Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Khwarazmi, Abu Ja‘far Muhammad ibn Musa al- (Abu Ja‘far Muhammad ibn Musa al-Khwarazmi) (Muhammad ibn Musa al-Khwarizmi) (Abu Abdullah Muhammad ibn Musa al-Khwarizmi) (Algorizm) (c,770-c.840). Mathematician, astronomer and geographer. His name still lies in the term algorithm. His Algebra (in Arabic, al-jabr) was translated partially by Robert of Chester as Liber algebras et almucabola, and shortly afterwards by Gerard of Cremona as De jebra et almucabola. In this way, there was introduced into Europe a science completely unknown until then. Almost at the same time an adaptation of his Arithmetic using Hindu-Arabic numerals, which today are “Arabic numerals,” was made known in Spain in a Latin version by John of Seville.
Al-Khwarazmi was born in Khwarizm (Kheva), a town south of the Oxus River in present day Uzbekistan. His parents migrated to a place south of Baghdad when he was a child. The exact date of his birth is not known. It has been established from his contributions that he flourished under Khalifah (Caliph) al-Mamun who reigned from 813 to 833 at Baghdad. Al-Khwarizmi is best known for introducing the mathematical concept algorithm, which is named after him.
Al-Khwarizmi was one of the greatest mathematicians that ever lived. He was the founder of several branches and basic concepts of mathematics. He is also famous as an astronomer and geographer. Al-Khwarizmi influenced mathematical thought to a greater extent than any other medieval writer. He is recognized as the founder of algebra, as he not only initiated the subject in a systematic form but also developed it to the extent of giving analytical solutions of linear and quadratic equations. The name algebra is derived from al-Khwarizmi’s famous book Al-Jabr wa-al-Muqabilah. Al-Khwarizmi developed in detail trigonometric tables containing the sine functions, which were later extrapolated to tangent functions. Al-Khwarizmi also developed the calculus of two errors, which led him to the concept of differentiation. He also refined the geometric representation of conic sections.
The influence of al-Khwarizmi on the growth of mathematics, astronomy and geography is well established in history. His approach was systematic and logical, and not only did he bring together the then prevailing knowledge on various branches of science but also enriched it through his original contributions. He synthesized Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. He adopted the use of zero, a numeral of fundamental importance, leading up to the so-called arithmetic of positions and the decimal system. His pioneering work on the system of numerals is well known as Algorithm, or Algorizm. In addition to introducing the Arabic numerals, he developed several arithmetical procedures, including operations on fractions.
In addition to an important treatise on astronomy, al-Khwarizmi wrote a book on astronomical tables. Several of his books were translated into Latin in the early twelfth century by Adelard of Bath and Gerard of Cremona. The treatise on arithmetic (Kitab al-Jam‘a wal-Tafreeq bil Hisab al-Hindi, and the one on algebra (al-Maqala fi Hisab al-Jabr wa-al-Muqabilah), are known only from Latin translations. It was this later translation which introduced the new mathematics to Europe -- to the West. Until this translation was made, the new math was unknown to Europeans. Al-Khwarizmi’s Al-Jabr wa-al-Muqabilah was used until the sixteenth century as the principal mathematical text book of European universities. His astronomical tables were also translated into European languages and, later, into Chinese.
The contribution of al-Khwarizmi to geography is also outstanding. He not only revised Ptolemy’s views on geography, but also corrected them in detail. Seventy geographers worked under Khwarizimi’s leadership and they produced the first map of the then known world in 830. He is also reported to have collaborated in the degree measurements ordered by khalifah (Caliph) Mamun al-Rashid that were aimed at measuring the volume and circumference of the earth. His geography book entitled Kitab Surat-al-Ard, including maps, was also translated. His other contributions include original work related to clocks, sundials and astrolabes. He also wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials). Muhammad ibn Musa al-Khwarizmi died around 840.
Very little is known of the life of Muhammad ibn Musa al-Khwarizmi. The name al-Khwarismi means literally “the man from Khwarizm;” the epithet may also, however, be interpreted to indicate the origin of one’s “stock.” The historian al-Tabari asserts that al-Khwarizmi actually came from Qutrubull, a district not far from Baghdad, between the Tigris and Euphrates rivers. Some sources even give his place of birth as Baghdad. Historians do agree that he lived in Baghdad in the early ninth century under the caliphates of al-Ma’mun and al-Mu‘tasim, whose reigns spanned the years from 813 to 842.
