Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī[1] (Arabic Arabic (العربية al-ʿarabīyah, ( Arabic pronunciation ) or عربي ʿarabi) is a Central Semitic language, thus related to and classified alongside other Semitic languages such as Hebrew and the Neo-Aramaic languages. Arabic has more speakers than any other language in the Semitic language family. It is spoken by more than 280 million: أبو عبد الله محمد بن موسى الخوارزمي) (c. 780, Khwārizm Khwarezm were a series of states centered on the Amu Darya river delta of the former Aral Sea, in Greater Iran , extending across the Ust-Urt plateau and possibly as far west as the eastern shores of the northern Caspian Sea[2][3][4] – c. 850) was a Persian The Persian people are defined by the use of the Persian language as their mother tongue. However, the term Persian has also a supra-ethnic significance and has been historically referred to a part of Iranian peoples. The origin of the Persian people is traced to the ancient Indo-Iranians , who arrived in parts of Greater Iran circa 2000-1500 BCE[5][2][6] mathematician In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics, is the mathematics developed in the Islamic world between 622 and 1600, during what is known as the Islamic Golden Age, in that part of the world where Islam was the dominant religion. Islamic science and mathematics flourished under the Islamic, astronomer In the history of astronomy, Islamic astronomy or Arabic astronomy refers to the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age , and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and geographer Islamic geography includes the advancement of geography, cartography and earth sciences under various Islamic civilizations. During the medieval ages, Islamic geography was driven by a number of factors: the Islamic Golden Age, parallel development of Islamic astronomy, translation of ancient texts into Arabic, increased travel due to commerce and, a scholar Scholarly method or scholarship — is the body of principles and practices used by scholars to make their claims about the world as valid and trustworthy as possible, and to make them known to the scholarly public in the House of Wisdom in Baghdad Baghdad is the capital of Iraq and of Baghdad Governorate, with which it is coterminous. Having a municipal population estimated between 7 and 7.5 million, it is the largest city in Iraq and the second largest city in the Arab World (after Cairo, Egypt).

His Kitab al-Jabr wa-l-Muqabala Al-Kitāb al-mukhtaṣar fī hīsāb al-ğabr wa’l-muqābala , 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 in Arabic, in approximately AD 820 by the Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī presented the first systematic solution of linear A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable and quadratic equations In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is. He is considered the founder of algebra Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure,[7] a credit he shares with Diophantus Diophantus of Alexandria , sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost. In studying Arithmetica, Pierre de Fermat concluded that a certain equation considered by. In the twelfth century, Latin Latin or sometimes Roman is an Italic language originally spoken in Latium and Ancient Rome. Although often considered a dead language, in view of the fact that it has no native, fluent speakers, Latin continues to be taught in schools and has been, and currently is, used in the process of new word production in modern languages from many translations of his work on the Indian numerals Most of the positional base 10 numeral systems in the world have originated from India, where the concept of positional numerology was first developed. The Indian numeral system is commonly referred to in the West as the Hindu-Arabic numeral system or even Arabic numerals, since it reached Europe through the Arabs, introduced the decimal The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations positional number system Positional notation or place-value notation is a generalization of decimal notation to arbitrary base. These include binary and hexadecimal (base 16) notations used by computers as well as the base 60 notation of Babylonian numerals. Indian mathematicians developed the Hindu-Arabic numeral system, the modern decimal positional notation, in the 9th to the Western world The Western world, also known as the West and the Occident , is a term that can have multiple meanings depending on its context (e.g., the time period, the region or social situation). Accordingly, the basic definition of what constitutes "the West" varies, expanding and contracting over time, in relation to various historical.[4] He revised Ptolemy Claudius Ptolemaeus , known in English as Ptolemy (pronounced /ˈtɒləmɪ/), was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer and a poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in's Geography and wrote on astronomy and astrology.

