Al-Khwarizmi

Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī ( Persian / Arabic : أبو عبد الله محمد بن موسى الخوارزمي ) (c. 780, Khwārizm – c. 850) was a Persian mathematician , astronomer and geographer , a scholar in the House of Wisdom in Baghdad . His Kitab al-Jabr wa-l-Muqabala presented the first systematic solution of linear and quadratic equations . He is considered the founder of algebra , a credit he shares with Diophantus . In the twelfth century, Latin translations of his work on the Indian numerals , introduced the decimal positional number system to the Western world . He revised Ptolemy 's Geography and wrote on astronomy and astrology. His contributions had a great impact on language. "Algebra" is derived from al-jabr , one of the two operations he used to solve quadratic equations . Algorism and algorithm stem from Algoritmi , the Latin form of his name. His name is the origin of ( Spanish ) guarismo and of ( Portuguese ) algarismo , both meaning digit . There is some confusion in the literature on whether al-Khwārizmī's full name is Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī or Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī . Ibn Khaldun notes in his encyclopedic work: "The first who wrote upon this branch (algebra) was Abu ʿAbdallah al-Khowarizmi, after whom came Abu Kamil Shojaʿ ibn Aslam." (MacGuckin de Slane). (Rosen 1831, pp. xi–xiii) mentions that "[Abu Abdallah Mohammed ben Musa] lived and wrote under the caliphat of Al Mamun, and must therefore be distinguished from Abu Jafar Mohammed ben Musa, likewise a mathematician and astronomer, who flourished under the Caliph Al Motaded (who reigned A.H. 279-289, A.D. 892-902)." Karpinski notes in his review on (Ruska 1917) that in (Ruska 1918): "Ruska here inadvertently speaks of the author as Abū Gaʿfar M. b. M., instead of Abū Abdallah M. b.

Abū ‘Abdallāh Muḥammad ibn Mūsā al-Khwārizmī ( ; c. 780 – c. 850 ), formerly Latinized as Algoritmi or Algaurizin , was a Persian mathematician , astronomer and geographer during the Abbasid Caliphate , a scholar in the House of Wisdom in Baghdad . In the twelfth century, Latin translations of his work on the Indian numerals introduced the decimal positional number system to the Western world . Al-Khwarizmi's The Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic. In Renaissance Europe, he was considered the original inventor of algebra , although it is now known that his work is based on older Indian or Greek sources. He revised Ptolemy 's Geography and wrote on astronomy and astrology. Some words reflect the importance of al-Khwārizmī's contributions to mathematics. "Algebra" is derived from al-jabr , one of the two operations he used to solve quadratic equations . Algorism and algorithm stem from Algoritmi , the Latin form of his name. His name is also the origin of ( Spanish ) guarismo and of ( Portuguese ) algarismo , both meaning digit . Rosen 1831 , p. v–vi harvnb error: no target: CITEREFRosen1831 ( help ) ; Toomer 1990 Daffa 1977 Knuth, Donald (1979). There are <ref group=note> tags on this page, but the references will not show without a template (see the help page ).

9th century Persian mathematician, astronomer and geographer "al-Khwārizmī" redirects here. Muḥammad ibn Mūsā al-Khwārizmī ( ; c. 780 – c. 850 ), Arabized as al-Khwarizmi and formerly Latinized as Algorithmi , was a Persian polymath who produced works in mathematics , astronomy , and geography . Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad . Al-Khwarizmi's popularizing treatise on algebra ( The Compendious Book on Calculation by Completion and Balancing , c. 813–833 CE ) presented the first systematic solution of linear and quadratic equations . One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square , for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra . The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm . His name is also the origin of ( Spanish ) guarismo and of ( Portuguese ) algarismo , both meaning digit . In the 12th century, Latin translations of his textbook on arithmetic ( Algorithmo de Numero Indorum ) which codified the various Indian numerals , introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing , translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities . In addition to his best-known works, he revised Ptolemy 's Geography , listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. He also made important contributions to trigonometry , producing accurate sine and cosine tables, and the first table of tangents. The Voyage and the Messenger: Iran and Philosophy . Take, for example, someone like Muhammad b. Musa al-Khwarizmi (fl. 850) who 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. Polynomials and equations in Arabic algebra. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation." Boyer, Carl B., 1985. "Diophantus sometimes is called the father of algebra, but this title more appropriately belongs to al-Khowarizmi..." , "...the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta..." S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277,"Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers." Katz, Victor J. 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. The Oxford History of Islam . Al-Khwarizmi is often considered the founder of algebra, and his name gave rise to the term algorithm. Encyclopaedia of Islam, THREE . A History of the Islamic World . "The Compendious Book on Calculation by Completion and Balancing" (Hisab al-Jabr wa H-Muqabala) on the development of the subject cannot be underestimated. Translated into Latin during the twelfth century, it remained the principal mathematics textbook in European universities until the sixteenth century Shawn Overbay, Jimmy Schorer, and Heather Conger, University of Kentucky. A history of algebra: from al – Khwarizmi to emmy noether. There are <ref group=note> tags on this page, but the references will not show without a template (see the help page ).

