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| Verdina J. — Projective Geometry and Point Tranformations |
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| Предметный указатель |
Plane of lines 23
Plane of points 23
Plane polarity 101
Plane, definition 1
Plane, homogeneous 3
Plueckerian coordinates of the line 20
Point at infinity 16
Point transformation 119 145
Point transformation, approximating another point transformation 122
Point transformation, between two r-dimensional spaces 155
Point transformation, characteristic curves 149
Point transformation, characteristic directions 148
Point transformation, characteristic projectivities 150
Point transformation, invariance of the contact 121
Point transformation, Jacobian 146
Point transformation, neighborhood of a pair of corresponding points 146
Point transformation, neighborhood of the rth-order 146
Point transformation, osculating another point transformation 153
Point transformation, osculating projectivity 121 122
Point transformation, quadratic transformations osculating a point transformation 155
Point transformation, regular pair of corresponding points 146
Point transformation, tangent 153
Point transformation, transformations which approximate others 152
Point, definition 1
Point, finite 16
Point, fundamental 3
Point, multiple 111
Point, real 2
Point, unit point 3
Points common to two conies 105
Polar line 99
Polarity as an involutory correlation 101
Polarity, plane 101
Pole 99
Principle of duality 23
Projective character of the contact 116
Projective plane 24
Projective spaces 7 23
Projectivity between directional pencils 147
Projectivity between lines 27
Projectivity between lines, characteristic invariant 39
Projectivity between lines, elliptic projectivity 39
Projectivity between lines, equations 27
Projectivity between lines, fixed points 38
Projectivity between lines, hyperbolic projectivity 39
Projectivity between lines, involution 40
Projectivity between lines, modulus 28
Projectivity between lines, parabolic projectivity 39
Projectivity between lines, the fundamental theorem 33
Projectivity between lines, united points 38
Projectivity between lines, vanishing points 39
Projectivity osculating a point transformation 121
Pyramid, fundamental 3
Quadratic transformation 127
Quadratic transformation of the first kind 131
Quadratic transformation of the second kind 131
Quadratic transformation of the third kind 131
Quadratic transformation, a line is transformed into a conic through the singular points 131
Quadratic transformation, definition 127
Quadratic transformation, equations 127
Quadratic transformation, equations in reduced form 141
Quadratic transformation, it transforms a point into a conic 129
Quadratic transformation, osculating a point transformation 155
Quadratic transformation, preserving ratios of corresponding areas 141
Quadratic transformation, singular lines 130 131
Quadratic transformation, singular points 129—131
Quadrics 13
| Quadrilateral in the projective plane 51
Quadrilateral in the projective plane, definition of 51
Range of points 23
Rank of matrix 168
Rational algebraic curves 123
Rational algebraic curves, definition 123
Reducible algebraic hypersurface 13
Riemannian geometry 164
Riemannian space 164
Riemannian variety 163
Sets 177
Similitude 163
Simple polygons 51
Singular points of a quadratic transformation 129
Singular points of the inversion in the complex plane 130
Singular projectivity 28
Space, complex 2
Space, definition 1
Space, Euclidean 162
Space, homogeneous 2
Space, n-dimensional homogeneous space 2
Space, n-dimensional space 1
Space, nonhomogeneous space 2
Space, projective 7
Space, real 2
Space, Riemannian 163
Special homology 60
Steiner, theorem 107
Subspaces, intersection of 12
Subspaces, skew 12
Subspaces, union of 12
Superposed lines 28
Superposed spaces 4
surface 2 161
Tangent collineations 153
Tangent line, indeterminate 96
Tangents to a conic 90
Tangents to a conic at a double point 114
Tangents to a conic at a multiple point 114
Tangents to a conic at a simple point 95
Tangents to a conic from a point 97
Tangents to a curve at the origin 113
Transformation 181
Transformation of projective coordinates 8
Transformation, birational 127 132
Transformation, conformal 160
Transformation, Cremona 127
Transformation, cubic 157 See
Transformation, group 4
Transformation, point transformation 111 119
Transformation, point transformation, algebraic 120
Transformation, point transformation, degenerate 120
Transformation, quadratic 127
Transformation, rational 132
Triangle in the projective plane 51
Triangle in the projective plane, definition 51
Triangle in the projective plane, sides 51
Triangle in the projective plane, vertices 51
Triple point of a curve 112
Two-dimensional forms 23
Unit point 47
Vanishing lines 55
Variety 161
Variety, k-dimensional 2
Variety, linear 161
Variety, parametric equations 161
Variety, Riemannian 163
Variety, t-dimensional linear 2
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