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Revision as of 09:24, 26 December 2006 view sourceBeh-nam (talk | contribs)8,290 editsm Please see discussion.← Previous edit Revision as of 04:48, 5 April 2007 view source Beh-nam (talk | contribs)8,290 edits ethnic Persians and/or Persian speakersliving in Khwarizm were commonly referred to as "Tajik" during Beruni's life, and today Persians and/or Persian-speakers in this region are still called "Tajik"Next edit →
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{{redirect|al-Khwarizmi}} {{redirect|al-Khwārizmī}}
{{Infobox Biography
⚫ ] issued ], ] in the ], commemorating al-Khwārizmī's (approximate) 1200th anniversary.]]
| subject_name = Muhammad ibn Mūsā al-Khwārizmī
⚫ '''{{Unicode|Muḥammad ibn Mūsā al-Khwārizmī}}''' (]: {{ar|محمد بن موسى الخوارزمي}}) was a ] ('']'') ], ], ] and ]. He was born around 780, in ] and died around 850.{{ref|oaks0000}}{{ref|hogendijk1998}}{{ref|toomer0000}}
| image_name = Abu Abdullah Muhammad bin Musa al-Khwarizmi edit.png
| image_size = 250px
⚫ | image_caption = A ] issued ], ] in the ], commemorating al-Khwārizmī's (approximate) 1200th anniversary.
| date_of_birth = c. 780
| date_of_death = c. 850
}}
⚫ '''{{Unicode|Muḥammad ibn Mūsā al-Khwārizmī}}''' ({{lang-ar|محمد بن موسى الخوارزمي}}) was a ] (])<ref>Toomer, Hogendijk 1997, Oaks</ref> ], ], ] and ]. He was born around 780 in ]<ref>Berggren, Hogendijk, Struik p. 93</ref> (now ], ]) and died around 850. He worked most of his life as a ] in the ] in ].


He was the author of ''{{Unicode|al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala}}'', the first book on the systematic solution of ] and ]s. Consequently he is considered to be the father of ]{{ref|gandz1936}}. The word algebra is derived from ''{{unicode|al-jabr}}'', one of the two operations used to solve ], as described in his book. ''Algoritmi de numero Indorum'', the ] translation of his other major work on the ], introduced the ] and the ] to the ] in the 12th century. The words ] and ] stem from ''Algoritmi'', the ] of his name.{{ref|aldaffa1978}} His name is also the origin of the ] word ''guarismo''{{ref|knuth1979}} and of the ] word ''algarismo'', both meaning ]. His ''Algebra'' was the first book on the systematic solution of ] and ]s. Consequently he is considered to be the father of ],<ref>Gandz 1936</ref> a title he shares with ]. ] translations of his ''Arithmetic'', on the ], introduced the ] ] to the ] in the 12th century.<ref>Struik p. 93</ref> He revised and updated ]'s ''Geography'' as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on our language as well. The word algebra is derived from ''al-jabr'', one of the two operations used to solve ], as described in his book. The words '']'' and '']'' stem from ''algoritmi'', the ] of his name.<ref>al-Daffa 1978</ref> His name is also the origin of the ] word ''guarismo''<ref>Knuith 1979</ref> and of the ] word ''algarismo'', both meaning ].


==Biography== ==Biography==
Few details about al-Khwārizmī's life are known, it is not even certain where he was born. His name indicates he has come from ] (Khiva) in the ] province of the ] ] (now ] of ]). Few details about al-Khwārizmī's life are known, it is not even certain where he was born. His name indicates he might have came from ] (Khiva) in the ] province of the ] empire (now ] of ]).


His name is often given as either ''{{Unicode|Abū ʿAbd Allāh Muḥammad ibn Mūsā al-Ḵwārizmī}}'' (Arabic: {{ar|أبو عبد الله محمد بن موسى الخوارزمي}} “Father of Abdullah, Muhammad, son of Moses, native of ]”{{ref|knuth1997}}) or ''{{Unicode|Abū Ǧaʿfar Muḥammad ibn Mūsā al-Ḵwārizmī}}'' (Arabic: {{ar| أبو جعفر محمد بن موسى الخوارزمي}}).<ref>possibly because it is mistaken with that of {{unicode|]}}. M. Dunlop. ''{{unicode|Muḥammad b. Mūsā al-Khwārizmī}}''. JRAS 1943 p. 248-250).</ref> His name is often given as either ''{{Unicode|Abū ʿAbd Allāh Muḥammad ibn Mūsā al-Khwārizmī}}'' (Arabic: {{ar|أبو عبد الله محمد بن موسى الخوارزمي}} “Father of Abdullah, Muhammad, son of Moses, native of ]”<ref>Knuth 1997</ref>) or ''{{Unicode|Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī}}'' (Arabic: {{ar|أبو جعفر محمد بن موسى الخوارزمي}}).<ref>possibly because it is mistaken with that of {{unicode|]}}. M. Dunlop. ''{{unicode|Muḥammad b. Mūsā al-Khwārizmī}}''. JRAS 1943 p. 248-250).</ref>


The ] ] gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: {{ar|محمد بن موسى الخوارزميّ المجوسيّ القطربّليّ}}). The ] ''al-Qutrubbulli'' indicates he might instead have came from ], a small town near ]. Regarding al-Khwārizmī's religion, Toomer writes: The ] ] gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: {{ar|محمد بن موسى الخوارزميّ المجوسيّ القطربّليّ}}). The ] ''al-Qutrubbulli'' indicates he might instead have came from ], a small town near ]. Regarding al-Khwārizmī's religion, Toomer writes:
<blockquote> <blockquote>
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 ], so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.{{ref|toomer0000}} 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 ], so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.<ref>Toomer</ref>
</blockquote> </blockquote>


In ]'s ''Kitāb al-Fihrist'' we find a short biography on al-Khwārizmī, together with a list the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the ], Baghdad became the centre of scientific studies and trade, and many merchants and scientists, from as far as China and India traveled to this city--as such apparently so did Al-Khwārizmī. He worked in Baghdad as a scholar at the ] established by ] {{unicode|]}}, where he studied and translated Greek scientific manuscripts. In ]'s ''Kitāb al-Fihrist'' we find a short biography on al-Khwārizmī, together with a list the books he wrote{{Fact|date=February 2007}}. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the ], Baghdad became the centre of scientific studies and trade, and many merchants and scientists, from as far as ] and ] traveled to this city--as such apparently so did Al-Khwārizmī. He worked in Baghdad as a scholar at the ] established by ] {{unicode|]}}, where he studied the sciences and mathematics, which included the translation of ] and ] scientific manuscripts.


==Contributions== ==Contributions==
] of Frederic Rosen's ''The Algebra of Mohammed ben Musa'' (1831)]] ] of Frederic Rosen's ''The Algebra of Mohammed ben Musa'' (1831)]]
His major contributions to ], ], ], ] and ] provided foundations for later and even more widespread innovation in ], ], and his other areas of interest. His systematic and logical approach to solving ] and ]s gave shape to the discipline of ''algebra'', a word that is derived from the name of his 830 book on the subject, ''al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala'' (الكتاب المختصر في حساب الجبر والمقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century. His major contributions to ], ], ], ] and ] provided foundations for later and even more widespread innovation in ], ], and his other areas of interest. His systematic and logical approach to solving ] and ]s gave shape to the discipline of ''algebra'', a word that is derived from the name of his 830 book on the subject, ''al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala'' (] الكتاب المختصر في حساب الجبر والمقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century.


His book ''On the Calculation with Hindu Numerals'' written about 825, was principally responsible for the diffusion of the ] in the ] and then ]. This book also translated into Latin in the twelfth century, as ''Algoritmi de numero Indorum''. From the name of the author, rendered in Latin as ''algoritmi'', originated the term ]. His book ''On the Calculation with Hindu Numerals'' written about 825, was principally responsible for the diffusion of the ] in the ] and then ]. This book also translated into Latin in the twelfth century, as ''Algoritmi de numero Indorum''. From the name of the author, rendered in Latin as ''algoritmi'', originated the term ].
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{{main|The Compendious Book on Calculation by Completion and Balancing}} {{main|The Compendious Book on Calculation by Completion and Balancing}}
] ]
''{{Unicode|al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala}}'' (Arabic: الكتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion <!-- <small>(variants: Restoring, Reuniting)</small> -->and Balancing”) is a ] book written approximately 830 AD. ''{{Unicode|al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala}}'' (Arabic: الكتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion <!-- <small>(variants: Restoring, Reuniting)</small> -->and Balancing”) is a ] book written approximately ] CE.