In Kitab al-Fihrist (Book of Chronicles -- c. 987), Ibn Abi Yaqub al-Nadim’s entry on al-Khwarizmi reads: al-Khwarizmi. His name was Muhammad ibn Musa and his family origin was from Khwarazm. He was temporarily associated with the Treasury of the “House of Wisdom” of al-Ma’mun. He was one of the leading scholars in astronomy. People both before and after the observations [conducted under al-Ma’mun] used to rely on his first and second zijes [astronomical tables] which were both known by the name Sindhind. His books are (as follows): (1) the Zij, in two [editions], the first and second; (2) the book on sundials; (3) the book on the use of the astrolabe; (4) the book on the construction of the astrolabe; and (5) the [chronicle].
Al-Nadim’s list is, however, incomplete. He mentions only the astronomical studies and omits an algebra, an arithmetic, a study of the quadrivium, and an adaptation of Ptolemy’s geography. Al-Khwarizmi was apparently well-known in Baghdad for his scholarly works on astronomy and mathematics. His inheritance tables on the distribution of money were widely used.
Al-Khwarizmi is credited by early Arab scholars Ibn Khaldun (1332-1406) and Katib Celebi (1609-1657) with being the first mathematician to write about algebra. The word “algebra” comes from the second word of the title, Kitab al-jabr wa al-muquabalah. It is his best known work. Literally, the title means “the book of integration and equation.” It contained rules for arithmetical solutions of linear and quadratic equations, for elementary geometry, and for inheritance problems concerning the distribution of wealth according to proportions. The algebra was based on a long tradition originating in Babylonian mathematics of the early second millennium B.C.T. When it was first translated into Latin in the twelfth century, the rules for the distribution of wealth, which had been so popular in the Near East, were omitted. Translated into English from a Latin version in 1915 by Louis Charles Karpinski, the book opens with a pious exhortation which reveals al-Khwarizmi’s belief in an ordered universe. In the same introduction, al-Khwarizmi describes three kinds of numbers, “roots, squares, and numbers.”
The first six chapters of al-Khwarizmi’s algebra deal with the following mathematical relationships: “Concerning roots equal to roots,” “Concerning squares equal to numbers,” “Concerning roots equal to numbers,” “Concerning squares and roots equal to numbers,” “Concerning squares and numbers equal to roots,” and “Concerning roots and numbers equal to a square.” These chapters are followed by illustrative geometrical demonstrations and then many problems with their solutions.Some of his problems are purely formal, whereas others appear in practical contexts. An interesting chapter on mercantile transactions asserts that “mercantile transactions and all things pertaining thereto involve two ideas and four numbers.”
For Muslims, al-Khwarizmis astronomical works are perhaps even more important than his algebra. His astronomical tables were used for accurate timekeeping. In Islam, the times of the five daily prayers are determined by the apparent position of the sun in the sky and vary naturally throughout the year. In al-Khwarizmi’s work on the construction and use of the astrolabe, the times of midday and afternoon prayers are determined by measuring shadow lengths. These timekeeping techniques were widely used for centuries.
Al-Khwarizmi also created tables to compute the local direction of Mecca. This is fundamental to Muslims because it is the direction in which they face when they pray, bury their dead, and perform various ritual acts. It is no wonder that in Islamic texts, al-Khwarizmi is referred to as “the astronomer.”
Al-Khwarizmi’s book on arithmetic has been preserved in only one version. Translated into Latin and published in Rome in 1857 by Prince Baldassare Boncompagni, al-Khwarizmi’s Algoritmi de numero indorum appears as part 1 of a volume entitled Tratti d’aritmetica. The title means “al-Khwarizmi concerning the Hindu art of numbering.” This is the derivation of the word “algorithm.” The arithmetic introduced Arabic numerals and the art of calculating by decimal notation. The only copy of this work is in the Cambridge University library.
