A page from the book

al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala (Arabic for "The Compendious Book on Calculation by Completion and Balancing"), 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 approximately 820 AD by the Persian mathematician Al-Khawarizmi. Image File history File links Al-Kitāb_al-muḫtaá¹£ar_fÄ«_ḥisāb_al-ÄŸabr_wa-l-muqābala. ... Image File history File links Al-Kitāb_al-muḫtaá¹£ar_fÄ«_ḥisāb_al-ÄŸabr_wa-l-muqābala. ... The Arabic language (Arabic: ‎ translit: ), or simply Arabic (Arabic: ‎ translit: ), is the largest member of the Semitic branch of the Afro-Asiatic language family (classification: South Central Semitic) and is closely related to Hebrew and Aramaic. ... Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of figures and numbers. Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. ... The Persians of Iran are an Iranian people who speak the Persian language and share a common culture and history. ... Soviet postage stamp commemorating the 1200th anniversary of Muhammad al‑Khwarizmi in 1983. ...

Several authors have also published texts under the name of Kitāb al-ğabr wa-l-muqābala, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil,^[1] Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, Ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr,^[2] and Šarafaddīn al-Ṭūsī. Abu Kamil Shuja ibn Aslam ibn Muhammad ibn Shuja (c. ... Sharafeddin Muzzafar-i Tusi, was a Persian mathematician of the middle ages, (1135 - 1213). ...

The book

The book was a compilation and extension of known rules for solving quadratic equations and for some other problems and considered to be the foundation of the modern algebra. The word algebra is derived from the name of one of the basic operations with equations (al-ğabr) described in this book. The book was translated in Latin as Liber algebrae et almucabala, hence "algebra". Graph of a quadratic function: y = x2−x−2 = (x+1)(x−2) The x-coordinates of the points where the graph crosses the x-axis, x = −1 and x = 2, are the roots of the quadratic equation: x2−x−2 = 0 In mathematics, a quadratic equation is a polynomial... Algebra is the current mathematics collaboration of the week! Please help improve it to featured article standard. ... Algebra is the current mathematics collaboration of the week! Please help improve it to featured article standard. ...

Since the book does not give any credits, it is not clearly known what earlier works were used by al-Khwarizmi, and modern mathematical historians put forth opinions based on the textual analysis of the book and the overall body of knowledge of the contemporary Muslim world. Most certain are connections with Indian and Hebrew texts.

Lacking modern abstract notations, the book reduces arbitrary quadratic equations to one of the six basic types, verbally described in terms of "squares" (what would be 'x²'), "roots" (i.e., 'x') and "numbers" (ordinary numbers, like 42), and provides algebraic and geometric methods to solve the basic ones. The six types, with modern notations, are:

• squares equal roots (ax² = bx)
• squares equal number (ax² = c)
• roots equal number (bx = c)
• squares and roots equal number (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots and number equal squares (bx + c = ax²)

The al-ğabr ("completion") operation is moving a negative quantity from one side of the equation to the other side with changing its sign. In an al-Khwarizmi's example (in modern notation), "x² = 40 x - 4 x²" is transformed by al-ğabr into "5x² = 40 x". Repeated application of this rule eleminates negative quantities from calculations.

Al-Muqabala ("balancing") means subtraction of the same positive quantity from both sides: "x² + 5 = 40 x + 4 x²" is turned into "5 = 40 x + 3 x²". Repeated application of this rule makes quantities of each type ("square"/"root"/"number") appear in the equation at most once, which helps to see that there are only 6 basic solvable types of the problem.

The second part of the book deals with applied problems of measuring areas and volumes. The last part deals with computations involved in convoluted Islamic rules of inheritance; as it turns out, they do require solutions of quadratic equations, e.g., to divide the land. Area is a physical quantity expressing the size of a part of a surface. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... Islam (Arabic: ; ( (help· info)), submission (to the will of God) is a monotheistic faith and the worlds second-largest religion with approximately 1. ... For other uses, see inheritance (disambiguation). ...

References

1. ↑ Rasāla fi l-ğabr wa-l-muqābala
2. ↑ Possibly.

• R. Rashed, The development of Arabic mathematics: between arithmetic and algebra, London, 1994.
• Robert of Chester's Latin Translation of Al-Khwarizmi's Al-Jabr: A New Critical Edition, (in Latin language) 1989, ISBN 3515045899

Robert of Chester (Robertus Castrensis) was an Englishman who lived around 1150. ... Latin was the language originally spoken in the region around Rome called Latium. ...

External link

• Al-Khwarizmi