The book is considered to have defined ]. The word '']'' is derived from the name of one of the basic operations with equations (''al-jabr'') described in this book. The book was translated in Latin as ''Liber algebrae et almucabala'' by ] (], 1145){{ref|mactutor-hanasi}} hence "algebra", and also by ]. The book is considered to have defined ]. The word '']'' is derived from the name of one of the basic operations with equations (''al-jabr'') described in this book. The book was translated in Latin as ''Liber algebrae et almucabala'' by ] (], 1145)<ref>mactutor-hanasi</ref> hence "algebra", and also by ].


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) 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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===Arithmetic=== ===Arithmetic===
] ]
''Algoritmi de numero Indorum'' ("al-Khwārizmī on the Hindu Art of Reckoning") on Arithmetic, which survived in a ] translation but was lost in the original ]. The translation was most likely done in the 12th century by ], who had also translated the astronomical tables in 1126. The original Arabic title was possibly ''{{unicode|Kitāb al-Ǧamʿ wa-al-tafrīq bi-ḥisāb al-Hind}}''.{{ref|ruska1917}} <!-- ("Book on the Addition and Subtraction according to the Indian Calculation") --> Al-Khwārizmī's second major work was on the subject of arithmetic, which survived in a ] translation but was lost in the original ]. The translation was most likely done in the 12th century by ], who had also translated the astronomical tables in 1126.

The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: ''Dixit algorizmi'' ("So said al-Khwārizmī"), or ''Algoritmi de numero Indorum'' ("al-Khwārizmī on the Hindu Art of Reckoning"), a name given to the work by ] in 1857. The original Arabic title was possibly ''{{unicode|Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind}}''<ref>Ruska 1917</ref> ("The Book of Addition and Subtraction According to the Hindu Calculation")<ref>Berggren, p. 7</ref>
{{sect-stub}} {{sect-stub}}


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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 ]'s '']'', consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.<ref>http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Cartography.html</ref> 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 ]'s '']'', consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.<ref></ref>


There is only one surviving copy of ''{{unicode|Kitāb ṣūrat al-Arḍ}}'', which is kept at the ]. A Latin translation is kept at the ] in ]. 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''.<ref>In al-Khwārizmī's opinion, "the Claudian" indicated that Ptolemy was a descendent of the emperor Claudius.</ref> There is only one surviving copy of ''{{unicode|Kitāb ṣūrat al-Arḍ}}'', which is kept at the ]. A Latin translation is kept at the ] in ]. 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''.<ref>In al-Khwārizmī's opinion, "the Claudian" indicated that Ptolemy was a descendent of the emperor Claudius.</ref>
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The book opens with the list of ] and ], in order of "]", that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As ] points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible. The book opens with the list of ] and ], in order of "]", that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As ] points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.


Neither the Arabic copy nor the Latin translation include the map of the world itself, however ] 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 ] 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|daunicht1968}} Neither the Arabic copy nor the Latin translation include the map of the world itself, however ] 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 ] 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 1968</ref>


One of the corrections which al-Khwārizmī made in Ptolemy's work is the reduction of the latitude of the ] 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 ]. The amount of inhabited land extends over 180°. <!--One of the corrections which al-Khwārizmī made in Ptolemy's work is the reduction of the latitude of the ] 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 ]. The amount of inhabited land extends over 180°.


The majority of the placenames used by al-Khwārizmī match those of Ptolemy, ] and ]. The general shape of the coastline is the same between ] and ]. The Atlantic coast of the ], 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 ] and on the later ] version. The majority of the placenames used by al-Khwārizmī match those of Ptolemy, ] and ]. The general shape of the coastline is the same between ] and ]. The Atlantic coast of the ], 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 ] and on the later ] version.-->

Finally, al-Khwarizmi also compiled a set of astronomical tables (Zij), based on a variety of Hindu and Greek sources. This work included a table of sines, evidently for a circle of radius 150 units. Like his treatises on algebra and Hindu-Arabic numerals, this astronomical work (or an Andalusian revision thereof) was translated into Latin.


===Astronomy=== ===Astronomy===
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{{unicode|Al-Khwārizmī's ''Zīj al-sindhind''}} <!-- Toomer --> (Arabic: زيج "astronomical tables") 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 ] values. {{unicode|Al-Khwārizmī's ''Zīj al-sindhind''}} <!-- Toomer --> (Arabic: زيج "astronomical tables") 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 ] values.


