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Behnke H., Bachmann F., Fladt K. Ч Fundamentals of Mathematics, Volume II: Geometry
Behnke H., Bachmann F., Fladt K. Ч Fundamentals of Mathematics, Volume II: Geometry

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Ќазвание: Fundamentals of Mathematics, Volume II: Geometry

јвторы: Behnke H., Bachmann F., Fladt K.

јннотаци€:

Volume II of a unique survey of the whole field of pure mathematic


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1974

 оличество страниц: 696

ƒобавлена в каталог: 26.02.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$T_1$-axiom      662
$\varepsilon$-covering      658
$\varepsilon$-neighborhood of a point p      638
Abelian group      11 62 619
Absolute circular point      414
Absolute conic section      414
Absolute figure      461 490
Absolute geometry      138Ч141 145Ч162
Absolute involution      413Ч414
Absolute polarity      413Ч414
Absolute simplex      611
Absolute sphere-circle      414n
Adjoint mapping      374
Adjoint representation      526
Adler, A.      228
Admissible mapping      535
Affine continuous metric plane      189
Affine geometry      180Ч182 297
Affine group      310Ч312 397 461Ч462
Affine line      527
Affine mapping      25 310Ч325 397Ч398
Affine plane      66Ч95 169 180
Affine plane, Desarguesian      182 310
Affine plane, Pappus      303Ч306
Affine point space      297Ч302
Affine reflection      316
Affine subspaces      335Ч345
Affine transormation      7 22
Affine-coordinate plane      85Ч90 114 124 300
Affinity      81Ч82 311Ч325
Affinity, algebraic description of      312Ч313
Affinity, axial      80Ч81 94 316 394
Affinity, classification of      314
Affinity, Euler      316Ч317
Affinity, representation of      93Ч95
Alexander lemma      651Ч652
Alexander, J.W.      631
Algebra, exterior, of Grassmann      294
Algebraic curves      438Ч453
Algebraic geometry      452
Algebraic surface      453Ч458
Algebraization, of Euclidean planes      124Ч127
Algebraization, of metric planes      168Ч173
Alternating product      360Ч365 486
Altitudes, of a tetrahedron      357Ч358
Altitudes, of a triangle      356
Altitudes, theorem of      125Ч126 152Ч153
angle      13Ч18 185Ч186 417Ч419
Angle, at the circumference of a circle      362
Angle, between vectors      346
Angle, bisection of      151 356Ч357
Angle, cosine theorem for      372
Angle, measure of      361 417n 495
Angle, of a polygon      239Ч242
Angle, of rotation      418
Angle, oriented      361
Angle, trisection of      230Ч233 235
Angle-sum      367Ч368 507
Annulus      598
Anti-prism      278
Antiparallel-equal      36Ч37
Apollonius      437
Apollonius contact problem (tangency problem)      480 485Ч486
Approximation, simplicial      631 665Ч666
Arc, cos function      347
Arc, Jordan      643Ч644
Arc, length      537Ч538 547
Arc, of a curve      640
Archimedes      233
Archimedes, axiom of      13 184Ч185
Archimedes, spiral of      437
Archimedes, system      13
Area      18Ч23
Area, of an oval      576
Area, surface      373 547Ч551
Asplund and Grunbaum theorem      584
Asymptote      440
Asystatic representation      525
Automorphism, group      24 460Ч461
Automorphism, inner      526
Automorphism, of Euclidean space      374
Axial affinity      80Ч81 94 316 394
Axial perspectivity      402
Axioms      11
Axioms, independence of      27Ч28
Axioms, model of, system      62Ч63
Axioms, of order      339
Axioms, system for absolute geometry      138Ч141 145Ч147
Axioms, system for affine planes      66Ч68
Axioms, system for Euclidean planes      113Ч114
Axioms, system for three-dimensional projective space      102Ч105
Axis, of a central collineation      393Ч395
Axis, of a conic section      422Ч424
Axis, of a pencil      148
Axis, of perspectivity      97
Axis, of reflection      378
Axis, of rotation      417
Axis, principal      380
Axis, radical      429
Banach space      349
Barycentric coordinates      344 390 665 667Ч668
Base points of a pencil      429
Base, ordered      340
Basis      296
Basis, conjugate      328
Basis, for a topological space      663
Basis, orthogonal      347
Basis, orthonormal      348 353 415
Bernoulli, Johann      562
Betti group      621
Betti number      621Ч622 631 650
Bilateral      6Ч7
Bilinear form      108Ч109 110 325Ч327 329 345Ч346 379Ч380
Bilinear outer product      486
Binormal      539
Birational correspondence      440
Birational equivalence of two curves      452Ч453
Birational transformation      438 454
Birationally related classes of surfaces      458
Blaschke's theorem      576 577Ч579 583Ч584
Bolyai, Janos      490
Boundary chain      616Ч617
Boundary curve      595
Boundary of a domain      648
Bounded set      639
Bounding line      573
Bourbaki, Nicolas      661
Branch of a curve      441
Breadth of a curve      574
Brianchon theorem      158Ч160 426
Brill, A.W.      438
Brouwer dimension theorem      654
Brouwer, L.E.J.      595 659
Brunn theorem      581
Bundle, dualization      408
Bundle, model of elliptic geometry      502Ч503
Bundle, of circles      473Ч474 484
Bundle, of cycles      479
Bundle, of Lie circles      484
Bundle, of lines      401 488
Bundle, of planes      401
Calculus of variation      559Ч560
Calculus, of segments (Hilbert)      90Ч93
