Izvorni kôd stranice Abu Abdullah Muhammad bin Musa al-Khwarizmi

{{Infokutija naučnik
| ime                     = Abu Abdullah Muhammad bin Musa al-Khwarizmi
| slika                   = 1983 CPA 5426 (1).png
| slika_širina            = 180px
| naslov                  = 
| datum_rođenja           = oko 780.
| mjesto_rođenja          = [[Khwarazm]]
| datum_smrti             = 850.
| mjesto_smrti            = 
| prebivalište            = <!-- [[Grad]], [[Država]] -->
| državljanstvo           = 
| narodnost               = [[Iran]]
| etnicitet               = Perzijanac
| polje                   = [[Matematika]], [[Geografija]], [[Astronomija]],
| radna_institucija       = 
| alma_mater              = 
| doktorski_mentor        = 
| doktorski_studenti      = 
| akademski_savjetnici    = 
| uticao_na               = Abu Kamil Shuja' ibn Aslam
| uticali_na_njega        = 
| poznat_po               = Traktati o algebri i indijskim brojevima
| autor_kratica_bot       = 
| autor_kratica_zoo       = 
| nagrade                 = 
| religija                = 
| fusnote                 = 
}}

'''Abu Abudllah Muhammad bin Musa al-Khwarizmi'''<ref>{{Cite web|url=https://www.britannica.com/biography/al-Khwarizmi|title=Al-Khwarizmi {{!}} Biography & Facts {{!}} Britannica|date=25. 8. 2023|website=www.britannica.com|language=en|access-date=21. 9. 2023}}</ref> (oko 780. - oko 840.) bio je [[Perzija|perzijski]] i [[musliman]]ski učenjak iz [[bagdad]]ske ''[[Kuća mudrosti|Kuće mudrosti]]''.

Proučavao je različite oblasti nauke kao što su: [[Matematika u srednjovjekovnom islamskom svijetu|matematika]], [[Astronomija u srednjovjekovnom islamu|astronomija]] i [[Geografija i kartografija u srednjovjekovnom islamu|geografija]] tokom perioda [[Abasidski halifat|Abasidskog halifata]].

Poznat je kao pronalazač [[Algebra|algebre]], koja je ime dobila po naslovu jedne njegove knjige. Zaslužan je za širenje [[arapski brojevi|indijskih brojeva]] po [[Zapad]]u. Zbog doprinosa u oblasti algebre smatra se kao ''otac''<ref>{{Cite book|last=Boyer|first=Carl B.|url=https://books.google.ba/books?redir_esc=y&id=bR9HAAAAQBAJ&q=al-Khwarizmi#v=snippet&q=al-Khwarizmi&f=false|title=A History of Mathematics|last2=Merzbach|first2=Uta C.|date=25. 1. 2011|publisher=John Wiley & Sons|isbn=978-0-470-63056-3|language=en}}</ref><ref>S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277</ref>  ili ''osnivač''<ref>https://eclass.uoa.gr/modules/document/file.php/MATH104/20010-11/HistoryOfAlgebra.pdf, {{Webarchive|url=https://web.archive.org/web/20190327085930/https://eclass.uoa.gr/modules/document/file.php/MATH104/20010-11/HistoryOfAlgebra.pdf |date=27. 3. 2019 }} "The first true algebra text which is still extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around 825"</ref><ref>{{Cite book|title=The Oxford History of Islam|last=Esposito|first=John L.|date=6. 4. 2000|publisher=Oxford University Press|isbn=978-0-19-988041-6|language=en|page=188}}</ref> algebre.

