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Muhammad ibn Musa al-Khwarizmi
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Muhammad ibn Musa Khwarizmi (???? ?? ???? ??? ???? ?????????? - Mu?ammad bin Musa Abu Ga?far al-?awarazmi) was a Persian mathematician, astronomer and geographer. He was born around 780 in Khwarizm, in contemporary Khiva, Uzbekistan, which was then part of the native Iranian-Khwarizmian Afrigid dynasty, and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
His Algebra, written around 820, was the first book on the systematic solution of linear and quadratic equations.
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Muhammad ibn Musa Khwarizmi (???? ?? ???? ??? ???? ?????????? - Mu?ammad bin Musa Abu Ga?far al-?awarazmi) was a Persian mathematician, astronomer and geographer. He was born around 780 in Khwarizm, in contemporary Khiva, Uzbekistan, which was then part of the native Iranian-Khwarizmian Afrigid dynasty, and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
His Algebra, written around 820, was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered by many to be the father of algebra, a title some scholars assign to Diophantus. In the twelfth century, Latin translations of his Arithmetic, which explained Arabic numerals, introduced decimal positional number system to the Western world. He was among the first to use zero as a place holder in positional base notation. The word algorithm derives from his name. He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.
His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book.
Etymology
The words algorism and algorithm stem from Algoritmi, the Latinization of his name. (In Finnish the term for algorithm is just that, "algoritmi".) His name is also the origin of the Spanish word guarismo and of the Portuguese word algarismo, both meaning digit.
Yaqut al-Hamawi in his Mu'jem al-baladan wrote that the name "Khwarezm" is a compound name (in Persian) of "Khwar", and "-razm", referring to the abundance of cooked fish meat as a main diet of the peoples of this area. C. E. Bosworth, however, believes the Persian name to be made up of ???, meaning "the sun," and ??, meaning "Earth", designating "the land from which the sun rises." More correctly, however, the Iranic compound stands for "lowland" from khwar/khar, "low" and zam/zem, "earth, land.". In the Avestan language it is "Xvairizem", in Old Persian "Huwarazmish", and in Modern Persian it is Khwarazm. The name also appears in Achaemenid inscriptions as "Huvarazmish", and declared to be part of the Persian Empire.
Life
Few details about al-Khwarizmi's life are known; it is not even certain where he was born. His name indicates he might have come from Khwarezm (Khiva), then part of Greater Khorasan, which at that time was part of the Persian Empire (the eastern part of the territory of Persia), now Xorazm Province of Uzbekistan. Abu Rayhan Biruni (a native Chorasmian) explicitly states: "The people of Khwarizm are a branch of the Persian tree".
His kunya is given as either (Arabic: ) or (??? ???? in Arabic). The historian Tabari gave his name as Muhammad ibn Musa al-Khwarizmi al-Majousi al-Katarbali (Arabic: ). The epithet al-Qutrubbulli indicates he might instead have come from Qutrubbull, a small town near Baghdad. However, Rashed points out that
Regarding al-Khwarizmi's religion, Toomer writes:
In Ibn al-Nadim's Kitab al-Fihrist we find a short biography on al-Khwarizmi, together with a list of the books he wrote. Al-Khwarizmi accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China and India traveled to this city—as such apparently so did Al-Khwarizmi. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph , where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit scientific manuscripts.
Contributions
His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book in the Arabic language on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (Arabic ?????? ??????? ?? ???? ????? ?????????) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century.
His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.
Some of his contributions were based on earlier Persian and Babylonian Astronomy, Indian numbers, and Greek sources.
Al-Khwarizmi systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.
He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".
When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the astrolabe and sundial.
Algebra
(Arabic: ?????? ??????? ?? ???? ????? ????????? “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE. The term algebra is derived from the name of one of the basic operations with equations (al-jabr) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and also by Gerard of Cremona. A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge.
