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In his book The Compendious Book on Calculation by Completion and Balancing, Al-Khwarizmi deals with ways to solve for the positive roots of first and second-degree (linear and quadratic) polynomial equations. He introduces the method of reduction, and unlike Diophantus, also gives general solutions for the equations he deals with. [7] [8] [9]
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 ...
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 systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, Al-Jabr. [ 40 ] On the Calculation with Hindu Numerals, written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe.
The Algebra is perhaps Abu Kamil's most influential work, which he intended to supersede and expand upon that of Al-Khwarizmi. [2] [11] Whereas the Algebra of al-Khwarizmi was geared towards the general public, Abu Kamil was addressing other mathematicians, or readers familiar with Euclid's Elements. [11]
Works by mathematicians who lived under the rule of Islam during the Middle Ages, irrespective of their religion, ethnicity or language. Pages in category "Mathematical works of the medieval Islamic world"
His commentaries of the Sphaerica covered book I and parts of book II, none of which survive today. His edition was later updated by Ahmad ibn Abi Said al-Harawi (10th century). Later, Nasir al-Din al-Tusi (1201–1274) dismissed Al-Mahani and Al-Harawi's edition and wrote his own treatment of the Sphaerica , based on the works on Abu Nasr Mansur .
The first book on the systematic algebraic solutions of linear and quadratic equations by the Persian scholar Muhammad ibn Mūsā al-Khwārizmī. The book is considered to be the foundation of modern algebra and Islamic mathematics. [10] The word "algebra" itself is derived from the al-Jabr in the title of the book. [11]