The Compendious Book On Calculation By Completion and Balancing

The Compendious Book On Calculation By Completion And Balancing

Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (Arabic for "The Compendious Book on Calculation by Completion and Balancing", in Arabic script 'الكتاب المختصر في حساب الجبر والمقابلة'), also known under a shorter name spelled as Hisab al-jabr w’al-muqabala, Kitab al-Jabr wa-l-Muqabala and other transliterations) is a mathematical book written in Arabic in approximately AD 820 by the Persian mathematician Muhammad ibn Mūsā al-Khwārizmī in Baghdad, the capital of the Abbasid Caliphate at the time.

The book was translated into Latin in the mid 12th century under the title Liber Algebrae et Almucabola. Today's term "algebra" is derived from the term al-ğabr in the title of this book. The al-ğabr provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree.

Several authors have also published texts under the name of Kitāb al-ğabr wa-l-muqābala, 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.