Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Semple J.G., Kneebone G.T. — Algebraic projective geometry
Semple J.G., Kneebone G.T. — Algebraic projective geometry

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Algebraic projective geometry

Авторы: Semple J.G., Kneebone G.T.

Аннотация:

First published in 1952, this book has proven a valuable introduction for generations of students. It provides a clear and systematic development of projective geometry, building on concepts from linear algebra.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1952

Количество страниц: 405

Добавлена в каталог: 07.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Absolute conic in euclidean geometry      255
Absolute conic in non-euclidean geometry      97
Absolute invariant      194
Absolute points      34 93
Absolute points, in trilinears      128 (Ex. 21)
Absolute quadric      356
Affine geometry 1-dimensional      64
Affine geometry 2-dimensional      91
Affine geometry 3-dimensional      254
Algebraic correspondences      176
Algebraic curves and envelopes      102
Allowable coordinate representations      41
Angle, modulus and Laguerre definition      93
Apolarity      184
Associated points, in space      339
Associated points, in the plane      321
Asymptotes      119 313
Auxiliary circle      127 (Ex. 20)
Axes, of a conic      121 169
Axes, of a quadric      284
Axes, of planes for a range of quadrics      336
Axes, of points for a pencil of quadrics      330
Biaxial collmeation      350
Bifocal plane-pair      269 278
Birational transformation      230
Bitangents of a/plane quartic      344
Brianchon's theorem      143
Cayley's notation      104
Centre locus of a pencil or range of conies      164
Centre, of a conic      119
Characteristic roots and vectors      211 286 365 16)
Chasles's Theorem      20 133
Circular points      32
Class of an envelope      102
Clifford parallels      357
Coaxal circles      158 165
Collinear fields and stare      254
Collinear fields and stare, reduced equations      259 (Ex. 12)
Collineations (plane)      205
Collineations (plane), a geometrical haracterization      238 (Ex. 6)
Collineations (plane), cyclic      218—221
Collineations (plane), involutory      218
Collineations (plane), permutable      239 (Ex. 12)
Collineations (plane), real      216
Collineations (plane), which leave a conic invariant      221 240
Collineations (space)      348
Collineations (space), involutory      353
Collineations (space), which leave a quadric invariant      354 364
Collineations (space), which leave a twisted cubic invariant      364 (Ex. 5)
Complex points      12
Complexes (of lines)      367 371
Concomitants      200
Confocal quadrics      336
Confocal quadrics, complex of normals      376
Confoeal conies      166 174
Congruence transformations      358
Congruences (of lines)      367 377
conic      19 27 103
Conic, as a one-dimensional projective domain      132
Conic, axes      121
Conic, canonical parametric representation      131
Conic, centre      119
Conic, conjugate diameters      120
Conic, degenerate forms      112 117
Conic, director circle      123
Conic, discriminant      112
Conic, foci      123 294
Conic, freedom      105
Conic, normals      150
Conic, projective generation      136
Conic, proper      116
Conic, self-duality      115
Conic, space dual of a quadric cone      269
Conic, special forms of equation      129
Conies, apolar      188
Conies, harmonically circumscribed or inscribed      148
Conies, invariants of a pair      194
Conies, nets of conies      170
Conies, pencils and ranges      156
Conies, reciprocation of one conic into another      148
Conies, representation by points of $S_6$      106 388
Conies, triangularly circumscribed or inscribed      147
Conjugate lines for a quadric      271
Conjugate points, for a conio      108
Conjugate points,, for a correlation      225
Coordinates, allowable systems      41
Coordinates, areal      25
Coordinates, dual (tangential)      79 244
Coordinates, homogeneous and non-homogeneous      40 41
Coordinates, homogeneous cartesian      14 22
Coordinates, homogeneous, projective      23
Coordinates, Plucker (or Graasmann)      246
Coordinates, tetrahedral      260 (Ex. 22)
Coordinates, trilinear      25
Correlations (plane)      224
Correlations (plane), generating (2, 2) correspondences on a conic      240 (Ex. 19)
Correlations (space)      359 364
Covariants and contra variants      199
Cremona transformations      230
Critical points of a correspondence      177
Cross axis, of related ranges on a conic      141
Cross axis, of related ranges on lines      89
Cross ratio      17 26 45
Cross ratio, of pairs of points on a conic      133
Cross ratio, six cross ratios of four numbers      47
Cross ratio, symmetric function of six cross ratios      69 (Ex. 18)
Cubic curves (plane), nodal      240 (Exx. 25 26)
Cubic curves (plane), projections of twisted cubic      299 325
Cubic curves (plane), property of non-singular cubic      346 (Ex. 10)
Cubic developable      310
Cubic surfaces      317
Cubic surfaces 4-nodal surface and cubic scroll      322 326 22)
Cubic surfaces, cubic ruled surface in $S_4$      384 394 3) 397
Cubic symmetroid      389
Curves in higher space, rational normal $C^{4}$      384 395
Curves in higher space, rational normal $C^{5}$ and projections      396 (Exx. 11—12)
Cylinder      283
Dandelin's Theorem      39 (Ex. 18)
Desargues, involution theorem for a pencil of conies      161
Desargues, theorem for tetrahedra in perspective      250
Desargues, Theorem for triangles in perspective      80 251
Desargues, Theorem for triangles in perspective, and failure in limiting case      99 (Ex. 14)
Descartes      7
Developable      268
Developable surface      379
Developable, cubic      310
Diameters, of conies      119
Diameters, of conies, of quadrics      283
Direct and opposite transformations      354
Director circle      123 127 165
Directrix of parabola      140
Disk quadric      265
Distance      96
Distance, non-euclidean      97 357
