In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities.

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 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.

His name gave rise to the terms algorism and algorithm, as well as Spanish, Italian and Portuguese terms algoritmo, and Spanish guarismo and Portuguese algarismo meaning ' digit'. The term algebra itself comes from the title of his book (the word al-jabr meaning 'completion' or 'rejoining'). : 14 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. 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. 813–833 CE : 171 ) presented the first systematic solution of linear and quadratic equations. : 14Īl-Khwarizmi's popularizing treatise on algebra ( The Compendious Book on Calculation by Completion and Balancing, c. Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad. 850), or al-Khwarizmi was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronomy, and geography. Treatises on algebra and Hindu–Arabic numeral system The Compendious Book on Calculation by Completion and Balancing, Book of the Description of the Earth, Astronomical tables of Siddhanta

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