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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Dowling L.W. - Projective Geometry |
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| Предметный указатель |
Affinity 170
Affinity, corresponding conies in 172
Affinity, fundamental property of 170
Algebraic equations of conies 100
Anti-polarity 190
Apollonius 36
Apollonius, circle of 34
Apollonius, theorem of 174
Area, of ellipse 175
Area, of parabolic segment 173
Assumption, fundamental 5
Asymptotes 66
Asymptotic cone 110
Axis, of a cone 200
Axis, of a conic 97
Axis, of a cylinder 104
Axis, of perspectivity 22 166
Bellavitis 209
Brianchon 80
Brianchon, theorem of 68
Bundle of lines, of planes 2
Center, of conies 94
Center, of perspectivity 22 166
Center, of projectivity 118
Center, of surfaces 110
Chains, of perspectivity 37 114 160
Chord of contact 83
Circle, auxiliary 156
Circle, director 158
Circle, of Apollonius 34
Circular involution 132
Circular involution, transformations 207
Circumscribing tetrahedrons 109
Classification, of conies 66
Classification, of polarities 187
Classification, of projectivities 120
Classification, of surfaces 109
Coaxial planes 22
Collinear points 22
Collineation 161
Collineation, limiting lines of 168
Collineation, self-corresponding elements 179
Complete, n-edge 13
Complete, n-face 13
Complete, n-plane 14
Complete, n-point 12 14
Complete, n-side 13
Concurrent lines 22
cones 79 199
Configuration, of Desargues 15
Configuration, of Pappus 70
Confocal, conies 157
Confocal, elements 196
Conform transformations 206
Congruence 178
Conic sections 66
Conjugate, diameters 94
Conjugate, diametral planes 104
Conjugate, of an ideal point 30
Conjugate, points and lines 86
Construction of confocal elements 196
Construction of curves and envelopes 62
Construction of cyclic projectivities 121
Construction of foci 146
Construction of harmonic ranges 27
Construction of perspectivity 166
Construction of polarity 184
Construction of poles and polar lines 84
Continuity, principle of 77
Continuity, theorem of 43
Converse theorems 22 40 69 122
Coplanar figures 22
Correlation of geometric figures 16
Cremona 209
Cross-ratio 31
Cross-ratio of harmonic range 32
Curves, classification of 66
Curves, of second order 56
Cyclic planes 201
Cyclic planes, projectivities 121
cylinders 79
Dandelin 209
Dedekind postulate 42
Desargues 15
Desargues, configuration of 15 22
Desargues, theorem of 20 134
Determination of projective relationship 50 163
Diagonal pyramid 92
Diagonal pyramid, triangle 91
Diameters 94
Diametral planes 104
Dimensions of primitive forms 19
Directrices 149
Duality 161
Duality in a plane 8
Duality in space 9
Duality, principle of 10
Elementary forms 55
Elementary forms, relations among 64
Elementary forms, totality of 66
Elements, the 1
Elements, the, common, of double polarity 193
Elements, the, confocal, of double polarity 196
Elements, the, double conjugate, of double polarity 194
Elements, the, double, of projectivity 119
Elements, the, dual 8
Elements, the, fundamental 202
Elements, the, homologous 16
Elements, the, ideal 5
Elements, the, reciprocal 8
Elements, the, self-corresponding 44 116
Elements, the, separated 39 40
ellipse 66
Envelope 56
Equation, of circle 102
Equation, of ellipse 100
Equation, of hyperbola 100
Equation, of parabola 103
Fermat 209
Field of points, of lines 2
Figures, complete 12
Figures, coplanar 22
Figures, geometric 16
Figures, in space 13
Figures, simple 10
Focal radii 150
Focal radii, axes 201
Focus 146
Forms, elementary 55
Forms, primitive 2
