The Compendious Book on Calculation by Completion and Balancing
The Compendious Book on Calculation by Completion and Balancing (Arabic: كتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; Latin: Liber Algebræ et Almucabola), also known as Al-Jabr (الجبر), is an Arabic mathematical treatise on algebra written by the polymath Muḥammad ibn Mūsā al-Khwārizmī around 820 CE while he was in the Abbasid capital of Baghdad, modern-day Iraq. Al-Jabr was a landmark work in the history of mathematics, establishing algebra as an independent discipline, and with the term "algebra" itself derived from Al-Jabr. The Compendious Book provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. It was the first text to teach algebra in an elementary form and for its own sake. It also introduced the fundamental concept of "reduction" and "balancing" (which the term al-jabr originally referred to), the transposition of subtracted terms to the other side of an equation, i.e. the cancellation of like terms on opposite sides of the equation. Mathematics historian Victor J. Katz regards Al-Jabr as the first true algebra text that is still extant. Translated into Latin by Robert of Chester in 1145, it was used until the sixteenth century as the principal mathematical textbook of European universities. Several authors have also published texts under this name, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil Shujā ibn Aslam, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī. (Wikipedia).
