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

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

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

јннотаци€:

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: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1988

 оличество страниц: 488

ƒобавлена в каталог: 27.10.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$e$, irrationality proofs      99
$n$-gon, rectilinear      28 31
$N$-stretch ($n$ Ч Streck)      303
$\check{C}$ahlenkova, Tamara GrigorТevna      377n.
$\check{C}$ahtauri, Ilya Adamovi$\check{c}$      405
$\check{C}$eby$\check{s}$ev, Pafnuti$\breve{\imath}$ LТvovi$\check{c}$      275Ч276
$\check{C}$ernikov, N. A.      272Ч273
$\check{S}$estryreva. L. V. (Rumyanceva)      379Ч380
$\check{S}$irokov, Petr Alekseevi$\check{c}$      363Ч364
$\check{S}\check{c}$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      328Ч329
Absolute      233Ч236 297Ч298 414 416 421Ч422
Acute-angle hypothesis      59 68 76 91 227 230
Acute-angle hypothesis, refuted      83 98 101 104 218Ч219
Adamu$\check{s}$ko, Nade$\check{z}$da Nikolaevna      415
AfanasТev, Vladimir Vasilevi$\check{c}$      424
Afrigids      16
Aghanis      42Ч44 56 58Ч59 92
Ahmedov, Ashraf Ahmedovic      81n.
al-Abh$\bar{a}$r$\bar{\imath}$, Ath$\bar{\imath}$r al-D$\bar{\imath}$n al-Mufaddal      85Ч87 105
al-Andalus$\bar{\imath}$      see al-Maghrib$\bar{\imath}$
al-B$\bar{u}$zj$\ddot{a}$n$\bar{\imath}$, Ab$\ddot{u}$-l Ч Waf$\bar{a}$      17 19 154
al-B$\bar{\imath}$r$\ddot{u}$n$\bar{\imath}$, Ab$\ddot{u}$Тl-Rayh$\bar{a}$n Ahmad (B$\bar{\imath}$r$\bar{u}$n$\bar{\imath}$, B$\bar{e}$r$\ddot{u}$n$\bar{\imath}$)      16Ч20 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      154Ч155 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$\bar{\imath}$, СAlam al-D$\bar{\imath}$n Qaysar      44 46 57 74 80 85Ч86
al-J$\bar{\imath}$l$\bar{\imath}$, K$\bar{u}$shy$\bar{a}$r ibn Labban      17
al-Jawhar$\bar{\imath}$, СAbb$\bar{a}$s      30 46Ч50 68Ч69 73Ч74 80 86 105
al-Jubb$\bar{a}$Т$\bar{\imath}$, Ab$\bar{u}$-l Ч 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-KaТbi, Ab$\bar{u}$-l Ч Q$\bar{a}$sim      193Ч194
al-Kh$\bar{a}$zin, Ab$\ddot{u}$ JaТfar Muhammad ibn al-Hussain      57 167
al-Khujand$\bar{\imath}$, Ab$\ddot{u}$ Mahm$\ddot{u}$d      17 19Ч20
al-Khw$\bar{a}$rizm$\bar{\imath}$, Muhammad ibn M$\bar{u}$s$\bar{a}$      14Ч16 20
al-M$\bar{a}$h$\bar{a}$n$\bar{\imath}$, Muhammad      15Ч16 20
al-Maghribl, Muhyl al-DIn Yahya      45Ч46 86Ч90
al-Maghribl, SamawТal      154
al-Nasawi, Abu-l Ч Hasan СAli      20
al-Nayr$\bar{\imath}$z$\bar{\imath}$, Ab$\ddot{u}$ l-ТAbb$\bar{a}$s al-Fadl      42Ч44 46 56Ч58 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$\bar{\imath}$ Ч Zada      86
al-S$\bar{a}$l$\bar{a}$r, Hus$\bar{a}$m al-D$\bar{\imath}$n      21 71Ч74 85
al-S$\bar{\imath}$jz$\bar{\imath}$, Ab$\ddot{u}$ SaТid      17 155Ч157
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$\ddot{u}$ СAbdall$\bar{a}$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 104Ч105 195
al-T$\bar{u}$s$\bar{\imath}$binomial formula for integer coefficients      154
al-T$\bar{u}$s$\bar{\imath}$parallel lines treatise      46Ч47
al-YaТq$\bar{u}$b$\bar{\imath}$, Ahmad      124
al-Zarq$\bar{a}$l$\bar{\imath}$, Ibr$\bar{a}$h$\bar{\imath}$m al-Qurt$\bar{u}$b$\bar{\imath}$      128Ч129
Albategnius      see al-Batt$\ddot{a}$ni
AlbategniusТ theorem      see Spherical cosine theorem
Albert, Abraham Adrian      413
Alberti, Leon Battista      134
Aleksandrov, (Alexandroff), Pavel Sergeevic      307Ч308
Alexander, James      304
Alfonso de Valiadolid      92
Algebra, geometric      152 157 169Ч171