The al-jabr is considered the foundational text of modern algebra. 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.
Al-Khwarizmi's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers)
- 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)
by dividing out the coefficient of the square and using the two operations (Arabic: ????? “restoring” or “completion”) and al-muqabala ("balancing"). is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x2 = 40x − 4x2 is reduced to 5x2 = 40x. Al-muqabala is the process of bringing quantities of the same type to the same side of the equation. For example, x2 + 14 = x + 5 is reduced to x2 + 9 = x.
Several authors have also published texts under the name of Kitab al-gabr wa-l-muqabala, including .
J. J. O'Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:
R. Rashed and Angela Armstrong write:
Arithmetic
Al-Khwarizmi's second major work was on the subject of arithmetic, which survived in a Latin translation but was lost in the original Arabic. The translation was most likely done in the twelfth century by Adelard of Bath, who had also translated the astronomical tables in 1126.
The Latin manuscripts are untitled, but are commonly referred to by the first two words with which they start: Dixit algorizmi ("So said al-Khwarizmi"), or Algoritmi de numero Indorum ("al-Khwarizmi on the Hindu Art of Reckoning"), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly ("The Book of Addition and Subtraction According to the Hindu Calculation")
Al-Khwarizmi's work on arithmetic was responsible for introducing the Arabic numerals, based on the Hindu-Arabic numeral system developed in Indian mathematics, to the Western world. The term "algorithm" is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwarizmi. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwarizmi's name, Algoritmi and Algorismi, respectively.
Astronomy
(Arabic: ??? "astronomical tables of Sind and Hind") is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. The work contains tables for the movements of the sun, the moon and the five planets known at the time. This work marked the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi's work marked the beginning of non-traditional methods of study and calculations.
The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslamah Ibn Ahmad al-Majriti (c. 1000) has survived in a Latin translation, presumably by Adelard of Bath (January 26, 1126). The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Bibliotheca Nacional (Madrid) and the Bodleian Library (Oxford).
Al-Khwarizmi made several important improvements to the theory and construction of sundials, which he inherited from his Indian and Hellenistic predecessors. He made tables for these instruments which considerably shortened the time needed to make specific calculations. His sundial was universal and could be observed from anywhere on the Earth. From then on, sundials were frequently placed on mosques to determine the time of prayer. The shadow square, an instrument used to determine the linear height of an object, in conjunction with the alidade for angular observations, was also invented by al-Khwarizmi in ninth-century Baghdad.
The first quadrants and mural instruments were invented by al-Khwarizmi in ninth century Baghdad. The sine quadrant, invented by al-Khwarizmi, was used for astronomical calculations. The first horary quadrant for specific latitudes, was also invented by al-Khwarizmi in Baghdad, then center of the development of quadrants. It was used to determine time (especially the times of prayer) by observations of the Sun or stars. The Quadrans Vetus was a universal horary quadrant, an ingenious mathematical device invented by al-Khwarizmi in the ninth century and later known as the Quadrans Vetus (Old Quadrant) in medieval Europe from the thirteenth century. It could be used for any latitude on Earth and at any time of the year to determine the time in hours from the altitude of the Sun. This was the second most widely used astronomical instrument during the Middle Ages after the astrolabe. One of its main purposes in the Islamic world was to determine the times of Salah.
Geography
Al-Khwarizmi's third major work is his (Arabic: ???? ???? ????? "Book on the appearance of the Earth" or "The image of the Earth" translated as Geography), which was finished in 833. It is a revised and completed version of Ptolemy's Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction.
There is only one surviving copy of , which is kept at the Strasbourg University Library. A Latin translation is kept at the Biblioteca Nacional de España in Madrid. The complete title translates as Book of the appearance of the Earth, with its cities, mountains, seas, all the islands and rivers, written by Abu Ja'far Muhammad ibn Musa al-Khwarizmi, according to the geographical treatise written by Ptolemy the Claudian.
