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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume II: Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Geometry, degenerate Cayley — Klein 497
Geometry, differential 504 534—542 576
Geometry, elementary 462
Geometry, elliptic 163—164 497 502—505
Geometry, equiform 498—499 501
Geometry, Euclidean 164—167 345—383 413—419 462 536
Geometry, hierarchy of 462
Geometry, higher 465
Geometry, hyperbolic 167—168 197 497—498 506—514
Geometry, in the group of motions 129—130
Geometry, Laguerre 465 475—482 484—485
Geometry, Lie 465 482—486
Geometry, Mobius 465—475 484—485 501—514
Geometry, non-Euclidean 490 532
Geometry, non-Legendrian 172
Geometry, nondegenerate Cayley — Klein 497
Geometry, of Abelian groups 62
Geometry, of continuity 596
Geometry, plane 355—357
Geometry, plane metric 145—162
Geometry, Plucker 486—490
Geometry, projective 182 345 397
Geometry, projective-metric 107—110
Geometry, pseudo-equiform 499—501
Geometry, real 391—393
Geometry, Riemannian 559 564
Geometry, similarity 462
Glide reflection 204—205 320 378—379
Golden section 246
Goniometry 14
Gram determinant 353
Grassmann, H.G., extended algebra of 294
Greater Desargues theorem 308—310
Gregory's formula 245
Group of motions 129 134—135 137 139 375
Group of motions, elliptic 163
Group of motions, Euclidean 166
Group of motions, geometry in the 129—130 134—136
Group of motions, hyperbolic 168
Group of motions, metric-Euclidean 166—167
Group of motions, projective-metric 108—109
Group plane 139—141
groups 23—28 516
Groups, affine 310—312 397 461—462
Groups, automorphism 24 460—461
Groups, Betti 621
Groups, connectivity 632
Groups, dihedral 283
Groups, elliptic 502
Groups, equiaffine 338 342
Groups, equiform 375 414 460—461
Groups, Euclidean 374—375 461—462
Groups, fixed 520n
Groups, free cyclic 619
Groups, fundamental 634
Groups, generated 61
Groups, hierarchy of 462
Groups, homology 616—631 650
Groups, icosahedral 282—283 286
Groups, isometric 375
Groups, Laguerre 477—479
Groups, Lie 533
Groups, Lorentz 481
Groups, Mobius 468—470
Groups, multiplicative 527
Groups, of similarities 25
Groups, of transformations 24 463
Groups, orthogonal 375
Groups, Plucker 488—489
Groups, principal 414 462
Groups, projective 396 461—462
Groups, representation of 516 519
Groups, rotation 377
Groups, stability 520—524 528—529
Groups, symmetric 463
Groups, topological 377 519
Groups, torsion 621
Habilitation Lecture of Riemann 532
Hadamard inequality for determinants 354
Hadwiger, H. 574
Half-elliptic plane 172
Halfline 5 8—10 185 475
Halfplane 5—6
Halfrotation 121—124 161—162 169—170 509
Halfspace 8 343
Handle 601—603 608—609 628
Harmonic conjugate 388—389
Harmonic point 388
Hausdorff axioms 660—663
Hausdorff space 662
Hausdorff, Felix 646
Heine — Bosel theorem 651
Helmholtz — Lie space problem 463 532
Helmholtz, H. von 532
Heptagon 234 236—237
Heptahedron 265
Hermes, identivity of 645 655
Hermitian form 554
Hermitian metric 414
Hesse normal form 350—351 475
Hesse transference principle 427
Hessenberg counterpairing theorem 157—158
Hexagon 44—55
Hexagon, A- 44 47—54
Hexagon, AC- 44 48—52
Hexagon, affine-regular 49 575
Hexagon, C- 44 47—52
Hexagon, simple 96
Hexagon, Thomsen 51 n
Hierarchy principle 464—465
Higher geometry 465
Hilbert axioms 4—5 175
Hilbert calculus of segments 90—93
Hilbert space 656
Hilbert, David 64 174 517—518 532
Hjelmslev, J. 224 228
Homaloidal net 455—457
Homeomorphism 593—594 605 631
Homogeneous coordinates 345 389—391
Homogeneous space 33
Homologous in an open subset 650
Homology 98 619 632 652
Homology class 619
Homology groups 616—631 650
Homomorphism 525
Homotopic mapping 664
Homotopic simplicial approximation 666
Homotopy 635
Homotopy class 664
Horocycles 510 530
Huyghens and Snell approximation to n 249
Hyperbola 329 421
Hyperbolic angle-sum 507
Hyperbolic axiom 168
Hyperbolic cylinder 329 433
Hyperbolic distance 513
Hyperbolic geometry 167—168 197 497—498 506—514
Hyperbolic group of motions 168
Hyperbolic involution 404
Hyperbolic line element 514
Hyperbolic measure of line 491—493
Hyperbolic paraboloid 332 383 433
Hyperbolic plane 168 169 173 189
