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| | Chance to encounter at all from the restaurant, Kelly was shown to Teresa's dad. Instantly, Kelly caught a peek at her own father. Simply serving coffee and exchanging several words and phraases offered convinced Kelly: Here is a good man, an outstanding man, who dearly is gets interested his family. Teresa must meet my in my situation own Dad.<br><br> |
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| {{Infobox scholar
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| | image = Abu Abdullah Muhammad bin Musa al-Khwarizmi edit.png
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| | image_size = 225px
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| | alt =
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| | caption = A [[commemorative stamp|stamp]] issued September 6, 1983 in the [[Soviet Union]], commemorating al-Khwārizmī's (approximate) 1200th birthday.
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| | name = Muḥammad ibn Mūsā al-Khwārizmī
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| | fullname =
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| | other_names =
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| | birth_date = 780
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| | birth_place = [[Khwarezm|Khwārizm]]<ref name="Hogendijk" /><ref>{{harvnb|Berggren|1986}}</ref><ref name="Struik 93">{{harvnb|Struik|1987| p= 93}}</ref>
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| | death_date = 850
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| | death_place =
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| | era = Medieval era ([[Islamic Golden Age]])
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| | region =
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| | alma_mater =
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| | school_tradition =
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| | main_interests =
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| | notable_ideas = Treatises on [[algebra]] and [[Indian numerals]]
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| | major_works =
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| | influences =
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| | influenced = [[Abu Kamil]]<ref name=MacTutor-AK>O'Connor, John J.; Robertson, Edmund F., [http://www-history.mcs.st-andrews.ac.uk/Biographies/Abu_Kamil.html "Abū Kāmil Shujāʿ ibn Aslam"], MacTutor History of Mathematics archive, University of St Andrews.</ref>
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| | awards =
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| '''{{transl|ar|ALA|Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī}}'''<ref group=note>There is some confusion in the literature on whether al-Khwārizmī's full name is '''{{transl|ar|ALA|Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī|أَبُو عَبْدَالله مُحَمَّد بِن مُوسَى اَلْخْوَارِزْمِی}}''' or '''{{transl|ar|ALA|Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī|أَبُو جَعْفَر مُحَمَّد بِن مُوسَى اَلْخْوَارِزْمِی}}'''. Ibn Khaldun notes in his encyclopedic work: "The first who wrote upon this branch (algebra) was Abu ʿAbdallah al-Khowarizmi, after whom came Abu Kamil Shojaʿ ibn Aslam." (MacGuckin de Slane). (Rosen 1831, pp. xi–xiii) mentions that "[Abu Abdallah Mohammed ben Musa] lived and wrote under the caliphat of Al Mamun, and must therefore be distinguished from Abu Jafar Mohammed ben Musa, likewise a mathematician and astronomer, who flourished under the Caliph Al Motaded (who reigned A.H. 279–289, A.D. 892–902)." In the introduction to his critical commentary on Robert of Chester's Latin translation of al-Khwārizmī's ''Algebra'', L.C. Karpinski notes that Abū Jaʿfar Muḥammad ibn Mūsā refers to the eldest of the [[Banū Mūsā]] brothers. Karpinski notes in his review on (Ruska 1917) that in (Ruska 1918): "Ruska here inadvertently speaks of the author as Abū Gaʿfar M. b. M., instead of Abū Abdallah M. b. M."</ref> ({{lang-ar| عَبْدَالله مُحَمَّد بِن مُوسَى اَلْخْوَارِزْمِي}}), earlier transliterated as '''Algoritmi''' or '''Algaurizin''', (c. 780 – c. 850) was a [[Persian people|Persian]]<ref name="Hogendijk">{{cite journal|first=Jan P.|last=Hogendijk|title=al-Khwarzimi|journal=Pythagoras|volume=38|issue=2|year=1998|pages=4–5|url=http://www.kennislink.nl/web/show?id=116543|format=|ref=harv|issn=0033–4766}} {{Dead link|date=March 2010}}</ref><ref name="Oaks">{{cite web|first=Jeffrey A.|last= Oaks|url=http://facstaff.uindy.edu/~oaks/MHMC.htm|title=Was al-Khwarizmi an applied algebraist?|publisher=[[University of Indianapolis]]|accessdate=2008-05-30}}</ref> [[Islamic mathematics|mathematician]], [[Islamic astronomy|astronomer]] and [[Islamic geography|geographer]] during the [[Abbasid Empire]], a [[scholar]] in the [[House of Wisdom]] in [[Baghdad]].
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| In the twelfth century, [[Latin]] translations of [[#Arithmetic|his work]] on the [[Indian numerals]] introduced the [[decimal]] [[Positional notation|positional number system]] to the [[Western world]].<ref name="Struik 93" /> His ''[[Compendious Book on Calculation by Completion and Balancing]]'' presented the first systematic solution of [[linear equation|linear]] and [[quadratic equation]]s in Arabic. In Renaissance Europe, he was considered the original inventor of [[algebra]], although it is now known that his work is based on older Indian or Greek sources.<ref>{{harvnb|Rosen|1831|p=v–vi}}; {{harvnb|Toomer|1990}}</ref> He revised [[Ptolemy]]'s ''[[Geography (Ptolemy)|Geography]]'' and wrote on astronomy and astrology.
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| Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is derived from ''al-jabr'', one of the two operations he used to solve [[quadratic equations]]. ''[[Algorism]]'' and ''[[algorithm]]'' stem from ''Algoritmi'', the [[Latin]] form of his name.<ref>{{harvnb|Daffa|1977}}</ref> His name is also the origin of ([[Spanish language|Spanish]]) ''guarismo''<ref>{{cite book|author=Knuth, Donald|url=http://historical.ncstrl.org/litesite-data/stan/CS-TR-80-786.pdf|title=Algorithms in Modern Mathematics and Computer Science|publisher=[[Springer-Verlag]]|year=1979|isbn= 0-387-11157-3|authorlink= Donald Knuth}}</ref> and of ([[Portuguese language|Portuguese]]) ''[[wikt:pt:algarismo|algarismo]]'', both meaning [[numerical digit|digit]].
