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Al-Khawarizmi was a mathematician, astronomer and geographer. He was perhaps one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics. In the words of Phillip Hitti:
"He influenced mathematical thought to a greater extent than any other mediaeval writer."
His work on algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra.
Hisab Al-jabr wAl-muqabala, contains analytical solutions of linear and quadratic equations and its author may be called one of the founders of analysis or algebra as distinct from geometry. He also gives geometrical solutions (with figures) of quadratic equations, for example X2 + 1OX = 39, an equation often repeated by later writers. The‘Liber ysagogarum Alchorismi in artem astronomicam a magistro A. [Adelard of Bath] compositus!' deals with arithmetic, geometry, music, and astronomy; it is possibly a summary of Al-Khawarzmi’s teachings rather than an original work.
His astronomical and trigonometric tables, revised by Maslama Al-Majrti (Second half of tenth century), were translated into Latin as early as l126 by Adelard of Bath. They were the first Muslim tables and contained not simply the sinefunction but also the tangent(Maslama's interpolation).
His arithmetic synthesised Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeral of fundamental importance developed by the Arabs. Similarly, he developed the decimal system so that the overall system of numerals, 'algorithm' or 'algorizm' is named after him. In addition to introducing the Indian system of numerals (now generally known as Arabic numerals), he developed at length several arithmetical procedures, including operations on fractions. It was through his work that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages.
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