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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Darboux, Gaston      343 361
Day-planes      127
De Lahire, Philippe      128n.
de Moivre formula      146
de Morgan, Augustus      382—383 398—399
Declinations      12—13 15
Dedekind, Richard      305 402—403
Deferents      175
Defrise, P.      378
Delian problem, classical      111
Dembowski, Peter      423
Democritus      182—183 190 194 196
Denisova, Natalya Serafimovna      411
Derivation, doctrine of      200
derivatives      197 281—284 292—294 310—311 316—317 351 364
Derivatives, partial      248 250 321
Desargues, Girard      136—140 416—417
Descartes, Ren $\acute{e}$       159 163 168—172 184—185
Determinants      250 255 342 352 389
Developability conditions      281
Dialectic method      198
Dickson, Leonard Eugene      411
Diderot      179—180
Differential equations      293 304 309 316 348 353
Differential equations, of geodesics      282 290
Differentials      197—198 270 282 302 317 324 334
Dilg $\hat{a}$ n, H $\hat{a}$ mit      86n.
Dimensionality, axiom of      263 279
Diodorus      42
Diophantus      153—155 167
Diopters      124
Dirac, Paul Adrian      278 418—419
Dirichlet, Peter Lejeune      380 401 402
Distance      211 229—238 241—244 255 258 264 272
Dodecahedra      256 345—346
Drum (tympanum astronomical instrument)      123—126 128—130
Du Val, Patrick      313—314
Duality principle      342 369—370
Dupin, Charles      281
Dynamics      141 202 265 266 268 312
Dynamis      152
Dynamodynamis      153
Dynamokybos      153
Dynkin, Eugene      355—357 360 369 371
D’Aguillon, Francois      124 134
d’Alembert, Jean le Rond      177—180 185
Ecliptics      1—3 10—11 123 125—126 129-130
Egyptians      1
Ehresmann, Charles      325 366 425—426
Eigenvalues      258 273 278 354—355 390—391
Eigenvectors      354—355 367 390—391
Einstein, Albert      212 265—266 268 309 319
Electrodynamics      265
Ellipses      34 113—115 122 127 131—148 246 347
Ellipsoids      113 246
Encke, Johann Franz      219
Engel, Friedrich      348
Engels, Friedrich      189—190 204 257n.
Enriques, Federigo      260
Epicycles      175
Equator      3 128—129
Equator, celestial      see Celestial equator
Equinoxes      2
Euclid      3—5 35—50 52—100 110 112 188 218 262 383 384
Euclid, axioms and four-dimensional rectangular coordinates      337
Euclid, definitions of square, cubic, plane, and solid numbers      152
Euclid, proportions “by equality”      119
Euclid, stereometric propositions      24
Euclid, straight line indefinite extension      183
Euclid, three-dimensional analogues      156
Eudemus      110
Eudoxus      35 89—90 92 123 191
Eudoxus, Eudoxus — Archimedes axiom      39 44 47 51 54 57—59 262n.
Euler curves classified by      258—259
Euler geometry of position      173 301—302
Euler Latin squares      421
Euler motion of fluids      178
Euler stereographic projection of sphere onto plane      130
Euler theorem      255 304
Euler, Leonhard      31—34 102 143—150 185 275 280—283 388- 391
Eutocius      65
Exhaustion, method of      35 131—132 191
Extensions      210 252 351 424
Faces      255—256
Fano, Gino      420
Farpetzi, Ghazar      42
Fedenko, Anatoli $\breve{\imath}$ Semenovi $\check{c}$       364
Fedorov, Evgraf Stepanovi $\check{c}$       347
Fermat, Pierre      162—163 168—170 401—402
Fibrations (fiber spaces)      321—323 418
Field quantization      278
Field theory, unified      317—320
Fields      395 400—402 404 408—409 420 425
Figures, concave and subconcave      162
Finikov, Sergei Pavlovi $\check{c}$       323
Flag      260
foci      34 135—136 149 296
Fomin, Viktor Egorovi $\check{c}$       279
Fourier, Jean Baptiste      274—275
Fractions, continued      95
Frames of reference      265 268
Francesca, Piero della      134
Frcchet, Maurice      304—306
Frenet, Frederic      324
Fresnel, Augustin J.      266
Freudenthal, Hans      387 416—418
Friedmann (Fridman), Aleksandr Aleksandrovi $\check{c}$       313
Frisius, Gemma      129n.