Algebras      382Ч418 passim
Algebras, alternative      411Ч412
Algebras, associative      398Ч399 403Ч404
Algebras, Jordan      412Ч415
Alidad      124 130
Almucantarats      125Ч126
Alternation symbol      396Ч397
Altitude of the Sun      12 15Ч16
Altitude of the Sun, spherical coordinate      128n.
Alyabeva, Valentina Georgievna      423
Ambarcumyan (Ambarzumian), Viktor Amazaspovi$\check{c}$      426
Analemmas      123
Analysis situs      173 302Ч304 307
Anatolius      155
Anaxagoras      190
Anderson, Alexander      165
Andreeva, Lyudmila Pavlovna      379
angles      5 6 11Ч12 35Ч94 102Ч103 108 122 168
Angles, stationary      258
Angular defect      214 225Ч226 295
Angular excess      225Ч226 286 291
Anthiniatus      42
Antiautomorphism      405
Anty$\bar{a}$      12
Apollonius      114Ч115 117 123 142 347
Apollonius, Conics      15 122 124 149 167Ч169
Application (parabol$\bar{e}$) of parallelogram      38
Arachne (spider)      123 127
Arc of half the day      13
Archimedes      15 30 40Ч41 112Ч114 132 153 156 168 175
Archimedes, Archimedes Ч Heron theorem      34
Archimedes, atomistic arguments      196
Archimedes, Eudoxus Ч Archimedes axiom      39 44 47 51 54 57 59 89 90 92 262
Archimedes, Eudoxus Ч Archimedes axiom, influence on Vi$\grave{e}$te      168
Archimedes, mechanical theorems method      191 193
Archimedes, On spirals      175
Architecture and geometry      116Ч121
Archytas      111
Arcs      11 45Ч46 99
Argand, Jean Robert      179
Aries constellation      2n.
Aristarchus of Samos      123 193
Aristotle      38Ч40 46 52 58 65Ч74 173Ч175 190-194
Aristotle, composition of continua      196
Aristotle, derivation doctrine      200
Aristotle, geometry notions origin      202
Aristotle, math conceptsТ teaching      186
Aristotle, motions in geometry debated      111Ч112
Aristotle, on infinity      182Ч184
Arrowsmith, A.      128n.
Assassins, state of      20Ч21 74
Astrolabes      17 123Ч130
Astrology      1 17 20 21 173n.
Astronomy      1Ч2 10ЧЧ12 14Ч17 22 52 101 117
Astronomy, and composition of motions      175
Asturl$\bar{a}$b      see Astrolabes
Asymptotes      136
Autolycus      2Ч3
Automorphisms      366 405 412 415 422Ч423
Averbah, V. L      411
Averroes      see Ibn Rushd
Avicenna      see Ibn S$\bar{\imath}$na
Azimuths      14Ч18 126 128n.
Ba$\check{s}$makova, Isabella GrigorТevna      163n. 167
Babylonians      1Ч2 10 15
Baltzer, Richard      221
Ban$\bar{\imath}$ СIr$\ddot{a}$q (dynasty)      16
Barbaro, Daniele      123
Barbilian, Dan (Ion Barbu)      405Ч406
Barlow, William      347
Barycenter (center of gravity)      149Ч150
Battaglini, Giuseppe      221
Bellavitis, Giusto      174
Beltrami, Eugenio      221 231 233 236Ч238 241 288Ч289 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      257Ч258 303Ч304 325Ч326 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      108Ч109 203Ч204 212 214-216
Bolyai, J$\acute{a}$nos      108 212Ч217 220
Bombelli, Raphael      177
Bonetus, Nicola      196
Borelli, Giovanni Alfonso      95Ч96
Bortolotti, Enea      378
Boscovich, Roger Josip      31
Boullough, R. K.      380
Boundedness      274 323 325
Boyer, Carl B.      379
Bradwardine, Thomas      161 183 195Ч196
Brahmagupta Khandakh$\ddot{a}$dyaka treatise and rule      12Ч15 34
Brauer, Richard      409
Braunmiihl, Anton von      14
Brethren of Purity, (Ikhw$\ddot{a}$n al-Saf$\bar{a}$Т)      191Ч194
Briggs, Henry      31
Brioschi, Francesco      387 388
Brouwer, Luitzen Egbertus Jan      308 309 349
Buckle (fibulle)      27Ч30
Buddhist doctrines      195 205
Bulgarin, Fadde$\breve{\imath}$ (Tadeusz) Benediktovi$\check{c}$      209
Bunyakovski$\breve{\imath}$, Victor Yakovlevi$\check{c}$      209Ч210
