Rosenfeld B.A. (Author), Shenitzer A. (Translator), Grant H. (Assistant) — A history of non-Euclidean geometry: evolution of the concept of a geometric space :: Электронная библиотека попечительского совета мехмата МГУ

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Rosenfeld B.A. (Author), Shenitzer A. (Translator), Grant H. (Assistant) — A history of non-Euclidean geometry: evolution of the concept of a geometric space

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Название: A history of non-Euclidean geometry: evolution of the concept of a geometric space

Авторы: Rosenfeld B.A. (Author), Shenitzer A. (Translator), Grant H. (Assistant)

Аннотация:

This book is an investigation of the mathematical and philosophical factors underlying the discovery of the concept of noneuclidean geometries, and the subsequent extension of the concept of space. Chapters one through five are devoted to the evolution of the concept of space, leading up to chapter six which describes the discovery of noneuclidean geometry, and the corresponding broadening of the concept of space. The author goes on to discuss concepts such as multidimensional spaces and curvature, and transformation groups. The book ends with a chapter describing the applications of nonassociative algebras to geometry.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 488

Добавлена в каталог: 27.10.2010

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Предметный указатель

Poncelet, Jean Victor      148—149 228 402
Pont, Jean Claude      109n. 302
Pontryagin, Lev Semenovi $\check{c}$       278 349—350 366
Posidonius      41—44
Positives (adfirmata)      163—164
Positivist philosophy      199—201 205
Power series      178 273
Pr $\bar{a}$ nas      12
Prad $\acute{e}$ sa (atom of space)      195
Principal character      407
Principal sections      280
Proclus      41—42 71 93 110—111
Progressions, geometric      160
Projections      116—121 127—128 134 140—142 147 149 341-342
Projective correspondence      121
Projective figure      149
Projective metrics      220 233 235—236 238
Projective ranges      121
Projective relations or properties      149
proportionality      225—226 318
Psellus, Michael      155—156 158—159
Pseudo vectors      167
Pseudo — T $\bar{u}$ s $\bar{\imath}$       81
Pseudosphere      287 289
Ptolemy, Claudius      8—17 passim 24 43 117 123—124 175 300
Pythagoras      38 196
Pythagoreans      35 111 152 185—186 191 194
Quadrants      27—30 235 298
Quadratic forms      284 324 358
Quadratic irrationalities      35
Quadratures      352—353
Quadrics      148 152 239—250 256 282—283 296—299 341—344 390-391
Quadrics, cardinalities of      421—422
Quadrics, Hermitian      362
Quadrilaterals      10 17 33—34 43 59—68 77—83 91—100
Quadrilaterals, complete, theorem of      7 11 71 119 120 148
Quadrilaterals, Ibn al-Haytham — Lambert      59 91 100
Quadrilaterals, Khayy $\bar{a}$ m — Saccheri      71 73 76 91 104 230
Qualities (linear, corporeal, surface)      161—162
Quantics      233
Quantifier, universal      172—173
quantum mechanics      276—278 418—419
Quantum physics      278 426
Quantum theory      318—319
Quaternary forms, theory of      342
Quaternions      179 250—251 358 385—386 388—389 395 409-412
Quaternions, biquaternions      298 395 398 403
Quaternions, duoquatemions      403
Qurb $\bar{a}$ n $\bar{\imath}$ , Ab $\bar{u}$ ’I — Q $\bar{a}$ sim      56
Qust $\bar{a}$ ibn L $\ddot{u}$ q $\bar{a}$       153
Ra $\check{s}$ evski $\breve{\imath}$ , Petr Konstantinovi $\check{c}$       366