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| ==Life==
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| He was born in a [[Persian people|Persian]]<ref name="Hogendijk"/><ref name="Oaks"/> family, and his birthplace is given as [[Chorasmia]]<ref>Cristopher Moore and Stephan Mertens, ''The Nature of Computation'', (Oxford University Press, 2011), 36.</ref> by [[Ibn al-Nadim]].
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| Few details of al-Khwārizmī's life are known with certainty. His name may indicate that he came from [[Khwarezm]] (Khiva), then in [[Greater Khorasan]], which occupied the eastern part of the [[Greater Iran]], now [[Xorazm Province]] in [[Uzbekistan]].
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| [[Muhammad ibn Jarir al-Tabari|Al-Tabari]] gave his name as Muhammad ibn Musa al-Khwārizmī al-[[Majousi]] al-Katarbali ({{lang|ar|محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ}}). The [[epithet]] ''al-Qutrubbulli'' could indicate he might instead have come from Qutrubbul (Qatrabbul),<ref>"Iraq After the Muslim Conquest", by [[Michael G. Morony]], ISBN 1-59333-315-3 (a 2005 facsimile from the original 1984 book), [http://books.google.com/books?id=uhjSiRAwGuEC&pg=PA145&dq=qatrabbul#v=onepage&q=qatrabbul&f=false p. 145 ]</ref> a [[viticulture]] district near [[Baghdad]]. However, Rashed<ref>{{Cite book | last = Rashed | first = Roshdi | contribution = al-Khwārizmī's Concept of Algebra | editor-last={{unicode|Zurayq}} | editor-first={{unicode|Qusṭanṭīn}} | editor2-last={{unicode|Atiyeh}} | editor2-first={{unicode|George Nicholas}} | editor3-last={{unicode|Oweiss}} | editor3-first={{unicode|Ibrahim M.}} | title = Arab Civilization: Challenges and Responses : Studies in Honor of Constantine K. Zurayk | publisher=SUNY Press|year= 1988|page=108 | isbn = 0-88706-698-4 | contribution-url = http://books.google.com/books?id=JXbXRKRY_uAC&pg=PA108&dq=Qutrubbulli#PPA108,M1 | url = http://books.google.com/?id=JXbXRKRY_uAC | ref = harv | postscript = <!--None--> }}</ref> suggests:
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| {{quote|There is no need to be an expert on the period or a philologist to see that al-Tabari's second citation should read "Muhammad ibn Mūsa al-Khwārizmī ''and'' al-Majūsi al-Qutrubbulli," and that there are two people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter ''wa'' [Arabic '{{lang|ar|و}}' for the article '[[wikt:ar:wa|and]]'] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning the personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made. Recently, [[G. J. Toomer]] ... with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader.}}
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| Regarding al-Khwārizmī's religion, Toomer writes:
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| {{quote|Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he was an adherent of the old [[Zoroastrian]] religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwārizmī's ''Algebra'' shows that he was an orthodox [[Muslim]], so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.<ref name="toomer">{{harvnb|Toomer|1990}}</ref>}}
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| [[Ibn al-Nadīm]]'s ''Kitāb al-Fihrist'' includes a short biography on al-Khwārizmī, together with a list of the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the [[Islamic conquest of Persia]], Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as [[China]] and [[History of India|India]] traveled to this city, as did Al-Khwārizmī. He worked in Baghdad as a scholar at the [[House of Wisdom]] established by [[Caliph]] {{unicode|[[al-Maʾmūn]]}}, where he studied the sciences and mathematics, which included the translation of [[Greek language|Greek]] and [[Sanskrit]] scientific manuscripts.
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| [[D. M. Dunlop]] suggests that it may have been possible that Muḥammad ibn Mūsā al-Khwārizmī was in fact the same person as [[Muḥammad ibn Mūsā ibn Shākir]], the eldest of the three [[Banū Mūsā]].<ref>Dunlop</ref>{{year missing|date=May 2011}}
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| ==Contributions==
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| [[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|A page from al-Khwārizmī's ''Algebra'']]
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| <!--[[File:The Algebra of Mohammed ben Musa (frontispiece).png|150px|thumb|The [[frontispiece]] of Frederic Rosen's ''The Algebra of Mohammed ben Musa'' (1831)]]-->
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| Al-Khwārizmī's contributions to [[mathematics]], [[geography]], [[astronomy]], and [[cartography]] established the basis for innovation in [[algebra]] and [[trigonometry]]. His systematic approach to solving [[linear equation|linear]] and [[quadratic equation]]s led to ''algebra'', a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (''al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala''الكتاب المختصر في حساب الجبر والمقابلة).
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| ''On the Calculation with Hindu Numerals'' written about 825, was principally responsible for spreading the [[Hindu-Arabic numeral system|Indian system of numeration]] throughout the [[Middle East]] and [[Europe]]. It was translated into Latin as ''Algoritmi de numero Indorum''. Al-Khwārizmī, rendered as (Latin) ''Algoritmi'', led to the term "[[algorithm]]".
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| Some of his work was based on [[Iran|Persian]] and [[Babylonia]]n [[astronomy]], [[Indian numerals|Indian numbers]], and [[ancient Greece|Greek]] mathematics.
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| Al-Khwārizmī systematized and corrected [[Ptolemy]]'s data for Africa and the Middle East. Another major book was ''Kitab surat al-ard'' ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of [[Ptolemy]] but with improved values for the [[Mediterranean Sea]], Asia, and Africa.
