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

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

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

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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.

Язык:

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

, irrationality proofs      99
-gon, rectilinear      28 31
-stretch ( — Streck)      303
$\check{C}$ ahlenkova, Tamara Grigor’evna      377n.
$\check{C}$ ahtauri, Ilya Adamovi $\check{c}$       405
$\check{C}$ eby $\check{s}$ ev, Pafnuti $\breve{\imath}$ L’vovi $\check{c}$       275—276
$\check{C}$ ernikov, N. A.      272—273
$\check{S}$ estryreva. L. V. (Rumyanceva)      379—380
$\check{S}$ irokov, Petr Alekseevi $\check{c}$       363—364
$\check{S}\check{c}$ erbatskoi, Fedor Ippolitovi $\check{c}$ (Stcherbatsky, theodor)      195 205
$\check{Z}$ elezina, Iraida Ivanovna      377n.
$\pi$ , irrationality proofs      99
2-gons      32
Abbasov, Nazim Tanriverdi oglu      405 411
Abel, Niels Henrik      328—329
Absolute      233—236 297—298 414 416 421—422
Acute-angle hypothesis      59 68 76 91 227 230
Acute-angle hypothesis, refuted      83 98 101 104 218—219
Adamu $\check{s}$ ko, Nade $\check{z}$ da Nikolaevna      415
Afanas’ev, Vladimir Vasilevi $\check{c}$       424
Afrigids      16
Aghanis      42—44 56 58—59 92
Ahmedov, Ashraf Ahmedovic      81n.
al-Abh $\bar{a}$ r $\bar{\imath}$ , Ath $\bar{\imath}$ r al-D $\bar{\imath}$ n al-Mufaddal      85—87 105
al-Andalus $\bar{\imath}$       see al-Maghrib $\bar{\imath}$
al-B $\bar{u}$ zj $\ddot{a}$ n $\bar{\imath}$ , Ab $\ddot{u}$ -l — Waf $\bar{a}$       17 19 154
al-B $\bar{\imath}$ r $\ddot{u}$ n $\bar{\imath}$ , Ab $\ddot{u}$ ’l-Rayh $\bar{a}$ n Ahmad (B $\bar{\imath}$ r $\bar{u}$ n $\bar{\imath}$ , B $\bar{e}$ r $\ddot{u}$ n $\bar{\imath}$ )      16—20 127 128 173 175 194 211
al-Batt $\bar{a}$ n $\bar{\imath}$ (Albategnius)      16 24 168
al-F $\bar{a}$ r $\bar{a}$ b $\bar{\imath}$ , Ab $\ddot{u}$ Nasr      154—155 161 173 183 200 211
al-Fargh $\bar{a}$ n $\bar{\imath}$ , Ahmad      124
al-H $\bar{a}$ d $\bar{\imath}$ , Muhammad      86
al-Hanaf $\bar{\imath}$ , ‘Alam al-D $\bar{\imath}$ n Qaysar      44 46 57 74 80 85—86
al-J $\bar{\imath}$ l $\bar{\imath}$ , K $\bar{u}$ shy $\bar{a}$ r ibn Labban      17
al-Jawhar $\bar{\imath}$ , ‘Abb $\bar{a}$ s      30 46—50 68—69 73—74 80 86 105
al-Jubb $\bar{a}$ ’ $\bar{\imath}$ , Ab $\bar{u}$ -l — H $\bar{a}$ shim      193
al-K $\bar{a}$ sh $\bar{\imath}$ , Ghiy $\bar{a}$ th al-D $\bar{\imath}$ n Jamsh $\bar{\imath}$ d      154
