Abu Abdullah Mohammed ben Musa Al-Khwarizmi was an Arab mathematician who was born around 780 and died around the year 850. Little is known about his life. There are indications that he or his family originated in Khowarezm, the region south of the Aral Sea, at the time part of Arab-occupied Persia (now part of Uzbekistan). He was one of the first mathematicians to work at the House of Wisdom in Baghdad during the reign of Caliph al-Mamum (813-833).

Al-Khwarizmi wrote treatises on arithmetic, algebra, astronomy, geography, and the calendar. You may have written a treatise on the astrolabe and another on sundials, but these last two have not come to our day. Both the treatise on arithmetic and algebra constituted the starting point for further work and exerted a strong influence on the development of mathematics, especially arithmetic and algebra.

The original version of Al-Khwarizmi's small treatise on arithmetic is lost, but it has come to Spain, and there are twelfth-century Latin translations. In his text al-Khwarizmi introduces the nine Indian symbols to represent the digits and a circle to represent the zero. It then explains how to type a number in the decimal position system using the 10 symbols. It describes the calculus operations (addition, subtraction, division and multiplication) according to the Indian method and explains the square root extraction. After calculating with integers, it approaches calculating with fractions (expressing them as the sum of unit fractions).

According to Youschkevitch, there are three twelfth-century Latin texts, which may be translations of al-Khwarizmi's treatise on arithmetic. The Liber Algorismi de pratica arismetrice (The Book of Algorismi on Practical Arithmetic), written by John of Seville (or Todelo), a Spanish Jew converted to Catholicism who worked in Todelo from 1135 to 1153. The Liber Ysagogarum Alchorismi in artem astronomicam (Algorismi's introduction to the art of astronomy), of which several copies are known, one dating from 1143. It is not known who was its author if the English Adelardus de Bada, or Bath (who belonged to the Toledo school), or Robert de Cherter, also English. Youschkevitch also mentions another untitled 13th-century translation in the Cambridge University Library, published by Boncompagni in 1857, under the title Algoritmi numero indorum and beginning with the words Dixit Algorismi ( ie Algorismi said).
The word algorithismi is therefore the Latin version of the name al-Khwarizmi and derived from the word algorithm.

Al-Khwarizmi's treatise on algebra dates from around 830 and is titled Hisab al-jabr w'al-muqabala, a possible translation would be the calculation by completion (or restoration) and reduction. Al-jabr is the operation of adding terms equal to both members of the equation in order to eliminate the negative coefficient terms, and al-quababalar the operation that follows, which is to add similar terms.

Al-Khwarizmi tells us, in the introduction of his algebra, with the title, that Caliph al-Mamum encouraged him to write a little work on calculus by the rules of completion and reduction, confining it to the simplest and most useful in arithmetic, such as that which men constantly need in the case of inheritances, shares, court proceedings, and trade, and in all their dealings with others, or when measuring land, channeling, geometric calculations, and other things of various kinds and types are involved.

Your book consists of three parts. The first on algebra, which precedes a brief chapter on business transactions; the second on geometry and the third on inheritance issues. In his book Al-Khwarizmi does not use any symbols, not even the symbols he will describe later in his arithmetic.

The book was also translated into Latin in the twelfth century, but these translations did not include the second and third parts. Robert de Chester, in his Latin translation of 1140, translates al-Khwarizmi's algebra treatise with title Liber algebrae and almucabala, so algebra derives from the Latin translation of al-jarb.