Bura$\check{c}$ek, S. A.      209
Burali Ч Forti, Cesare      393
Burleigh, Walter      183
Burnside, William      408
Bussey, W.      420
Busurina, Anna Evgerievna      40n.
Calculus      141 174Ч180 197Ч198 310 311 393-394
Calendars      1 93
Cancer, Tropic of      2 125Ч126
Candry, P. J.      380
Cantor, Georg      161 262 308 426
Capricorn, Tropic of      2 125Ч126
Carbonaro, Carmela      405
Cardano, Girolamo      157 177 327
Carnot, Lazare      148Ч150 174 301
Carra de Vaux, Bernard      17n.
Cartan, $\acute{E}$lie      228 320Ч325 353 367 380 396 404 408- 412
Cartography      127 130 178 283
Cataldi, Pietro Antonio      95
Catton, Walter      196
Cauchy, Augustin Louis      178Ч179 306 328 391 399
Cavalieri, Bonaventura      31 196Ч197
Cayley abstract groups      333
Cayley general reduction of matrices      391
Cayley, Arthur      220 233Ч236 249Ч251 296Ч297 398
Cayley, Cayley numbers or octaves      386Ч389
Cayley, Cayley Ч Dickson numbers      411
Celestial equator      2Ч3 10 12 125 129 130
Celestial mechanics      136
Celestial meridian      12 15 130
Celestial poles      12 14 129
Celestial spheres      2Ч3 14 18 117 124 126 128Ч130
Chasles, Michel      117n. 393
Chevalier, Auguste      329
Chevalley, Claude      350 362 423 425Ч426
chords      9Ч11 24 45 85Ч86 232-233
Christoffel, Edwin Bruno      294 311
ChristoffТs cube      160
Chronology      17
circles      2Ч5 12 92 109Ч110 115 129Ч141 235Ч246
Circles, as blocks      424
Circles, circumference, area computed      219
Circles, great      8 19Ч39 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 364Ч366
Classes      425
Classes, exceptional      412
Classes, residue      400Ч403 420
Clavius, Christopher      93Ч95
Clebsch, Alfred      259 302
Clifford, William Kingdon      203 290 298Ч301 363 394Ч399 408Ч409
Closure operation      307Ч308
Coding theory      425
Collection of rules of the science of astronomy      20
Collineations      150 235 238 297 339Ч343 417 422
Collineations, groups of      405Ч406
Collineations, matrices of      369
Collineations, of projective spaces      361
Commandino, Federigo      93 168
Complements      21Ч22 25
Completeness Condition      274Ч276
Comte, Auguste      199Ч202
cones      110 117 134Ч149 233Ч250 267Ч268 285Ч286 297Ч298 340-341
Cones, circular      122
Cones, conic sections      127
Cones, cylinderТs third part      191
Cones, light      420
Configuration, flat      337
Congruence      172 211 239Ч240 262 400
Conjugations      406Ч407
Connections      262 319Ч321 323 325
Conservation of matter and motion      185
Continua      254Ч256
Continuity axioms      112 171 262Ч263 301 420
Contravariant systems      310Ч311
Coolidge, Julian Lowell      362
Coordinates and coordinate systems      112Ч113 128Ч131 149Ч150 167 228Ч229 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      167Ч168 232 234 281 282 337
Coordinates and coordinate systems, skew      141Ч142
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      148Ч150
Cosine theorems      27 29 272
Cossists      158Ч159
Countable basis of a space      306
Coxeter, Harold Scott Macdonald      345 357 421Ч423
Crelle, August      102 288
Cremona, Luigi      347 415
Crystallographic groups      346Ч347
Curvature      280Ч301 passim 311 313Ч314 317 324 326 337-338
CURVES      141 143Ч144 259 282 297 302
Curves, equidistant      93Ч94 101 109 230 244
Curves, geodesic      286
Curves, isothermal      293
Curves, osculation of      280n. 297
CYCLE      414Ч415
cylinders      110Ч111 131 191 281 285Ч286 322
D$\ddot{u}$rer, Albrecht      134
Damaskius      42
1 2 3 4 5
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