al-Karaj $\bar{\imath}$ , Ab $\ddot{u}$ Bakr Muhammad      154
al-Ka’bi, Ab $\bar{u}$ -l — Q $\bar{a}$ sim      193—194
al-Kh $\bar{a}$ zin, Ab $\ddot{u}$ Ja’far Muhammad ibn al-Hussain      57 167
al-Khujand $\bar{\imath}$ , Ab $\ddot{u}$ Mahm $\ddot{u}$ d      17 19—20
al-Khw $\bar{a}$ rizm $\bar{\imath}$ , Muhammad ibn M $\bar{u}$ s $\bar{a}$       14—16 20
al-M $\bar{a}$ h $\bar{a}$ n $\bar{\imath}$ , Muhammad      15—16 20
al-Maghribl, Muhyl al-DIn Yahya      45—46 86—90
al-Maghribl, Samaw’al      154
al-Nasawi, Abu-l — Hasan ‘Ali      20
al-Nayr $\bar{\imath}$ z $\bar{\imath}$ , Ab $\ddot{u}$ l-’Abb $\bar{a}$ s al-Fadl      42—44 46 56—58 65 92
al-Naysh $\bar{a}$ bur $\bar{\imath}$ , Ab $\ddot{u}$ R $\bar{a}$ shid      193
al-Naysh $\bar{a}$ bur $\bar{\imath}$ , Niz $\bar{a}$ m al-D $\bar{\imath}$ n      81
al-Q $\bar{a}$ ss, Yuhann $\bar{a}$ ibn Y $\ddot{u}$ suf al-H $\bar{a}$ rith ibn al-Bitr $\bar{\imath}$ q      57
al-R $\bar{a}$ z $\bar{\imath}$ , Ab $\bar{u}$ Bakr Muhammad ibn Zakariy $\bar{a}$       194
al-R $\bar{u}$ m $\bar{\imath}$ , Q $\bar{a}$ d $\bar{\imath}$ — Zada      86
al-S $\bar{a}$ l $\bar{a}$ r, Hus $\bar{a}$ m al-D $\bar{\imath}$ n      21 71—74 85
al-S $\bar{\imath}$ jz $\bar{\imath}$ , Ab $\ddot{u}$ Sa’id      17 155—157
al-Sagh $\bar{a}$ n $\bar{\imath}$ , Ab $\bar{u}$ H $\bar{a}$ mid      127
al-Samarqand $\bar{\imath}$ , Shams al-D $\bar{\imath}$ n Muhammad Ashraf al-Husay $\breve{\imath}$       86
al-Sh $\bar{\imath}$ r $\bar{a}$ z $\bar{\imath}$ , Qutb al-D $\bar{\imath}$ n      90 195
al-Shann $\bar{\imath}$ , Ab $\ddot{u}$ ‘Abdall $\bar{a}$ h      57 65
al-T $\bar{u}$ s $\bar{\imath}$ , Nas $\bar{\imath}$ r al-D $\bar{\imath}$ n      5 20 22 44 57 71 98 104—105 195
al-T $\bar{u}$ s $\bar{\imath}$ binomial formula for integer coefficients      154
al-T $\bar{u}$ s $\bar{\imath}$ parallel lines treatise      46—47
al-Ya’q $\bar{u}$ b $\bar{\imath}$ , Ahmad      124
al-Zarq $\bar{a}$ l $\bar{\imath}$ , Ibr $\bar{a}$ h $\bar{\imath}$ m al-Qurt $\bar{u}$ b $\bar{\imath}$       128—129
Albategnius      see al-Batt $\ddot{a}$ ni
Albategnius’ theorem      see Spherical cosine theorem
Albert, Abraham Adrian      413
Alberti, Leon Battista      134
Aleksandrov, (Alexandroff), Pavel Sergeevic      307—308
Alexander, James      304
Alfonso de Valiadolid      92
Algebra, geometric      152 157 169—171
Algebras      382—418 passim
Algebras, alternative      411—412
Algebras, associative      398—399 403—404
Algebras, Jordan      412—415
Alidad      124 130
Almucantarats      125—126
Alternation symbol      396—397
Altitude of the Sun      12 15—16
Altitude of the Sun, spherical coordinate      128n.