== Dostignuća ==
[[File:Image-Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala.jpg|thumb|Stranica iz al-Khwarizmijeve ''Algebre'']]

Al-Khwarizmi doprinosi matematici, geografiji, astronomiji i kartografiji postavili su osnovu razvoja u algebri i trigonometriji. Njegov sistematski pristup rješavanju linearnih i kvadratnih jednačina doveo je do algebre, riječi koja je izvedena iz naslova njegove knjige o ovoj temi, "Komendijska knjiga o izračunavanju dovršavanjem i balansiranjem".<ref>{{Cite web |url=http://sharif.edu/~tabesh/math-education.pdf |title=Mathematics Education in Iran From Ancient to Modern |author=Yahya Tabesh |author2=Shima Salehi |website=Sharif University of Technology |access-date=16. 4. 2018 |archive-date=16. 4. 2018 |archive-url=https://web.archive.org/web/20180416200423/http://sharif.edu/~tabesh/math-education.pdf |url-status=live }}</ref>

Izračun s hinduističkim brojevima, napisan oko 820, bio je uglavnom odgovoran za širenje hinduističko-arapskog numeričkog sistema po Bliskom istoku i Evropi. Na latinski je preveden kao Algoritmi de numero Indorum. Ime Al-Khwarizmi, prevedeno kao (latinski) Algoritmi, doveo je do izraza "algoritam".

Neki od njegovih radova bili su zasnovani na perzijskoj i babilonskoj astronomiji, indijskim brojevima i grčkoj matematici.

Al-Khwarizmi je sistematizirao i ispravio Ptolomejeve podatke za Afriku i Bliski istok. Druga velika knjiga bila je Kitab surat al-ard ("Slika Zemlje"; prevedeno kao Geografija), koja predstavlja koordinate mjesta zasnovane na onima iz Ptolomejeve geografije, ali s poboljšanim vrijednostima za Sredozemno more, Aziju i Afriku.

Pisao je i o mehaničkim uređajima kao što su astrolab[<ref>Joseph Frank, ''al-Khwarizmi über das Astrolab'', 1922.</ref> i sunčani sat. Pomagao je u projektu za određivanje obima Zemlje i u izradi mape svijeta za al-Ma'muna, halifu, nadgledajući 70 geografa.<ref>{{cite encyclopedia|access-date=30. 5. 2008|url=https://www.britannica.com/eb/article-9045366|title=al-Khwarizmi|encyclopedia=[[Encyclopædia Britannica]]|archive-date=5. 1. 2008|archive-url=https://web.archive.org/web/20080105123350/http://www.britannica.com/eb/article-9045366|url-status=live}}</ref> Kada su se u 12. vijeku njegova djela proširila Evropom preko latinskih prevoda, to je imalo dubok uticaj na napredak matematike u Evropi.

Al-Khwarizmi (Abu Jafar Muhammad ibn Musa al-Khwarizmi) je uveo modernu numeričku notaciju. Malo se zna o njegovom životu; bio je član [[bagdad]]ske Akademije nauka i pisao o [[matematika|matematici]], [[Astronomija|astronomiji]] i [[Geografija|geografiji]]. Njegova knjiga '''Algebra''' (Hisab al-jabr w’al-muqabala) uvela je ovo ime, mada se veliki dio knjige bavi računanjem. On daje opći metod (al-Khwarizmijevo rješenje) za nalaženje dva korijena kvadratne jednačine. Naime, pokazao je da jednačina oblika:

<math>ax^2 + bx + c = 0</math>

gdje je <math>a \neq 0</math> ima korijene:

<math>x_1 = \frac {-b + \sqrt {b^2 - 4ac}} {2a}</math>

<math>x_2 = \frac {-b - \sqrt {b^2 - 4ac}} {2a}</math>

U svojoj knjizi o indijskim numeralima on je opisao [[Indija|indijsku]] notaciju (pogrešno nazvanu "arapskim" numeralima), u kojoj vrijednost numerala zavisi od njegovog položaja, te koja, također, uključuje i [[Nula|nulu]].

Riječ '''[[algoritam]]''' potiče od njegovog imena prilagođenom [[latinski jezik|latinskom jeziku]], ''algoritmi''.<ref>al-Daffa 1978</ref> Od njegovog imena također vode porijeklo [[Španski jezik|španska]] riječ<ref>[[Donald Knuth|Donald E. Knuth]], [http://historical.ncstrl.org/litesite-data/stan/CS-TR-80-786.pdf ''Algorithms in Modern Mathematics and Computer Science''] {{Webarchive|url=https://web.archive.org/web/20061107213306/http://historical.ncstrl.org/litesite-data/stan/CS-TR-80-786.pdf |date=7 Novembar 2006 }}. Springer-Verlag. 1979. {{ISBN|0-387-11157-3}}.</ref> ''guarismo'' i [[Portugalski jezik|portugalska]] riječi ''algarismo''. Obje riječi nose značenje ''[[cifra]]''.<ref>{{Cite journal|last=Gandz|first=Solomon|date=1926|title=The Origin of the Term "Algebra"|url=https://www.jstor.org/stable/2299605|journal=The American Mathematical Monthly|volume=33|issue=9|pages=437–440|doi=10.2307/2299605|issn=0002-9890}}</ref>