Calculus, reflection      30
Calculus, vector      30
Calculus, with points      30
Canonical system of generators      62
Cantor definition of a curve      660
Cantor discontinuum      637
Carpenter's square      235Ч237
Carrier      148 167Ч168 387 401
Carrier simplex      665
Cartan, E.      533
Cartesian coordinate system      415
Cartesian product      176n
Castelnuovo, Guido      438
Cauchy theorem on polyhedra      266
Cauchy Ч Schwarz inequality      346
Cavalieri principle      20
Cayley, A.      107 490
Cayley-Klein geometries      490Ч501
Center      317 393Ч395
Center of a conic section      421Ч422
Center of a pencil      148
Center of a quadric      432
Center of curvature      540
Center of gravity      54Ч61 356 390 580Ч581
Center of perspectivity      97
Central collineation      395
Central dilation      316Ч317
Central line of a penicl      430
Central ovoid      580Ч584
Central quadric      328 381
Central-elliptic geometry      501
Central-hyperbolic geometry      501
Ceulen, von, doubling formula of      243Ч245
Chain      616Ч635
Change of direction      478 485
Chasles relation      33 55
Christoffel three-index symbols      556
circle      351 381 423 584Ч588
Circle, bundle of      473Ч474 484
Circle, inversion in a      456Ч457 471
Circle, Lie      466 483^84
Circle, limit      510
Circle, linear set of      473Ч474
Circle, measurement of      248Ч252
Circle, of constant geodesic distance      568
Circle, oriented      465
Circle, pencil of      429Ч431 473Ч474 484
Circular point, absolute      414
Circular transformation      469
Circumcircle of a polygon      242
Circumference of an oval      576Ч577
Cissoid of Diodes      437
Clebsch, R.F.A.      457
Closed chain      617Ч619
Closed halfspaces      343
Closed manifold      604Ч609
Closed path      635
Closed set      517 639
Closure      638
Closure, theorems      68Ч76 82Ч84 91Ч92 150Ч153
Cloverleaf loop      593Ч594
Collinear      66
Collineation      76Ч82 94 306Ч307 393Ч400 461
Collineation, central      395
Collineation, involutory      394
Collineation, of a projective plane      98Ч99
Collineation, orthogonal      132Ч133
Collineation, perspective      98 393
Collineation, projective      99 395Ч397 400Ч401
Combinatorial geometry      574
Combinatorial topology      595 616
Compact      647 651
Compactum      659Ч660
Comparativity      11 179
Compass construction      199Ч210 222Ч229
Complement      244 639
Complete quadrangle, theorem of the      388
Complete quadrilateral      107 335Ч336
COMPLEX      595Ч596 609Ч616
Complex geometry      391Ч393
Conchoid of Nicomedes      437
Cone      329 381 412 457^58 482
Congruence      298 349 375 379 512
Congruence, axioms      183Ч189
Congruence, class of segments      24
Congruence, invariance of an area under      22
Congruence, relation      183Ч189
Congruence, theorem      512
Conic section      100 325 332 412 419Ч431
Conic section, absolute      414
Conic section, axis of      422Ч424
Conic section, diameter of      421Ч422
Conic section, proper      381
Conic section, vertex of      423Ч424
Conies, as an algebraic curve      438Ч440
Conies, homaloidal net of      457
Conies, imaginary      421
Conies, line      496Ч497
Conies, nondegenerate      439
Conies, point      496Ч497
Conies, projective generation of      425Ч427
conjugate      388Ч389 410 421
Conjugate basis      328
Conjugate midline      590
Conjugate pair      403Ч405
Connected set      639
Connective relation      517
Connectivity      631Ч635 649Ч650
Constructible problems      199
Constructible regular n-gon      257Ч259
Construction, Mascheroni      224Ч229
Construction, methods of      200Ч201
Construction, Mohr      224Ч229
Construction, of classes      24
Construction, of higher degree      229Ч237
Construction, problems      208Ч209
Construction, Steiner      214Ч218
Construction, von Staudt's pentagon      253
Construction, with compass      224Ч229
Construction, with straightedge alone      210Ч224
Construction, with straightedge and compass      199Ч210
Construction, with straightedge and gauge      220Ч223
Contact (tangency) problem of Apollonius      485Ч486
Contact point      638
Continuity      180
Continuity, axiom of      178Ч180
Continuity, Dedekind      22
Continuity, geometry of      596
Continuity, of mappings      517
Continuous function      642
Continuous mapping      664Ч670
Continuous plane      143Ч145 180 182 189
Continuous representation      519Ч520
Continuously ordered set      646
Continuum      639 641 642Ч644
Contravariant tensor      545
Contravariant vector      545
Convex body      572
Convex hull      265Ч266
Convex point      572
Convex polygon      239 241Ч242
Convex polyhedra      265Ч272 343Ч344
Convex sets      342Ч345
Convexity      343Ч345
Coordinate      85Ч95
Coordinate plane      124Ч127 389
Coordinate plane, affine      85Ч90 114 124
Coordinate simplex      313
Coordinate system      313 392 415
Coordinate vector      385Ч387
Coordinate, affine      300
Coordinate, barycentric      344 390 665 667Ч668
Coordinate, geodesic polar      567
Coordinate, homogeneous      345 389Ч391
Coordinate, in projective space      385Ч393
Coordinate, line      439 487
Coordinate, normal      569
1 2 3 4 5 6 7
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