Al-Khwarizmi writes the book of al-jabr
Around 820 in Baghdad Muhammad ibn Musa al-Khwarizmi wrote for the caliph al-Ma'mun ‘The Compendious Book on Calculation by Restoration and Balancing’, which taught how to reduce linear and quadratic equations to six standard forms and solve them, with geometric proofs and practical problems of inheritance, trade and surveying. It is regarded as the first book to treat algebra as a discipline in its own right, and its title gave the subject its name.
- Date
- c. 820year known, approximate
- Place
- Baghdadtoday: Baghdad, Iraq · Middle East and Egypt
- Participants
- Muhammad ibn Musa al-Khwarizmi, Al-Ma'mun
- Threads
- Middle East and Egypt (6th–10th c.)
- Also known as
- Al-Jabr; Kitab al-jabr wa'l-muqabala; The Compendious Book on Calculation by Completion and Balancing; Hisab al-jabr wa'l-muqabala; Китаб аль-джабр ва-ль-мукабала; Аль-джебр
Al-Khwarizmi, a scholar associated with al-Ma'mun’s House of Wisdom, dedicated the book to the caliph and explained in its preface that it contained ‘what is easiest and most useful in arithmetic’, such as people need in cases of inheritance, legacies, partition, lawsuits and trade and in measuring land and digging canals. The first part shows how any problem leading to a linear or quadratic equation can be brought to one of six standard forms — squares equal to roots, squares equal to numbers, roots equal to numbers and three compound forms — by the two operations that gave the work its title: al-jabr, ‘restoration’, which removes a subtracted quantity by adding it to both sides, and al-muqabala, ‘balancing’, which cancels equal quantities on both sides. Each rule is justified by a geometric construction such as completing the square.
The text is entirely rhetorical: there are no symbols, and even numbers are written out in words. Al-Khwarizmi then turns to the measurement of areas and volumes, and about half of the book deals with problems of the Islamic law of inheritance. Historians debate how far he drew on earlier traditions — Babylonian, Greek and Indian — but his book is regarded as the first to present algebra systematically, in an elementary form and for its own sake, as Solomon Gandz put it, which is why al-Khwarizmi is often called the father of algebra.
Translated into Latin by Robert of Chester in 1145, the book made al-jabr the European word ‘algebra’. Al-Khwarizmi’s separate treatise on calculation with the Indian decimal numerals survives only in Latin, as Algoritmi de numero Indorum, and the Latinised form of his name became ‘algorithm’. Through such translations the mathematics of al-Ma'mun’s Baghdad reached medieval Europe.
Connections
Related events
- Brahmagupta writes the Brahmasphutasiddhanta628 · South Asiaal-Khwarizmi’s separate treatise taught calculation with the Indian decimal numerals, which had reached Baghdad with Indian astronomy
- Indian astronomy in Arabic: the Zij al-Sindhindbetween 771 and 773 · Middle East and Egyptal-Khwarizmi’s own astronomical tables, also called Zij al-Sindhind, continued the Indian tradition brought to Baghdad in the 770s
- The House of Wisdom and the translation movement in Baghdadc. 800 – c. 900 · Middle East and Egyptal-Khwarizmi is said to have worked at al-Ma'mun’s House of Wisdom
Same participants
- Fourth Fitna: al-Amin against al-Ma'mun and the siege of BaghdadJanuary 811 – September 813 · Middle East and Egyptvia Al-Ma'mun
- The mihna: the Abbasid inquisition over the createdness of the Qur’an833 – between 848 and 852 · Middle East and Egyptvia Al-Ma'mun
Same place
- Reign of Vologases I51–78 · Middle East and Egypt
- Trajan’s Parthian campaign114–117 · Middle East and Egypt
- Roman–Parthian War of 161–166161–166 · Middle East and Egypt
- Reign of Vologases IV147–191 · Middle East and Egypt
- Mani begins his mission240 · Middle East and Egypt
- Reign of Shapur II309–379 · Middle East and Egypt
- Julian’s Persian expedition and the Peace of 3635 March 363 – July 363 · Middle East and Egypt
- Council of Seleucia-Ctesiphon410 · Middle East and Egypt
- Reign of Bahram V Gurbetween 420 and 421 – 438 · Middle East and Egypt
- Suppression of the Mazdakitesbetween 524 and 529 · Middle East and Egypt
- Reign of Khosrow I Anushirvan531–579 · Middle East and Egypt
- Revolt of Bahram Chobin and the restoration of Khosrow II589–591 · Middle East and Egypt
- Founding of Baghdad: al-Mansur’s Round Citybetween 30 July and 2 August 762 – between 766 and 767 · Middle East and Egypt
- Paper comes to Baghdadbetween 794 and 795 · Middle East and Egypt
- Siege of Baghdad29 January – 10 February 1258 · Middle East and Egypt
- Capture of Baghdad by Suleiman Ibetween November and December 1534 · Middle East and Egypt
Adjacent events in the thread
- Al-Mu'tasim founds Samarra, the new Abbasid capital836 · Middle East and Egypt
Meanwhile in the world
Other regions, within a year of this event
Eastern Europe
- Saltovo-Mayaki culturec. 750 – between 900 and 950
- The Khazar rulers adopt Judaismbetween 740 and 861
- Volyntsevo culture: the Slavs of the Dnieper Left Bank in the Khazar agebetween 700 and 750 – between 813 and 833
Balkans and Anatolia
- Byzantine Iconoclasmbetween 726 and 730 – 11 March 843
Africa
- Ifriqiya under the Aghlabids800 – March 909
- Igbo-Ukwu: bronze casting in the West African forest800–899 – 1100–1199
Central and Northern Asia
- The Tang–Tibet treaty of 821–822 and the treaty pillar in Lhasa8 November 821 – March 823
- The rise of the Samanids in Transoxiana819–900
South Asia
- Dharmapala founds the monasteries of Somapura and Vikramashilabetween 770 and 821
- The tripartite struggle for Kannaujbetween 783 and 790 – between 915 and 918
Southeast Asia and Oceania
- Building of Borobudurc. 780 – c. 833
North America
- Pueblo I: villages of surface rooms on the Colorado Plateauc. 750 – c. 900
- Plum Bayou Mounds: a planned ceremonial centre in the Arkansas valleyc. 650 – c. 1050
- The Late Woodland period in eastern North Americac. 500 – c. 1000
Latin America
- Wari culture and the Middle Horizon state in the Central Andesc. 600 – c. 1000
- Tiwanaku culture at its height by Lake Titicacac. 600 – c. 1000
- Cacaxtla and Xochicalco: the Epiclassic cities of central Mexicoc. 650 – c. 900
- Classic Maya collapse in the southern lowlandsc. 800 – c. 950
- Rise of Chichén Itzá in northern Yucatánc. 800 – between 900 and 1000
The same period
Sources
- Wikipedia (English): Al-Jabr
- Wikipedia (English): Al-Khwarizmi
- Wikipedia (Russian): Китаб аль-джебр ва-ль-мукабала
- Wikipedia (Russian): Аль-Хорезми
- O'Connor J. J., Robertson E. F. Abu Ja'far Muhammad ibn Musa Al-Khwarizmi // MacTutor History of Mathematics Archive. — University of St Andrews
- Rosen F. (ed., trans.) The Algebra of Mohammed ben Musa. — London: Oriental Translation Fund, 1831.
- Rashed R. Al-Khwārizmī: The Beginnings of Algebra. — London: Saqi, 2009.
- Wikidata: Q8369