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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]
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.
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 ...
In the history of mathematics, Arabic mathematics or Islamic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600.While most scientists in this period were Muslims and Arabic was the dominant language, contributions were made by people of many religions (Muslims as well as Christians, Jews, and Zoroastrians) and ethnicities (Arabs as well as Persian ...
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]
Only a chapter called "Logical Necessities in Mixed Equations", on the solution of quadratic equations, has survived. The manuscript gives exactly the same geometric demonstration as is found in Al-Jabr , and in one case the same example as found in Al-Jabr , and even goes beyond Al-Jabr by giving a geometric proof that if the discriminant is ...
Systemic algebraic solution and completing the square: Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE [48]: 171 ) presented the first systematic solution of linear and quadratic equations.
The Tusi couple, a mathematical device invented by the Persian polymath Nasir al-Din Tusi to model the not perfectly circular motions of the planets. Science in the medieval Islamic world was the science developed and practised during the Islamic Golden Age under the Abbasid Caliphate of Baghdad, the Umayyads of Córdoba, the Abbadids of Seville, the Samanids, the Ziyarids and the Buyids in ...