The book opens with the list of latitudes and longitudes, in order of "weather zones", that is to say in blocks of latitudes and, in each weather zone, by order of longitude. As Paul Gallez points out, this excellent system allows us to deduce many latitudes and longitudes where the only document in our possession is in such a bad condition as to make it practically illegible.
Neither the Arabic copy nor the Latin translation include the map of the world itself, however Hubert Daunicht was able to reconstruct the missing map from the list of coordinates. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. He transferred the points onto graph paper and connected them with straight lines, obtaining an approximation of the coastline as it was on the original map. He then does the same for the rivers and towns.
Al-Khwarizmi corrected Ptolemy's gross overestimate for the length of the Mediterranean Sea (from the Canary Islands to the eastern shores of the Mediterranean); Ptolemy overestimated it at 63 degrees of longitude, while al-Khwarizmi almost correctly estimated it at nearly 50 degrees of longitude. He "also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done." Al-Khwarizmi thus set the Prime Meridian of the Old World at the eastern shore of the Mediterranean, 10–13 degrees to the east of Alexandria (the prime meridian previously set by Ptolemy) and 70 degrees to the west of Baghdad. Most medieval Muslim geographers continued to use al-Khwarizmi's prime meridian.
Jewish calendar
Al-Khwarizmi wrote several other works including a treatise on the Hebrew calendar ( "Extraction of the Jewish Era"). It describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishri shall fall; calculates the interval between the Jewish era (creation of Adam) and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Jewish calendar. Similar material is found in the works of al-Biruni and Maimonides.
Other works
Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwarizmi. The Istanbul manuscript contains a paper on sundials, which is mentioned in the Fihirst. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy.
Two texts deserve special interest on the morning width (Ma?rifat sa?at al-mashriq fi kull balad) and the determination of the azimuth from a height (Ma?rifat al-samt min qibal al-irtifa?).
He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his (an index of Arabic books) also mentions (the book on sundials) and (the book of history) but the two have been lost.The shaping of our mathematics can be attributed to Al-Khwarizmi (c.780-c.850), the chief librarian of the observatory, research center and library called the House of Wisdom in Baghdad. His treatise, "Hisab al-jabr w'al-muqabala" (Calculation by Restoration and Reduction), which covers linear and quadratic equations, solved trade imbalances, inheritance questions and problems arising from land surveyance and allocation. In passing, he also introduced into common usage our present numerical system, which replaced the old, cumbersome Roman one.
See also
His treatise, "Hisab al-jabr w'al-muqabala" (Calculation by Restoration and Reduction), which covers linear and quadratic equations, solved trade imbalances, inheritance questions and problems arising from land surveyance and allocation. In passing, he also introduced into common usage our present numerical system, which replaced the old, cumbersome Roman one.
Further reading
- Barnabas Hughes. Robert of Chester's Latin translation of al-Khwarizmi's al-Jabr: A new critical edition. In Latin. F. Steiner Verlag Wiesbaden (1989). ISBN 3-515-04589-9.**
- Roshdi Rashed, The development of Arabic mathematics: between arithmetic and algebra, London, 1994.*
- Fuat Sezgin. Geschichte des arabischen Schrifttums. 1974, E. J. Brill, Leiden, the Netherlands.
- Sezgin, F., ed., Islamic Mathematics and Astronomy, Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997–9.
- Suter, H. [Ed.]: Die astronomischen Tafeln des Muhammed ibn Mûsâ al-Khwârizmî in der Bearbeitung des Maslama ibn Ahmed al-Madjrîtî und der latein. Übersetzung des Athelhard von Bath auf Grund der Vorarbeiten von A. Bjørnbo und R. Besthorn in Kopenhagen. Hrsg. und komm. Kopenhagen 1914. 288 pp. Repr. 1997 (Islamic Mathematics and Astronomy. 7). ISBN 3-8298-4008-X.
- Van Dalen, B. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time.
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