Islamic

The Islamic Empire established建立 across Persia波斯, the Middle East, Central Asia, North Africa, Iberia伊比利亚, and in parts of India in the 8th century made significant contributions towards mathematics. Although most Islamic texts on mathematics were written in Arabic阿拉伯语, most of them were not written by Arabs, since much like the status of Greek in the Hellenistic world希腊世界, Arabic was used as the written language of non-Arab scholars throughout the Islamic world at the time. Persians contributed to the world of Mathematics alongside Arabs. In the 9th century, the Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī穆阿迈德·伊本·穆斯海瓦里兹姆 wrote several important books on the Hindu–Arabic numerals and on methods for solving equations. His book On the Calculation with Hindu Numerals, written about 825, along with the work of Al-Kindi, were instrumental起重要作用 in spreading Indian mathematics and Indian numerals to the West. The word algorithm算法，计算程序 is derived from the Latinization拉丁化 of his name, Algoritmi, and the word algebra from the title of one of his works, Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (The Compendious概括的，简明扼要的 Book on Calculation by Completion and Balancing). He gave an exhaustive详尽的 explanation for the algebraic solution of quadratic equations二次方程 with positive roots, and he was the first to teach algebra in an elementary基本的 form and for its own sake. He also discussed the fundamental基础的 method of "reduction" and "balancing", referring to the transposition of subtracted terms减项 to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. This is the operation which alKhwārizmī originally described as al-jabr. His algebra was also no longer concerned "with a series of problems to be resolved, but an exposition which starts with primitive原始的 terms in which the combinations must give all possible prototypes原形 for equations, which henceforward explicitly明确地 constitute（被看作）是 the true object of study." He also studied an equation for its own sake and "in a generic通用的 manner, insofar在…范围下 as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."