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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume II: Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Representation, similar 522
Representation, spherical 551
Residue class field 452
Rhombi-cubo-octahedron 278
Rhombi-icosi-dodecahedron 279
Riemann curvature tensor 557 566
Riemann geometry 559 564
Riemann number sphere 598—599
Riemann space 563—564
Riemann, Georg Friedrich B. 490
Riemann, Habitation Lecture 532
Right bisector 118—119
Right bisector, theorem of 125 151
Right-angle involution 413
Rigid mapping 24 375 415 462
Rigid surface 557
Root of unity 254—255
Rossel, Theophil 233
Rotation 203 377—378 417 472
Rotation group 377
Rotation vector 541
Rotation, about a point 115 204
Rotation, angle of 418
Rotation, axis of 417
Rotation, dilative 206
Rotation, half- 121—124 161—162 169—170 509
Rotation, in Cayley — Klein geometry 509
Rotation, limit 510
Rotation, n-fold pole of 284
Rotation, pseudo- 500
Rotation, sense of 10
Rotation, surface 435
Ruled surface 457—458
Scalar product 345—347 415
Schema 261 598
Schmidt, Erhard 347 586
Schwab formulas 251
Schwab, J.C 251
Schwarz, H.A. 549
Scissors theorem 69
Screw 8—9
Screw displacement 417
Screw motion 378
Secant-tangent theorem 359—360
Second fundamental form 552—553
Section, principal 555
segments 4 342—343
Segments, congruence class of 24
Segments, Hilbert calculus of 90—93
Segments, triply covered 45
Segre, Corrado 438
Self-dual 408
Self-polar 99—100
Semi-Euclidean plane 166 168 172
Semi-order 645
Semiaxes 380
Semiregular polyhedra 277—279
Semisimple Lie group 533
Sense 6
Sense of rotation 10
Sense of traversal 340
Sense-preserving transformation 471
Separable set 639 646
Separation, axiom of 661—662
Separation, point 645
Separation, relation 182
Set, bounded 639
Set, closed 517 639
Set, connected 639
Set, convex 342—345
Set, disjoint 639
Set, interior of a 647
Set, open 639
Set, separable 639 646
Set, totally ordered 5
Set, zero 639
Set-theoretic topology 596
Severi, Francesco 438
SHAPE 594
Shear 315 394
Shift 319 510
Shift reflection 511
Sides, cosine theorems for 372
Similar representation 522
Similarity 24 25 375 414 461—462
Similarity, geometry 462
Similarity, transformation 133
Simple hexagon 96
Simple point 441
Simple polygon 239
simplex 343—344 595—596 610—615 655
Simplex, carrier 665
Simplex, coordinate 313
Simplicial approximation 631 665—666
Simplicial complex 611
Simplicial mapping 664—665
Sines, law of 367 512—513
Singular affinity 322—323
Singular point 334 438—439 441
Singular projective-metric plane 109—110 172
Skew field 85—90
Skew line 8
Skew polygon 238
Space 27 655
Space curve 447 450 452
Space problem 463 532
Space, affine point 297—302
Space, complex 391—392
Space, covering of a 658—659
Space, dual 349 408—409
Space, empirical 3
Space, Euclidean 374 375 563
Space, Frechet 656
Space, Hausdorff 662
Space, Hilbert 656
Space, homogeneous 33
Space, image 322—324
Space, Laguerre geometry of 481
Space, metric 350 517 654—660
Space, metrizable 663
Space, Minkowski 349
Space, normal 662
Space, null 326
Space, octahedral 628—630
Space, projective 102 391—392
Space, regular 662
Space, Riemannian 563—564
Space, topological 654—670
Spacelike pencil of cycles 479
SPEAR 465 475—477 479 481 482
Special complex 489
Special theory of relativity 479n 480 500
Sperner, Emanuel 659
Sperner, lemma of 669
Sphere 351—352 433
Sphere isometry 502
Sphere model of elliptic geometry 503—505
Sphere model of hyperbolic geometry 506
Sphere, one-dimensional 648
Sphere, pseudo- 514
Sphere, Riemann number 598—599
Sphere, surface of the 628
Sphere, unit 349
Sphere-circle, absolute 414n
Spherical excess 373
Spherical representation 551
Spherical trigonometry 369—374
Spiral of Archimedes 437
Spiric curves of Perseus 437
Square 574—575
| Stability group 520—524 528—529
Staudt, pentagon construction of 253
Staudt, Ñ. von 374 490
Steiner formulas 577
Steiner symmetrization 586
Steiner, Jacob 228—229
Stereographic projection 196 435—436 466—468 650
Straightedge 199—224 232—235
Stroke relation 137—138
Subspaces 298—299