Notacija (koja je u [[Evropa|Evropu]] stigla u [[Latinski jezik|latinskom]] prijevodu poslije 1240.) od ogromne je praktične vrijednosti i njeno prihvatanje je jedan od velikih koraka u [[Matematika|matematici]]. Iz sačuvanih rukopisa vidi se da je deset znakova (1-9 i 0) imalo skoro svoj sadašnji oblik sredinom 14. vijeka.

Iranska istraživačka organizacija za nauku i tehnologiju svake godine dodijeljuje Internacionalnu nagradu Khwarizmi za dostignuća u oblasti matematike, čiji su internacionalni sponzori svjetska organizacija za intelektualnu svojinu, [[UNESCO]], Međunarodna federacija udruženja pronalazača, Stalni komitet za naučnu i tehnološku saradnju OIK-a, Komisija za nauku i tehnologiju za održivi razvoj, Akademija nauka sa sjedištem u Trstu, Islamska organizacija za obrazovanje, nauku i kulturu, te UNDP.

U godini 2007. dobitnik ove nagrade je bio prof. dr. Muharem Avdispahić, redovni profesor na Prirodno - Matematičkom fakultetu Univerziteta u Sarajevu za izuzetna naučna dostignuća.<ref>http://old.unsa.ba/s/images/stories/AMOB/VI/Biografija.pdf</ref><ref>{{Cite web|url=http://www.infobiro.ba/article/307143|title=Nagrada “Khwarizmi” Muharemu Avdispahiću|last=d.o.o|first=OliveBH|website=infobiro.ba|access-date=21. 9. 2023}}{{Mrtav link}}</ref>

== Reference ==
{{reference}}

== Izvori ==

* {{Cite journal|last=Arndt|first=A. B.|title=Al-Khwarizmi |url=https://archive.org/details/sim_mathematics-teacher_1983-12_76_9/page/668|journal=The Mathematics Teacher |date=decembar 1983 |pages=668–670|volume=76|issue=9 |doi=10.5951/MT.76.9.0668|jstor=27963784}}
* {{cite book|first=Carl B.|last=Boyer|author-link=Carl Benjamin Boyer|title=A History of Mathematics|edition=Second|publisher=John Wiley & Sons, Inc.|date=1991|chapter=The Arabic Hegemony|isbn=978-0-471-54397-8|url=https://archive.org/details/historyofmathema00boye}}
* {{citation |first=Charles |last=Burnett |chapter=Arabic Numerals |editor=Thomas F. Glick |title=Routledge Revivals: Medieval Science, Technology and Medicine (2006): An Encyclopedia |chapter-url=https://books.google.com/books?id=zTQrDwAAQBAJ&pg=PA39 |year=2017 |publisher=Taylor & Francis |isbn=978-1-351-67617-5 |access-date=5. 5. 2019 |archive-date=28. 3. 2023 |archive-url=https://web.archive.org/web/20230328222536/https://books.google.com/books?id=zTQrDwAAQBAJ&pg=PA39 |url-status=live }}
* {{Cite book|last=Daffa|first=Ali Abdullah al-|author-link=Ali Abdullah Al-Daffa|title=The Muslim contribution to mathematics|date=1977|publisher=[[Croom Helm]]|location=[[London]]|isbn= 978-0-85664-464-1}}
* {{cite journal |last1=Dunlop |first1=Douglas Morton |title=''Muḥammad b. Mūsā al-Khwārizmī'' |journal=The Journal of the Royal Asiatic Society of Great Britain and Ireland |date=1943 |volume=2 |issue=3–4 |pages=248–250 |doi=10.1017/S0035869X00098464 |jstor=25221920 |s2cid=161841351 |url=https://www.jstor.org/stable/25221920 |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625061227/https://www.jstor.org/stable/25221920 |url-status=live }}
* {{cite journal |last1=Kennedy |first1=E. S. |title=A Survey of Islamic Astronomical Tables |journal=Transactions of the American Philosophical Society |year=1956 |volume=46 |issue=2 |pages=123–177 |doi=10.2307/1005726 |jstor=1005726 |hdl=2027/mdp.39076006359272 |url=https://www.jstor.org/stable/1005726 |hdl-access=free |access-date=24. 6. 2021 |archive-date=4. 6. 2021 |archive-url=https://web.archive.org/web/20210604153154/https://www.jstor.org/stable/1005726 |url-status=live }}
*{{Citation
 |last2=Morelon
 |first2=Régis
 |last1=Rashed
 |first1=Roshdi
 |author1-link=Roshdi Rashed
 |year=1996
 |title=Encyclopedia of the History of Arabic Science
 |url=https://books.google.com/books?id=dIWtmfwvItkC
 |volume=1
 |publisher=[[Routledge]]
 |isbn=0-415-12410-7
 }}

