Muhammad ibn Musa al-Khwarizmi
{{Infobox academic|image=era=Medieval era ([[Islamic Golden Age]])|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 Shujā‘ ibn Aslam"], MacTutor History of Mathematics archive, University of St Andrews.</ref>|influences=|major_works=[[The Compendious Book on Calculation by Completion and Balancing]], Book of the Description of the Earth, Astronomical tables of Siddhanta|notable_ideas=Treatises on [[algebra]] and [[Indian numerals]]|main_interests=[[Mathematics]], [[Geography]], [[Astronomy]]|school_tradition=|alma_mater=|region=|death_place=[[Baghdad]], [[Iraq]]|image_size=|death_date={{circa|lk=no|850}} (aged c. 70)|birth_place=[[Khwarezm]]<ref>{{harvnb|Berggren|1986}}; {{harvnb|Struik|1987| p= 93}}</ref>|birth_date={{circa|lk=no|780}}|other_names=|birth_name=|native_name=|name=Muḥammad ibn Mūsā al-Khwārizmī|caption=Statue of al-Khwārizmī carrying an [[astrolabe]] in [[Amir Kabir University]], [[Tehran]], [[Iran]]|alt=|awards=}}Si '''Muḥammad ibn Mūsā al-Khwārizmī'''{{refn|There is some confusion in the literature on whether al-Khwārizmī's full name is {{lang|ar|rtl=yes|ابو عبد الله محمد بن موسى الخوارزمي}} {{transl|ar|ALA|Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī}} or {{lang|ar|rtl=yes|ابو جعفر محمد بن موسی الخوارزمی}} {{transl|ar|ALA|Abū Ja‘far Muḥammad ibn Mūsā al-Khwārizmī}}. [[Ibn Khaldun]] notes in his Prolegomena: "The first to write on this discipline [algebra] was Abu 'Abdallah al-Khuwarizmi. After him, there was Abu Kamil Shuja' b. Aslam. People followed in his steps."<ref>[http://www.muslimphilosophy.com/ik/Muqaddimah/Table_of_Contents.htm Ibn Khaldūn, The Muqaddimah : An introduction to history, Translated from the Arabic by Franz Rosenthal, New York: Princeton (1958), Chapter VI:19]</ref> 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 Ja‘far 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 Ga‘far M. b. M., instead of Abū Abdallah M. b. M." Donald Knuth writes it as {{transl|ar|ALA|Abū ’Abd Allāh Muḥammad ibn Mūsā al-Khwārizmī}} and quotes it as meaning "literally, 'Father of Abdullah, Mohammed, son of Moses, native of Khwārizm,'" citing previous work by Heinz Zemanek. <ref>{{citation |first=Donald |last=Knuth |chapter=Basic Concepts |title=The Art of Computer Programming |volume=1 |edition=3rd |year=1997 |publisher=Addison-Wesley |isbn=978-0-201-89683-1 |page=1}}</ref>|group=note}} ({{lang-fa|محمد بن موسی خوارزمی|Moḥammad ben Musā Khwārazmi}}; {{circa|780|850|lk=no}}), naka-Arabiko na al-Khwarizmi asin dating naka-Latin  ''Algorithmi'', iyo sarong [[Persians|Persyano]]<ref name="Corbin 1998 44">{{Cite book|url=https://books.google.com/books?id=_VF0AgAAQBAJ&pg=PA44|title=The Voyage and the Messenger: Iran and Philosophy|last=Corbin|first=Henry|date=1998|publisher=North Atlantic Books|isbn=978-1-55643-269-9|page=44|language=en}}</ref><ref>{{cite book|url=https://books.google.com/books?id=JrslMKTgSZwC&pg=PA84|title=The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics|author=Clifford A. Pickover|publisher=Sterling Publishing Company, Inc.|year=2009|isbn=978-1-4027-5796-9|page=84}}</ref><ref name="Science and medicine">{{cite journal|last1=Saliba|first1=George|title=Science and medicine|journal=Iranian Studies|date=September 1998|volume=31|issue=3–4|pages=681–690|doi=10.1080/00210869808701940|quote=Take, for example, someone like Muhammad b. Musa al-Khwarizmi (fl. 850) may present a problem for the EIr, for although he was obviously of Persian descent, he lived and worked in Baghdad and was not known to have produced a single scientific work in Persian.}}</ref> na [[polymath]] na may impluwensiyal na gibo sa [[matematika]], [[astronomiya]], asin [[heograpiya]]. Mga  820 CE, siya nagin astronomo asin pamayo kan library kan [[House of Wisdom]] sa [[Baghdad]].<ref name="Maher">Maher, P. (1998). From Al-Jabr to Algebra. Mathematics in School, 27(4), 14–15.</ref>

Pinasikat ni Al-Khwarizmi an treatise sa [[alhebra]] (''[[The Compendious Book on Calculation by Completion and Balancing]]'', c. 813–833 CE<ref name="Oaks">Oaks, J. (2009). Polynomials and equations in Arabic algebra. Archive for History of Exact Sciences, 63(2), 169–203.</ref>) pigpresentar an enot na sitematikong solusyon sa mga linyar asin kwadratikong ekwasyon.

== Mga nota ==
{{reflist|group=note}}

== Mga toltolan ==
{{Reflist}}

== Magbasa pa lalo ==

=== Ispesipikong mga toltolan ===
{{Refbegin|2}}
====Biographical====
* {{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}}
* [[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.&nbsp;631–633. ([http://islamsci.mcgill.ca/RASI/BEA/Khwarizmi_BEA.pdf PDF version])
* {{cite journal|last=Dunlop|first=Douglas Morton|author-link=Douglas Morton Dunlop|date=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|jstor=25221920|issue=2|doi=10.1017/S0035869X00098464}}
* Hogendijk, Jan P., [http://www.alkhwarizmi.nl/ Muhammad ibn Musa (Al-)Khwarizmi (c. 780–850 CE)] – bibliography of his works, manuscripts, editions and translations.
* {{MacTutor Biography|id=Al-Khwarizmi|title=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}
* [[Fuat Sezgin]]. ''Geschichte des arabischen Schrifttums''. 1974, E.J. Brill, Leiden, the Netherlands.
* 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|last=Gandz|first=Solomon|author-link=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|issn=0002-9890|jstor=2299605}}
* {{cite journal|last=Gandz|first=Solomon|date=1936|title=The Sources of al-Khowārizmī's Algebra|journal=Osiris|volume=1|pages=263–277|jstor=301610|doi=10.1086/368426|issue=1|s2cid=60770737|issn=0369-7827}}
* {{cite journal|last=Gandz|first=Solomon|date=1938|title=The Algebra of Inheritance: A Rehabilitation of Al-Khuwārizmī|journal=Osiris|volume=5|pages=319–391|jstor=301569|issue=5|doi=10.1086/368492|s2cid=143683763|issn=0369-7827}}
* {{cite journal|last=Hughes|first=Barnabas|author-link=Barnabas Hughes|title=Gerard of Cremona's Translation of al-Khwārizmī's al-Jabr: A Critical Edition|date=1986|journal=Mediaeval Studies|volume=48|pages=211–263|doi=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|url=https://library.albany.edu/preservation/brittlebooks|title=Robert of Chester's Latin Translation of the Algebra of Al-Khowarizmi: With an Introduction, Critical Notes and an English Version|last=Karpinski|first=L.C.|date=1915|publisher=The Macmillan Company|author-link=L. C. Karpinski}}
* {{cite book|url=https://archive.org/details/algebraofmohamme00khuwrich|title=The Algebra of Mohammed Ben Musa|last=Rosen|first=Fredrick|date=1831|publisher=Kessinger Publishing|isbn=978-1-4179-4914-4|author-link=Frederick Rosen}} <!-- 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. -->
* {{cite journal|last=Ruska|first=Julius|author-link=Julius Ruska|title=Zur ältesten arabischen Algebra und Rechenkunst|journal=[[Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse]]|pages=1–125|date=1917|url=http://catalog.hathitrust.org/Record/001653568|series=Sitzungsberichte der Heidelberger Akademie der Wissenschaften. Philologisch-historische Klasse. Jahr. 1917,2. Abh}}
==== Arithmetic ====
* {{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}}
* {{cite book|title=Die älteste lateinische Schrift über das indische Rechnen nach al-Ḫwārizmī|last=Folkerts|first=Menso|date=1997|publisher=Bayerische Akademie der Wissenschaften|isbn=978-3-7696-0108-4|location=München|language=de, la|author-link=Menso Folkerts}} <!-- / 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. -->
* [[Kurt Vogel (historian)|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.
==== Astronomy ====
* {{cite book|title=Commentary on the Astronomical Tables of Al-Khwarizmi: By Ibn Al-Muthanna|last=Goldstein|first=B.R.|date=1968|publisher=Yale University Press|isbn=978-0-300-00498-4|author-link=B. R. Goldstein}}
* {{cite journal|first=Jan P.|last=Hogendijk|author-link=Jan Hogendijk|title=Al-Khwārizmī's Table of the "Sine of the Hours" and the Underlying Sine Table|date=1991|journal=Historia Scientiarum|volume=42|pages=1–12}}
* {{cite book|title=Al-Khwārizmī and New Trends in Mathematical Astronomy in the Ninth Century|last=King|first=David A.|date=1983|publisher=Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East 2|location=New York University|bibcode=1983antm.book.....K|lccn=85150177|author-link=David A. King (historian)}} <!-- Description and analysis of seven recently discovered minor works related to al-Khwarizmi. -->
* {{cite book|title=The Astronomical Tables of al-Khwarizmi|last=Neugebauer|first=Otto|date=1962|author-link=Otto Neugebauer}}
* {{cite book|title="Geometric trigonometry" in treatises of al-Khwārizmī, al-Māhānī and Ibn al-Haytham|last=Rosenfeld|first=Boris A.|date=1993|journal=Vestiga Mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H.L.L. Busard|publisher=Rodopi|isbn=978-90-5183-536-6|editor=Menso Folkerts|location=Amsterdam|author-link=Boris A. Rosenfeld|editor2=J.P. Hogendijk}}
* [[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}}.
* [[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. -->
==== Spherical trigonometry ====
* B.A. Rozenfeld. "Al-Khwarizmi's spherical trigonometry" (Russian), ''Istor.-Mat. Issled.'' '''32–33''' (1990), 325–339.
==== Jewish calendar ====
* {{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 -->
==== Geography ====
* {{cite book|title=Der Osten nach der Erdkarte al-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens|last=Daunicht|first=Hubert|date=1968–1970|publisher=Bonner orientalistische Studien. N.S.; Bd. 19|language=de|lccn=71468286|author-link=Hubert Daunicht}}
* {{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|title=Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa'far Muḥammad ibn Mūsā al-Ḫuwārizmī|last=Mžik|first=Hans von|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|last=Spitta|first=W.|author-link=W. Spitta|title=Ḫuwārizmī's Auszug aus der Geographie des Ptolomaeus|journal=Zeitschrift Deutschen Morgenl. Gesell.|volume=33|date=1879}}
{{Refend}}

=== Pangkagabsan na toltolan ===
{{Refbegin|2}}
* {{Cite journal|last=Arndt|first=A. B.|title=Al-Khwarizmi|date=1983|publisher=National Council of Teachers of Mathematics|pages=668–670|volume=76|issue=9|url=http://www.personal.psu.edu/users/e/c/ecb5/Courses/M475W/WeeklyReadings/Week%2013/Al-Khwarizmi.pdf|access-date=2021-05-25|archivedate=2021-04-13|archiveurl=https://web.archive.org/web/20210413095521/http://www.personal.psu.edu/users/e/c/ecb5/Courses/M475W/WeeklyReadings/Week%2013/Al-Khwarizmi.pdf}}
* {{Cite book|title=Episodes in the Mathematics of Medieval Islam|last=Berggren|first=J. Lennart|date=1986|publisher=[[Springer Science+Business Media]]|isbn=978-0-387-96318-1|location=New York|author-link=Len Berggren}}
* {{cite book|url=https://archive.org/details/historyofmathema00boye|title=A History of Mathematics|last=Boyer|first=Carl B.|date=1991|publisher=John Wiley & Sons, Inc.|isbn=978-0-471-54397-8|edition=Second|chapter=The Arabic Hegemony|author-link=Carl Benjamin Boyer}}
* {{Cite book|title=The Muslim contribution to mathematics|last=Daffa|first=Ali Abdullah al-|date=1977|publisher=[[Croom Helm]]|isbn=978-0-85664-464-1|location=[[London]]|author-link=Ali Abdullah Al-Daffa}}
* {{Cite book|title=The Oxford History of Islam|last=Dallal|first=Ahmad|date=1999|publisher=[[Oxford University Press]], [[New York City|New York]]|editor-last=Esposito|editor-first=John|contribution=Science, Medicine and Technology|author-link=Ahmad Dallal}}
* {{Cite journal|last=Kennedy|first=E.S.|author-link=Edward Stewart Kennedy|title=A Survey of Islamic Astronomical Tables; Transactions of the American Philosophical Society|date=1956|location=[[Philadelphia]]|publisher=[[American Philosophical Society]]|volume=46|issue=2}}
* {{Cite book|title=Astronomy before the telescope|last=King|first=David A.|date=1999a|publisher=[[British Museum]] Press|isbn=978-0-7141-2733-0|editor-last=Walker|editor-first=Christopher|editor-link=Christopher J. Walker|pages=143–174|contribution=Islamic Astronomy|author-link=David A. King (historian)}}
* {{Cite journal|last=King|first=David A.|date=2002|title=A Vetustissimus Arabic Text on the Quadrans Vetus|journal=Journal for the History of Astronomy|volume=33|issue=112|pages=237–255|bibcode=2002JHA....33..237K|doi=10.1177/002182860203300302|s2cid=125329755}}
* {{Cite book|url=https://archive.org/details/concisehistoryof0000stru_m6j1|title=A Concise History of Mathematics|last=Struik|first=Dirk Jan|date=1987|publisher=[[Dover Publications]]|isbn=978-0-486-60255-4|edition=4th|author-link=Dirk Jan Struik|url-access=registration}}
<!-- *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).-->
<!-- muslim<ref name="Britannica">Britannica, [http://www.britannica.com/eb/article-9045366 ''al-Khw<u>a</u>rizm<u>i</u>'']
</ref> -->
<!-- * [http://www.iranica.com Encyclopaedia Iranica] what page/chapter/article??? -->
<!-- * 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?? -->
* {{MacTutor Biography|id=Abraham|title=Abraham bar Hiyya Ha-Nasi}}
* {{MacTutor Biography|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?}}
* [[Roshdi Rashed]], ''The development of Arabic mathematics: between arithmetic and algebra'', London, 1994.
{{Refend}}
{{tamboan}}
[[Kategorya:Mga matematiko]]
Si Muḥammad ibn Mūsā al-Khwārizmī (; ), naka-Arabiko na al-Khwarizmi asin dating naka-Latin  Algorithmi, iyo sarong Persyano na polymath na may impluwensiyal na gibo sa matematika, astronomiya, asin heograpiya. Mga  820 CE, siya nagin astronomo asin pamayo kan library kan House of Wisdom sa Baghdad.Maher, P. (1998). From Al-Jabr to Algebra. Mathematics in School, 27(4), 14–15.

