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Archbold J.W. — Introduction to the Algebraic Geometry of a Plane
Archbold J.W. — Introduction to the Algebraic Geometry of a Plane



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Название: Introduction to the Algebraic Geometry of a Plane

Автор: Archbold J.W.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1948

Количество страниц: 313

Добавлена в каталог: 21.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $E_{C}$      22
Co-ordinates, of a line in $E_{M}$      29
Co-ordinates, of a line in $E_{R}$      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, ($I$, $J$)      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 $E_{C}$      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 $E_{R}$      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$\acute{e}$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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