* {{Cite book|last=Struik|first=Dirk Jan|author-link=Dirk Jan Struik|title=A Concise History of Mathematics|date=1987|isbn=978-0-486-60255-4|edition=4th|publisher=[[Dover Publications]]|url-access=registration|url=https://archive.org/details/concisehistoryof0000stru_m6j1}}
* {{cite encyclopedia
  | last = Toomer
  | first = Gerald
  | author-link = Gerald Toomer
  | title = Al-Khwārizmī, Abu Ja'far Muḥammad ibn Mūsā
  | encyclopedia = [[Dictionary of Scientific Biography]]
  | volume = 7
  | editor = Gillispie, Charles Coulston
  | publisher = Charles Scribner's Sons
  | location = New York
  | date = 1990
  | isbn = 978-0-684-16962-0
  | url = http://www.encyclopedia.com/doc/1G2-2830902300.html
  | access-date = 31. 12. 2010
  | archive-date = 2. 7. 2016
  | archive-url = https://web.archive.org/web/20160702040538/http://www.encyclopedia.com/doc/1G2-2830902300.html
  | url-status = live
  }}

== Dodatna literatura ==
==== Bibliografija ====
* [[Sonja Brentjes|Brentjes, Sonja]] (2007). "[http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.htm Khwārizmī: Muḥammad ibn Mūsā al‐Khwārizmī] {{Webarchive|url=https://web.archive.org/web/20110706185327/http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.htm |date=6. 7. 2011 }}" in Thomas Hockey et al.(eds.). ''[[The Biographical Encyclopedia of Astronomers]]'', Springer Reference. New York: Springer, 2007, pp.&nbsp;631–633. ([http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.pdf PDF version] {{Webarchive|url=https://web.archive.org/web/20120114103045/http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.pdf |date=14. 1. 2012 }})
* [[Jan Hogendijk|Hogendijk, Jan P.]], [http://www.alkhwarizmi.nl/ Muhammad ibn Musa (Al-)Khwarizmi (c. 780–850 CE)] {{Webarchive|url=https://web.archive.org/web/20180203102909/http://alkhwarizmi.nl/ |date=3. 2. 2018 }} – bibliography of his works, manuscripts, editions and translations.
* {{MacTutor Biography|id=Al-Khwarizmi|title=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}
* {{cite book |last1=Sezgin |first1=Fuat |title=Geschichte des arabischen Schrifttums, Band V: Mathematik. Bis ca. 430 H |date=1974 |publisher=Brill |location=Leiden |pages=228–241}}
*{{cite book |last1=Sezgin |first1=Fuat |title=Geschichte des arabischen Schrifttums, Band VI: Astronomie. Bis ca. 430 H |date=1978 |publisher=Brill |location=Leiden |pages=140–143|bibcode=1978gasb.book.....S }}
*{{cite book |last1=Sezgin |first1=Fuat |title=Geschichte des arabischen Schrifttums, Band VII: Astrologie – Meteorlogie und Verwanndtes Bis ca. 430 H |date=1979 |publisher=Brill |location=Leiden |pages=128–129}}
* Sezgin, F., ed.,  ''Islamic Mathematics and Astronomy'',  Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997–99. <!-- 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. -->