His contributions had a great impact on language. "Algebra" is derived from al-jabr, one of the two operations he used to solve quadratic equations In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is. Algorism Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This system largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude and in some and algorithm In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields stem from Algoritmi, the Latin Latin or sometimes Roman is an Italic language originally spoken in Latium and Ancient Rome. Although often considered a dead language, in view of the fact that it has no native, fluent speakers, Latin continues to be taught in schools and has been, and currently is, used in the process of new word production in modern languages from many form of his name.[8] His name is the origin of (Spanish Countries where Spanish has official status. States of the U.S. where Spanish has no official status but is spoken by 25% or more of the population. States of the U.S. where Spanish has no official status but is spoken by 10-20% of the population. States of the U.S. where Spanish has no official status but is spoken by 5-9.9% of the population) guarismo[9] and of (Portuguese Portuguese ( português or língua portuguesa) is a Romance language that grew from the Latin descended Galician-Potuguese language that was spoken in the mediaeval Kingdom of Galicia; whose territory is now divided between northern Portugal, Galicia and Asturias. It also absorbed influences from the Latin and Arabic languages spoken in the areas) algarismo, both meaning digit A digit is a symbol used in numerals (combinations of symbols, e.g. "37"), to represent numbers, (integers or real numbers) in positional numeral systems. The name "digit" comes from the fact that the 10 digits (ancient Latin digita meaning fingers) of the hands correspond to the 10 symbols of the common base 10 number system,.

Contents

Life

Statue of Khwarizmi in front of the Faculty of Mathematics of Amirkabir University of Technology in Tehran Tehran , is the capital of Iran and Tehran Province. With a population of 18,429,807; it is also Iran's largest urban area and city, one of the largest cities in Western Asia, and is the 20th largest city in the world, Persia Iran (Persian: ایران [ʔiˈɾɒn] ), officially the Islamic Republic of Iran, and formerly known as Persia, is a country in Central Eurasia and Western Asia. The name Iran has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was widely known as Persia. Both Persia and Iran are/Iran Iran (Persian: ایران [ʔiˈɾɒn] ), officially the Islamic Republic of Iran, and formerly known as Persia, is a country in Central Eurasia and Western Asia. The name Iran has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was widely known as Persia. Both Persia and Iran are.

Few details of al-Khwārizmī's life are known with certainty, even his birthplace is unsure. His name may indicate that he came from Khwarezm Khwarezm were a series of states centered on the Amu Darya river delta of the former Aral Sea, in Greater Iran , extending across the Ust-Urt plateau and possibly as far west as the eastern shores of the northern Caspian Sea (Khiva), then in Greater Khorasan Greater Khorasan (also written Khorasaan, Khurasan and Khurasaan) is a modern term for a historical geographic region spanning (in clockwise order) north-eastern and east of Iran, Turkmenistan, Uzbekistan, Tajikistan, western and northern Afghanistan. The name "Khorasan" is said to derive from Middle Persian khor "sun" + ayan &, which occupied the eastern part of the Persian Empire The Achaemenid Empire , also known as the Persian Empire, was the successor state of the Median Empire, ruling over significant portions of what would become Greater Iran. The Persian and the Median Empire taken together are also known as the Medo-Persian Empire, which encompassed the combined territories of several earlier empires, now Xorazm Province in Uzbekistan Uzbekistan, officially the Republic of Uzbekistan is one of the six independent Turkic states. It is a doubly landlocked country in Central Asia, formerly part of the Soviet Union. It shares borders with Kazakhstan to the west and to the north, Kyrgyzstan and Tajikistan to the east, and Afghanistan and Turkmenistan to the south. Abu Rayhan Biruni Abū Rayḥān Muḥammad ibn Aḥmad Bīrūnī , often known as Alberuni, Al Beruni or variants, (born 5 September 973 in Kath, Khwarezm (now in Uzbekistan), died 13 December 1048 in Ghazni, today's Afghanistan) was a Persian scholar and polymath of the 11th century calls the people of Khwarizm "a branch of the Persian The Persian people are defined by the use of the Persian language as their mother tongue. However, the term Persian has also a supra-ethnic significance and has been historically referred to a part of Iranian peoples. The origin of the Persian people is traced to the ancient Indo-Iranians , who arrived in parts of Greater Iran circa 2000-1500 BCE tree".[10]

Al-Tabari Abu Ja'far Muhammad ibn Jarir al-Tabari was one of the earliest, most prominent and famous Persian historian and exegete of the Qur'an,who wrote exclusively in Arabic , most famous for his Tarikh al-Tabari (History of the Prophets and Kings) and Tafsir al-Tabari gave his name as Muhammad ibn Musa al-Khwārizmī al-Majousi al-Katarbali (Arabic: محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epithet An epithet is a descriptive term (word or phrase) accompanying, or occurring in place of, a name, and having entered common usage. It has various shades of meaning when applied to seemingly real or fictitious people, divinities, objects, and binomial nomenclature. It is also a descriptive title al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul)[11], a viticulture Viticulture is the science, production and study of grapes which deals with the series of events that occur in the vineyard. When the grapes are used for winemaking, it is also known as viniculture. It is one branch of the science of horticulture district near Baghdad Baghdad is the capital of Iraq and of Baghdad Governorate, with which it is coterminous. Having a municipal population estimated between 7 and 7.5 million, it is the largest city in Iraq and the second largest city in the Arab World (after Cairo, Egypt). However, Rashed[12] points out that:

There is no need to be an expert on the period or a philologist to see that al-Tabari's second citation should read “Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli,” and that there are two people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic ‘و’ for the article ‘and’] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning the personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made. Recently, G. J. Toomer … with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader.