RADIANS      31
Ranks      310
Rashed, Roshdi      155
Ratios      8—9 15 18 35 131 137 290- 291
Ratios, composite      20—21 97
Ratios, cross      118 121 136—137 148 236—246 296—297 362 406
Ratios, theory of      15 64 65 195
Rays      254—255
Rectangles      136—137 152
Rectangles, existence proved      54 57 59 68 83 87 91—99
Reflections      112 115 122 146 180 344—345 357
Reflections, along geodesics      317 364
Regiomontanus (Johann M $\ddot{u}$ ller)      22—24
Relationship      150
Relativity, general theory of      212 309—314 316 317
Relativity, Special Theory of      229 265—268 270 273 309 316 372
Rest, absolute      265
Reye, Theodor      174
Rham, Georges de      325
Rhomboid      37
Rhombus      37
Ricci — Curbastro, Gregorio      310—311 319
Richard of Middleton      183
Riemann topology      301—304
Riemann, Bernhard      173 203—204 257 266—267 276 321
Riemann, Cauchy — Riemann conditions      178 399
Riemann, Riemann symbols, four-inxed      294 411
Riemann, Riemann — Roch theorem      259—260
Riese, Adam      158
Riesz, Frigyes      274—275 308
Right-angle hypothesis      59 91 92 98
Rigid bodies      335—336 338
Ring theory      400—403 424
Roch, Gustav      259—260
Root extraction      154 170—171
Rosenfeld (Rozenfel’d), Boris Abramovi $\check{c}$       81n. 361n. 362 362n. 363 367 377 378 405 406 415—418
Rotation      126—127 258
Rudolff, Christoff      157 159—160
Ruffini, Paolo      154 327—328
Rule of four magnitudes      17—18
Rumyanceva, Lyudmila Viktorovna      362
Sabians (star worshippers)      15 24
Sabra, Abdelhamid Ibrahim      44 46 81 86n. 87n.
Saccheri, Girolamo      80 98—100 107 203
Saccheri, Khayyam — Saccheri quadrilaterals      71—73 76 83 94 104 230
Sagle, A. A.      412
Saint Venant, Ademar Jean Claude Barre’ de      177
Satake, Ichir $\hat{o}$ , diagrams      359—360 369—371 422—423 425
Sayf al-Dawla      57
Scenography (perspective)      117 134
Sch $\ddot{o}$ nflies, Arthur      347
Scheffers, Georg      399 403 404
Schellekens, Gerhard Johan      416
Schl $\bar{a}$ fli, Ludwig      253 257 289
Schlt $\ddot{u}$ ssel      see Clavius Christopher
Schmidt, Otto Yulevi $\check{c}$       333
Schoute, Peter Hendrik      256
Schouten, Jan Arnoldus      310—311 319 321
Schubert, Hermann      260
Schumacher, Heinrich Christian      215 220
Schur, Friedrich      295
Schutbert, Friedrich Theodor (Fedor Ivanovic $\check{S}$ ubert)      147
Schweikart, Ferdinand Carl      217—218 220
Sciences, Academy of      209—210
Sebokt, Severus      124
Secants, figure of      17—21
segments      174 252—253
Segre, Beniamino      422
Segre, Corrado      392—393
Seljuq dynasty      20
Semenova, Irina Nikolaevna      379—380
Semichord conjugate      115
Semicircles      5—6 8 110
Semiellipse      281
Series, convergent      104
Serre, Jean Pierre      425
Servois, Francois Joseph      138n.
Sets, topological      306—308
Severi, Francesco      260
Sexagesimals      10
Shadow      12 15
Shkolenok, Galina      142n.
Siddhantas      11—12 14
Silberstein, Ludwik      375—376 427
Simplices      308—309 345—346
Simplicius      42—46 68 69 85 86 89 105 190
Sindhind      11
SINEs      10—19 passim 23—26 31 214
Sitter, Willem de      313 314
Skew-symmetry condition      150
Skopec, Zalman Alterovi $\check{c}$       415
Slavutin, Evgeni! Iosifovi $\check{c}$       155n. 163n.
Smorodinskil, Yakov Abramovi $\check{c}$       272 273
Snyder, Hartland      427
Socrates      186—187
Sohnke, Leonhard      346—347
Sokolov, A. A.      426 427
Solitons      380—381
Solstices      2 129