==== Algebra ====
* {{cite journal |last1=Gandz |first1=Solomon |author1-link=Solomon Gandz |title=''The Origin of the Term "Algebra'' |journal=The American Mathematical Monthly |date=novembar 1926 |volume=33 |issue=9 |pages=437–440 |doi=10.2307/2299605 |jstor=2299605 |url=https://www.jstor.org/stable/2299605 |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625055507/https://www.jstor.org/stable/2299605 |url-status=live }}
* {{cite journal |last1=Gandz |first1=Solomon |author1-link=Solomon Gandz |title=''The Sources of al-Khowārizmī's Algebra'' |journal=Osiris |date=1936 |volume=1 |issue=1 |pages=263–277 |doi=10.1086/368426 |jstor=301610 |s2cid=60770737 |url=https://www.jstor.org/stable/301610 |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625080209/https://www.jstor.org/stable/301610 |url-status=live }}
* {{cite journal |last1=Gandz |first1=Solomon |author1-link=Solomon Gandz |title=''The Algebra of Inheritance: A Rehabilitation of Al-Khuwārizmī'' |journal=Osiris |date=1938 |volume=5 |issue=5 |pages=319–391 |doi=10.1086/368492 |jstor=301569 |s2cid=143683763 |url=https://www.jstor.org/stable/301569 |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625054923/https://www.jstor.org/stable/301569 |url-status=live }}
* {{cite journal |last1=Hughes |first1=Barnabas |title=Gerard of Cremona's Translation of al-Khwārizmī's al-Jabr, A Critical Edition |journal=Mediaeval Studies |date=1986 |volume=48 |pages=211–263 |doi=10.1484/J.MS.2.306339 |url=https://doi.org/10.1484/J.MS.2.306339 }}
* 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}}.
* {{cite book|first=L.C.|last=Karpinski|author-link=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|date=1915|publisher=The Macmillan Company|url=https://library.albany.edu/preservation/brittlebooks|access-date=21. 5. 2020|archive-date=24. 9. 2020|archive-url=https://web.archive.org/web/20200924032358/https://library.albany.edu/preservation/brittlebooks|url-status=live}}
* {{cite book |last1=Rosen |first1=Fredrick |title=The Algebra of Mohammed Ben Musa |date=1831 |location=London |url=https://archive.org/details/algebraofmohamme00khuwuoft }}
* {{cite journal |last1=Ruska |first1=Julius |title=''Zur ältesten arabischen Algebra und Rechenkunst'' |journal=Sitzungsberichte der Heidelberger Akademie der Wissenschaften. Philologisch-historische Klasse |date=1917 |volume=2 |pages=1–125 |url=https://archive.org/details/ruska1917algebra }}

==== Artimetika ====
* {{cite book |last1=Folkerts |first1=Menso |title=Die älteste lateinische Schrift über das indische Rechnen nach al-Ḫwārizmī |date=1997 |publisher=Bayerische Akademie der Wissenschaften |location=München |isbn=978-3-7696-0108-4 |url=http://publikationen.badw.de/de/011407256 |access-date=24. 6. 2021 |archive-date=24. 6. 2021 |archive-url=https://web.archive.org/web/20210624211923/http://publikationen.badw.de/de/011407256 |url-status=live }} (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).
* {{cite book |last1=Vogel |first1=Kurt |title=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 |series=Milliaria.3 |date=1963 |publisher=Aalen, O. Zeller |url=https://catalog.hathitrust.org/Record/000404668/Home |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625101707/https://catalog.hathitrust.org/Record/000404668/Home |url-status=live }}