Al-Khwarizmi’s study of the quadrivium -- the medieval curriculum of arithmetic, music, astronomy, and geometry -- is entitled Liber y sagogarum Alchorismi in artem astronomican a magistro A. compositus (1126). It was the first of al-Khwarizmi’s writings to appear in Europe. The identity of the writer “A” is not certain, but he is assumed to be the scholar Adelard of Bath, who is known as the translator of al-Khwarizmi’s tables. These trigonometric tables were among the first of the Arabic studies in mathematics to appear in Europe.
Al-Khwarizmi enjoyed an excellent reputation among his fellow Arab scholars. Some of his numerical examples were repeated for centuries, becoming so standardized that many subsequent mathematicians did not consider it necessary to acknowledge al-Khwarizmi as the source.
The geography Kitab surat al-ard (Book of the Form of the Earth) differs in several respects from Ptolemy’s geography. Like Ptolemy’s, it is a description of a world map and contains a list of the coordinates of the principal places on it, but al-Khwarizmi’s arrangement is radically different, and it is clear that the map to which it refers is not the same as the map which Ptolemy described. It is supposed that al-Khwarizmi’s world map was the one constructed for al-Ma’mun. This map was an improvement over Ptolemy’s, correcting distortions in the supposed length of the Mediterranean. It was far more accurate, too, in its description of the areas under Islamic rule. Because it contained errors of its own, however, the geography written by al-Khwarizmi failed to replace the Ptolemaic geography used in Europe.
Al-Khwarizmi’s importance in the history of mathematics is not debatable. Two notable arithmetic books, Alexander de Villa Dei’s Carmen de Algorismo (twelfth century) and Johannes de Sacrobosco’s Algorismus vulgaris (thirteenth century), owe much to al-Khwarizmi’s arithmetic and were widely used for several hundred years. In the ninth century, Abu Kamil drew on al-Khwarizmi’s works for his own writings on algebra. In turn, Leonardo of Pisa, a thirteenth century scholar, was influenced by Abu Kamil. Numerous commentaries on Abu Kamil’s work kept al-Khwarizmi’s influence alive in the Middle Ages and throughout the Renaissance.
Abu Ja'far Muhammad ibn Musa al-Khwarazmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Muhammad ibn Musa al-Kharizmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Kharizmi, Muhammad ibn Musa al- see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Abu Abdullah Muhammad ibn Musa al-Khwarizmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Khwarizmi, Abu Abdullah Muhammad ibn Musa see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Algorizm see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Al-Khwarazmi was born in Khwarizm (Kheva), a town south of the Oxus River in present day Uzbekistan. His parents migrated to a place south of Baghdad when he was a child. The exact date of his birth is not known. It has been established from his contributions that he flourished under Khalifah (Caliph) al-Mamun who reigned from 813 to 833 at Baghdad. Al-Khwarizmi is best known for introducing the mathematical concept algorithm, which is named after him.
Al-Khwarizmi was one of the greatest mathematicians that ever lived. He was the founder of several branches and basic concepts of mathematics. He is also famous as an astronomer and geographer. Al-Khwarizmi influenced mathematical thought to a greater extent than any other medieval writer. He is recognized as the founder of algebra, as he not only initiated the subject in a systematic form but also developed it to the extent of giving analytical solutions of linear and quadratic equations. The name algebra is derived from al-Khwarizmi’s famous book Al-Jabr wa-al-Muqabilah. Al-Khwarizmi developed in detail trigonometric tables containing the sine functions, which were later extrapolated to tangent functions. Al-Khwarizmi also developed the calculus of two errors, which led him to the concept of differentiation. He also refined the geometric representation of conic sections.
The influence of al-Khwarizmi on the growth of mathematics, astronomy and geography is well established in history. His approach was systematic and logical, and not only did he bring together the then prevailing knowledge on various branches of science but also enriched it through his original contributions. He synthesized Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. He adopted the use of zero, a numeral of fundamental importance, leading up to the so-called arithmetic of positions and the decimal system. His pioneering work on the system of numerals is well known as Algorithm, or Algorizm. In addition to introducing the Arabic numerals, he developed several arithmetical procedures, including operations on fractions.