Sommerfeld, Arnold      270 272
Sommerville, Duncan Maclaren Young      372 375 376
spaces      179—211 passim 228—245 247—279 290—325 334 351 359 372 375-377
Spaces, finite      424
Spaces, G-elliptic and G-hyperbolic      415
Spaces, Galilean      381
Spaces, Hermitian elliptic      406—407
Spaces, Hjelmslev      406
Spaces, imaginary      161
Spaces, Minkowski’s space      418
Spaces, multidimensional      162
Spaces, parabolic      368
Spaces, reductive      368
Spaces, symmetric      363
Spacetime      277 309 311—313 317—318 418—419 426-427
Spampinato, Nicol $\acute{o}$       405
Spatial chain      228
Spatial complexes      302
Species      304
Spheres      3—4 27—33 229—235 280 302—303 321—326 344
Spheres, -dimensional      256
Spheres, armillary      124
Spheres, as blocks      424
Spheres, Euclid’s definition      110
Spheres, Loba $\check{c}$ evskii’s definition      211
Spheres, real, pure imaginary, or null radii      229 302—303 321—326 344
Spheres, volume computed      219
Spherical astronomy      17
Spherical cosine theorem      12—15 19 22—25 29 170 223—224
Spherical Pythagoras theorem      13 223
Spherical sine theorem      11—20 22 223—224
Spherical tangent theorem      11 16—17 19—20 223
Spherical triangles      5—34 passim 39—40 83 101 206 222—226 295
Spherical trigonometry      see Trigonometry
Spheroid      33
Spider      see Arachne
Spinor representations      397 409—410 415 418
spirals      167 175 337
Spiritualists      204
Spivak, Michael      256
Stab (directed segments)      253
Staudt, Christian von      174
Steenrod, Norman      322
Steiner, Jacob      423—424
Steklov, Vladimir Andreevi $\check{c}$       275—276
Stepa $\check{s}$ ko, Tamara Andreevna      417
Stereographic projection      121—130 134 147 242 244 342—343
Stereography      134
Stereometric propositions      5 24
Stevin, Simon      175—176
Stevin’s parallelogram      176
Stifel, Michael      159—161
Stipani $\acute{c}$ , Ernest      93
Stretch      251
Stringham, Washington Irving      256
Strubecker, Karl      376
Structure      398 416
Study, Eduard      299n. 361—366 395—398 409 420
Substitutions, real      239
Sude, Barbara Huper      59
Sufficient reason      185—186
Suida      124
Sums, partial      104
Sun      12 14 19—20
Sundials      15 123 167—168
Superposition      52 112 294 334—338
Surface-direction      293
Surfaces      111 160 201—204001 211 230—245 281—304 326
Sursolida      158—159
Symmetric forms      22
Symmetry      122 144 146 256 306 323 368—370
Tangency      156 197—198 246 270—271 280 281 286—287 322-323
Tangency, and cyclic points      149
Tangency, conics      116 135 235
Tangency, double      259
Tangency, ecliptic representation      126
Tangency, plane      242
Tangency, point of      122 140
Tangency, transformations mapping spheres onto spheres      344
Tapero, Tatyana Borisovna      279
Tartaglia, Niccolo      157
Taurinus, Franz Adolf      217—219 224
Taylor series      226
Tensors      310—311 321 323 325 364 366 420
Terminology, origins      11 22—23 156 158 159 168 187 302
Tetrads      120 148 420
Tetrahedra      195 256 345 347
Thales      110—111
Thas, Jacques      424
Theaetetus      35
Theodosius      3—5 110
Theon      123—124
Tihonov, Andrei Nikolaevi $\check{c}$ (Tychonoff)      309
Time      19—20 199 201—202 205
Tits, Jacques      367 416 424—425
Tlla $\check{s}$ ev, Hamid Hasanovi $\check{c}$       81
Tlupova, Rimma Gumarovna      415—416
Toghr $\bar{u}$ l, B $\bar{e}$ k      20
topology      203 212 257 268—269 301—309 322 325
Topology, combinatorial      173 260
Topology, groups      349—350
Torus      111 302 303 326
Totality      254—255 273 297 349
Toth, Imre      40n.
Touching      211
Toupin, R. A.      378
Tractrix      287
Trajectories, orthogonal      146 178 230
Transfmite      161
Transformations      136—138 142—151 264 274 320 338—344 413 415
Transformations, affine      130—133 320 323 393
Transformations, affine, affinities, axial      112—114 130 140
Transformations, affine, dilatations, central      112 115 30 40
Transformations, birationai      116 40—42 347—348
Transformations, circular      244
Transformations, conformal      323 361 418 420
Transformations, coordinate      278 310—311
Transformations, equiaffine      131
Transformations, fractional linear      237 239 346
transformations, geometric      134 348
Transformations, infinitesimai      351 353
Transformations, linear      297 348 354 388 407—408
Transformations, Lorentz      418
Transformations, projective      133—134 135—150 323
Transformations, symplectic      362 406
Triangles      22 50 78—91 100—111 163—168 206—208 214—228 286- 292
Triangles, angle sums      244
Triangles, equal      64
Triangles, homologous      140 417
Triangles, right      12 17—19 92 122 186
Triangles, spherical      see Spherical triangles
Trigonometry      7 11—27 31 33 36 219—228 230
Triplets      179
Tympanums      123 126
Unguru, Sabetai      90
Unit disk      241
Unit segment      163
Unit sphere      249 415
Uryson, Pavel Samuilovi $\check{c}$ (Urysohn)      308
Utkramajya      12
VACUUM      182—183 185 194
Valences      310—311
Van der Waerden, Bartel Lendert      260 355
Van Roomen, Adrian      165—167
Van Schooten, Franz      159
Var $\bar{a}$ hamihira      14
Vari $\check{c}$ ak, Vladimir      272
Variables      178 239 254 257 273—274 276 343
Veblen, Oswald      318 321 420
Vectors      167—179 passim 251—253 263—264 316—325 351—368 385 403 418 420

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