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| He also wrote on mechanical devices like the <!-- [[clock]], al-Biruni? -->[[astrolabe]] and [[sundial]]. <!-- His other contributions include tables of [[trigonometric function]]s, refinements in the geometric representation of [[conic sections]], and aspects of the [[calculus of two errors]]. More al-Biruni? al-Khwārizmī's made a table of sien values. -->
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| He assisted a project to determine the circumference of the Earth and in making a world map for [[al-Ma'mun]], the caliph, overseeing 70 geographers.<ref>{{cite web|accessdate=2008-05-30|url=http://www.britannica.com/eb/article-9045366|title=al-Khwarizmi|publisher=[[Encyclopædia Britannica]]}}</ref>
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| When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.<ref>[http://www.oxfordislamicstudies.com/article/opr/t125/e1305 "Khwarizmi, Abu Jafar Muhammad ibn Musa al-" in Oxford Islamic Studies Online]</ref>
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| ===Algebra===
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| {{Main|The Compendious Book on Calculation by Completion and Balancing}}
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| {{Further|Latin translations of the 12th century|Islamic science}}
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| {{double image|right|The Algebra of Mohammed ben Musa (Arabic).png|130|The Algebra of Mohammed ben Musa (English).png|120|Left: The original Arabic print manuscript of the Book of Algebra by [[Al-Khwarizmi]]. Right: A page from The Algebra of [[Al-Khwarizmi]] by Fredrick Rosen, in [[English language|English]].}}
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| ''{{transl|ar|ALA|Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala}}''
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| ({{lang-ar|الكتاب المختصر في حساب الجبر والمقابلة}}, 'The Compendious Book on Calculation by Completion <!-- <small>(variants: Restoring, Reuniting)</small> -->and Balancing') is a mathematical book written approximately 830 CE. The book was written with the encouragement of the [[Al-Ma'mun|Caliph al-Ma'mun]] as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance.<ref name=Algebra_1831_translation_rosen>{{cite web
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| |url=http://www.wilbourhall.org/index.html#algebra The Compendious Book on Calculation by Completion and Balancing
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| |work=1831 English Translation
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| |title=The Compendious Book on Calculation by Completion and Balancing, al-Khwārizmī
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| |first=Frederic
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| |last=Rosen
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| |accessdate=2009-09-14
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| }}</ref> The term ''[[algebra]]'' is derived from the name of one of the basic operations with equations ({{transl|ar|ALA|al-jabr}}, meaning completion, or, subtracting a number from both sides of the equation) described in this book. The book was translated in Latin as ''Liber algebrae et almucabala'' by [[Robert of Chester]] ([[Segovia]], 1145) hence "algebra", and also by [[Gerard of Cremona]]. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.<ref>{{cite journal|author=Karpinski, L. C.|year=1912|title=History of Mathematics in the Recent Edition of the Encyclopædia Britannica|journal=[[American Association for the Advancement of Science]]|ref=harv|authorlink=L. C. Karpinski}}</ref>
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| It provided an exhaustive account of solving polynomial equations up to the second degree,<ref>{{cite book|first=Carl B.|last=Boyer|authorlink=Carl Benjamin Boyer|title=A History of Mathematics|edition=Second|publisher=John Wiley & Sons, Inc.|year=1991|chapter=The Arabic Hegemony|pages=228|isbn=0-471-54397-7}}
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| {{quote|"The Arabs in general loved a good clear argument from premise to conclusion, as well as systematic organization — respects in which neither Diophantus nor the Hindus excelled."}}</ref> and discussed the fundamental methods of "reduction" and "balancing", referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation.<ref name=Boyer-229>{{Harv|Boyer|1991|loc="The Arabic Hegemony" p. 229}} "It is not certain just what the terms ''al-jabr'' and ''muqabalah'' mean, but the usual interpretation is similar to that implied in the translation above. The word ''al-jabr'' presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word ''muqabalah'' is said to refer to "reduction" or "balancing" — that is, the cancellation of like terms on opposite sides of the equation."</ref>
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| Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where ''b'' and ''c'' are positive integers)
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| * squares equal roots (''ax''<sup>2</sup> = ''bx'')
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| * squares equal number (''ax''<sup>2</sup> = ''c'')
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| * roots equal number (''bx'' = ''c'')
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| * squares and roots equal number (''ax''<sup>2</sup> + ''bx'' = ''c'')
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| * squares and number equal roots (''ax''<sup>2</sup> + ''c'' = ''bx'')
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| * roots and number equal squares (''bx'' + ''c'' = ''ax''<sup>2</sup>)
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| by dividing out the coefficient of the square and using the two operations ''{{transl|ar|ALA|al-jabr}}'' ({{lang-ar|الجبر}} "restoring" or "completion") and ''{{transl|ar|ALA|al-muqābala}}'' ("balancing"). {{transl|ar|ALA|Al-jabr}} is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, ''x''<sup>2</sup> = 40''x'' − 4''x''<sup>2</sup> is reduced to 5''x''<sup>2</sup> = 40''x''. {{transl|ar|ALA|Al-muqābala}} is the process of bringing quantities of the same type to the same side of the equation. For example, ''x''<sup>2</sup> + 14 = ''x'' + 5 is reduced to ''x''<sup>2</sup> + 9 = ''x''.
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| The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in al-Khwārizmī's day, most of this notation [[History of mathematical notation|had not yet been invented]], so he had to use ordinary text to present problems and their solutions. For
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| example, for one problem he writes, (from an 1831 translation)
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| {{quote|"If some one say: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts."<ref name=Algebra_1831_translation_rosen />}}
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| In modern notation this process, with 'x' the "thing" (shay') or "root", is given by the steps,
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| :<math>(10-x)^2=81 x</math>
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| :<math>x^2 - 20 x + 100 = 81 x</math>
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| :<math>x^2+100=101 x</math>
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| Let the roots of the equation be 'p' and 'q'. Then <math>\tfrac{p+q}{2}=50\tfrac{1}{2}</math>, <math>pq =100</math> and
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| :<math>\frac{p-q}{2} = \sqrt{\left(\frac{p+q}{2}\right)^2 - pq}=\sqrt{2550\tfrac{1}{4} - 100}=49\tfrac{1}{2}</math>
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| So a root is given by
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| :<math>x=50\tfrac{1}{2}-49\tfrac{1}{2}=1</math>
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| Several authors have also published texts under the name of ''{{transl|ar|ALA|Kitāb al-jabr wa-l-muqābala}}'', including |[[al-Dinawari|Abū Ḥanīfa al-Dīnawarī]], [[Abū Kāmil Shujā ibn Aslam]], Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, [['Abd al-Hamīd ibn Turk]], Sind ibn ʿAlī, Sahl ibn Bišr, and [[Sharaf al-Dīn al-Tūsī|Šarafaddīn al-Ṭūsī]].
