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Ifrah G., Bellos D. — The Universal History of Numbers: From Prehistory to the Invention of the Computer
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Íàçâàíèå: The Universal History of Numbers: From Prehistory to the Invention of the ComputerÀâòîðû: Ifrah G., Bellos D. Àííîòàöèÿ: "Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly
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Ïðåäìåòíûé óêàçàòåëü
'Abbas, Caliph Abu'l 520 'Ali, Abu'l Hassan 58 'Ali, caliph 519—520 555 'Ammar 525 'Attar, Farid ad din 527 'Isa, 'Ali ibn 525 'n' roots 528 'Umar, caliph 515 519 'Umayyad dynasty 512 'Uthman, Abu 523 'Uthman, Caliph 519—520 Aba, tomb of 52 abacus 125—133 207—211 333—334 366 556—562 Abacus, abacists and algorists 578 590—591 Abacus, Akkadian 139—141 Abacus, Assyro-Babylonian 140 Abacus, Chinese 125 211 283—294 556 Abacus, French 290 Abacus, Gerbert's 579 581—586 588 Abacus, Greek 200—203 208 Abacus, Inca 308 Abacus, Indian 434 559 Abacus, Latin 542—543 Abacus, Liber Abaci 361—362 588—589 Abacus, Mesopotamian tablet 155 Abacus, multiplication 208—209 557—559 Abacus, Persian 556 562—563 Abacus, Roman 187 202—207 209—211 577 579—580 582 Abacus, Russian 290 Abacus, suan pan 288—294 Abacus, Sumerian sexagesimal 126—133 140 Abacus, Table of Salamis 201—203 Abacus, wax or sand 207—209 563 Abbasid caliphs 512 514 520 Abel, Niels Henrik 596 Abenragel 356 363 524 Abjad numerals (ABC) 244 248 250 261—262 548—555 Aboriginals, Australian 6 18 Abraham 73 253—254 257 364 Abrasax 259 Absolute quantity 21 Abstraction 16 see "Model "Place-value "Zero" Abstraction, counting 10 19—20 76 Abstraction, numbers 5 23 Abulcassis 522 Abusir 390 Abyssinia 96 246 387 Academy of Sciences (France) 42 accounting 101—120 187 541—543 see "Calculi" "Quipus" "Tablet" "Tally Accounting, balance sheet 109—111 Accounting, Cretan 178 Accounting, Elamite 102—107 Accounting, Japan 288—289 Accounting, Jews 236 Accounting, Mayan 304—305 Accounting, Mesopotamian 132 Accounting, pocket calculator 209—211 Accounting, Roman 187 209—211 Accounting, Sumerian 122—124 131 Acor 406 Acrophonic number systems 186 214 387 ad Dahabi, Ahmad 252 Adab 81 Adad 161 Adam (first man) 254 Addition, abacus 127 204—206 285 Addition, calculi, Sumerian use 122 Addition, Egypt, Ancient 174 Addition, suan pan 291—292 Additive principle 231 325—329 333—336 347—351 Additive principle, Americas 306 308 Additive principle, India 397 434 Additive principle, Roman numerals 187 Additive principle, Sheban 186 Adelard of Bath 207 362 587 Afghanistan 377 386 522—523 528 Afghanistan and Arabs 512 520 523 Afghanistan, counting 94 290 Afghanistan, numerals 228 368 534 Afghanistan, writing 376 539 Aflah, Jabir ibn 526 Africa, Arabian provinces 521 Africa, base five in 36 Africa, Central 5 22 Africa, counting 10 96 125 Africa, East 72 Africa, Maghribi script 539 Africa, North, and Arab-Islamic world 520 528 587 Africa, North, calculation 559 Africa, North, counting 47 214 Africa, North, Goths 226 Africa, North, Morra 51 Africa, North, number