==== Astronomija ====
* {{cite book|title=Commentary on the Astronomical Tables of Al-Khwarizmi: By Ibn Al-Muthanna|first=B.R.|last=Goldstein|author-link=B. R. Goldstein|publisher=Yale University Press|date=1968|isbn=978-0-300-00498-4}}
* {{cite journal |last1=Hogendijk |first1=Jan P. |author1-link= Jan Hogendijk |title=Al-Khwārizmī's Table of the "Sine of the Hours" and the Underlying Sine Table |journal=Historia Scientiarum |date=1991 |volume=42 |pages=1–12 |url=http://www.jphogendijk.nl/publ.html#English |access-date=24. 6. 2021 |archive-date=7. 5. 2021 |archive-url=https://web.archive.org/web/20210507023229/http://www.jphogendijk.nl/publ.html#English |url-status=live }} (Hogendijk's homepage. Publication in English, no. 25).
* {{cite book |last1=King |first1=David A. |author-link=David A. King (historian) |title=Al-Khwārizmī and New Trends in Mathematical Astronomy in the Ninth Century |date=1983 |publisher=Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East 2 |location=New York University |url=https://davidaking.academia.edu/research#muslimastronomers |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625030900/https://davidaking.academia.edu/research#muslimastronomers |url-status=live }} (Description and analysis of seven recently discovered minor works related to al-Khwarizmi).
* {{cite book|last=Neugebauer|first=Otto|author-link=Otto Neugebauer|title=The Astronomical Tables of al-Khwarizmi|date=1962}}
* {{cite book |last1=Rosenfeld |first1=Boris A. |editor1-last=Folkerts |editor1-first=Menso |editor2-last=Hogendijk |editor2-first=Jan P. |editor2-link=Jan Hogendijk |title=Vestigia Mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H.L.L. Busard |url=https://archive.org/details/vestigiamathemat0000unse |date=1993 |publisher=Brill |location=Leiden |isbn=978-90-5183-536-6 |pages=[https://archive.org/details/vestigiamathemat0000unse/page/n308 305]–308 |chapter='Geometric trigonometry' in treatises of al-Khwārizmī, al-Māhānī and Ibn al-Haytham}}
* [[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}}.
* {{cite book |last1=Van Dalen |first1=Benno |editor1-last=Casulleras |editor1-first=Josep |editor2-last=Samsó |editor2-first=Julio |title=From Baghdad to Barcelona, Studies on the Islamic Exact Sciences in Honour of Prof. Juan Vernet |date=1996 |publisher=Instituto Millás Vallicrosa de Historia de la Ciencia Arabe |location=Barcelona |pages=195–252 |url=http://www.bennovandalen.de/Publications/publications.html |chapter=al-Khwârizmî's Astronomical Tables Revisited: Analysis of the Equation of Time |chapter-url=http://www.bennovandalen.de/Publications/publications.html |access-date=24. 6. 2021 |archive-date=24. 6. 2021 |archive-url=https://web.archive.org/web/20210624203439/http://www.bennovandalen.de/Publications/publications.html |url-status=live }} (Van Dalen's homepage. List of Publications, Articles – no. 5).

==== Trigonometrija sfera ====
* B.A. Rozenfeld. "Al-Khwarizmi's spherical trigonometry" (Russian), ''Istor.-Mat. Issled.'' '''32–33''' (1990), 325–339.

==== Jevrejski kalendar  ====
* {{cite journal|last=Kennedy|first=E. S.|author-link=Edward Stewart Kennedy|title=Al-Khwārizmī on the Jewish Calendar|date=1964|journal=[[Scripta Mathematica]]|volume=27|pages=55–59}} <!-- reprinted in Studies in the Islamic Exact Sciences. Beirut 1983, 661–665 -->