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| J. J. O'Conner and E. F. Robertson wrote in the ''[[MacTutor History of Mathematics archive]]'':
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| {{quote|"Perhaps one of the most significant advances made by [[Mathematics in medieval Islam|Arabic mathematics]] began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed [[rational numbers]], [[irrational number]]s, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before."<ref name=MacTutor>{{MacTutor|id=Al-Khwarizmi|name=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}</ref>}}
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| R. Rashed and Angela Armstrong write:
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| {{quote|"Al-Khwarizmi's text can be seen to be distinct not only from the [[Babylonian mathematics|Babylonian tablets]], but also from [[Diophantus]]' ''[[Arithmetica]]''. It no longer concerns a series of [[problem]]s to be resolved, but an [[Expository writing|exposition]] which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."<ref>{{Cite book | last1=Rashed | first1=R. | last2=Armstrong | first2=Angela | year=1994 | title=The Development of Arabic Mathematics | publisher=[[Springer Science+Business Media|Springer]] | isbn=0-7923-2565-6 | oclc=29181926 | pages=11–2 | ref=harv | postscript=<!--None-->}}</ref>}}
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| [[File:Dixit algorizmi.png|thumb|Page from a Latin translation, beginning with "Dixit algorizmi"]]
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| ===Arithmetic===
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| Al-Khwārizmī's second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original [[Arabic language|Arabic]]. The translation was most likely done in the twelfth century by [[Adelard of Bath]], who had also translated the astronomical tables in 1126.
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| The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: {{lang|la|''Dixit algorizmi''}} ("So said al-Khwārizmī"), or {{lang|la|''Algoritmi de numero Indorum''}} ("al-Khwārizmī on the Hindu Art of Reckoning"), a name given to the work by [[Baldassarre Boncompagni]] in 1857. The original Arabic title was possibly ''{{unicode|Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind}}''<ref>Ruska</ref> ("The Book of Addition and Subtraction According to the Hindu Calculation").<ref>{{harvnb|Berggren|1986|p=7}}</ref>
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| Al-Khwarizmi's work on arithmetic was responsible for introducing the [[Arabic numerals]], based on the [[Hindu-Arabic numeral system]] developed in [[Indian mathematics]], to the [[Western world]]. The term "[[algorithm]]" is derived from the [[algorism]], the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both "algorithm" and "algorism" are derived from the [[List of Latinised names|Latinized forms]] of al-Khwarizmi's name, ''Algoritmi'' and ''Algorismi'', respectively.
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| ===Astronomy===
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| [[File:Corpus Christ College MS 283 (1).png|thumb|Page from ''Corpus Christi College MS 283''. A Latin translation of al-Khwārizmī's ''Zīj''.]]
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| {{unicode|Al-Khwārizmī's ''Zīj al-Sindhind''}}<ref name="toomer" /> (Arabic: زيج "astronomical tables of [[Sindh|Sind]] and [[Indian subcontinent|Hind]]") is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of [[sine]] values. This is the first of many Arabic ''[[Zij]]es'' based on the [[Indian astronomy|Indian astronomical]] methods known as the ''sindhind''.<ref name=Kennedy-1956>{{harvnb|Kennedy|1956|pp= 26–9}}</ref> The work contains tables for the movements of the [[sun]], the [[moon]] and the five [[planet]]s known at the time. This work marked the turning point in [[Islamic astronomy]]. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. <!-- Al-Khwarizmi's work marked the beginning of non-traditional methods of study and calculations.<ref>{{Harv|Dallal|1999|p=163}}</ref> ?????? -->
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| The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer [[Maslamah Ibn Ahmad al-Majriti]] (c. 1000) has survived in a Latin translation, presumably by [[Adelard of Bath]] (January 26, 1126).<ref>{{harvnb|Kennedy|1956|p=128}}</ref> The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) and the Bodleian Library (Oxford).
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| <!-- FAILED VERIFICATION!!!
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| Al-Khwarizmi made several important improvements to the theory and construction of [[sundial]]s, which he inherited from his [[Indian astronomy|Indian]] and [[Hellenistic civilization|Hellenistic]] predecessors. He made tables for these instruments which considerably shortened the time needed to make specific calculations. His sundial was universal and could be observed from anywhere on the Earth. From then on, sundials were frequently placed on mosques to determine the [[Salah|time of prayer]].<ref>{{Harv|King|1999a|pp=168–9}}</ref> The shadow square, an instrument used to determine the linear height of an object, in conjunction with the [[alidade]] for angular observations, was also invented by al-Khwārizmī in ninth-century [[Baghdad]].<ref>{{cite journal | last1 = King | first1 = David A. | year = 2002 | title = A Vetustissimus Arabic Text on the Quadrans Vetus | url = | journal = Journal for the History of Astronomy | volume = 33 | issue = | pages = 237–255 [238–9] |bibcode = 2002JHA....33..237K }}</ref>{{Failed verification|date=April 2010}}
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| The first [[Quadrant (instrument)|quadrants]] and [[mural instrument]]s were invented by al-Khwarizmi in ninth century Baghdad.<ref name=King>[[David A. King]], "Islamic Astronomy", in Christopher Walker (1999), ed., ''Astronomy before the telescope'', p. 167-168. [[British Museum]] Press. ISBN 0-7141-2733-7.</ref>{{Failed verification|date=April 2010}} The sine quadrant, invented by al-Khwārizmī, was used for astronomical calculations.<ref name=King-2002/>{{Failed verification|date=April 2010}} The first horary [[Quadrant (instrument)|quadrant]] for specific [[latitude]]s, was also invented by al-Khwārizmī in Baghdad, then center of the development of quadrants.<ref name=King-2002/>{{Failed verification|date=April 2010}} It was used to determine time (especially the times of prayer) by observations of the Sun or stars.<ref>{{Harv|King|1999a|pp=167–8}}</ref> The ''Quadrans Vetus'' was a universal horary quadrant, an ingenious mathematical device invented by al-Khwarizmi in the ninth century and later known as the ''Quadrans Vetus'' (''Old Quadrant'') in medieval Europe from the thirteenth century. It could be used for any [[latitude]] on Earth and at any time of the year to determine the time in hours from the [[altitude]] of the Sun. This was the second most widely used astronomical instrument during the [[Middle Ages]] after the [[astrolabe]]. One of its main purposes in the Islamic world was to determine the times of [[Salah]].<ref name=King-2002>{{Harv|King|2002|pp=237–238}}</ref>{{Failed verification|date=April 2010}}