Regarding al-Khwārizmī's religion, Toomer writes:

Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he was an adherent of the old Zoroastrian religion. This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwārizmī's Algebra shows that he was an orthodox Muslim A Muslim or Moslem is an adherent of the religion of Islam. Literally, the word means "one who submits (to God)". Muslim is the participle of the same verb of which Islam is the infinitive. All Muslims observe Sunnah, but differences in the definition of what is and what is not Sunnah has led to the emergence of sectarian movements.[, so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.[5]

In Ibn al-Nadīm's Kitāb al-Fihrist we find a short biography on al-Khwārizmī, together with a list of the books he wrote. Al-Khwārizmī accomplished most of his work in the period between 813 and 833. After the Islamic conquest of Persia The Muslim conquest of Persia led to the end of the Sassanid Empire in 644, the fall of Sassanid dynasty in 651 and the eventual decline of the Zoroastrian religion in Persia. The Sassanid Empire was first invaded by Arabs in present day Iraq in 633 under general Khalid ibn Walid resulting in the Muslim conquest of Iraq. Following the transfer of, Baghdad became the centre of scientific studies and trade, and many merchants and scientists from as far as China China is seen variously as an ancient civilization extending over a large area in East Asia, a nation and/or a multinational entity and India The history of India begins with evidence of human activity of Homo sapiens as long as 75,000 years ago hominids from about 500,000 years ago. The Indus Valley Civilization, which spread and flourished in the north-western part of the Indian subcontinent from c. 3300 to 1300 BCE, was the first major civilization in India. A sophisticated and traveled to this city, as did Al-Khwārizmī. He worked in Baghdad as a scholar at the House of Wisdom established by Caliph The Caliph is the head of state in a Caliphate, and the title for the leader of the Islamic Ummah, an Islamic community ruled by the Shari'ah. It is a transcribed version of the Arabic word خليفة Khalīfah (help·info) which means "successor" or "representative". The early leaders of the Muslim nation following Muhammad's ( al-Maʾmūn, where he studied the sciences and mathematics, which included the translation of Greek Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical ancient Greek literature and the New Testament of and Sanskrit Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism and Buddhism[note 1]. Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand. Sanskrit has been declared a classical language by the Government of India scientific manuscripts.

Contributions

Al-Khwārizmī's contributions to mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions, geography Geography is the study of the Earth and its lands, features, inhabitants, and phenomena. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes (276-194 B.C.). Four historical traditions in geographical research are the spatial analysis of natural and, astronomy Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation). It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the formation and development of the universe, and cartography Cartography is the study and practice of making maps (also can be called mapping). Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively established the basis for innovation in algebra and trigonometry. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his 830 book on the subject, "The Compendious Book on Calculation by Completion and Balancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabalaالكتاب المختصر في حساب الجبر والمقابلة).

On the Calculation with Hindu Numerals written about 825, was principally responsible for spreading the Indian system of numeration throughout the Middle East and Europe. It was translated into Latin as Algoritmi de numero Indorum. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm".

Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle east. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy but with improved values for the Mediterranean Sea, Asia, and Africa.

He also wrote on mechanical devices like the astrolabe and sundial.

He assisted a project to determine the circumference of the Earth and in making a world map for al-Ma'mun, the caliph, overseeing 70 geographers.[13]

When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. He introduced Arabic numerals into the Latin West, based on a place-value decimal system developed from Indian sources.[14]

Algebra

Main article: The Compendious Book on Calculation by Completion and Balancing A page from al-Khwārizmī's Algebra

Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (Arabic: الكتاب المختصر في حساب الجبر والمقابلة “The Compendious Book on Calculation by Completion and Balancing”) is a mathematical book written approximately 830 CE. The book was written with the encouragement of the Caliph Al-Ma'mun as a popular work on calculation and is replete with examples and applications to a wide range of problems in trade, surveying and legal inheritance[15]. 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.[16]

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,[17] 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.[18]

Al-Khwārizmī'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)

by dividing out the coefficient of the square and using the two operations al-ǧabr (Arabic: الجبر “restoring” or “completion”) and al-muqābala ("balancing"). Al-ǧabr 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-muqābala 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.