In addition to an important treatise on astronomy, al-Khwarizmi wrote a book on astronomical tables. Several of his books were translated into Latin in the early twelfth century by Adelard of Bath and Gerard of Cremona. The treatise on arithmetic (Kitab al-Jam‘a wal-Tafreeq bil Hisab al-Hindi, and the one on algebra (al-Maqala fi Hisab al-Jabr wa-al-Muqabilah), are known only from Latin translations. It was this later translation which introduced the new mathematics to Europe -- to the West. Until this translation was made, the new math was unknown to Europeans. Al-Khwarizmi’s Al-Jabr wa-al-Muqabilah was used until the sixteenth century as the principal mathematical text book of European universities. His astronomical tables were also translated into European languages and, later, into Chinese.
The contribution of al-Khwarizmi to geography is also outstanding. He not only revised Ptolemy’s views on geography, but also corrected them in detail. Seventy geographers worked under Khwarizimi’s leadership and they produced the first map of the then known world in 830. He is also reported to have collaborated in the degree measurements ordered by khalifah (Caliph) Mamun al-Rashid that were aimed at measuring the volume and circumference of the earth. His geography book entitled Kitab Surat-al-Ard, including maps, was also translated. His other contributions include original work related to clocks, sundials and astrolabes. He also wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials). Muhammad ibn Musa al-Khwarizmi died around 840.
Very little is known of the life of Muhammad ibn Musa al-Khwarizmi. The name al-Khwarismi means literally “the man from Khwarizm;” the epithet may also, however, be interpreted to indicate the origin of one’s “stock.” The historian al-Tabari asserts that al-Khwarizmi actually came from Qutrubull, a district not far from Baghdad, between the Tigris and Euphrates rivers. Some sources even give his place of birth as Baghdad. Historians do agree that he lived in Baghdad in the early ninth century under the caliphates of al-Ma’mun and al-Mu‘tasim, whose reigns spanned the years from 813 to 842.
In Kitab al-Fihrist (Book of Chronicles -- c. 987), Ibn Abi Yaqub al-Nadim’s entry on al-Khwarizmi reads: al-Khwarizmi. His name was Muhammad ibn Musa and his family origin was from Khwarazm. He was temporarily associated with the Treasury of the “House of Wisdom” of al-Ma’mun. He was one of the leading scholars in astronomy. People both before and after the observations [conducted under al-Ma’mun] used to rely on his first and second zijes [astronomical tables] which were both known by the name Sindhind. His books are (as follows): (1) the Zij, in two [editions], the first and second; (2) the book on sundials; (3) the book on the use of the astrolabe; (4) the book on the construction of the astrolabe; and (5) the [chronicle].
Al-Nadim’s list is, however, incomplete. He mentions only the astronomical studies and omits an algebra, an arithmetic, a study of the quadrivium, and an adaptation of Ptolemy’s geography. Al-Khwarizmi was apparently well-known in Baghdad for his scholarly works on astronomy and mathematics. His inheritance tables on the distribution of money were widely used.
Al-Khwarizmi is credited by early Arab scholars Ibn Khaldun (1332-1406) and Katib Celebi (1609-1657) with being the first mathematician to write about algebra. The word “algebra” comes from the second word of the title, Kitab al-jabr wa al-muquabalah. It is his best known work. Literally, the title means “the book of integration and equation.” It contained rules for arithmetical solutions of linear and quadratic equations, for elementary geometry, and for inheritance problems concerning the distribution of wealth according to proportions. The algebra was based on a long tradition originating in Babylonian mathematics of the early second millennium B.C.T. When it was first translated into Latin in the twelfth century, the rules for the distribution of wealth, which had been so popular in the Near East, were omitted. Translated into English from a Latin version in 1915 by Louis Charles Karpinski, the book opens with a pious exhortation which reveals al-Khwarizmi’s belief in an ordered universe. In the same introduction, al-Khwarizmi describes three kinds of numbers, “roots, squares, and numbers.”