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| -->
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| ===Trigonometry===
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| Al-Khwārizmī's ''Zīj al-Sindhind'' also contained tables for the [[trigonometric functions]] of sines and cosine.<ref name=Kennedy-1956/> <!-- CITATION NEEDED alongside the first tables for tangents. -->A related treatise on [[spherical trigonometry]] is also attributed to him.<ref name=MacTutor/>
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| ===Geography===
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| [[File:al-Khwarizmi's map.png|thumb|Hubert Daunicht's reconstruction of al-Khwārizmī's [[planisphere]].]] <!--[[File:PtolemyWorldMap.jpg|thumb|A fifteenth century map based on Ptolomy's ''Geography'' for comparison.]]-->
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| Al-Khwārizmī's third major work is his ''{{unicode|Kitāb ṣūrat al-Arḍ}}'' (Arabic: كتاب صورة الأرض "Book on the appearance of the Earth" or "The image of the Earth" translated as ''Geography''), which was finished in 833. It is a revised and completed version of [[Ptolemy]]'s ''[[Geographia (Ptolemy)|Geography]]'', consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.<ref>{{cite web|accessdate=2008-05-30|url=http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Cartography.html|title=The history of cartography|publisher=[[GAP computer algebra system]]}}</ref>
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| There is only one surviving copy of ''{{unicode|Kitāb ṣūrat al-Arḍ}}'', which is kept at the [[Strasbourg University Library]]. A Latin translation is kept at the [[Biblioteca Nacional de España]] in [[Madrid]].{{citation needed|date=September 2013}} The complete title translates as ''Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja'far Muhammad ibn Musa al-Khwārizmī, according to the geographical treatise written by Ptolemy the Claudian''.
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| The book opens with the list of [[latitudes]] and [[longitudes]], in order of "weather zones", that is to say in blocks of latitudes and, in each [[weather]] zone, by order of longitude. As [[Paul Gallez]]{{Dubious|date=January 2011}} points out, this excellent system allows the deduction of many latitudes and longitudes where the only extant document is in such a bad condition as to make it practically illegible.
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| Neither the Arabic copy nor the Latin translation include the map of the world itself; however, Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto [[graph paper]] and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.<ref>Daunicht.</ref>
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| Al-Khwārizmī corrected Ptolemy's gross overestimate for the length of the [[Mediterranean Sea]]<ref name=Kennedy-188>Edward S. Kennedy, ''Mathematical Geography'', p. 188, in {{Harv|Rashed|Morelon|1996|pp=185–201}}</ref> from the [[Canary Islands]] to the eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of [[longitude]], while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He "also depicted the [[Atlantic Ocean|Atlantic]] and [[Indian Ocean]]s as [[Ocean|open bodies of water]], not land-locked [[sea]]s as Ptolemy had done."<ref name=Covington>{{Cite journal|first=Richard|last=Covington|journal=[[Saudi Aramco World]], May–June 2007|year=2007|pages=17–21|url=http://www.saudiaramcoworld.com/issue/200703/the.third.dimension.htm|accessdate=2008-07-06|ref=harv|postscript=<!--None-->}}</ref> Al-Khwarizmi thus set the [[Prime Meridian]] of the [[Old World]] at the eastern shore of the Mediterranean, 10–13 degrees to the east of [[Alexandria]] (the prime meridian previously set by Ptolemy) and 70 degrees to the west of [[Baghdad]]. Most medieval Muslim geographers continued to use al-Khwarizmi's prime meridian.<ref name=Kennedy-188/>
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| <!--One of the corrections which al-Khwārizmī made in Ptolemy's work is the reduction of the latitude of the [[Mediterranean]] from 62° to 52° when, in actual fact, it should be only 42°. The Arab opts for the same zero meridian as Ptolemy, that of the [[Canaries]]. The amount of inhabited land extends over 180°.
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| The majority of the placenames used by al-Khwārizmī match those of Ptolemy, [[Martellus]] and [[Behaim]]. The general shape of the coastline is the same between [[Taprobane]] and [[Cattigara]]. The Atlantic coast of the [[Dragon's Tail]], which does not exist in Ptolemy's map, is traced in very little detail on al-Khwārizmī's map, but is clear and precise on the [[Martellus map]] and on the later [[Behaim]] version.-->
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| ===Jewish calendar===
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| [[File:Khwarizmi Amirkabir University of Technology.png|thumb|150px|Statue of Muḥammad ibn Mūsā al-Khwārizmī in [[Amir Kabir University of Technology]] in [[Tehran]]]]
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| Al-Khwārizmī wrote several other works including a treatise on the [[Hebrew calendar]] (''{{unicode|Risāla fi istikhrāj taʾrīkh al-yahūd}}'' "Extraction of the Jewish Era"). It describes the [[Metonic cycle|19-year intercalation cycle]], the rules for determining on what day of the week the first day of the month [[Tishrei|Tishrī]] shall fall; calculates the interval between the [[Anno Mundi|Jewish era]] (creation of Adam) and the [[Seleucid era]]; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar material is found in the works of [[al-Bīrūnī]] and [[Maimonides]].<ref name="toomer" /> <!-- Folkerts / More in Kenedy / Only Sezgin mentions "risala fi" -->
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| ===Other works===
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| [[Ibn al-Nadim]] in his ''{{unicode|[[Kitab al-Fihrist]]}}'' (an index of Arabic books) mentions al-Khwārizmī's ''{{unicode|Kitab al-Tarikh}}'', a book of annals. No direct manuscript survives; however, a copy had reached [[Nisibis]] by the 1000s, where its metropolitan, Elias bar Shinaya, found it. Elias's chronicle quotes it from "the death of the Prophet" through to 169 AH, at which point Elias's text itself hits a lacuna.<ref>{{cite book
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| |author= LJ Delaporte
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| |title=Chronographie de Mar Elie bar Sinaya
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| |year=1910
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| |location=Paris
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| |page=xiii}}</ref>
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| Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwārizmī. The Istanbul manuscript contains a paper on sundials; the ''[[Ibn_al-Nadim#Fihrist|Fihrist]]'' credits al-Khwārizmī with ''{{unicode|Kitāb ar-Rukhāma(t)}}''.<!-- This is likely an error in the Fihirst (Dunlop) --> Other papers, such as one on the determination of the direction of [[Mecca]], are on the [[spherical astronomy]].
