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| Авторизация |
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| Поиск по указателям |
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| Archbold J.W. — Introduction to the Algebraic Geometry of a Plane |
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| Предметный указатель |
Harmonic pole and polar, relative to a conic 93 94 96 98
Harmonic pole and polar, relative to a triangle 80
Harmonic, conic 177
Harmonic, conic-envelope 179
Harmonic, conjugate 63 79
Harmonic, cross-ratio 63
Harmonic, homology 204
Hesse, X. O. 101 194
Hessian point and line 103
Homaloidal net of curves 273
Homogeneous co-ordinates 29
Homogeneous co-ordinates, generalised 70 ff.
Homogeneous parameters 30
Homography 197
Homology 201
Homology, equations of a 202
Homology, harmonic 202
Homology, homothetic 204
Hudson, H. P. 273
Hyperbola 145 156
Hyperbola, conjugate 159
Hyperbola, its branches 158 161 167
Hyperbola, rectangular, of Apollonius 150
Identity collineation 198
Identity element of a group 34
Identity, projectivity 51
Inaccessible points and line 27
Incidence condition of, for a point and line 29
Incidence conic and conic-envelope of a correlation 226
Indeterminate 38
Indices of a correspondence 246
Infinity, points and line at 40
Infinity, the number 38
Inflexion 260 269
Inflexion, simple 269
Inflexion, tangent at an 260
Inpolar conic-envelope 192
Interior chord 144
Interior point 143
Intersections of a conic and a line 90
Intersections of a curve and a line 259
Intersections of two conics 115
Intersections of two curves 272 275
Interval from one line to another 68
Intervals, bisectors of the, between two lines 70
Intervals, with the same or opposite senses 68 69
Invariant, distance as an 18
Invariant, points of a collineation 200
Invariants, projective 60 219 230
Invariants, projective, fundamental, of a pair of conics 231
Invariants, projective, of a group of transformations 44 60
Invariants, projective, relative and absolute 230 ff.
Inverse curve 274
Inverse element of a group 35
Inverse points 274
Inverse projectivity on a line 47 61
inversion 274
Involution 54 ff.
Involution, of pairs of points on a conic 125
Involution, of sets of points on a curve 250
Involution, orthogonal 136
Involutory pair of a correlation 226
Irreducible algebraic curves and envelopes 41
Irreducible conic-envelopes 95
Irreducible conics 90
Isomorphism, simple 31
Isotropic lines 25 41
Joachimstal, F. 5 22
Limiting points 180
Line, fundamental 264
Line, in  21
Line, in  27
Line, in  6 ff.
Line, inaccessible 27
Line, of centres 181 183
Line, point equation of a 29
Line, polar 80 93 148 168
Line, real 24
Line, tangent 91 93 261
Line, unit 71
Line, unreal 24
Line-at-infinity 40
Linear branch 263
Linear conditions 113 258
Linear dependence 113
Linear system of conics 112
Lines, isotropic 25 41
Lines, Luroth, J. 57 253
Lines, perpendicular 12 24 41 69
Map of the sets of an involution 253
Mates in an involution 55
Matrix, characteristic 217 231
Median 132
Menelaus 174
Mid point of a diagonal of a quadrilateral 83
Mid point of two accessible points 66
Miquel, A. 165
Modified co-ordinates 27
Modified number systems 39
Modified plane 27
Modulus of a collineation 230
Monoid 262
Multiple correspondence 245 ff.
Multiple point 124 244 260 261
Multiplication 30
Multiplicity, virtual 220
Neighbourhood 264 275
Nine point circle 140
Node 261
Non-singular curve 261
Normals to a conic 141 160 163
Opposite foci of a conic 137
Opposite sides of a quadrangle 81
Opposite vertices of a quadrilateral 81
Order of a branch 263
Order of a finite group 33
Order of an algebraic curve 41
Order of an involution 250
Origin of co-ordinates 2
Orthocentre 133
Orthogonal circles 180
Orthogonal involution 136
Orthogonal property of confocal conics 185
Orthogonal systems of curves 195
Orthoptic locus 139
Outpolar conic 192
Pair, associated in cross-ratio 61
Pappus 76 131
parabola 133
Parabola, improper 133
Parabola, real 145 ff.
Parallel lines 9 23
Parallelogram 130
Parameter, non-homogeneous 40 105
Parameter, regular or representative 244
Parameters, homogeneous 30
Parametric equations see Equations
Pascal, B. 108 ff.