Subspaces, affine 335—345
Subspaces, parallelism of 299
Subspaces, vector 294—295
Sum, angle- 367—368 507
Sum, of two vector spaces 294
Summation theorem of dimension theory 659
Supplementwise equality 19
Support line 69 573
Support strip 573—574
Supremum 179
Surface area 373 547—551
Surface transformation 453—458
Surfaces 542—570
Surfaces, algebraic 453—458
Surfaces, birational 458
Surfaces, deformation of 596—604
Surfaces, degenerate quadric 432
Surfaces, genus of 634
Surfaces, intrinsic geometry of 546—547
Surfaces, mapping 557
Surfaces, of rotation 435
Surfaces, orientable 604
Surfaces, oriented 543
Surfaces, quadric 431—436 453—454
Surfaces, rational 453—454
Surfaces, ruled 457—458
Surfaces, topology of 596—635
Sylvester law of inertia 329
Symmetric bilinear form 325—326 379—380
Symmetric group 463
Symmetric polyhedra 279—286
Symmetrization, Steiner 586
Symmetry 11 279—281 655
Taking bearings 224
Tangent 332—334 419—421 483
Tangent distance 478
Tangent plane 333—334 432 543—544
Tangent problem, of Apollonius 480 485—486
Tangent problem, of Malfatti 222
Tangent representation of a curve 539
Tangent to a quadric 432
Tangent vector 538 543
Tangent, cuspidal 444
Tangent, point of contact of a 333 420—421 432 642
Tangent, position of 535
Tangent, secant 359—360
Tangential hyperplanes 333—334
Tensor, contravariant 545
Tensor, covariant 546
Tensor, fundamental 546 559
Tensor, of fourth order 557
Tensor, of second order 565
Tensor, Riemann curvature 557 566
Tetracyclic coordinate 467 469 531
Tetrahedral group 281 286
tetrahedron 8 52—54 278 357—358
Thales, theorem of 431
Theorema egregium of Gauss 557
Thickness of a curve 574
Thomsen hexagon 51 n
Three-dimensional projective space 102—107
Three-reflections theorem 113 115 136—137 147—148 153—154
Threefold point 445
Timelike pencil of cycles 479
Tits, J. 532—533
Topological group 377 519
Topological mapping 517 593
Topological product 657
Topological properties of shape 594
Topological relation 518
Topological space 654—670
topology 516—517 593—670
Topology, combinatorial 595 616
Topology, of curves 635—654
Topology, of surfaces 596—635
Topology, set-theoretic 596
Torsion coefficient 621—622 633
Torsion group 621
Torsion of a curve 541
Torus 619
Total curvature 567 570
Total flag 533
Total order 645
Total order relation 179
Trace 77 79 80
Tractrix 547
Transference principle 427 463—464
transform 78n
Transform, of a group element 31
Transformation 133—135 137 516
Transformation group 463
Transformation, affine 7 22
Transformation, birational 438 454
Transformation, circular 469
Transformation, coordinates of 536
Transformation, Cremona 454—457
Transformation, elementary 201—202
Transformation, fractional linear 527
Transformation, group of 24
Transformation, involutory 456
Transformation, Lie line-sphere 489—490
Transformation, linear 472—473
Transformation, Lorentz 500
Transformation, of motions 133—134
Transformation, orientation-preserving 472
Transformation, quadratic 455—456
Transformation, sense-preserving 471
Transformation, similarity 133
Transformation, surface 453—458
Transitive representation 520
Transitivity 179 645
Transitivity theorem 153—155
Translation 31 77—79 117—121 166—167 319 321—322 378 416 472
Translation plane 92
Translation vector 321
Translation, by a vector 33
Translation, Desargues theorem 310
Translation, in Laguerre geometry 479
Translation, in the g-direction 78
Translation, invariance of an area under 22
Translation, parallel 201—202 565
Translation-congruent 298
trapezoid 343
Triadic expansion 636
triangle 23—24
Triangle inequality 346 372 655
Triangle, altitudes of 356
Triangle, doubly covered 45—46
Triangle, Euler 370 503—504
Triangle, excess of 570
Triangle, in the Euclidean plane 366—369
Triangle, metric closure theorems and 150—153
Triangle, Mobius concept of 370
Triangle, oriented 6
Triangle, polar 143 145—146 370—371 411
Triangle, spherical 369—374
Trigonometry 366—374
Trigonometry, elliptic 503—504
Trigonometry, hyperbolic 512—513
Trigonometry, projection theorems of 367
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