The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer ] (c. 1000) has survived in a Latin translation, presumably by ] (January 26, 1126).{{ref|neugebauer1962|2}} The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford). The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer ] (c. 1000) has survived in a Latin translation, presumably by ] (January 26, 1126).<ref>Neugebauer 1962</ref> The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).


=== Jewish calendar === === Jewish calendar ===
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{{commonscat|Muhammad ibn Musa al-Khwarizmi}} {{commonscat|Muhammad ibn Musa al-Khwarizmi}}
* ] &mdash; A crater on the far side of the moon named after al-Khwārizmī. * ] &mdash; A crater on the far side of the moon named after al-Khwārizmī.
* ] * ] &mdash; An Iranian award named after al-Khwārizmī.
* ]

==Notes==
<div class="references-2column"><references /></div>


==References and further reading== ==References==
<div class="references-2column"> <div class="references-2column">
*{{cite book|last=Berggren|first=J. Lennart|title=Episodes in the Mathematics of Medieval Islam|year=1986|publisher=Springer-Verlag|location=New York|id=ISBN 0-387-96318-9}}
#{{note|KADI1992}}Ibrahim A. Al-Kadi "The origins of cryptology: The Arab contributions”, '']'', 16(2) (April 1992) pp. 97&ndash;126.
⚫ *{{cite book|last=Daffa'|first=Ali Abdullah al-|title=The Muslim contribution to mathematics|year=1977|publisher=Croom Helm|location=London|id=ISBN 0-85664-464-1}} <!-- ''In the foremost rank of mathematicians of all time stands Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world...'' -->
#{{note|encarta}}, Encarta.
⚫ *{{cite book|last=Daunicht|first=Hubert|title=Der Osten nach der Erdkarte al-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens|year=1968&ndash;1970|publisher=Bonner orientalistische Studien. N.S. ; Bd. 19|language=German|id={{LCCN|71||468286}}}} <!-- I. Rekonstruktion der Karte, Interpretation der Karte: Südasien. II. Die ost- und südostasiatische Inselwelt und die Meere. III. Der Süden des festländischen Ostasiens. IV. 1. Der Norden des festländischen Ostasiens und Nord- und Mittelasien. 2. Der Norden des festländischen Ostasiens und Nord- und Mittelasien -->
#{{note|britannica}}, Encyclopedia Britannica.
*{{cite journal|last=Dunlop|first=Douglas Morton|year=1943|title=Muhammad ibn-Musa al-Khwarizmi|journal=Journal of the Royal Asiatic Society of Great Britain & Ireland|pages=248&ndash;250}}
#{{note|American}}, The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
⚫ *{{cite book|last=Folkerts|first=Menso|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|id=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. -->
#{{note|columbia}}, The Columbia Encyclopedia, Sixth Edition. 2001-05.
⚫ *{{cite journal|last=Gandz|first=Solomon|title=The Origin of the Term "Algebra"|journal=The American Mathematical Monthly|volume=33|issue=9|year=1926|month=November|pages=437&ndash;440|id={{ISSN|0002-9890}}|url=http://links.jstor.org/sici?sici=0002-9890%28192611%2933%3A9%3C437%3ATOOTT%22%3E2.0.CO%3B2-0}}
⚫ #{{note|daffa1977}}{{cite book|last = Daffa | first = Ali | authorlink =Ali Abdullah Al-Daffa |title=The Muslim contribution to mathematics|year=1977|publisher=Croom Helm|location=London|id=ISBN 0-85664-464-1}} <!-- ''In the foremost rank of mathematicians of all time stands Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world...'' -->
⚫ *{{cite journal|last=Gandz|first=Solomon|year=1936|title=The Sources of al-Khowārizmī's Algebra|journal=Osiris|volume=1|pages=263&ndash;277|id={{ISSN|0369-7827}}|url=http://links.jstor.org/sici?sici=0369-7827%28193601%291%3A1%3C263%3ATSOAA%3E2.0.CO%3B2-3}} <!-- *:''Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, Khwarizmi is more entitled to be called "the father of algebra" than ] because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, ] is primarily concerned with the theory of numbers.'' -->
⚫ #{{note|daunicht1968}}{{cite book|last=Daunicht|first=Hubert|title=Der Osten nach der Erdkarte al-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens|year=1968&ndash;1970|publisher=Bonner orientalistische Studien. N.S. ; Bd. 19|language=German|id={{LCCN|71||468286}}}} <!-- I. Rekonstruktion der Karte, Interpretation der Karte: Südasien. II. Die ost- und südostasiatische Inselwelt und die Meere. III. Der Süden des festländischen Ostasiens. IV. 1. Der Norden des festländischen Ostasiens und Nord- und Mittelasien. 2. Der Norden des festländischen Ostasiens und Nord- und Mittelasien -->
*{{cite journal|last=Gandz|first=Solomon|year=1938|title=The Algebra of Inheritance: A Rehabilitation of Al-Khuwārizmī|journal=Osiris|volume=5|pages=319&ndash;391|id={{ISSN|0369-7827}}|url=http://links.jstor.org/sici?sici=0369-7827%281938%291%3A5%3C319%3ATAOIAR%3E2.0.CO%3B2-2}}
⚫ #{{note|folkerts1997}}{{cite book|last=Folkerts|first=Menso|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|id=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. -->
⚫ *{{cite journal|First=Jan P.|last=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&ndash;12}}
⚫ #{{note|gandz1926}}{{cite journal|last=Gandz|first=Solomon|year=1926|title=The Origin of the Term "Algebra"|journal=The American Mathematical Monthly|volume=33|issue=9|year=1926|month=November|pages=437&ndash;440|id={{ISSN|0002-9890}}|url=http://links.jstor.org/sici?sici=0002-9890%28192611%2933%3A9%3C437%3ATOOTT%22%3E2.0.CO%3B2-0}}
⚫ *{{cite journal|first=Jan P.|last=Hogendijk|title=al-Khwarzimi|journal=Pythagoras|volume=38|issue=2|year=1998|pages=4&ndash;5|id={{ISSN|0033-4766}}|url=http://www.kennislink.nl/web/show?id=116543}}
⚫ #{{note|gandz1936}}{{cite journal|last=Gandz|first=Solomon|year=1936|title=The Sources of al-Khowārizmī's Algebra|journal=Osiris|volume=1|pages=263&ndash;277|id={{ISSN|0369-7827}}|url=http://links.jstor.org/sici?sici=0369-7827%28193601%291%3A1%3C263%3ATSOAA%3E2.0.CO%3B2-3}} <!-- #:''Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, Khwarizmi is more entitled to be called "the father of algebra" than ] because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, ] is primarily concerned with the theory of numbers.'' -->
#{{note|gandz1938}}{{cite journal|last=Gandz|first=Solomon|year=1938|title=The Algebra of Inheritance: A Rehabilitation of Al-Khuwārizmī|journal=Osiris|volume=5|pages=319&ndash;391|id={{ISSN|0369-7827}}|url=http://links.jstor.org/sici?sici=0369-7827%281938%291%3A5%3C319%3ATAOIAR%3E2.0.CO%3B2-2}} *{{cite journal|last=Hughes|first=Barnabas B.|title=Gererd of Cremona's Translation of al-Khwārizmī's al-Jabr: A Critical Edition|year=1986|journal=Mediaeval Studies|volume=48|pages=211&ndash;263}}
⚫ *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.
⚫ #{{note|hogendijk1991}}{{cite journal|First=Jan P.|last=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&ndash;12}}
⚫ *{{cite journal|last=Kennedy|first=E. S.|title=Al-Khwārizmī on the Jewish Calendar|year=1964|journal=Scripta Mathematica|volume=27|pages=55&ndash;59}} <!-- reprinted in Studies in the Islamic Exact Sciences. Beirut 1983, 661-665 -->
⚫ #{{note|hogendijk1998}}{{cite journal|first=Jan P.|last=Hogendijk|title=al-Khwarzimi|journal=Pythagoras|volume=38|issue=2|year=1998|pages=4&ndash;5|id={{ISSN|0033-4766}}|url=http://www.kennislink.nl/web/show?id=116543}}
⚫ *{{cite book|last=King|first=David A.|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|id={{LCCN|85||150177}}}} <!-- Description and analysis of seven recently discovered minor works related to al-Khwarizmi. -->
#{{note|huges1986}}{{cite journal|last=Hughes|first=Barnabas B.|title=Gererd of Cremona's Translation of al-Khwārizmī's al-Jabr: A Critical Edition|year=1986|journal=Mediaeval Studies|volume=48|pages=211&ndash;263}}
⚫ *Donald E. Knuth, . Springer-Verlag. 1979. ISBN 0-387-11157-3.
⚫ #{{note|huges1989}}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.
⚫ *Donald E. Knuth, '']: Fundamental Algorithms'' 3rd edition. Addison-Wesley. 1997. ISBN 0-201-89683-4.
⚫ #{{note|kennedy1964}}{{cite journal|last=Kennedy|first=E. S.|title=Al-Khwārizmī on the Jewish Calendar|year=1964|journal=Scripta Mathematica|volume=27|pages=55&ndash;59}} <!-- reprinted in Studies in the Islamic Exact Sciences. Beirut 1983, 661-665 -->
⚫ *{{cite book|last=Mžik|first=Hanz von|title=Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa‘far Muḥammad ibn Mūsā al-Ḫuwārizmī|year=1926|location=Leipzig}}
⚫ #{{note|king1983}}{{cite book|last=King|first=David A.|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|id={{LCCN|85||150177}}}} <!-- Description and analysis of seven recently discovered minor works related to al-Khwarizmi. -->
⚫ *{{cite book|last=Neugebauer|first=Otto|title=The Astronomical Tables of al-Khwarizmi|year=1962}} Historisk-filosofiske Skrifter. Bind 4, nr. 2. <!-- Based on the medieval Latin translation by Adelard of Bath. The Arabic original is lost. See the review by G.J. Toomer in ''Centaurus'' 10 (1964), pp. 202-212. -->
⚫ #{{note|knuth1979}}Donald E. Knuth, . Springer-Verlag. 1979. ISBN 0-387-11157-3.
⚫ *Jeffrey A. Oaks. . The University of Indianapolis.
⚫ #{{note|knuth1997}}Donald E. Knuth, '']: Fundamental Algorithms'' 3rd edition. Addison-Wesley. 1997. ISBN 0-201-89683-4.