mysticism 248 250 262 553 Africa, North, numerals 242 244 356 534—537 Africa, North, writing 248 539 Africa, number mysticism 93—94 554 Africa, South 5 Africa, West 19 24—25 70 74 Agade see "Akkadian Empire" Ages of the world 426 Aggoula, B. 335 Ah Puch, god of death 312 Aharoni, Y. 236 Ahmad, Abu Hanifa 522 Ahmad, Ali ibn 523 Ahmed 363 511 519 Ainus 36 305 Akhiram 213 Akkad 135 Akkadian Empire 81 134—146 see "Babylonian Akkadian Empire, bullae 100—101 Akkadian Empire, counting 139—141 Akkadian Empire, Mari 74 81 134 142—146 336 Akkadian Empire, number mysticism 93 159—160 Akkadian Empire, numbers 90 134 136—139 142—146 Akkadian Empire, writing 130—133 135—136 159—160 Aksharapalli numerals 388 Aksum 246 387 al Hanbali, Mawsili 55 58 al Harran, Sinan ibn al Fath min ahl 364 al Kalwadzani, Abu Nasr Muhammad Ben Abdullah 364 al Karabisi, Ahmad ben 'Umar 364 al Ma'ali, Abu 556 al Maklati, Muhammad Ben Ahmed 252 al Malik, 'Abd 252 al Misri, Abu Kamil Shuja' ibn Aslam ibn Muhammad al Hasib 364 al Mu'aliwi, 'Ali Ben Ahmad Abu'l Qasim al Mujitabi al Antaki 364 al Mulk, Nizam 58 al Mustadi 252 al Shamishi system 248 al Tadmuri system 248 al Tarabulusi, Ahmad al Barbir 58—59 al Tirmidhi, Abu Dawud 51 al umam, Tabaqat 515 al Wahab Adaraq, Abd 252 al Yaman, Hudaifa ibn 58 al-'Amuli, Beha ad din 363 528 al-'Umari 527 al-Abbas 521 al-Adami, ibn 523 529—530 al-Akhtal 520 al-Andalusi, Sa'id 515—516 al-Ansari 528 al-Antaki 541—542 al-Ash'ari, Abul Hasan 'Ali ibn Ismail 522 al-Asma'i 521 al-Asturlabi, Ali ibn 'Isa 521 al-Asturlabi, Badi al-Zaman 518 526 al-Atahiya, Abu 521 al-Ba'albakki, Qusta ibn Luqa 518 522 al-Baghdadi, "Abd al-Qadir 528 al-Baghdadi, Muwaffaq al din Abu Muhammad 363 527 542 al-Bakri 525 al-Baqi, Muhammad ibn "Abd 525 al-Baqilani, Abu Bakr Ahmad ibn "Ali 524 al-Barakat, Abu 526 al-Basri, Hasan 520 al-Battani (Albategnus) 514 522 al-Bayasi, 'Abu Zakariyya Yahya 518 526 al-Baytar, Ibn 527 al-Biruni, Muhammad ibn Ahmed Abu'l Rayhan 513—515 519 524 588 al-Biruni, Muhammad ibn Ahmed Abu'l Rayhan, Indian numerals 418 438 al-Biruni, Muhammad ibn Ahmed Abu'l Rayhan, Kitab fi tahqiq i ma li'lhind 363—365 368 409 426—429 530 534 al-Biruni, Muhammad ibn Ahmed Abu'l Rayhan, Tarikh ul Hind 251 al-Bujzani, Abu'l Wafa' 523 548 Al-Buni 553—554 al-Daffa, A.A. 519 al-Darir, Abu Sa'id 521 al-Fadl 520 al-Faqih, ibn 523 al-Farabi 514 517 523 al-Farazdaq 58 520 al-Farghani 521 al-Farid, Ibn 527 al-Farrukhan, "Umar ibn 521 al-Fath, Sinan ibn 524 al-Fazzari, Abu Ishaq Ibrahim 513—514 520 530 al-Fazzari, Muhammad Ben Ibrahim 520 529—530 al-Ghafur, "Abd ar Rashid Ben "Abd 528 al-Ghazali, Abu Hamid 525 al-Gili 549 al-Gili, Abu'l Hasan Kushiyar ibn Labban 363 513 524 534 549 560—562 al-Hajjami 525 al-Hakam II, caliph 523 al-Hallaj, Abu Mansur ibn Husayn 523 al-Hamdani 523 al-Harb, Urjuza fi hasab al "uqud 542 al-Hasib, Hasbah 521 al-Hassar 563 al-Haytham, Abu Ali al Hasan ibn al Hasan ibn 363 514 518 524 al-Himsi 522 al-Husayn, Abu Ja'far Muhammad ibn 520 al-Idrisi 526 al-Imrani 523 al-Istakhri 524 al-Jahiz 364 521 541 al-Jamali, Badr 525 al-Jauhari 