About 830 CE, Persian mathematician, astronomer and geographer Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī, a scholar in the House of Wisdom in Baghdad, published Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة The Compendious Book on Calculation by Completion and Balancing. This was written "with the encouragement of the Caliph Al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance. The term algebra is derived from the name of one of the basic operations with equations (al-jabr) described in this book. It provided an exhaustive account of solving polynomial equations up to the second degree, and introduced the fundamental methods of 'reduction' and 'balancing', referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation" (Wikipedia article on Muhammad ibn Mūsā al-Khwārizmī, accessed 01-23-2010).
The work was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, circa 1145) from which our word "algebra" originates, and also by Gerard of Cremona. Robert of Chester's translation was translated into English as Robert of Chester's Latin Translation of the Algebra of Al-Khowarizmi with an Introduction, Critical Notes and an English Version by Louis Charles Karpinski (1915). As Chapter VII Karpinski included a survey of the manuscripts of Chester's text available to him. The primary texts that Karpinski could use were the Dresden Codex C.80, that dates from the mid-15th century, and the Codex Vindobonensis 4770 (Rec.3246) dating from the 14th century.