Pencil of conics 113 116
Pencil of conics, base points of a 117
Pencil of lines 12 23 30
Period of a projectivity 54
Perpendicular lines 12 24 41 69
Perspective collineation 201
Perspective projectivity 59
Perspective, space 206
Place 245
Place, branch 248
Place, double 248
Place, simple 248
| Place, united 247
Plane, complex euclidean 19 ff.
Plane, modified euclidean (real or complex) 27 ff.
Plane, projective 242
Plane, real euclidean 1 ff.
Point, accessible 27
Point, cuspidal 261
Point, double 261
Point, exterior 143
Point, Fr gier 142
Point, fundamental 264
Point, inaccessible 27
Point, inflexional 260
Point, interior 143
Point, invariant 200
Point, line-equation of 29
Point, mid 66 83
Point, Miquel 165
Point, multiple 124 260
Point, nodal 261
Point, ordinary 261 275
Point, real 21
Point, simple 260
Point, tacnodal 265
Point, triple 261
Point, unit 71
Point, united 52
Point, unreal 20
Point, variant 200
Point-at-infinity 40
Points, limiting 180
Polar co-ordinates 165 ff.
Polar curve, first 270
Polar line 80 93 148 168
Polar quadrangle 194
Polar triangles 101
Pole 80 96
Poncelet, J. F. 187 188 256
Power of a projectivity 53
Principal angle 9 ff.
PRODUCT 36 49 200
Projective aspect of a metrical theorem 173
Projective collineation 33 197
Projective equivalence of collineations 223
Projective equivalence of configurations 230
Projective generation of a conic 104
Projective generation of a conic -envelope 105
Projective geometry 241
Projective group 33
Projective invariant 60 219 230
Projective plane 33 242
Projective space 33 242
Projective transformation of a collineation 219
Projective transformation on a line 47
Projectivities between lines and pencils 58
Projectivities between rational curves and envelopes 125
Projectivity 47 58
Projectivity, group property 49
Projectivity, incidence 58
Projectivity, induced 197
Projectivity, involutory 54 ff. 58
Projectivity, on a conic 125
Projectivity, parabolic 52
Projectivity, periodic 54
Projectivity, perspective 59
Projectivity, united points of 52
Quadrangle 81
Quadrangle, polar 194
Quadratic, fundamental for a conic 90
Quadratic, fundamental for a conic-envelope 95
Quadratic, transformation 263 274
Quadrilateral 81
Quartic curve 41 263 268
Radical axis of a coascal system of circles 180 183
Radical axis of two circles 182
Radius of curvature 152
Range of conic-envelopes 121
Rank of a branch 263
Rational curve 123 244
Rational envelope 124 268
Rational function 124
Rationality of an involution on a rational curve 253
Real conic 142
Real line in 24
Real parabola 145
Reciprocal conics 150 189 190
Reciprocal element in a field 36
Reciprocal figures 189
Reciprocation 189
rectangle 130
Rectangular conic 133
Reduced transform 205
Reducible algebraic curves and envelopes 41
Reducible conic 90 92
Reducible conic-envelope 95
Reflection in a line 205
Reflection in a point 204
Regular, or representative, parameter 244
Relative invariants 230 ff.
Representation of the sets of an involution 253
Rhombus 130
Rotations, negative and positive 2
Scale of measurement 16
Self-polar or self-conjugate triangle 99
Seven, F. 276
Simeon, R. 174
Similar configurations 69
Similar conics 237
Similarity group 215 238
Similitude 215
Similitude, contra 214
Similitude, direct 213
Simple inflexion 269
Simple place 248
Simple point 260
Simply invariant line or pencil 201
Souare 130
Staudt, van, K. G. C. 197 208
Steiner, J. 164
Stretch, uniform 205
Sturm, C. 120
Subfield 37
Subgroup 32
Subgroup, cyclic 54
Subnormal 163
Successive points 3
Summation convention 199
Supplemental chords 149
System, modified, of real or complex numbers 39
Syzygy 45
Tacnode 265
Tangent 91 93 148 159 162 167 260
Tangent, inflexional 260
Terset, affine 7
Terset, complex 22
Terset, real 7
Totally invariant line or pencil 200
Transform of one bilinear equation by another 47
Transform, reduced 264
Transformation, birational 276
Transformation, Cremona 273
Transformation, inverse projective 47
Transformation, negative 19
Transformation, positive 19
Transformation, projective 32
Transformation, projective, of a collineation 219
Transformation, quadratic 263
Translation 205
triangle 43
Triangle, diagonal, of a quadrangle 81
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