==== Geografija ====
* {{cite book |last1=Daunicht |first1=Hubert |title=Der Osten nach der Erdkarte al-Ḫuwārizmīs. Beiträge zur historischen Geographie und Geschichte Asiens. Bd 1: Rekonstruktion der Karte, Interpretation der Karte: Südasien; Teil 2: Die ost- und südostasiatische Inselwelt und die Meere; Teil 3: Der Süden des festländischen Ostasiens; Teil 4, 1 u. 2: Der Norden des festländischen Ostasiens und Nord- und Mittelasien |date=1968–1970 |publisher=Diss.--Bonn: Bonner Orientalistische Studien. N. S. Bd 19. 19a—d |jstor=43370513 |url=https://www.jstor.org/stable/43370513 |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625051225/https://www.jstor.org/stable/43370513 |url-status=live }}
* {{cite journal|last=Mžik|first=Hans von|author-link=Hans von Mžik|title=Ptolemaeus und die Karten der arabischen Geographen|journal=Mitteil. D. K. K. Geogr. Ges. In Wien|volume=58|date=1915|page=152}}
* {{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|date=1916}}
* {{cite book|last=Mžik|first=Hans von|title=Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa'far Muḥammad ibn Mūsā al-Ḫuwārizmī|date=1926|location=Leipzig}}
* {{citation|last=Nallino|first=C.A.|author-link=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|date=1896}}
* {{cite journal|last=Ruska |first=Julius|title=Neue Bausteine zur Geschichte der arabischen Geographie|journal=Geographische Zeitschrift|volume=24|date=1918|pages=77–81|author-link=Julius Ruska}}
* {{cite journal |last1=Spitta |first1=Wilhelm |title=Huwârazmî's Auszug aus der Geographie des Ptolemaios |journal=Zeitschrift der Deutschen Morgenländischen Gesellschaft |date=1879 |volume=33 |pages=294–297 |url=http://menadoc.bibliothek.uni-halle.de/dmg/periodical/titleinfo/49140 |access-date=24. 6. 2021 |archive-date=24. 6. 2021 |archive-url=https://web.archive.org/web/20210624205734/http://menadoc.bibliothek.uni-halle.de/dmg/periodical/titleinfo/49140 |url-status=live }}
{{Refend}}

=== Opste reference ===
* {{cite book |last1=Berggren |first1=John L. |title=Episodes in the Mathhematics of Medieval Islam |url=https://archive.org/details/episodesinmathem0000berg_y2l9 |date=2016 |publisher=Springer |location=New York |isbn=978-1-4939-3778-3 |edition=2nd}}
* {{cite book |last1=Dallal |first1=Ahmad |editor1-last=Esposito |editor1-first=John L. |editor1-link=John Esposito |title=The Oxford History of Islam |url=https://archive.org/details/oxfordhistoryofi00john |date=1999 |publisher=Oxford University Press |location=New York |isbn=978-0-19-510799-9 |chapter=Science, Medicine and Technology: The Making of a Scientific Culture}}
* {{cite book |last1=King |first1=David A. |author1-link=David A. King (historian) |editor1-last=Walker |editor1-first=Christopher |title=Astronomy before the telescope |date=1999a |publisher=British Museum Press |isbn=978-0-7141-2733-0 |pages=143–174 |chapter=Islamic Astronomy |chapter-url=https://davidaking.academia.edu/research#islamicastronomygeneralsurveys |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625030900/https://davidaking.academia.edu/research#islamicastronomygeneralsurveys |url-status=live }}
* {{cite journal |last1=King |first1=David A |author1-link=David A. King (historian) |title=A Vetustissimus Arabic Text on the Quadrans Vetus |journal=Journal for the History of Astronomy |date=2002 |volume=33 |issue=112 |pages=237–255 |doi=10.1177/002182860203300302 |s2cid=125329755 |url=https://davidaking.academia.edu/research#miscellaneousinstrumentsquadrantscompass |access-date=24. 6. 2021 |archive-date=25. 6. 2021 |archive-url=https://web.archive.org/web/20210625030900/https://davidaking.academia.edu/research#miscellaneousinstrumentsquadrantscompass |url-status=live }}
* {{MacTutor Biography|id=Abraham|title=Abraham bar Hiyya Ha-Nasi}}
* {{MacTutor Biography|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?}}
* {{cite book |last1=Rashed |first1=Roshdi |author1-link=Roshdi Rashed |last2=Armstrong |first2=Angela F.W. |title=The Development of Arabic Mathematics: Between Arithmetic and Algebra |date=1994 |publisher=Springer |location=New York |isbn=978-90-481-4338-2}}
{{Refend}}

{{Commonscat|Muhammad ibn Musa al-Khwarizmi}}
{{Astronomija u srednjovjekovnom islamu}}
{{Geografija i kartografija u srednjovjekovnom islamu}}

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