griinwald)
Generalized perspectivity 86
Gergonne, J. D. 13—14 59 66 70
Glide reflection 132
Gnomonic projection 50
Godel, Kurt 159
Grassmann, Robert 169
Graustein, W. C. 78 162 189
Griinwald, T. (alias Gallai) 26
Half-turn 105 129
Hamilton, Sir W. R. 187
Hardy, G. II. 5 189
Harmonic conjugate 16—17 29 101 162
Harmonic homology 56—57 66 92 105
Harmonic mean 105
Harmonic net 139—143 152
Harmonic set 16 30—21 37 104—105 152
Heffter, Lothar 1 5 5 189
Hesse, L. O. 60 175 189
Hexagon of lirianchon 80 89
Hexagon of Pappus 40
Hexagon of Pascal 80 88 95 147 150
Hilbert, David 106 138 145 180
History of conics 60
Hodge, W. V. I 39 180
Holgate, T. F. 8 5 04 119 133 135 180
Homogeneous coordinates 154—157 160—188
Homol belie 105
Homology 52 54 57 00 57 84—85 170
Hyperbola 109 110 133 181—183
Hyperbola, branches of a 3 110
Hyperbolic involution 28 46 93 111 146 151
Hyperbolic polarity 70
Hyperbolic projectivity 42 19 151—152
Ideal elements 4—5
Identity 18
Ilessenberg, Gerhard 41—42 145 189
Incenter of a triangle 128 184 186
incidence 11 160
Incircle of a triangle 185
Inflexions of a cubic 188
Interior of a conic 72
Interior of a triangle 100 167
Interior of an interval 24
Intermediacy 99
Internal convexity 188
Intersection 11
interval 24
Invariant point 27 81—33 42 91—92 153 170
Inverse correspondence 18
inversion 53 124 179
Involution 46—50 77 81 103—104 145—154 172 Elliptic Hyperbolic Orthogonal
Involution on a conic 93
Involutory collineation 56—57
Involutory correlation (see Polarity)
Jenkins, James 95
Johnson, R, A. 8 127 189
Join 11
Kepler, Johann 4 69—70
Kronecker, Leopold 168
La Hire, Philippe de 52 70 99 111 132
Lehmer, D. N 99 189
Leibniz, G. W. 88
Leisenring, Kenneth 90 180
Length 106 124
Levi, F. W. 42 189
Liiroth, Jakob 142
LIMIT 137—143 152
Line 10 160
Line at infinity 5 98 182 184
Line coordinates 157 160
Linear fractional transformation 151
Linear homogeneous transformation 167
Maclaurin, Colin 40 69—70 78
Major axis of an ellipse 124
Mathews, G. B. 49 75 142 189
Maurolycus 13
Median class of a set of points 142
Medians of a triangle 101
Menaechmus 69
Menger, Karl 14
Meobius, A. F. 52 169
Mid-point 101 140
Minkowski, Hermann 1
Minor axis of an ellipse 124
Model 158—159
Monotonic sequence 137—143 147 165 167
Moore, J. C. 135
Multiplication of points 148—150
Mydorge, Claude 70
Net of rationality 139 143 152
Newton, Sir Isaac 52 69
Nine-point center 122 18
Nine-point circle 121 186
Nine-point conic 84 85 110 11 5
Non — Euclidean geometry 1 189
Normal to a conic 119
Oblique triangle 117—118
One-dimensional geometry 22—34 42 41 145—154
Opposite correspondence 28 130
Opposite projectivity 42
Order in a pencil 34
Order on a conic 86
Order on a line 22—34 150
Ordered correspondence 27—32 142—144
orthocenter 118 121—122 135—136 186
Orthogonal involution 117
O’Hara, C. W. 40 145 189
Pappus 40—42 66 69 88 91 109 135 145 169 174
parabola 3 78 109—110 122 133—135 181 183
Parabolic projectivity 42 45 50 91 100—101 111 151—152
Parallel lines 2 4 98 103
Parallel projection 1 99
Parallelogram 98 107
Parameter for a point on a conic 176
Pascal, Blui.se 70 86 88—91 95 147 150 178
Pasch, Moritz 41 109 189
Pedal triangle 118 128
Pedoe, Daniel 39 189
Pencil of conics 83 85 177
Pencil of lines 18 31
Pencil of parallel linos 4
Pencil of polarities 66—67 81 83 174
Pentagon 04
Perfect set 139
Periodic projectivity 45 170
Perpendicular lines 117 181—18 5
Perspective ollincation 54—57
Perspectivily 19 39
Picken, IX K. 8 1 27
Pieri, Mario 12 33 142 104 189
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