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The word "algebra" is derived from the Arabic word الجبر al-jabr, and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī, whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala, can be translated as The Compendious Book on Calculation by Completion and Balancing.
His Book of Algebra (Kitāb fī al-jabr wa al-muqābala) is "essentially a commentary on and elaboration of al-Khwārizmī's work; in part for that reason and in part for its own merit, the book enjoyed widespread popularity in the Muslim world". [31] It contains 69 problems, which is more than al-Khwārizmī who had 40 in his book. [31]
Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...
Further developments in algebra were made by Al-Karaji in his treatise al-Fakhri, where he extends the methodology to incorporate integer powers and integer roots of unknown quantities. Something close to a proof by mathematical induction appears in a book written by Al-Karaji around 1000 AD, who used it to prove the binomial theorem , Pascal's ...
Al-Samaw'al wrote the mathematical treatise al-Bahir fi'l-jabr, meaning "The brilliant in algebra", at the age of nineteen. He also used the two basic concepts of mathematical induction, though without stating them explicitly. He used this to extend results for the binomial theorem up to n=12 and Pascal's triangle previously given by al-Karaji. [5]
Bhaskara Acharya writes the “Bijaganita” (“Algebra”), which is the first text that recognizes that a positive number has two square roots 1130: Al-Samawal gives a definition of algebra: “[it is concerned] with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.” [16] c ...
Abu Kamil made important contributions to algebra and geometry. [4] He was the first Islamic mathematician to work easily with algebraic equations with powers higher than x 2 {\displaystyle x^{2}} (up to x 8 {\displaystyle x^{8}} ), [ 3 ] [ 5 ] and solved sets of non-linear simultaneous equations with three unknown variables . [ 6 ]
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. [52]