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| Two texts deserve special interest on the [[morning width]] (''Maʿrifat saʿat al-mashriq fī kull balad'') and the determination of the [[azimuth]] from a height <!-- Bestimmung des Azimuts aus der Höhe --> (''Maʿrifat al-samt min qibal al-irtifāʿ''). <!-- see Rosenfeld 1993 -->
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| He also wrote two books on using and constructing [[astrolabe]]s.
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| ==See also==
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| {{wikiquote|al-Khwārizmī}}
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| {{Commons category|Muhammad ibn Musa al-Khwarizmi}}
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| * [[Al-Khwarizmi (crater)]] — A crater on the far side of the moon named after al-Khwārizmī.
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| * [[Khwarizmi International Award]] — An Iranian award named after al-Khwārizmī.
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| * [[Mathematics in medieval Islam]]
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| * [[Astronomy in medieval Islam]]
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| * [[Hindu and Buddhist contribution to science in medieval Islam]]
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| {{Break}}
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| ==Notes==
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| {{reflist|2|group=note}}
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| ==References==
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| {{Reflist|2}}
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| ==Further reading==
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| {{Refbegin|2}}
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| ;Biographical
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| * {{cite encyclopedia
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| | last = Toomer
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| | first = Gerald
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| | authorlink = Gerald Toomer
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| | title = Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā
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| | encyclopedia = [[Dictionary of Scientific Biography]]
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| | volume = 7
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| | editor = Gillispie, Charles Coulston
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| | publisher = Charles Scribner's Sons
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| | location = New York
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| | year = 1990
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| | isbn = 0-684-16962-2
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| | ref=harv
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| | url=http://www.encyclopedia.com/doc/1G2-2830902300.html
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| }}
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| * [[Sonja Brentjes|Brentjes, Sonja]] (2007). "[http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.htm Khwārizmī: Muḥammad ibn Mūsā al‐Khwārizmī]" in Thomas Hockey et al. (eds.). ''[[The Biographical Encyclopedia of Astronomers]]'', Springer Reference. New York: Springer, 2007, pp. 631–633. ([http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.pdf PDF version])
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| *{{cite journal|last=Dunlop|first=Douglas Morton|authorlink=Douglas Morton Dunlop|year=1943|title=Muḥammad b. Mūsā al-<u>Kh</u>wārizmī|journal=[[The Journal of the Royal Asiatic Society of Great Britain and Ireland]]|pages=248–250|publisher=Cambridge University|ref=harv|jstor=25221920|issue=2}}
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| *{{MacTutor Biography|id=Al-Khwarizmi|title=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}
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| *[[Fuat Sezgin]]. ''Geschichte des arabischen Schrifttums''. 1974, E. J. Brill, Leiden, the Netherlands.
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| *Sezgin, F., ed., ''Islamic Mathematics and Astronomy'', Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997–9. <!-- This is a collection of (mostly) reprints, consisting of 112 volumes to date. Practically all the literature on Islamic mathematics published before 1960 will be reprinted in these volumes. The volumes are compiled thematically, for example vols. 1–4 are about Al-Khwarizmi, vols. 14–20 on Euclid in the Arabic tradition, vols. 21–22 on Tabit ibn Qurra, vol. 23 on Abu Kamil, vols. 24–25 on Ibn Yunis, vols. 32–36 on al-Biruni, etc. -->
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| ;Algebra
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| *{{cite journal|last=Gandz|first=Solomon|authorlink=Solomon Gandz|title=The Origin of the Term "Algebra"|journal=The American Mathematical Monthly|volume=33|issue=9|date=November 1926|pages=437–440|doi=10.2307/2299605|publisher=The American Mathematical Monthly, Vol. 33, No. 9|ref=harv|issn=0002–9890|jstor=2299605}}
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| *{{cite journal|last=Gandz|first=Solomon|year=1936|title=The Sources of al-Khowārizmī's Algebra|journal=Osiris|volume=1|pages=263–277|url=http://links.jstor.org/sici?sici=0369-7827%28193601%291%3A1%3C263%3ATSOAA%3E2.0.CO%3B2–3|doi=10.1086/368426|issue=1|ref=harv|issn=0369–7827}}
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| *{{cite journal|last=Gandz|first=Solomon|year=1938|title=The Algebra of Inheritance: A Rehabilitation of Al-Khuwārizmī|journal=Osiris|volume=5|pages=319–391|url=http://links.jstor.org/sici?sici=0369-7827%281938%291%3A5%3C319%3ATAOIAR%3E2.0.CO%3B2–2|issue=5|doi=10.1086/368492|ref=harv|issn=0369–7827}}
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| *{{cite journal|last=Hughes|first=Barnabas|authorlink=Barnabas Hughes|title=Gerard of Cremona's Translation of al-Khwārizmī's al-Jabr: A Critical Edition|year=1986|journal=Mediaeval Studies|volume=48|pages=211–263|ref=harv}}
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| *Barnabas Hughes. ''Robert of Chester's Latin translation of al-Khwarizmi's al-Jabr: A new critical edition''. In Latin. F. Steiner Verlag Wiesbaden (1989). ISBN 3-515-04589-9.