Duality      21
Duality, principle      79 248
Elation      54
ellipse      119
Ellipsoid      282
Elliptic paraboloid      283
Equianharmonic tetrads      48
Euclidean geometry 1-dimensional      66
Euclidean geometry 2-dimensional      93
Euclidean geometry 3-dimensional      255
Euclidean transformations      256—257
False position, method of      182
Fifth associated plane      384
Focal conies      337
Foci and directrices of a conic      38 123
Fregier point      153 (Ex. 16)
Fregier point, extension for a quadric      293 (Ex. 20)
Fundamental points (of a transformation)      232
Generators      273
Gordan's Theorem      198
Grassmann coordinates      246
Group      4 9 10
Group, projective      41
Harmonic construction      82
Harmonic locus and envelope      181
Harmonic pole and polar, for a tetrahedron      249
Harmonic pole and polar, for a triangle      78
Harmonic relation      18 48
Hesse, quadrilateral      185
Hesse, Theorem for a conic      150
Homaloidal net      232
Homographic correspondences      28 50
Homographic correspondences of period 3 or 4      68 (Ex. 9)
Homographic correspondences, canonical forms      55—57
Homographic correspondences, cyclic      58
Homographic correspondences, elliptic, hyperbolic, or parabolic      67
Homographic correspondences, generation of elliptic type      101 (Ex. 25)
Homographic correspondences, on a conic      137
Homographic correspondences, representation as product of involutions      61
Homographic correspondences, representation in Argand plane      69 (Ex. 19)
Homographic ranges and pencils      82 86
Homographies, permutable      62
Homologies (plane)      214
Homologies (plane), general equations      238 (Ex. 3)
Homologies (plane), transforming one conic into another      223
Homologies (space)      351
Hyperbola      119
Hyperbola of Apollonius      151
Hyperboloid, hyperbolic paraboloid      282
Ideal elements      12 92
Incidence constructions with a conic      142
Inpolar relation      188 306
Invariants      191
inversion      39 (Ex. 20) 236 291
Involution      55
Involution, on a conic      138
Involution, on a twisted cubic      301
Involution, quaternary      305
Involution, ternary      304
Isotropic lines      93
Isotropic lines, planes      255
Jacobian curve, of a net of conies      171
Jacobian curve, of a net of conies, of a net of quadrics      342
Joachimsthars equation      107 265
Klein, Erlangen Programme      6
Laguerre's formula      95
Length      97
Line at infinity      13 92
Line systems      367
Line-coordinates      22 75 244 366
Linear dependence of points      73 242
Linear transformations, basic theorem      398
Mobius net      207
Net, of conies      170
Net, of quadrics      339
Non-euclidean geometry 1-dimensional      70 (Ex. 21)
Non-euclidean geometry 2-dimensional      97 223
Non-euclidean geometry 3-dimensional      356
Normals, to a conic      150
Normals, to a quadric      293 (Exx. 16 18) 338 376
Null polarity      311 361 364
Order, of a Cremona transformation      232
Order, of a plane curve      102
Order, of a twisted cubic      296
Orthocentre      99 (Ex. 15) 172
Orthogonality      see “Perpendicularity”
Outpolar relation      188 306
Pappus's Theorem      81
parabola      119
Parabolic cylinder      283
Parallels      13 92 254
Parallels, right and left      357
Pascal's theorem      143
Pencil, of conics      156
Pencil, of lines      83
Pencil, of quadrics      327
Perpendicularity      34 93 255
Perpendicularity, non-euclidean      97 357
Perspective (relation), conies      333
Perspective (relation), perspective ranges and pencils      86
Perspective (relation), triangles      81
Perspectives (transformations)      see “Homologies”
Perspectives (transformations), perspectivity      86
Perspectives (transformations), skew perspective      350
Points at infinity      13 92
Polar k-points and k-sides      184
Polar lines for a quadric      271
Polarity, for a conic      108
Polarity, for a quadric      266
Polarity, for a twisted cubic      311
Polarization      198
Poncelet      5
Poncelet, Porism      147 181
Position ratio      10 44
Primal      383 388
Prime      387
Principal axes, transformation to      285
Projection      15
Projection, in $S_{4}$      383
Projection, in $S_{5}$      388
Projection, of a quadric      278
Projection, of a twisted cubic      299
Projective equivalence      15
Projective geometry      10
Projective geometry 1-dimensional      42
Projective geometry 2-dimensional      72
Projective geometry 3-dimensional      241
Projective geometry, general definition      40
Projective geometry, subordinate      76 134 247
Projective hierarchy      6 9
Projective parameter      25 43
Projective transformation      29
Pseudo-invariant      194
Quadrangle      18 88
Quadratic complex      372
Quadratic forms, reduction to sum of squares      400
Quadratic transformation      233
Quadratic transformation, by incidence construction      259 (Ex. 13)
Quadric      263
Quadric systems, centre locus of a net      346 (Ex. 11)
Quadric systems, net      339
Quadric systems, pencil      327
Quadric systems, range      335
Quadric, centre, diameter, axes      283
Quadric, circular sections      284
Quadric, cone and disk quadric      264 277
Quadric, curves on the surface      281
Quadric, focal conies      337
Quadric, foci      338 347
Quadric, generators      273
Quadric, projection      278
Quadric, reduction to principal axes      285
Quadric, surface of revolution      285 293 346
Quadrilateral, complete      19
Quadrilateral, complete, Hesse      185
Quadrilateral, complete, metrical properties      203 (Ex. 14)
Radial expansion      217
Radial expansion, product of two expansions      239 (Ex. 10)
Range, of conies      156
Range, of conies, of quadrics      335
Rational curve      132
Reciprocal transformation      231
Reciprocation      230
Reciprocation, of one conic into another      148
Rectangular hyperbola      122
Rectangular hyperbola, orthocentric property      172 (Exx. 1 2)
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте