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| Авторизация |
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| Archbold J.W. — Introduction to the Algebraic Geometry of a Plane |
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| Предметный указатель |
Abelian group 34
Absolute invariants 230 ff.
Absolute points 41
Accessible points and lines 27
Addition 34
Additive group 34
Affine linear equation 21
Affine terset 7
Algebraic co-ordinates 16
Algebraic correspondence 246
Algebraic curve 41
Algebraic distance from a line 8
Algebraic envelope 42
angle 9 ff.
Angle, eccentric 147
Apollonius 150 151 160
Aspect, projective, of a metrical theorem 173
Associated conic and conic-envelope 97
Associated pairs in a cross-ratio 61
Asymptotes 134
Attached collineation 225
Attached collineation, its projective invariants 227
Automorphism 34
Auxiliary circles 146 157
Axes of a conic 136
Axes of co-ordinates 1
Axes of co-ordinates, angle between 3
Axes of co-ordinates, formulae for change of 15ff.
Axes of co-ordinates, oblique 3
Axes of co-ordinates, rectangular 3 25
Axes of co-ordinates, with same or opposite senses, pairs of 14
Axes, major and minor, of an ellipse 146
Axes, transverse and conjugate, of a hyperbola 157
Axis of perspective 60 201
Axis, radical 180 183
Baker, H. F. 3 242 244 276
Base points of a pencil of conics 117
Base points of a pencil of conics, line equation of 121
Bertini, E. 242
Bilinear equation 46
Bilinear equation, in homogeneous form 46
Bilinear equation, non-singular and singular 46
Bilinear equation, transform of one by another 47
Birational transformation 276
Bisector of an angle 13
Bisectors of the intervals between two lines 70
Biset 30
Bitangent 272
BOND 45
Branch element of a correspondence 253
Branch of a curve 245 265 268 273
Branch of a curve, linear 263
Branch of a curve, order of 263
Branch of a curve, origin of 263
Branch of a curve, rank of 263
Branch of an envelope 268
Branch of an envelope, class of 268
Branch of an envelope, rank of 268
Branch place of a correspondence 248
Branches of a hyperbola 158 161 167
Brianchon, C. J. 109
Bussey, W. H. 243
Cauchy, A. L. 243
Centre of a conic 134
Centre of an involution 125
Centre of perspective 59 75 201
Centres, line of 181 183
Ceva, G. 174
Characteristic determinant 231
Characteristic equation 217 231
Characteristic matrix 217 231
Chasles, M 247
circle 41 42 133 169 170
Circle, auxiliary 146
Circle, director 139
Circle, improper 133
Circle, nine-point, of triangle 140
Circle, of curvature 152
Circle, point 41 133
Circle, proper 133
Circles, coaxal 180 191
Circular points 41
Class of an envelope 42 267
Cluster of multiple points 275
Co-ordinates, algebraic 16
Co-ordinates, areal 74
Co-ordinates, axes of 1
Co-ordinates, confocal 187
Co-ordinates, distance 2
Co-ordinates, homogeneous 29
Co-ordinates, modified 27
Co-ordinates, of a line in  22
Co-ordinates, of a line in  29
Co-ordinates, of a line in  7
Co-ordinates, polar 165
Co-ordinates, tangential 40
Co-ordinates, trilinear 74 169
Collineation 197
Collineation, affine 201
Collineation, attached to a correlation 225
Collineation, equations of a 207
Collineation, identity 198
Collineation, invariant points of 200 210ff.
Collineation, modulus of 230
Collineation, non-projective 198
Collineation, perspective 201
Collineation, projective 197 199
Collineation, similitude 212
Collineation, simplified forms of the equation 211
Collineation, uniqueness theorem 205
Collineations, algebraic classification 217
Collineations, general 210
Collineations, group property of 200
Collineations, non-special 220 221 227
Collineations, product of two 200
Collineations, projective equivalence of 223
Collineations, special 220 222 228
Collineations, von Staudt’s theorem for 208
Commutative group 34
Concyclic points 151 160 163
Conditions, linear 113 258
Confocal co-ordinates 187
Confocal conics 183
conic 41
Conic, central 134
Conic, director 177
Conic, eleven point 120
Conic, harmonic 179
Conic, irreducible or proper 90
Conic, outpolar 192
Conic, parabolic 133
Conic, real 142
Conic, rectangular 133 171
Conic, reducible or degenerate 90
Conic-envelope 42
Conic-envelope, ( ,  ) 170
Conic-envelope, harmonic 192
Conic-envelope, inpolar 192
Conic-envelope, irreducible 95
Conic-envelope, reducible 95
Conics, confocal 183
Conics, reciprocal 150
Conics, similar 237
Conjugate harmonic 63
Conjugate hyperbolas 159
Conjugate lines -with respect to a conic-envelope 96
Conjugate paints and lines in 24
Conjugate points with respect to a conic 94
Conormal points 142 150 160 163
Contact of two conics 115
| Contact, point of, of a tangent 93
Continuous function 151
Correlation 189 224
Correlation, attached collineation 225
Correlation, equations of 225
Correlation, its incidence conic and conic-envelope 226
Correlation, polarity 228
Correlation, projective 225
Correlation, projective invariants of its attached collineation 227
Correlation, uniqueness theorem 225
Correlations, classification of 227
Correspondence, algebraic 246
Correspondence, algebraic (2, 2) 255
Correspondence, birational 276
Correspondence, branch places of a 248
Correspondence, direct 246
Correspondence, identical 246
Correspondence, indices of a 246
Correspondence, inverse 246
Correspondence, involutory 250
Correspondence, involutory (2, 2) on a conic 257
Correspondence, one-one 1
Correspondence, symmetrical 248
Correspondence, symmetrical (2, 2) on a conic 255
Correspondence, united places of a 247
Corresponding points on an ellipse and its auxiliary circle 147
Covering of one plane or line by another 21 27
Cremona, L. 273
Cross-axis 86 127
Cross-ratio 32
Cross-ratio, equianharmonic 63
Cross-ratio, harmonic 63
Cross-ratio, in relation to angles 67
Cross-ratio, of four elements 61
Cross-ratio, of four lines 66
Cross-ratio, of four numbers 61
Cross-ratio, of four points on a conic 107
Cubic, discriminating 231
Cubic-envelope or class cubic 42
Curve, algebraic 41
Curve, covariant 236
Curve, cubic 41
Curve, first polar 270
Curve, irreducible 41
Curve, order of an algebraic 41
Curve, rational or unicursal 123
Curve, reducible 41
CYCLE 273
Cyclic subgroup 54
Desargues 75 120 131 172
Determinant 6
Determinant, characteristic 231
Diagonal points of a quadrangle 81
Diagonal points of a quadrilateral 81
Diagrams 175
Diameters, conjugate 135 148
Diameters, of a conic 135 136
Diameters, principal 136
Dilatation 204 212
Director circle of a central conic 139
Director conic 177
Director line of a parabola 139
Director locus 139
Directrix 140
Distance, as an invariant 18
Distance, between two points 2
Distance, co-ordinates 2
Distance, function 26
Distance, of a point from a line 8
Distance, sensed 3
Double place of a correspondence, Double point of a curve 261
Double points in an involution 55
Duality, principle of 42
Eccentric angle 147
Eccentricity 154 160 164 165
Elation 201
Elation, equations of an 203
Element, identity 34
Element, inverse 35
Element, reciprocal 36
Element, unit 36
Element, unreal 20
Element, zero 35
Eleven point conic 120
ellipse 145 ff.
Elliptic functions 124
Embedding of one plane in another 21 27
Envelope, algebraic 42
Envelope, algebraic, class of an 42
Envelope, algebraic, contravariant 237
Envelope, algebraic, irreducible and reducible 42
Envelope, algebraic, rational 124
equal 31
Equation, bilinear 46
Equation, characteristic 217
Equation, of a conic 90
Equation, of a hyperbola 156
Equation, of a line 6 7 28
Equation, of a real parabola 162
Equation, of an ellipse 145
Equation, polar, of a real conic 167
Equation, tangential 40
Equations, fundamental, of a collineation 217
Equations, parametric, ffor points on a conic 105 106
Equations, parametric, ffor points on a hyperbola 158 159
Equations, parametric, ffor points on a line 30
Equations, parametric, ffor points on a monoid 262
Equations, parametric, ffor points on a real parabola 162
Equations, parametric, ffor points on an ellipse 147
Equations, parametric, for lines through a point 31
Equianaharmonic cross-ratio 63
Equivalence between fields 37
Equivalence between groups 34
Equivalence of unreal elements attached to 21
Equivalence projective, of collineations 223
Euler, L. 260
Evolute 153
Extension of a field 37
Exterior chord 144
Exterior point 143
Fano, G. 242
Field 36
Finite geometry 44
Foci of a conic 137 138 154 160
Foci of a hyperbola 160
Foci of an ellipse 154
Foci, opposite or associated or corresponding 137
Focus of a real parabola 164
Fr gier 142
Frame of reference 71
Frame of reference, formulae for change of 73
Freedom of a linear system 113 258
Function, elliptic 124
Function, holomorphic 194
Function, rational 124
Fundamental theorem of algebra 20
Gaskin, T. 194
General,collineation 210
Genus of a curve 276
Geometry, Euclidean 172
Geometry, finite 44
Geometry, on a curve 245
Geometry, projective 241
Gradient of a line 10
Group 31
Group, abelian or commutative 34
Group, additive 34
Group, finite 33
Group, infinite 33
Group, similarity 215
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