⚫ *{{MacTutor Biography|id=Al-Khwarizmi|title=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}
⚫ #{{note|mzik1926}}{{cite book|last=Mžik|first=Hanz von|title=Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa‘far Muḥammad ibn Mūsā al-Ḫuwārizmī|year=1926|location=Leipzig}}
⚫ *{{MacTutor Biography|id=Abraham|title=Abraham bar Hiyya Ha-Nasi}}
⚫ #{{note|neugebauer1962}}{{cite book|last=Neugebauer|first=Otto|title=The Astronomical Tables of al-Khwarizmi|year=1962}} Historisk-filosofiske Skrifter. Bind 4, nr. 2. <!-- Based on the medieval Latin translation by Adelard of Bath. The Arabic original is lost. See the review by G.J. Toomer in ''Centaurus'' 10 (1964), pp. 202-212. -->
⚫ *{{MacTutor Biography|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?}}
⚫ #{{note|oaks0000}}Jeffrey A. Oaks. . The University of Indianapolis.
⚫ *Roshdi Rashed, ''The development of Arabic mathematics: between arithmetic and algebra'', London, 1994.
⚫ #{{note|mactutor-alkhwarizmi}}{{MacTutor Biography|id=Al-Khwarizmi|title=Abu Ja'far Muhammad ibn Musa Al-Khwarizmi}}
⚫ *{{cite book|last=Rosen|first=Fredrick|title=The Algebra of Mohammed Ben Musa|date=2004-09-01|publisher=Kessinger Publishing|id=ISBN 1-4179-4914-7}} <!-- 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. -->
⚫ #{{note|mactutor-hanasi}}{{MacTutor Biography|id=Abraham|title=Abraham bar Hiyya Ha-Nasi}}
⚫ *{{cite journal|first=Boris A.|last=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|id=ISBN 90-5183-536-1}}
⚫ #{{note|mactutor-arabic}}{{MacTutor Biography|class=HistTopics|id=Arabic_mathematics|title=Arabic mathematics: forgotten brilliance?}}
⚫ *]. ''Zur ältesten arabischen Algebra und Rechenkunst''. ISBN 3-533-03817-3.
⚫ #{{note|rashed1994}}Roshdi Rashed, ''The development of Arabic mathematics: between arithmetic and algebra'', London, 1994.
⚫ *Fuat Sezgin. ''Geschichte des arabischen Schrifttums''. 1974, E. J. Brill, Leiden, the Netherlands.
⚫ #{{note|rosen2001}}{{cite book|last=Rosen|first=Fredrick|title=The Algebra of Mohammed Ben Musa|date=2004-09-01|publisher=Kessinger Publishing|id=ISBN 1-4179-4914-7}} <!-- 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. -->
⚫ *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. -->
⚫ #{{note|rosenfeld1993}}{{cite journal|first=Boris A.|last=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|id=ISBN 90-5183-536-1}}
*{{cite book|last=Struik|first= Dirk Jan|title=A Concise History of Mathematics|year=1948|id=ISBN 0486602559|edition=4th|year=1987|publisher=Dover Publications}}
⚫ #{{note|ruska1917}}Julius Ruska. ''Zur ältesten arabischen Algebra und Rechenkunst''. ISBN 3-533-03817-3.
⚫ *Suter, H. : 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.
⚫ #{{note|sezgin1974}}Fuat Sezgin. ''Geschichte des arabischen Schrifttums''. 1974, E. J. Brill, Leiden, the Netherlands.
⚫ *{{cite encyclopedia|last=Toomer|first=Gerald|title=Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā|encyclopedia=Dictionary of Scientific Biography|volume=7|pages=358&ndash;365|editor=Charles Coulston Gillispie|publisher=Charles Scribner's Sons|location=New York|year=1970&ndash;1990|id=ISBN 0-684-16962-2}} <!-- Gillispie, Charles C. ed. ''The Dictionary of Scientific Biography'', 16 vols. 2 supps. New York: Charles Scribner's Sons, 1970-1990. S.v. "Al-Khwarizmi, Abu Ja'far Muhammad ibn Musa" by Gerald Toomer. -->
⚫ #{{note|sezgin1997}}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. -->
⚫ *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. -->
⚫ #{{note|suter1914}}Suter, H. : 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.
⚫ <!-- *Nito Verdera. . Comment: Contains a bit of useful info on the Geography, but also presents a crank theory (see talk page).-->
⚫ #{{note|toomer0000}}{{cite encyclopedia|last=Toomer|first=Gerald|title=Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā|encyclopedia=Dictionary of Scientific Biography|volume=7|pages=358&ndash;365|editor=Charles Coulston Gillispie|publisher=Charles Scribner's Sons|location=New York|year=1970&ndash;1990|id=ISBN 0-684-16962-2}} <!-- Gillispie, Charles C. ed. ''The Dictionary of Scientific Biography'', 16 vols. 2 supps. New York: Charles Scribner's Sons, 1970-1990. S.v. "Al-Khwarizmi, Abu Ja'far Muhammad ibn Musa" by Gerald Toomer. -->
⚫ #{{note|vandalen1996}}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. -->
⚫ <!-- #{{note|vereda0000}}Nito Verdera. . Comment: Contains a bit of useful info on the Geography, but also presents a crank theory (see talk page).-->
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Revision as of 04:48, 5 April 2007