The first six chapters of al-Khwarizmi’s algebra deal with the following mathematical relationships: “Concerning roots equal to roots,” “Concerning squares equal to numbers,” “Concerning roots equal to numbers,” “Concerning squares and roots equal to numbers,” “Concerning squares and numbers equal to roots,” and “Concerning roots and numbers equal to a square.” These chapters are followed by illustrative geometrical demonstrations and then many problems with their solutions.Some of his problems are purely formal, whereas others appear in practical contexts. An interesting chapter on mercantile transactions asserts that “mercantile transactions and all things pertaining thereto involve two ideas and four numbers.”
For Muslims, al-Khwarizmis astronomical works are perhaps even more important than his algebra. His astronomical tables were used for accurate timekeeping. In Islam, the times of the five daily prayers are determined by the apparent position of the sun in the sky and vary naturally throughout the year. In al-Khwarizmi’s work on the construction and use of the astrolabe, the times of midday and afternoon prayers are determined by measuring shadow lengths. These timekeeping techniques were widely used for centuries.
Al-Khwarizmi also created tables to compute the local direction of Mecca. This is fundamental to Muslims because it is the direction in which they face when they pray, bury their dead, and perform various ritual acts. It is no wonder that in Islamic texts, al-Khwarizmi is referred to as “the astronomer.”
Al-Khwarizmi’s book on arithmetic has been preserved in only one version. Translated into Latin and published in Rome in 1857 by Prince Baldassare Boncompagni, al-Khwarizmi’s Algoritmi de numero indorum appears as part 1 of a volume entitled Tratti d’aritmetica. The title means “al-Khwarizmi concerning the Hindu art of numbering.” This is the derivation of the word “algorithm.” The arithmetic introduced Arabic numerals and the art of calculating by decimal notation. The only copy of this work is in the Cambridge University library.
Al-Khwarizmi’s study of the quadrivium -- the medieval curriculum of arithmetic, music, astronomy, and geometry -- is entitled Liber y sagogarum Alchorismi in artem astronomican a magistro A. compositus (1126). It was the first of al-Khwarizmi’s writings to appear in Europe. The identity of the writer “A” is not certain, but he is assumed to be the scholar Adelard of Bath, who is known as the translator of al-Khwarizmi’s tables. These trigonometric tables were among the first of the Arabic studies in mathematics to appear in Europe.
Al-Khwarizmi enjoyed an excellent reputation among his fellow Arab scholars. Some of his numerical examples were repeated for centuries, becoming so standardized that many subsequent mathematicians did not consider it necessary to acknowledge al-Khwarizmi as the source.
The geography Kitab surat al-ard (Book of the Form of the Earth) differs in several respects from Ptolemy’s geography. Like Ptolemy’s, it is a description of a world map and contains a list of the coordinates of the principal places on it, but al-Khwarizmi’s arrangement is radically different, and it is clear that the map to which it refers is not the same as the map which Ptolemy described. It is supposed that al-Khwarizmi’s world map was the one constructed for al-Ma’mun. This map was an improvement over Ptolemy’s, correcting distortions in the supposed length of the Mediterranean. It was far more accurate, too, in its description of the areas under Islamic rule. Because it contained errors of its own, however, the geography written by al-Khwarizmi failed to replace the Ptolemaic geography used in Europe.
Al-Khwarizmi’s importance in the history of mathematics is not debatable. Two notable arithmetic books, Alexander de Villa Dei’s Carmen de Algorismo (twelfth century) and Johannes de Sacrobosco’s Algorismus vulgaris (thirteenth century), owe much to al-Khwarizmi’s arithmetic and were widely used for several hundred years. In the ninth century, Abu Kamil drew on al-Khwarizmi’s works for his own writings on algebra. In turn, Leonardo of Pisa, a thirteenth century scholar, was influenced by Abu Kamil. Numerous commentaries on Abu Kamil’s work kept al-Khwarizmi’s influence alive in the Middle Ages and throughout the Renaissance.
Abu Ja'far Muhammad ibn Musa al-Khwarazmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Muhammad ibn Musa al-Kharizmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Kharizmi, Muhammad ibn Musa al- see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Abu Abdullah Muhammad ibn Musa al-Khwarizmi see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Khwarizmi, Abu Abdullah Muhammad ibn Musa see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
Algorizm see Khwarazmi, Abu Ja‘far Muhammad ibn Musa al-
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