Hyperbolic plane, continuous 144—145
Hyperbolic plane, differential geometric properties of 513—514
Hyperbolic plane, Klein model of 191—195
Hyperbolic plane, of lines 529
Hyperbolic plane, of points 529—530
Hyperbolic plane, Poincare model of 529—530 656
Hyperbolic polarity 99
| Hyperbolic reflection 508—509
Hyperbolic trigonometry 512—513
Hyperbolically congruent 512
Hyperboloid 329 381 432—433
Hypercone 328 334 380
Hyperplane 299 325 333—334
Hypersphere 351
Icosahedral group 282—283 286
icosahedron 278
Icosi-dodecahedron 278 279
Ideal line 169—170
Ideal plane 168—173
Ideal points 26 141 168—170
Ideal, prime 452
Idempotent 324
Identification of vertices or sides of a polyhedron 261
Identivity of Hermes 645 655
Image space 322—324
Imaginary conic 421
Imaginary quadric 432
Improper line 461
Improper pencil 148
Improper plane 461
Improper point 385 482
Inaccessible elements 211—214
incidence 103—104 140 176—178 517
Incidence, matrix 622—625 633
Incidence, relation 176
Incidence, structure 176—177
Incircle of a polygon 242
Incommensurable 11
INDEX 329 551—552
Inertia, law of 329
Inner automorphism 526
Inner product 346 415
Interior, of a polyhedron 265—266
Interior, of a quadric 345
Interior, of a set 647
Intersection 145
Intrinsic geometry of a surface 546—547
Intrinsic opological property 594
Invariant complex 134
Invariant factors of a matrix 624
Invariants 473—474 546
inversion 207—210
Inversion in a circle 456—457 471
Inversion in the plane 456—457
Inversion, Laguerre 477—479
Inversion, Lie 483
Inversion, Mobius 470—472
Involution 402—405
Involution, absolute 413—414
Involution, diameter 421
Involution, elliptic 404—405
Involution, hyperbolic 404
Involution, line 421
Involution, on a conic section 427
Involution, right angle 413
Involutory collineation 394
Involutory correlation 99
Involutory group element 31 137—138
Involutory transformation 456
Irreducibility of a continuum 641
Isobaric «-tuples of points 54—57
Isogonal correspondence 455—456
Isogonality theorem 151—152
Isometric group 375
Isometric mapping 374—379 462 517
Isometry 375—379 415—417
Isometry, opposite 375 510—512
Isometry, orientation-preserving 375 462
Isometry, sphere 502
Isomorphism 196—197
Isoperimetric inequality 588
Isoperimetric problem 585—588
Isotropic line 414
Isotropic pencil 479
Isotropic plane 481
Iterated reflection 39—41
Jacobi identity 364
Jacobian functional determinant 543
Jordan arc 643—644
Jordan content 341—342
Jordan curve 647—654
Jordan curve, theorem 595 647—654
Jordan normal form 315
Jordan theorem 314—316
Jump 646
Jung's theorem 575
k-dimensional volume 354—355
Kernel 322 324
Kernel of a homomorphism 525
Klein bottle 600—604 621
Klein four-group 281 283
Klein model of hyperbolic plane 191—195
Klein, Felix 107 460 462—465 490 532 533 593
Knaster, Kuratowski, and Mazurkiewicz theorem 668—669
Knottedness 594
Kock, Í. von 644
Kolmogorov, A.N. 532
Kortum, H. 231
Kowner's theorem 579—580
Lagrange identity 338 353
Laguerre equation 419
Laguerre geometry 465 475—482 484—485
Laguerre group 477—479
Laguerre inversions 477—479
Laguerre plane 475—477
Least upper bound 179—180
Lebesgue measure 638
Lebesgue paving theorem 659
Left side 6
Leibniz 562
Length of a vector 414—415
Length, elliptic measurement of 491—493
Levi-Civita parallel displacement 563—567
Lie circle 466 483—484
Lie geometry 465 482—486
Lie group 533
Lie line-sphere transformation 489—490
Lie plane 482
Lie sphere 486
Lie, Sophus 532—533
Lightcone 482
LIMIT 518
Limit circle 510
Limit point 639
Limit rotation 510
Line conic 496—497
Line coordinate 439 487
Line element 350 479 514
Line involution 421
Line reflection 113—117 129 131—137 471 508 510
Line-geometry, Plucker 486—490
Line-sphere transformation 489—490
linear combination 295
Linear complex 489
Linear dependence 295—296
Linear differential form 558
Linear family of curves 457
Linear form 325 558
Linear independence 295—296
Linear Pfaffian form 558
Linear set of circles 473—474
Linear transformation 472—473 527
Linearization 464 468 477
Linearly transitive 78 80
lines 298
Lines, affine 527
Lines, at infinity 96
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