"al-Khwārizmī" redirects here. For other uses, see al-Khwārizmī (disambiguation).
Al-Khwarizmi

Muḥammad ibn Mūsā al-Khwārizmī (Template:Lang-ar) was a Persian (Tajik) mathematician, astronomer, astrologer and geographer. He was born around 780 in Khwārizm (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.

His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered to be the father of algebra, a title he shares with Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the 12th century. He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.

His contributions not only made a great impact on mathematics, but on our language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book. The words algorism and algorithm stem from algoritmi, the Latinization of his name. His name is also the origin of the Spanish word guarismo and of the Portuguese word algarismo, both meaning digit.

Biography

Few details about al-Khwārizmī's life are known, it is not even certain where he was born. His name indicates he might have came from Khwarizm (Khiva) in the Khorasan province of the Abbasid empire (now Xorazm Province of Uzbekistan).

His name is often given as either Abū ʿAbd Allāh Muḥammad ibn Mūsā al-Khwārizmī (Arabic: Template:Ar “Father of Abdullah, Muhammad, son of Moses, native of Khwārizm”) or Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī (Arabic: Template:Ar).

The historian al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: Template:Ar). The epithet al-Qutrubbulli indicates he might instead have came from Qutrubbull, a small town near Baghdad. Regarding al-Khwārizmī's religion, Toomer writes:

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.

In Ibn al-Nadīm's Kitāb al-Fihrist we find a short biography on al-Khwārizmī, together with a list 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 India traveled to this city--as such apparently so did Al-Khwārizmī. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph al-Maʾmūn, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.

Contributions

The frontispiece of Frederic Rosen's The Algebra of Mohammed ben Musa (1831)

His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (Arabic الكتاب المختصر في حساب الجبر والمقابلة) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century.

His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.