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| *{{cite book|first=L. C.|last=Karpinski|authorlink=L. C. Karpinski|title=Robert of Chester's Latin Translation of the Algebra of Al-Khowarizmi: With an Introduction, Critical Notes and an English Version|year=1915|publisher=The Macmillan Company|url=http://library.albany.edu/preservation/brittle_bks/khuwarizmi_robertofchester/}}
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| *{{cite book|last=Rosen|first=Fredrick|authorlink=Frederick Rosen|title=The Algebra of Mohammed Ben Musa|year=1831|publisher=Kessinger Publishing|isbn=1-4179-4914-7|url=http://www.archive.org/details/algebraofmohamme00khuwrich|ref=harv}} <!-- Arabic text of the Algebra of al-Khwarizmi, with English translation. Various medieval Latin translations of the Algebra of al-Khwarizmi have also been published. -->
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| *{{cite journal|author=Ruska, Julius|title=Zur ältesten arabischen Algebra und Rechenkunst|journal=[[Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse]]|pages=1–125|year=1917|ref=harv|url=http://catalog.hathitrust.org/Record/001653568|authorlink=Julius Ruska}}
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| ;Arithmetic
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| *{{cite book|last=Folkerts|first=Menso|authorlink=Menso Folkerts|title=Die älteste lateinische Schrift über das indische Rechnen nach al-Ḫwārizmī|year=1997|publisher=Bayerische Akademie der Wissenschaften|location=München|language=German and Latin|isbn=3-7696-0108-4}} <!-- / Ed., Übers. und Kommentar von Menso Folkerts unter Mitarb. von Paul Kunitzsch --><!-- This is a new edition of the complete medieval Latin translation of the Arithmetic of al-Khwarizmi (previous editions are all incomplete). This work is lost in Arabic. -->
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| *[[Kurt Vogel|Vogel, Kurt]] (1968). ''[http://catalog.hathitrust.org/Record/000404668 Mohammed ibn Musa Alchwarizmi's Algorismus; das früheste Lehrbuch zum Rechnen mit indischen Ziffern. Nach der einzigen (lateinischen) Handschrift (Cambridge Un. Lib. Ms. Ii. 6.5) in Faksimile mit Transkription und Kommentar herausgegeben von Kurt Vogel.]'' Aalen, O. Zeller.
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| ;Astronomy
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| *{{cite book|title=Commentary on the Astronomical Tables of Al-Khwarizmi: By Ibn Al-Muthanna|first=B. R.|last=Goldstein|authorlink=B. R. Goldstein|publisher=Yale University Press|year=1968|isbn=0-300-00498-2}}
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| *{{cite journal|first=Jan P.|last=Hogendijk|authorlink=Jan Hogendijk|title=Al-Khwārizmī's Table of the "Sine of the Hours" and the Underlying Sine Table|year=1991|journal=Historia Scientiarum|volume=42|pages=1–12|ref=harv}}
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| *{{cite book|last=King|first=David A.|authorlink=David A. King|title=Al-Khwārizmī and New Trends in Mathematical Astronomy in the Ninth Century|year=1983|publisher=Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East '''2'''|location=New York University|lccn=85150177}} <!-- Description and analysis of seven recently discovered minor works related to al-Khwarizmi. -->
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| *{{cite book|last=Neugebauer|first=Otto|authorlink=Otto Neugebauer|title=The Astronomical Tables of al-Khwarizmi|year=1962}}
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| *{{cite journal|first=Boris A.|last=Rosenfeld|authorlink=Boris A. Rosenfeld|title="Geometric trigonometry" in treatises of al-Khwārizmī, al-Māhānī and Ibn al-Haytham|journal=Vestiga mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H. L. L. Busard|editor=Menso Folkerts and J. P. Hogendijk|publisher=Rodopi|location=Amsterdam|year=1993|isbn=90-5183-536-1|ref=harv}}
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| *[[Heinrich Suter|Suter, Heinrich]]. [Ed.]: Die astronomischen Tafeln des Muhammed ibn Mûsâ al-Khwârizmî in der Bearbeitung des Maslama ibn Ahmed al-Madjrîtî und der latein. Übersetzung des Athelhard von Bath auf Grund der Vorarbeiten von A. Bjørnbo und R. Besthorn in Kopenhagen. Hrsg. und komm. Kopenhagen 1914. 288 pp. Repr. 1997 (Islamic Mathematics and Astronomy. 7). ISBN 3-8298-4008-X.
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| *[[Benno van Dalen|Van Dalen, B]]. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time. <!-- Published in "Casulleras, J, Samsó, J., eds., ''From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet''. 2 vols. Barcelona: Universitat de Barcelona 1996.", pp. 195–252. With survey of all work done on the tables of al-Khwarizmi. -->
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| ;Jewish calendar
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| *{{cite journal|last=Kennedy|first=E. S.|authorlink=Edward Stewart Kennedy|title=Al-Khwārizmī on the Jewish Calendar|year=1964|journal=[[Scripta Mathematica]]|volume=27|pages=55–59|ref=harv}} <!-- reprinted in Studies in the Islamic Exact Sciences. Beirut 1983, 661–665 -->
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| ;Geography
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| *{{cite book|last=Daunicht|first=Hubert|authorlink=Hubert Daunicht|title=Der Osten nach der Erdkarte al-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens|year=1968–1970|publisher=Bonner orientalistische Studien. N.S.; Bd. 19|language=[[German language|German]]|lccn=71468286}}
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| *{{cite journal|last=Mžik|first=Hans von|authorlink=Hans von Mžik|title=Ptolemaeus und die Karten der arabischen Geographen|journal=Mitteil. D. K. K. Geogr. Ges. In Wien|volume=58|year=1915|page=152|ref=harv}}
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| *{{cite journal|last=Mžik|first=Hans von|title=Afrika nach der arabischen Bearbeitung der γεωγραφικὴ ὑφήγησις des Cl. Ptolomeaus von Muh. ibn Mūsa al-Hwarizmi|journal=Denkschriften d. Akad. D. Wissen. In Wien, Phil.-hist. Kl.|volume=59|year=1916|ref=harv}}
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| *{{cite book|last=Mžik|first=Hans von|title=Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa‘far Muḥammad ibn Mūsā al-Ḫuwārizmī|year=1926|location=Leipzig}}
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| *{{citation|last=Nallino|first=C. A.|authorlink=Carlo Alfonso Nallino|title=Al-Ḫuwārizmī e il suo rifacimento della Geografia di Tolemo|journal=Atti della R. Accad. dei Lincei, Arno 291, Serie V, Memorie, Classe di Sc. Mor., Vol. II, Rome|year=1896}}
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| *{{cite journal|author=Ruska, Julius|title=Neue Bausteine zur Geschichte der arabischen Geographie|journal=Geographische Zeitschrift|volume=24|year=1918|pages=77–81|ref=harv|authorlink=Julius Ruska}}
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| *{{cite journal|last=Spitta|first=W.|authorlink=W. Spitta|title=Ḫuwārizmī's Auszug aus der Geographie des Ptolomaeus|journal=Zeitschrift Deutschen Morgenl. Gesell.|volume=33|year=1879|ref=harv}}
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| ;Spherical trigonometry
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| *B. A. Rozenfeld. "Al-Khwarizmi's spherical trigonometry" (Russian), ''Istor.-Mat. Issled.'' '''32–33''' (1990), 325–339.