Frobenius, Georg      403 404 407—408
Fubini, Guido Ghirin      361 363
Fuchs, Lazarus      239 241 346
Functions      1 142 219—232 271—278 289—292 305 346-347
Functions, abelian      259 302
Functions, analytic      147 150 178 399
Functions, curvilinear coordinates introduced by Gauss      283
Functions, exponential      31
Functions, Hamilton’s      380—381
Functions, homogeneous      248—250 334
Functions, linear      255
Functions, linear vector function      393
Functions, monodromy property      336
Functions, point      309 319—320
Functions, quadratic      250
Functions, wave      419
Fuss, Nicolai Ivanovi $\check{c}$       33—34
Galen      300
Galilei, Galileo      375
Galois, Evariste      328—333 348 352 400—401 420 424
Gauss intrinsic geometry of a surface      291—292 294
Gauss quadratic forms      324
Gauss topological investigations      302
Gauss, Carl Friedrich      108 179 202—204 214—220 283—286 386 400-401
Gel’fand, Izrail Moiseevi $\check{c}$       366—367 377
Generators      93 299 342 410
Genus (of a curve)      259 302—303 347
Geodesy and geodesics      17 233 282—293 311—312 320 364
Geometric notions, origin of      200 202
Geometric theorems, auxiliary      22
geometries      1 34 85—101 152 180 204—246 279 289—302 420-427
Geometries, analytic      253—254 256
Geometries, atomistic      194
Geometries, elliptic      266
Geometries, enumerative      260
Geometries, existence doubted by Gauss      215
Geometries, Loba $\check{c}$ evskian      207
Geometries, multidimensional      251 254 256—258 260 276
Geometries, non — Euclidean      59 65 106—107 109 268 269 312—313 341
Geometries, plane      262 337 341—342
Geometries, projective      121 147—148 250 341- 343
Geometries, pseudo — Euclidean      266 309

Geometries, quaternion symplectic      362
Geometries, Riemannian      316 359
Geometries, spherical      39 287
Geometries, symplectic      415
Geometries, synthetic projective      147—149 256
Geometry of position      173—174
Gergonne, Joseph Diaz      138n.
Gerling, Christian Ludwig      215 217 218
Gerson, Levi ben      see Levi ben Gerson
Ghaznawl, Mahmud      16
Gibbs, Josiah Willard      393—394
Giordano, Vitale      96 173 211
Girard, Albert      27—31 34
Glagolev, Nil Aleksandrovi $\check{c}$       378
Gleason, Andrew      350
Gluskov, Viktor Miha $\breve{\imath}$ lovi $\check{c}$       350
Gnomon, vertical      12
Gois, Manuel de      161 183
Goldbach, Christian      385
Goldstein, Bernard R      90
Gondavo, Henry de      183
Gordon, Walter      381
Gosset, Thorold      346
Gottingen Scientific Society      220
Grassmann, Hermann G $\ddot{u}$ nther      174 251—261 289 301 393—399 408
Graves, Charles      383—384 386—387 398-399
Graves, John Thomas      386—387 398
Gravitation      149 150 185 311—312 317
Gre $\check{c}$ , Nikolai Ivanovi $\check{c}$       209
Greeks      1—2 10—11 181
Grigoryan, Edik, Sarkisovi $\check{c}$       56
Grisogono, Federik Bartola $\acute{c}$ i $\acute{c}$       93
Grosseteste, Robert (Robert of Lincoln)      196
Grossmann, Marcel      309—310
groups      305 325 327—381 407—427
Gur’ev, Semen Emel’yanovi $\check{c}$       104 107—108
H $\ddot{u}$ l $\bar{a}$ gu Kh $\bar{a}$ n      21
Half-chord (j $\bar{\imath}$ va)      11
Half-turn      112
Hamilton, William Rowan      166—167 179 250 380—382 385—387 393—394 398
Haritonova, Nade $\check{z}$ da Ivanovna      424
Harley, Henry      196
Harmonic mean      30
Harriot, Thomas      31
Hausdorff, Felix      306—308
Heaviside, Oliver      390 393—394
Hegel, Georg Wilhelm Friedrich      198 199
Heisenberg, Werner      318—319
Helgason, Sigurdur      364
Helmholtz, Hermann      267 333—338 348
hemisphere      123 128
Hermite, Charles      275
Hermitian forms      358 361—362 378—379
Heron      34 65 153
Hesse, Otto      341 362
hexagons      121
Hilbert, David      261—262 273—276 333 349—350 402 416—417 426
Hippocrates of Chios      35
Hjelmslev, Juhannes      406
Ho $\bar{u}$ el, Jules      220—221
Homeomorphisms      255 306 331
Homogeneity principle      163 169
Homologies      140 143 304 308
Homomorphisms      403 407
Homotheties      112
Hoppe, Reinhold      256
Horizon      2—3 12 117 123 125 127
Horocycles      109 230—231 244 289
horoscopes      123
Horospheres      230—231 245
Hour angle      129—130
Hour lines      123 126n.