521 al-Jayyani, Ibn Mu'adh Abu "Abdallah 518 524 al-Jazzari, Isma'il ibn al-Razzaz 518 527—528 Al-Karaji 511 514 516 524 526 530 548 Al-Kashi 516 al-Kashi, Ghiyat ad din Ghamshid ibn Mas'ud 513 528 561 571 al-Kathi 525 al-Khazini, Abu Ja'far 523 al-Khujani 524 al-Khuwarizmi, Abu Ja'far Muhammad Ben Musa 364—365 513—514 516 521 523—524 529—531 533 539 548 560 562 588 al-Khuwarizmi, Abu Ja'far Muhammad Ben Musa, algorithms 531 587 al-Kilwadhi 522 al-Kindi 364 514 519 521 556 al-Kirmani 524 al-Koyunlu 528 al-Kuhi, Ibn Rustam 523 al-Ma'ari, Abu'l 'ala 525 al-Ma'mun, Caliph 512 521 529 531 al-Maghribi, As Samaw'al ibn Yahya 55 363 511 514 516 526 534 Al-Mahani 522—523 al-Mansur, Caliph 512 520 529—530 al-Mansur, Sultan Abu Yusuf Ya'qub 526 528 550 al-Maqrizi 528 al-Maradini 542 al-Mardini, Massawayh 513 525 al-Marrakushi, Abu'l Abbas Ahmad ibn al-Banna 363 527 568 al-Marwarradhi 521 al-Mas'udi 514 523 al-Mawardi 525 al-Meqi, al-Amuni Saraf ad din 363 526 al-Mu'min, 'Abd 525 al-Mu'tamin 525 al-Muhasibi 522 al-Muqaddasi 524 al-Muqafa', ibn 520 al-Muqafa, Abu Shu'ayb 521 al-Mustawfi, Hamdallah 527 al-Nadim, Ya'qub ibn 364 524 al-Nadim, Ya'qub ibn, Fihrist 364 531 539 al-Nafis, Ibn 527 al-Nahawandi, Ahmad 521 al-Nawabakht 520 al-Nayrizi (Anaritius) 522 al-Nazzam 521 al-Qalasadi 539 al-Qalasadi, Abu'l Hasan 'Ali ibn Muhammad 363 516 528 563 567 al-Qasim, Muhammad Ben 529 al-Qass, Nazif ibn Yumn 523 al-Qays, Imru' 520 al-Qifti, Abu'l Hasan 527 529—530 al-Rashid, Harun 512 520 al-Razi, Fakhar ad din 363 513—514 526 al-Razi, Muhammad Abu Bakr Ben Zakariyya (Razhes) 522 al-Samh, Ibn 524 al-Shanshuri 536 al-Sijzi, 'Abdjalil 524 534 al-Sufi, Abu Musa Ja'far 364 521 al-Sufin, 'Abd ar-Rahman 524 al-Tabari, Marshallah 514 al-Tabari, Sahl 514 521 al-Uqlidisi, Abu'l Hasan Ahmad ibn Ibrahim 364 523 563 al-Wafid, Ibn 525 al-Ya'qubi 522 al-Yamani, Yahya ibn Nawfal 58 520 al-Zarqali 525 Albania 33—35 528 Albategnus 522 Albright, W.F. 142 Alchemy 518—519 553—554 Alexander the Great 135 256 386 407 Alexandria 515 522 Algazel 525 Algebra 588 597—598 Algebra, Arabs and 521 524 527—528 531 Algebra, Arabs and Brahmagupta 419 439 530 Algebraic numbers 596—597 Algeria 248 521 528 Algeria, counting 49 66 555 Algorists 587—590 Algorithms 559 587 Algorithms, al-Khuwarizmi 531 587 Alhazen 524 Ali (language) 22 Alien intervention theory 593—594 Allah 47 59 214 514—515 553 Allah, Abu Sa'id 'Ubayd 525 Allah, attributes of 11 50—51 71 261—262 542 553 Allah, Sa'id ibn Hibat 525 Allard, A.L. 365 434 533 562—563 589 Alleton, V.G. 266—268 272 almanacs 195—196 Alphabet 212—214 Alphabet, Greek 190 Alphabet, Hebrew 215—218 Alphabet, palaeo-Hebrew 212 233 Alphabet, Samaritans 212 Alphabetic numerals 156—157 212—262 329 483—484 see Alphabetic numerals, Arabic 158 241—246 516 548—555 Alphabetic numerals, Aryabhata's 432 Alphabetic numerals, Ethiopian 246—247 Alphabetic numerals, Greek 218—223 227 232—233 238—239 329 333 360 Alphabetic numerals, Hebrew 158 227 233—236 238—239 346 362 Alphabetic numerals, Indian 389
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