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| {{Refend}}
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| ===General references===
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| :''For a more extensive bibliography see: [[History of mathematics]], [[Mathematics in medieval Islam]], and [[Astronomy in medieval Islam]].''
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| {{Refbegin|2}}
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| * {{Cite book|last=Berggren|first=J. Lennart|authorlink=Len Berggren|title=Episodes in the Mathematics of Medieval Islam|year=1986|publisher=[[Springer Science+Business Media]]|location=[[New York]]|isbn= 0-387-96318-9|ref=harv|postscript=<!--None-->}}
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| * {{cite book|first=Carl B.|last=Boyer|authorlink=Carl Benjamin Boyer|title=A History of Mathematics|edition=Second|publisher=John Wiley & Sons, Inc.|year=1991|chapter=The Arabic Hegemony|isbn=0-471-54397-7}}
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| * {{Cite book|last=Daffa|first=Ali Abdullah al-|authorlink=Ali Abdullah Al-Daffa|title=The Muslim contribution to mathematics|year=1977|publisher=[[Croom Helm]]|location=[[London]]|isbn= 0-85664-464-1|ref=harv|postscript=<!--None-->}}
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| * {{Cite book|last=Dallal |first=Ahmad |authorlink=Ahmad Dallal|contribution=Science, Medicine and Technology |editor-last=Esposito |editor-first=John |title=The Oxford History of Islam |year=1999 |publisher=[[Oxford University Press]], [[New York]]|ref=harv|postscript=<!--None--> }}
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| * {{Cite journal|last=Kennedy|first=E. S.|authorlink=Edward Stewart Kennedy|title=A Survey of Islamic Astronomical Tables; Transactions of the American Philosophical Society| year=1956|location=[[Philadelphia]]| publisher=[[American Philosophical Society]]|volume=46|issue=2|ref=harv|postscript=<!--None-->}}
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| * {{Cite book|last=King |first=David A. |authorlink=David A. King (historian)|year=1999a |contribution=Islamic Astronomy |title=Astronomy before the telescope |editor-first=Christopher |editor-last=Walker |publisher=[[British Museum]] Press |pages=143–174 |isbn=0-7141-2733-7 |editor-link=Christopher Walker|ref=harv|postscript=<!--None--> }}
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| * {{Cite journal|last=King |first=David A. |year=2002 |title=A Vetustissimus Arabic Text on the Quadrans Vetus |journal=Journal for the History of Astronomy |volume=33 |pages=237–255|ref=harv|postscript=<!--None--> |bibcode = 2002JHA....33..237K }}
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| * {{Cite book|last=Struik|first= Dirk Jan|authorlink=Dirk Jan Struik|title=A Concise History of Mathematics|year=1987|isbn= 0-486-60255-9|edition=4th|publisher=[[Dover Publications]]|ref=harv|postscript=<!--None-->}}
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| <!-- *Nito Verdera. [http://www.cristobalcolondeibiza.com/2eng/2eng00.htm ''South America on ancient, medieval and Renaissance maps'']. Comment: Contains a bit of useful info on the Geography, but also presents a crank theory (see talk page).-->
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| <!-- muslim<ref name="Britannica">Britannica, [http://www.britannica.com/eb/article-9045366 ''al-Khw<u>a</u>rizm<u>i</u>'']</ref> -->
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| <!-- * [http://www.iranica.com Encyclopaedia Iranica] what page/chapter/article??? -->
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| <!-- * William Muir (revised edition by T. H. WEIR, M.A., D.D.). [http://answering-islam.org.uk/Books/Muir/Caliphate/ The Caliphate Its Rise, Decline, and Fall]. relevance?? -->
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| *{{MacTutor Biography|id=Abraham|title=Abraham bar Hiyya Ha-Nasi}}
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| *{{MacTutor Biography|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?}}
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| *[[Roshdi Rashed]], ''The development of Arabic mathematics: between arithmetic and algebra'', London, 1994.
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| {{Refend}}
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| {{Islamic mathematics}}
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| {{Islamic astronomy}}
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| {{Islamic geography}}
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| {{Scholars of Khorasan}}
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| {{Authority control|LCCN=n/84/020660}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Khwarizmi, Muhammad ibn Musa
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Persian mathematician and astronomer
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| | DATE OF BIRTH = ca. 780
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| | PLACE OF BIRTH =
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| | DATE OF DEATH = ca. 850
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Khwarizmi, Muhammad Ibn Musa}}
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| [[Category:780s births]]
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| [[Category:850s deaths]]
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| [[Category:Medieval Persian astrologers]]
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| [[Category:Medieval Persian astronomers]]
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| [[Category:Astronomers of medieval Islam]]
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| [[Category:Persian geographers]]
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| [[Category:Medieval Persian mathematicians]]
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| [[Category:Mathematicians of medieval Islam]]
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| [[Category:Medieval Persian people]]
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| [[Category:Scientists who worked on Qibla determination]]
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| [[Category:Geographers of medieval Islam]]
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| [[Category:9th-century geographers]]
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| [[Category:Mathematicians who worked on Islamic inheritance]]
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| [[Category:9th-century astronomers]]
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| [[Category:World Digital Library related]]
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| [[Category:8th-century Iranian people]]
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| [[Category:9th-century Iranian people]]
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