Hours      126—127
Hua, Loo Keng      405 415
Hudson, Hilda      347—348
Huygens, Christian      171—172 211—212 253
Hyperbolas      115 127 134—148 246 267—268 337 347
Hyperbolisms      142 347
Hyperboloids      93 113 229—230 245—246 266—267 297—298 344
Hypercones      376
Hypercycles      217
Hypergeometry      261
Hyperplanes      313 344—345 362 370 406—407 420
Hyperquadrics      376
Hyperspace      260—261
Hyperspheres      217 291 424
Hypersurfaces      291 313 324
Ibn al-Haytham, Abu ‘Al $\bar{\imath}$ (Alhazen)      57 59—65 74—96 100 112 134—135 175
Ibn al-Nad $\bar{\imath}$ m, Ab $\bar{u}$ l — Faraj Muhammad      40—41
Ibn Fath, Sin $\bar{a}$ n      155
Ibn Qurra motion used in geometry      92 112
Ibn Qurra parallel postulate proof      77 83
Ibn Qurra rules for coordinate systems’ transitions      167 168
Ibn Qurra, Th $\bar{a}$ bit      15—16 20 23—24 41 49—60 96 131
Ibn Rushd (Averroes)      183 196
Ibn S $\bar{\imath}$ na, Ab $\ddot{u}$ ‘Al $\bar{\imath}$ (Avicenna)      16 58—59 194
Ibn Sin $\bar{a}$ n, Ibr $\bar{a}$ h $\bar{\imath}$ m      131—133
Ibn Y $\bar{u}$ nis. Kam $\bar{a}$ l al-D $\bar{\imath}$ n      85
Ibn ‘Ir $\bar{a}$ q, Ab $\ddot{u}$ Nasr Mans $\ddot{u}$ r      5 16—20
Ichnography (plan)      117
Icosahedra      256 345—346
Ideae      117
Ideal      403—405
Idempotents      406
Identity axiom      306
Images      133 243—244
In $\ddot{o}$ n $\bar{u}$ , Erdal      377
Incendiary mirror (parabola)      135—136
Incidence axioms      262
Inclination of two planes, equal      3
India and Indian science      17
Indices (of a space)      264 279 313—314 361—362 399 409
Indivisibles      112 196—197
Inertia      312
infinity      39 98 102 143 161 181—183 296—297
Infinity, divisibility      85 190 192
Infinity, plane at      235
Infinity, points at      133—134 136 140 149—150 237
Infinity, simple      257
Initius Algebras      158
Integrals and integration      15 208—210 240 259 274 276—277 302
Integrals and integration, multiple      247—249 256 323
Invariance under rotation property      7
Invariants of algebraic forms      233 235 258 340
Inversions      114—116 118—119 142 242—245 340 347 415
Involutions      138—139 413
Involutive correlations      421—422
Involutory property      20—21
Isometries      146 320
Isomorphisms      333 346 351 361—363 403—410 420
Ivanenko, Dmitri $\breve{\imath}$ Dmitrievi $\check{c}$       426—427
Jacobi, Carl Gustav Jacob      248—251 275 321 351 386
Jacobson, F. D.      413
Jacobson, Nathan      413
Jankiewicz, Czes ${\l}$ aw (Yankevi $\check{c}$ )      378
Javadov, Maqsud Ali Simran oglu (D $\check{z}$ avadov)      405 410—411 415
Jordan, Camille      257—258 324 333 338 346 348 392
Jordan, Paskual      412—415 417
Jung, F.      310 393
Kagan, Veniamin Fedorovi $\check{c}$       80n.
Kallenberg, G. W. M      376
Kaluza, Theodor      318
Kant, Immanuel      179 187—188 203 208—210 215 218
Kantor, Isa $\breve{\imath}$ L’vovi $\check{c}$       367 413 417
Kapralova, Sofya Borisovna      424
Karpova, Lyudmila Mihailovna      377 411
Kepler, Johann      31 134—136 196
Khayy $\bar{a}$ m, Khayy $\bar{a}$ m — Saccheri quadrilaterals      71—73 76 83 91—98 104 230
Khayy $\bar{a}$ m, theory of parallels      64—77 90—91 94—95
Khayy $\bar{a}$ m, ‘Umar      38 46 57—58 95 112 154 195

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