9th-century mathematician and astronomer For other uses, see Al-Khwarizmi (disambiguation) . Muḥammad ibn Mūsā al-Khwārizmī ( ; c. 780 – c. 850 ), or al-Khwarizmi , was a Persian polymath from Khwarazm , who produced vastly influential works in mathematics , astronomy , and geography . Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad . Al-Khwarizmi's popularizing treatise on algebra ( The Compendious Book on Calculation by Completion and Balancing , c. 813–833 CE ) presented the first systematic solution of linear and quadratic equations . One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square , for which he provided geometric justifications. Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra . The term algebra itself comes from the title of his book (the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms algorism and algorithm , the Spanish, Italian, and Portuguese terms algoritmo , and the Spanish guarismo and Portuguese algarismo , both meaning " digit ". In the 12th century, Latin translations of his textbook on arithmetic ( Algorithmo de Numero Indorum ) which codified the various Indian numerals , introduced the decimal positional number system to the Western world. The Compendious Book on Calculation by Completion and Balancing , translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities . In addition to his best-known works, he revised Ptolemy 's Geography , listing the longitudes and latitudes of various cities and localities. He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial . He also made important contributions to trigonometry , producing accurate sine and cosine tables, and the first table of tangents . In Gillispie, Charles Coulston (ed.). Dictionary of Scientific Biography . The Encyclopaedia of Islam . 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. "Mohammed ibn Musa al-Khwarizmi (780–850) was a Persian astronomer and mathematician from the district of Khwarism (Uzbekistan area of Central Asia)." Ben-Menahem, Ari (2009). Historical Encyclopedia of Natural and Mathematical Sciences (1st ed.). A History of World Societies (11th ed.). Near the beginning of this period the Persian scholar al-Khwarizmi (d. ca. 850) harmonized Greek and Indian findings to produce astronomical tables that formed the basis for later Eastern and Western research. (1998), "From Al-Jabr to Algebra", Mathematics in School , 27(4), 14–15. (2009), "Polynomials and Equations in Arabic Algebra", Archive for History of Exact Sciences , 63(2), 169–203. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation." Corbin, Henry (1998). The Voyage and the Messenger: Iran and Philosophy . "Diophantus sometimes is called the father of algebra, but this title more appropriately belongs to al-Khowarizmi...", "...the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta..." S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277, "Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers." Katz, Victor J. 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. The Oxford History of Islam . Al-Khwarizmi is often considered the founder of algebra, and his name gave rise to the term algorithm. Encyclopaedia of Islam, THREE . Scientifica Historica: How the world's great science books chart the history of knowledge . "The Origin of the Term "Algebra" " . History of the Arabs . A History of the Islamic World . "The Compendious Book on Calculation by Completion and Balancing" (Hisab al-Jabr wa H-Muqabala) on the development of the subject cannot be underestimated. Translated into Latin during the twelfth century, it remained the principal mathematics textbook in European universities until the sixteenth century Shawn Overbay; Jimmy Schorer; Heather Conger. A History of Algebra: From al–Khwarizmi to Emmy Noether .

Islamic mathematician (c. 780 – c. 850) For other uses, see Al-Khwarizmi (disambiguation) . Muhammad ibn Musa al-Khwarizmi c. 780 – c. 850 , or simply al-Khwarizmi , was a mathematician active during the Islamic Golden Age , who produced Arabic-language works in mathematics , astronomy , and geography . Around 820, he worked at the House of Wisdom in Baghdad , the contemporary capital city of the Abbasid Caliphate . One of the most prominent scholars of the period, his works were widely influential on later authors, both in the Islamic world and Europe. His popularizing treatise on algebra , compiled between 813 and 833 as Al-Jabr ( The Compendious Book on Calculation by Completion and Balancing ), presented the first systematic solution of linear and quadratic equations . One of his achievements in algebra was his demonstration of how to solve quadratic equations by completing the square , for which he provided geometric justifications. Because al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise ( الجبر Al-Jabr , transl. His name gave rise to the English terms algorism and algorithm ; the Spanish, Italian, and Portuguese terms algoritmo ; and the Spanish term guarismo and Portuguese term algarismo , all meaning ' digit '. In the 12th century, Latin translations of al-Khwarizmi's textbook on Indian arithmetic ( Algorithmo de Numero Indorum ), which codified the various Indian numerals , introduced the decimal -based positional number system to the Western world . Al-Khwarizmi revised Geography , the 2nd-century Greek-language treatise by Ptolemy , listing the longitudes and latitudes of cities and localities. He further produced a set of astronomical tables and wrote about calendric works, as well as the astrolabe and the sundial . Al-Khwarizmi made important contributions to trigonometry , producing accurate sine and cosine tables. In Gillispie, Charles Coulston (ed.). Dictionary of Scientific Biography . The Encyclopaedia of Islam . The Art of Computer Programming . (2009), "Polynomials and Equations in Arabic Algebra", Archive for History of Exact Sciences , 63(2), 169–203. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation." Corbin, Henry (1998). The Voyage and the Messenger: Iran and Philosophy . "Diophantus sometimes is called the father of algebra, but this title more appropriately belongs to al-Khowarizmi...", "...the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta..." Gandz, Solomon , The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277, "Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers." Katz, Victor J. 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. The Oxford History of Islam . Al-Khwarizmi is often considered the founder of algebra, and his name gave rise to the term algorithm. Encyclopaedia of Islam (3rd ed.). "The Origin of the Term "Algebra" ". History of the Arabs . A History of the Islamic World . "The Compendious Book on Calculation by Completion and Balancing" (Hisab al-Jabr wa H-Muqabala) on the development of the subject cannot be underestimated. Translated into Latin during the twelfth century, it remained the principal mathematics textbook in European universities until the sixteenth century Overbay, Shawn; Schorer, Jimmy; Conger, Heather. A History of Algebra: From al–Khwarizmi to Emmy Noether .