Al-Jabr

The Concise Book of Calculation by Restoration and Balancing , commonly abbreviated Al-Jabr or Algebra (<a href="/facts/Arabic/A1e66hVV">Arabic</a>: الجبر), is an <a href="/facts/Arabic_mathematics/TACUEnlp">Arabic mathematical</a> treatise on <a href="/facts/Algebra/nMdqczjo">algebra</a> written in <a href="/facts/Baghdad/RbtLzzHe">Baghdad</a> around 820 by the Persian polymath <a href="/facts/Al-Khwarizmi/24KdxyEQ">Al-Khwarizmi</a>. It was a landmark work in the <a href="/facts/History_of_mathematics/18h5rQA5">history of mathematics</a>, with its title being the ultimate etymology of the word "algebra" itself, later borrowed into <a href="/facts/Medieval_Latin/gyLMjaCX">Medieval Latin</a> as algebrāica.
Al-Jabr provided an exhaustive account of solving for the positive <a href="/facts/Root_of_a_function/mlK3dhoT">roots</a> of <a href="/facts/Polynomial_equations/1QauIGxs">polynomial equations</a> up to the second degree. It was the first text to teach <a href="/facts/Elementary_algebra/973nufT7">elementary algebra</a>, and the first to teach algebra 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.{{efn|"It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation, which is evident in the treatise; the word muqabalah is said to refer to "reduction" or "balancing"—that is, the cancellation of like terms on opposite sides of the equation." The mathematics historian <a href="/facts/Victor_J._Katz/kgcIWQDM">Victor J. Katz</a> regards Al-Jabr as the first true algebra text that is still extant. Translated into Latin by <a href="/facts/Robert_of_Chester/jgf8rTdt">Robert of Chester</a> 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 <a href="/facts/Abu_Hanifa_Dinawari/QI88GIm3">Abu Hanifa Dinawari</a>, <a href="/facts/Abu_Kamil/rL52YrHL">Abu Kamil</a>, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, <a href="/facts/%2527Abd_al-Ham%25C4%25ABd_ibn_Turk/g9uHTKN3">'Abd al-Hamīd ibn Turk</a>, Sind ibn ʿAlī, Sahl ibn Bišr, and <a href="/facts/Sharaf_al-D%25C4%25ABn_al-T%25C5%25ABs%25C4%25AB/uYR64wm4">Šarafaddīn al-Ṭūsī</a>.

Al-Jabr open-in-new

Al-Jabr