Some of his contributions were based on earlier Persian and Babylonian Astronomy, Indian numbers, and Greek sources.

Al-Khwārizmī systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.

He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".

When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the astrolabe and sundial.

Algebra

Main article: The Compendious Book on Calculation by Completion and Balancing
File:Al-Kitab al-mukhtasar fi hisab al-jabr wa-l-muqabala.jpg
A page from al-Khwārizmī's Algebra

al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE.

The book is considered to have defined algebra. The word algebra is derived from the name of one of the basic operations with equations (al-jabr) 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.

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)

  • squares equal roots (ax = bx)
  • squares equal number (ax = c)
  • roots equal number (bx = c)
  • squares and roots equal number (ax + bx = c)
  • squares and number equal roots (ax + c = bx)
  • roots and number equal squares (bx + c = ax)

by dividing out the coefficient of the square and using the two operations al-ǧabr (Arabic: الجبر “restoring” or “completion”) and al-muqābala ("balancing"). Al-ǧabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x = 40x - 4x is reduced to 5x = 40x. Al-muqābala is the process of bringing quantities of the same type to the same side of the equation. For example, x+14 = x+5 is reduced to x+9 = x.

Several authors have published texts under the name of Kitāb al-ǧabr wa-l-muqābala, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil (Rasāla fi al-ǧabr wa-al-muqābala), Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, Ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr (author uncertain), and Šarafaddīn al-Ṭūsī.

Arithmetic

Page from a Latin translation, beginning with "Dixit algorizmi"

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. The translation was most likely done in the 12th century by Adelard of Bath, who had also translated the astronomical tables in 1126.

The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi ("So said al-Khwārizmī"), or 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 Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind ("The Book of Addition and Subtraction According to the Hindu Calculation")

This section needs expansion. You can help by making an edit requestadding to it .

Geography

Hubert Daunicht's reconstruction of al-Khwārizmī's planisphere.
A 15th century map based on Ptolomy's Geography for comparison.

Al-Khwārizmī's third major work is his 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 Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.

There is only one surviving copy of 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. 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.

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 points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.

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.


Astronomy

Corpus Christi College MS 283

Al-Khwārizmī's Zīj al-sindhind (Arabic: زيج "astronomical tables") 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.

The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslama al-Majrīṭī (c. 1000) has survived in a Latin translation, presumably by Adelard of Bath (January 26, 1126). The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).

Jewish calendar

Al-Khwārizmī wrote several other works including a treatise on the Jewish calendar (Risāla fi istikhrāj taʾrīkh al-yahūd "Extraction of the Jewish Era"). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall; calculates the interval between the 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.

Other works

Several Arabic manuscripts in Berlin, Istanbul, Taschkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwārizmī. The Istanbul manuscript contains a paper on sundials, which is mentioned in the Fihirst. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy.

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 (Maʿrifat al-samt min qibal al-irtifāʿ).

He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his Kitab al-Fihrist (an index of Arabic books) also mentions Kitāb ar-Ruḵāma(t) (the book on sundials) and Kitab al-Tarikh (the book of history) but the two have been lost.

See also

Notes

  1. Toomer, Hogendijk 1997, Oaks
  2. Berggren, Hogendijk, Struik p. 93
  3. Gandz 1936
  4. Struik p. 93
  5. al-Daffa 1978
  6. Knuith 1979
  7. Knuth 1997
  8. possibly because it is mistaken with that of Ǧaʿfar Muḥammad ibn Mūsā ibn Šākir. M. Dunlop. Muḥammad b. Mūsā al-Khwārizmī. JRAS 1943 p. 248-250).
  9. Toomer
  10. Encyclopedia Britannica. al-Khwarizmi.
  11. mactutor-hanasi
  12. Ruska 1917
  13. Berggren, p. 7
  14. MacTutor: Cartography
  15. In al-Khwārizmī's opinion, "the Claudian" indicated that Ptolemy was a descendent of the emperor Claudius.
  16. Daunicht 1968
  17. Neugebauer 1962

References

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  • Suter, H. : 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.
  • Toomer, Gerald (1970–1990). "Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā". In Charles Coulston Gillispie (ed.). Dictionary of Scientific Biography. Vol. 7. New York: Charles Scribner's Sons. pp. 358–365. ISBN 0-684-16962-2. {{cite encyclopedia}}: Check date values in: |year= (help)CS1 maint: year (link)
  • Van Dalen, B. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time.
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