Alyabeva, Valentina Georgievna      423
Ambarcumyan (Ambarzumian), Viktor Amazaspovi $\check{c}$       426
Analemmas      123
Analysis situs      173 302—304 307
Anatolius      155
Anaxagoras      190
Anderson, Alexander      165
Andreeva, Lyudmila Pavlovna      379
angles      5 6 11—12 35—94 102—103 108 122 168
Angles, stationary      258
Angular defect      214 225—226 295
Angular excess      225—226 286 291
Anthiniatus      42
Antiautomorphism      405
Anty $\bar{a}$       12
Apollonius      114—115 117 123 142 347
Apollonius, Conics      15 122 124 149 167—169
Application (parabol $\bar{e}$ ) of parallelogram      38
Arachne (spider)      123 127
Arc of half the day      13
Archimedes      15 30 40—41 112—114 132 153 156 168 175
Archimedes, Archimedes — Heron theorem      34
Archimedes, atomistic arguments      196
Archimedes, Eudoxus — Archimedes axiom      39 44 47 51 54 57 59 89 90 92 262
Archimedes, Eudoxus — Archimedes axiom, influence on Vi $\grave{e}$ te      168
Archimedes, mechanical theorems method      191 193
Archimedes, On spirals      175
Architecture and geometry      116—121
Archytas      111
Arcs      11 45—46 99
Argand, Jean Robert      179
Aries constellation      2n.
Aristarchus of Samos      123 193
Aristotle      38—40 46 52 58 65—74 173—175 190-194
Aristotle, composition of continua      196
Aristotle, derivation doctrine      200
Aristotle, geometry notions origin      202
Aristotle, math concepts’ teaching      186
Aristotle, motions in geometry debated      111—112
Aristotle, on infinity      182—184
Arrowsmith, A.      128n.
Assassins, state of      20—21 74
Astrolabes      17 123—130
Astrology      1 17 20 21 173n.
Astronomy      1—2 10——12 14—17 22 52 101 117
Astronomy, and composition of motions      175
Asturl $\bar{a}$ b      see Astrolabes
Asymptotes      136
Autolycus      2—3
Automorphisms      366 405 412 415 422—423
Averbah, V. L      411
Averroes      see Ibn Rushd
Avicenna      see Ibn S $\bar{\imath}$ na
Azimuths      14—18 126 128n.
Ba $\check{s}$ makova, Isabella Grigor’evna      163n. 167
Babylonians      1—2 10 15
Baltzer, Richard      221
Ban $\bar{\imath}$ ‘Ir $\ddot{a}$ q (dynasty)      16
Barbaro, Daniele      123
Barbilian, Dan (Ion Barbu)      405—406
Barlow, William      347
Barycenter (center of gravity)      149—150
Battaglini, Giuseppe      221
Bellavitis, Giusto      174
Beltrami, Eugenio      221 231 233 236—238 241 288—289 295
Benz, Walter      405
Berezin, Feliks Aleksandrovi $\check{c}$       377
Berger, Marcel      364
Bergson, Henri      205
Bernoulli, Jacob      282
Bernoulli, Johann      280n. 282