Generation of elementary "forms of particular conies and envelopes 78
Generation of elementary forms 55
Generator of ruled surface 105
Geometric figures 16
Geometric figures, mean 33
Gergonne 15
| Harmonic elements 112
Harmonic elements, conjugates 27
Harmonic elements, mean 32
Harmonic elements, pencils 28
Harmonic elements, ranges 25
Harmonic elements, scales 38
Hyperbola 66
Hyperboloids 110
Imaginary elements 141
Imaginary elements, lines 138 141
Imaginary elements, planes 139
Imaginary elements, points 137
Infinitely distant 6
Invariant of perspectivity 167
inversion 204
Involution 127 168
Involution, circular 132
Involution, determined by quadrangle 133
Involution, determined by quadrilateral 133
Involution, elliptic 128
Involution, hyperbolic 128
Involution, on a sheaf of rays 132
Involution, on a straight line 130
Involution, parabolic 129
Kreis - Verwandshaft 209
Limiting lines of a collineation 168
Linear complex, special 3
Magnus 209
Moebius 54 209
Normal conjugate rays 30
Notation 2 19
Order, effect of 26
orthocenter 137
Orthogonal circles 34
Orthogonally correlated bundles 160
Pappus 36
Pappus, configuration of 70
parabola 66
parallel 5
Pascal 80
Pascal, theorem of 68
Pencil, harmonic 28
Pentagon theorem 73
Perspective position 16 113 159
Perspectivity 165
Perspectivity, harmonic 168
Perspectivity, invariant of 167
Planes, cyclic 201
Planes, diametral 200
Planes, of symmetry 104
Planes, principal 104
Pluecker 209
Point of contact 58
Point-row 2
Polar figures 89
Polar figures, planes 108
Polarity, absolute 192
Polarity, double 192
Polarity, in a bundle 189
Polarity, in a plane 183
Polarity, orthogonal 190
Polarity, self-conjugate elements of 185
Pole-rays and polar planes 91
Poles and polar lines 81
Poles and polar lines, special positions of 83
Poncelet 15
Postulate, Dedekind 42
Primitive forms, of the first kind 37
Primitive forms, of the second kind 159
Principle of continuity 77
Principle of duality 10
Projection and section 3
Projection, central 1
Projective relationship 38 114 160
Projective relationship, determination of 50 115 163
Projectivity 38 165
Projectivity, cyclic 121
Projectivity, elliptic 120
Projectivity, hyperbolic 120
Projectivity, parabolic 120
Projector 3
Projector of regulus 65
Properties of curves and envelopes 57
Properties of the similitude 176
Properties, reflection 154
Quadrangle, complete 12
Quadrangle, theorem 76
Quadrangles in perspective position 23
Quadric transformations 202
Quadric transformations, perspective 203
Quadrilateral, complete 13
Radical axis 177
Ranges, harmonic 25
Reflection properties 154
Regulus 57
Section 3
Section of regulus 65
Section of surface 106
Self-conjugate elements 185 190
Self-corresponding elements 44 179*
Self-polar figures 91
Seydewitz 209
Sheaf, of lines or planes 2
Sheaf, of planes of second class 56
Similarly projective 79
Similitude 176
Similitude, inverse points 177.
Similitude, properties of 176
Simple n-edge 13
Simple n-face 13
Simple n-point 11
Simple n-side 11
Space, of points, of rays, of planes 3
Steiner 93 209
Superposition 44 116
Surfaces, classification of 109
Surfaces, ruled 105
Tangent cones 108
Tangent cones, line 58
Tangent cones, lines and planes 107
Theorem, of Apollonius 174
Theorem, of Brianchon 08
Theorem, of continuity 43
Theorem, of Desargues 20 134
Theorem, of Pascal 68
Theorem, of Von Staudt 46
Theory of involution 127
Trace 3
Transformation, birational 207
Transformation, circular 207
Transformation, conform 206
Transformation, Cremona 209
Transformation, quadric 202
Vertices of a conic 99
Vieta 209
Von Staudt 54
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