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| Ïîèñê ïî óêàçàòåëÿì |
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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume II: Geometry |
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| Ïðåäìåòíûé óêàçàòåëü |
Perpendicular 115—117 124—127 186—188 355 413—414
Perpendicular, -equal 165
Perpendicular, existence of 146
Perpendicular, pencil of 148
Perpendicular, theorem of 148—150
Perpendicular, uniqueness of 146
Perspective collineative 98 393n
Perspectivity 97—98 105—106 393n 402
Pfaffian form 558
Plane algebraic curves 438—446
Plane coordinate 389
Plane curve 660
Plane dualization 408—409
Plane geometry 355—357
Plane polygon 238
Plane rational cubic 448—449
Planes 299
Planes, affine 66—84 169 180 182 189 303—306
Planes, affine-coordinate 85—90 114 124
Planes, bundle of 401
Planes, complex 391
Planes, connectivity of 649—650
Planes, continuous 143—145 180 182 189
Planes, Desargues 84 85—93 180 182
Planes, directed 6
Planes, double 412
Planes, elliptic 143—145 163—164 169 172 195—196
Planes, elliptic projective-metric 172
Planes, equatorial 466—467
Planes, Euclidean 114 124—128 166 169 172 189 190—191
Planes, group 139—141
Planes, half- 5—6
Planes, half-elliptic 172
Planes, hyperbolic 144—145 168 169 173 189 191—195 513—514 656
Planes, ideal 168—173 improper 461
Planes, isotropic 481
Planes, Laguerre 475—477
Planes, Lie 482
Planes, metric 142—143 168—173 183—185 189
Planes, metric-Euclidean 166
Planes, Moebius 467
Planes, of lines 401 529
Planes, of points 401 529—530
Planes, ordered 177
Planes, ordered hyperbolic projective-metric 173
Planes, ordinary projective-metric 108 172
Planes, oriented 6—8 10
Planes, osculating 538—539
Planes, Pappus 85 87 93 97 101—102 107—109 303—306
Planes, pencil of 387 401 479
Planes, projective 26 101—102 108 109—110 169—173 182
Planes, rational 142
Planes, real 392
Planes, semi-Euclidean 166 168 172
Planes, singular projective-metric 109—110 172
Planes, tangent 333—334 432 543—544
Planes, translation 92
Planes, with constant negative Gauss curvature 514
Pluecker equation of a line 365
Pluecker group 448—489
Pluecker line coordinates 487
Pluecker line geometry 486—490
Pluecker quadric 487—488
Pluecker, Julius 437 442 446
Poincare fundamental polygon 597
Poincare model of a hyperbolic plane 529—530 656
Poincare model of elliptic geometry 504—505
Poincare model of hyperbolic geometry 197 506—507 509
Poincare, Henri 27
Poinsot definition of a polygon 239
Poinsot, Louis 238
Point conic 496—497
Point space 297—302 350—352
Point-direction form 302
Point-line analogy 164
POINTS 32 655
Points, absolute circular 414
Points, at infinity 96 385
Points, base 429
Points, calculus with 30
Points, convex 572
Points, diagonal 107
Points, double 403—404 441
Points, fixed 77 98
Points, fourth harmonic 388
Points, ideal 26 141 168—170
Points, improper 385 482
Points, limit 639
Points, Moebius 465 467
Points, neighborhood of 596
Points, nonabsolute 491
Points, of contact 333 420—421 432 638 642
Points, of inflection 442
Points, ordinary 441—442
Points, plane of 401
Points, power of 359 429
Points, proper ideal 168
Points, range of 97—98 401
Points, reflection in 31 34 115 117 129 131—137 316 395 509
Points, regular 333—334
Points, rotation about 115 204
Points, self-polar 99—100
Points, separation 645
Points, simple 441
Points, singular 334 438—439 441
Points, threefold 445
Points, umbilical 554
Points, unit 300—301 389—391
polar 99—100 109 140 169 410 419—421
Polar coordinates 567
Polar triangle 143 145—146 370—371 411
Polar trilateral 140 163
Polarity 99—100 405—412
Polarity, absolute 413—414
Polarity, condition for 469 483 487
Polarity, degenerate 411—412
Polarity, elliptic 99
Polarity, hyperbolic 99
Polarity, real 420
Pole 99 140 410 440
Pole of rotation 284
Polygon 238—260
Polygon, circumcircle of 242
Polygon, complement of the side of 244
Polygon, convex 239 241—242
Polygon, definition of 238—239
Polygon, fundamental 597 608—609
Polygon, incircle of 242
Polygon, interior of 239
Polygon, orientation of 239—242
Polygon, plane 238
Polygon, Poincare fundamental 597
Polygon, radius of 242
Polygon, regular 242—260
Polygon, simple 239
Polygon, skew 238
Polygon, type of 240
Polyhedra 260—286 609—616
Polyhedra, Cauchy theorem on 266
Polyhedra, continuous mapping of 664—670
Polyhedra, convex 265—272 343—344
Polyhedra, curvilinear 648
Polyhedra, duality for 268