Berosus the Chaldean      123
Bertrand, Louis      102
Betti, Enrico      257—258 303—304 325—326 366 426
Bianchi, Luigi      295
Binary linear forms      292 341 343
Binomial coefficients      154 160 165
Blaschke, Wilhelm      375 378
BLOCKS      423
Bochner, Salomon      326
Bohl (Bol), Piers      309
Bolyai, Farkas      108—109 203—204 212 214-216
Bolyai, J $\acute{a}$ nos      108 212—217 220
Bombelli, Raphael      177
Bonetus, Nicola      196
Borelli, Giovanni Alfonso      95—96
Bortolotti, Enea      378
Boscovich, Roger Josip      31
Boullough, R. K.      380
Boundedness      274 323 325
Boyer, Carl B.      379
Bradwardine, Thomas      161 183 195—196
Brahmagupta Khandakh $\ddot{a}$ dyaka treatise and rule      12—15 34
Brauer, Richard      409
Braunmiihl, Anton von      14
Brethren of Purity, (Ikhw $\ddot{a}$ n al-Saf $\bar{a}$ ’)      191—194
Briggs, Henry      31
Brioschi, Francesco      387 388
Brouwer, Luitzen Egbertus Jan      308 309 349
Buckle (fibulle)      27—30
Buddhist doctrines      195 205
Bulgarin, Fadde $\breve{\imath}$ (Tadeusz) Benediktovi $\check{c}$       209
Bunyakovski $\breve{\imath}$ , Victor Yakovlevi $\check{c}$       209—210
Bura $\check{c}$ ek, S. A.      209
Burali — Forti, Cesare      393
Burleigh, Walter      183
Burnside, William      408
Bussey, W.      420
Busurina, Anna Evgerievna      40n.
Calculus      141 174—180 197—198 310 311 393-394
Calendars      1 93
Cancer, Tropic of      2 125—126
Candry, P. J.      380
Cantor, Georg      161 262 308 426
Capricorn, Tropic of      2 125—126
Carbonaro, Carmela      405
Cardano, Girolamo      157 177 327
Carnot, Lazare      148—150 174 301
Carra de Vaux, Bernard      17n.
Cartan, $\acute{E}$ lie      228 320—325 353 367 380 396 404 408- 412
Cartography      127 130 178 283
Cataldi, Pietro Antonio      95
Catton, Walter      196
Cauchy, Augustin Louis      178—179 306 328 391 399
Cavalieri, Bonaventura      31 196—197
Cayley abstract groups      333
Cayley general reduction of matrices      391
Cayley, Arthur      220 233—236 249—251 296—297 398
Cayley, Cayley numbers or octaves      386—389
Cayley, Cayley — Dickson numbers      411
Celestial equator      2—3 10 12 125 129 130
Celestial mechanics      136
Celestial meridian      12 15 130
Celestial poles      12 14 129
Celestial spheres      2—3 14 18 117 124 126 128—130
Chasles, Michel      117n. 393
Chevalier, Auguste      329
Chevalley, Claude      350 362 423 425—426
chords      9—11 24 45 85—86 232-233
Christoffel, Edwin Bruno      294 311
Christoff’s cube      160
Chronology      17
circles      2—5 12 92 109—110 115 129—141 235—246
Circles, as blocks      424
Circles, circumference, area computed      219
Circles, great      8 19—39 100 125 246 282 291
Circles, imaginary at infinity      297
Circles, osculating      280
Circles, prad $\acuter{e}$ sas for      195
Clairaut, Alexis Claude      99 103 143 146
class      259 362 364—366
Classes      425
Classes, exceptional      412
Classes, residue      400—403 420
Clavius, Christopher      93—95
Clebsch, Alfred      259 302
Clifford, William Kingdon      203 290 298—301 363 394—399 408—409
Closure operation      307—308
Coding theory      425
Collection of rules of the science of astronomy      20
Collineations      150 235 238 297 339—343 417 422
Collineations, groups of      405—406
Collineations, matrices of      369
Collineations, of projective spaces      361
Commandino, Federigo      93 168
Complements      21—22 25
Completeness Condition      274—276
Comte, Auguste      199—202
cones      110 117 134—149 233—250 267—268 285—286 297—298 340-341
Cones, circular      122
Cones, conic sections      127
Cones, cylinder’s third part      191
Cones, light      420
Configuration, flat      337
Congruence      172 211 239—240 262 400
Conjugations      406—407
Connections      262 319—321 323 325
Conservation of matter and motion      185
Continua      254—256
Continuity axioms      112 171 262—263 301 420
Contravariant systems      310—311
Coolidge, Julian Lowell      362
Coordinates and coordinate systems      112—113 128—131 149—150 167 228—229 231 290
Coordinates and coordinate systems, affine      134 138
Coordinates and coordinate systems, Beltrami      231
Coordinates and coordinate systems, Cartesian      169 269
Coordinates and coordinate systems, curvilinear      281 283
Coordinates and coordinate systems, Grassmann      253 408
Coordinates and coordinate systems, homogeneous point      296 299
Coordinates and coordinate systems, inertial      265
Coordinates and coordinate systems, local, system of      321
Coordinates and coordinate systems, Pl $\ddot{u}$ cker      253 342 408
Coordinates and coordinate systems, polar      269
Coordinates and coordinate systems, projective      250 318 341 343 347 404
Coordinates and coordinate systems, rectangular      167—168 232 234 281 282 337
Coordinates and coordinate systems, skew      141—142
Coordinates and coordinate systems, space      202 265
Coordinates and coordinate systems, tangential      235
Coordinates and coordinate systems, tetracyclic      343
Coordinates and coordinate systems, time      202 265
Coordinates and coordinate systems, Weierstrass      231
Copernicus, Nicolaus      24 28 300
Corpus      402
Correlations      148—150
Cosine theorems      27 29 272
Cossists      158—159
Countable basis of a space      306
Coxeter, Harold Scott Macdonald      345 357 421—423
Crelle, August      102 288
Cremona, Luigi      347 415
Crystallographic groups      346—347
Curvature      280—301 passim 311 313—314 317 324 326 337-338
CURVES      141 143—144 259 282 297 302
Curves, equidistant      93—94 101 109 230 244
Curves, geodesic      286
Curves, isothermal      293
Curves, osculation of      280n. 297
CYCLE      414—415
cylinders      110—111 131 191 281 285—286 322
D $\ddot{u}$ rer, Albrecht      134
Damaskius      42

1 2 3 4 5

О проекте