The above discussion uses modern mathematical notation for the types of problems which the book discusses. However, in Al-Khwārizmī's day, most of this notation had not yet been invented, so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an 1831 translation)

"If some one say: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts."[15]

In modern notation this process, with 'x' the "thing" (shay') or "root", is given by the steps,

(10 − x)2 = 81x
x2 + 100 = 101x

Let the roots of the equation be 'p' and 'q'. Then , pq = 100 and

So a root is given by

Several authors have also published texts under the name of Kitāb al-ğabr wa-l-muqābala, including Abū Ḥanīfa al-Dīnawarī, Abū Kāmil Shujā ibn Aslam, Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī.

J. J. O'Conner and E. F. Robertson wrote in the MacTutor History of Mathematics archive:

"Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before."[19]

R. Rashed and Angela Armstrong write:

"Al-Khwarizmi's text can be seen to be distinct not only from the Babylonian tablets, but also from Diophantus' Arithmetica. It no longer concerns a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in a generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems."[20]
Page from a Latin translation, beginning with "Dixit algorizmi"

Arithmetic

Al-Khwārizmī'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-Khwārizmī"), or Algoritmi de numero Indorum ("al-Khwārizmī on the Hindu Art of Reckoning"), a name given to the work by Baldassarre Boncompagni in 1857. The original Arabic title was possibly Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind[21] ("The Book of Addition and Subtraction According to the Hindu Calculation")[22]

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

Corpus Christi College MS 283

Al-Khwārizmī's Zīj al-Sindhind[5] (Arabic: زيج "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.[23] 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.[24]

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).[25] 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.[26] 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-Khwārizmī in ninth-century Baghdad.[27]

The first quadrants and mural instruments were invented by al-Khwarizmi in ninth century Baghdad.[28] The sine quadrant, invented by al-Khwārizmī, was used for astronomical calculations.[29] The first horary quadrant for specific latitudes, was also invented by al-Khwārizmī in Baghdad, then center of the development of quadrants.[29] It was used to determine time (especially the times of prayer) by observations of the Sun or stars.[30] 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.[29]

Geography

Hubert Daunicht's reconstruction of al-Khwārizmī's planisphere.

Al-Khwārizmī's third major work is his Kitāb ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض "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.[31]

There is only one surviving copy of Kitāb ṣūrat al-Arḍ, 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-Khwārizmī, 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.[32]

Al-Khwārizmī corrected Ptolemy's gross overestimate for the length of the Mediterranean Sea[33] (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."[34] 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.[33]

Jewish calendar

Al-Khwārizmī wrote several other works including a treatise on the Hebrew calendar (Risāla fi istikhrāj taʾrīkh al-yahūd "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 Tishrī 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-Bīrūnī and Maimonides.[5]

Other works

Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo and Paris contain further material that surely or with some probability comes from al-Khwārizmī. 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 (Maʿrifat saʿat al-mashriq fī kull balad) and the determination of the azimuth from a height (Maʿrifat al-samt min qibal al-irtifāʿ).

He also wrote two books on using and constructing astrolabes. Ibn al-Nadim in his Kitab al-Fihrist (an index of Arabic books) also mentions Kitāb ar-Ruḵāma(t) (the book on sundials) and Kitab al-Tarikh (the book of history) but the two have been lost.

The shaping of our mathematics can be attributed to Al-Khwarizmi, 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

Wikiquote has a collection of quotations related to: al-Khwārizmī
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Notes