Polyhedra, Euler formula for 266—267 634
Polyhedra, identification of 261
Polyhedra, interior of 265—266
Polyhedra, morphology of 260—265
Polyhedra, nonorientable 261—265
Polyhedra, orientable 261—265
Polyhedra, outline of 266
| Polyhedra, schema of 261
Polyhedra, semiregular 277—279
Polyhedra, symmetric 279—286
Polyhedral group 281—285
Polyhedral net 261
Polynomial ideal 452
Polynomial of root of unity 255
POSITION 535 594
Position vectors 301—302
Positive definite form 327 345—346
Postulates 11
Power of a point 359 429
Prime field of characteristic p 305
Prime ideal 452
Primitive geometric form 401
Primitive pole-polar pair 170
Primitive root of unity 254—255
Principal axes 380
Principal curvature 555
Principal group 414 462
Principal normal 538
Principal section 555
Principal semiaxes 380
prism 41 44—47 277—278
Product, bilinear outer 486
Product, cartesian 176n
Product, cross 363
Product, inner 346 415
Product, metric 657
Product, outer 360 363 486
Product, scalar 346—347 415
Product, topological 657
Product, vector 360—366
Projection theorems of trigonometry 367
Projection, parallel 322—324
Projection, stereographic 196 435—436 466—468 650
Projective collineation 99 395—397 400—401
Projective coordinate plane 100—102
Projective correlation 407
Projective Desargues theorem 96 105—107 308—310
Projective geometry 182 345 397
Projective group 396 461—462
Projective mapping 97—100 401 461
Projective measure 503
Projective plane 26 95—102 107—109 169—170 182
Projective reflection 470—471
Projective space 102—107 385—393
Projective theorem 409
Projective-metric geometry 107—110 145—162
Projective-metric plane 108—110 172—173
Projectivity 26 400—405
Projectivity on a conic section 426—427
Proper central quadric 381
Proper conic section 381
Proper ideal line 169—170
Proper ideal point 168
Proper orthogonal mapping 375
Proper pencil 148
Proper quadric 327
Pseudo-equiform geometry 499—501
Pseudo-hyperbolic group 528
Pseudorotation 500
Pseudosphere 514
Pyramid 283
Pythagorean Theorem 415
Quadrangle 388
Quadratic transformation 455—456
Quadric 325—334
Quadric cone 458
Quadric in Euclidean geometry 379—383
Quadric surface 431—436 453—454
Quadric with center 327—329
Quadric without center 381—383
Quadric, imaginary 432
Quadric, interior of a 345
Quadric, nonregular point of a 334
Quadric, Plucker 487—488
Quadric, proper 327
Quadrilateral, complete 107 335—336
Quadsatic form 325—326
Quartic curve 445
Quaternion 505—506 531
r-dimensional homology group 619
r-dimensional side of a simplex 610
Radical axis 429
Radius of a polygon 242
Radius of curvature 540
Raising an index 551—552
Range of points 97—98 401
Rank, of a bilinear form 108—109 110 326
Rank, of a mapping 324—325
ratio 300—301
Ratio, cross 387—389 461 473
Rational curve 440 447
Rational parametric representation of a conic section 425
Rational parametrization 439—440 453
Rational plane 142
Rational space curve 447
Rational surface 453—454
Rausenberger, O. 269
Rayleigh quotient 379
Real coordinate system 392
Real geometry 391—393
Real line 392
Real plane 392
Real polarity 420
Real projective collineation 397
Real projective space 391—392
Rectangular parallelotope 354
Rectifiable curve 537
Rectilateral 165—166
Reduction of a complex 615
Reference point 389—391
Reflection calculus 30
Reflections 7 202 416
Reflections, affine 316
Reflections, axis of 378
Reflections, elliptic 505
Reflections, geodesic 533
Reflections, glide 204—205 320 378—379
Reflections, hyperbolic 508—509
Reflections, in a point 31 34 115 117 129 131—137 316 395 509
Reflections, iterated 39—41
Reflections, line 113—117 129 131—137 471 508 510
Reflections, of the group plane 141
Reflections, orthogonal 378
Reflections, projective 470—471
Reflections, shift 511
Reflections, three- 113 115 136—137 147—148 153—154
Reflexivity 11 645
Regular 15-gon 247—248 259—260
Regular affine mapping 311—325
Regular decagon 245—247
Regular heptagon 234 236—237
Regular n-gon 257—259
Regular outer product 486
Regular point 333—334
Regular polygon 242—260
Regular polygon of nine sides 234—235
Regular prism 277—278
Regular space 662
Regulus 434 458
Representation of a curve 535 539
Representation of a group 516 519 526
Representation of affinities 93—95
Representation, asystatic 525
Representation, continuous 519—520
Representation, faithful 525
Representation, normal 477n 551—552
Representation, parametric 302
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