Pinasikat ni Al-Khwarizmi an treatise sa alhebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CEOaks, J. (2009). Polynomials and equations in Arabic algebra. Archive for History of Exact Sciences, 63(2), 169–203.) pigpresentar an enot na sitematikong solusyon sa mga linyar asin kwadratikong ekwasyon.

 Mga nota 

 Mga toltolan 

 Magbasa pa lalo 

 Ispesipikong mga toltolan 

Biographical
 
 Brentjes, Sonja (2007). "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. (PDF version)
 
 Hogendijk, Jan P., Muhammad ibn Musa (Al-)Khwarizmi (c. 780–850 CE) – bibliography of his works, manuscripts, editions and translations.
 
 Fuat Sezgin. Geschichte des arabischen Schrifttums. 1974, E.J. Brill, Leiden, the Netherlands.
 Sezgin, F., ed.,  Islamic Mathematics and Astronomy,  Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997–99. 
 Algebra 
 
 
 
 
 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). .
 
  
 
 Arithmetic 
 
  
 Vogel, Kurt (1968). 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.
 Astronomy 
 
 
  
 
 
 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). .
 Van Dalen, B. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time. 
 Spherical trigonometry 
 B.A. Rozenfeld. "Al-Khwarizmi's spherical trigonometry" (Russian), Istor.-Mat. Issled. 32–33 (1990), 325–339.
 Jewish calendar 
  
 Geography 
 
 
 
 
 
 
 

 Pangkagabsan na toltolan 

 
 
 
 
 
 
 
 
 

 
 
 Roshdi Rashed, The development of Arabic mathematics: between arithmetic and algebra, London, 1994.

Kategorya:Mga matematiko