  1. ^ There is some confusion in the literature on whether al-Khwārizmī's full name is Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī or Abū Jaʿfar Muḥammad ibn Mūsā al-Khwārizmī. Ibn Khaldun notes in his encyclopedic work: "The first who wrote upon this branch (algebra) was Abu ʿAbdallah al-Khowarizmi, after whom came Abu Kamil Shojaʿ ibn Aslam." (MacGuckin de Slane). (Rosen 1831, pp. xi–xiii) mentions that "[Abu Abdallah Mohammed ben Musa] lived and wrote under the caliphat of Al Mamun, and must therefore be distinguished from Abu Jafar Mohammed ben Musa, likewise a mathematician and astronomer, who flourished under the Caliph Al Motaded (who reigned A.H. 279-289, A.D. 892-902)." Karpinski notes in his review on (Ruska 1917) that in (Ruska 1918): "Ruska here inadvertently speaks of the author as Abū Gaʿfar M. b. M., instead of Abū Abdallah M. b. M."
  2. ^ a b Hogendijk, Jan P. (1998). "al-Khwarzimi". Pythagoras 38 (2): 4–5. ISSN 0033–4766. http://www.kennislink.nl/web/show?id=116543.
  3. ^ Berggren 1986
  4. ^ a b Struik 1987, p. 93
  5. ^ a b c d Toomer 1990
  6. ^ Oaks, Jeffrey A.. "Was al-Khwarizmi an applied algebraist?". University of Indianapolis. http://facstaff.uindy.edu/~oaks/MHMC.htm. Retrieved 2008-05-30.
  7. ^ Gandz 1936
  8. ^ Daffa 1977
  9. ^ Knuth, Donald (1979). Algorithms in Modern Mathematics and Computer Science. Springer-Verlag. ISBN 0-387-11157-3. http://historical.ncstrl.org/litesite-data/stan/CS-TR-80-786.pdf.
  10. ^ Abu Rahyan Biruni, "Athar al-Baqqiya 'an al-Qurun al-Xaliyyah"(Vestiges of the past: the chronology of ancient nations), Tehran, Miras-e-Maktub, 2001. Original Arabic of the quote: "و أما أهل خوارزم، و إن کانوا غصنا ً من دوحة الفُرس" (pg. 56)
  11. ^ "Iraq After the Muslim Conquest", by Michael G. Morony, ISBN 1593333153 (a 2005 facsimile from the original 1984 book), p. 145
  12. ^ Rashed, Roshdi (1988), "al-Khwārizmī's Concept of Algebra", in Zurayq, Qusṭanṭīn; Atiyeh, George Nicholas; Oweiss, Ibrahim M., Arab Civilization: Challenges and Responses : Studies in Honor of Constantine K. Zurayk, SUNY Press, p. 108, ISBN 0887066984, http://books.google.com/books?id=JXbXRKRY_uAC&pg=PA108&dq=Qutrubbulli#PPA108,M1
  13. ^ "al-Khwarizmi". Encyclopædia Britannica. http://www.britannica.com/eb/article-9045366. Retrieved 2008-05-30.
  14. ^ "Khwarizmi, Abu Jafar Muhammad ibn Musa al-" in Oxford Islamic Studies Online
  15. ^ a b Rosen, Frederic. The Compendious Book on Calculation by Completion and Balancing "The Compendious Book on Calculation by Completion and Balancing, Al-Khwārizmī". 1831 English Translation. http://www.wilbourhall.org/index.html#algebra The Compendious Book on Calculation by Completion and Balancing. Retrieved 2009-09-14.
  16. ^ Karpinski, L. C. (1912). "History of Mathematics in the Recent Edition of the Encyclopædia Britannica". American Association for the Advancement of Science.
  17. ^ Boyer, Carl B. (1991). "The Arabic Hegemony". A History of Mathematics (Second Edition ed.). John Wiley & Sons, Inc.. pp. 228. ISBN 0471543977.
    "The Arabs in general loved a good clear argument from premise to conclusion, as well as systematic organization — respects in which neither Diophantus nor the Hindus excelled."
  18. ^ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" — that is, the cancellation of like terms on opposite sides of the equation."
  19. ^ O'Connor, John J.; Robertson, Edmund F., "Muhammad ibn Mūsā al-Khwārizmī", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Khwarizmi.html .
  20. ^ Rashed, R.; Armstrong, Angela (1994), The Development of Arabic Mathematics, Springer, pp. 11–2, ISBN 0792325656, OCLC 29181926
  21. ^ Ruska
  22. ^ Berggren 1986, p. 7
  23. ^ Kennedy 1956, pp. 26–9
  24. ^ (Dallal 1999, p. 163)
  25. ^ Neugebauer
  26. ^ (King 1999a, pp. 168-9)
  27. ^ David A. King (2002), "A Vetustissimus Arabic Text on the Quadrans Vetus", Journal for the History of Astronomy 33: 237-255 [238-9]
  28. ^ David A. King, "Islamic Astronomy", in Christopher Walker (1999), ed., Astronomy before the telescope, p. 167-168. British Museum Press. ISBN 0-7141-2733-7.
  29. ^ a b c (King 2002, pp. 237-238)
  30. ^ (King 1999a, pp. 167-8)
  31. ^ "The history of cartography". GAP computer algebra system. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Cartography.html. Retrieved 2008-05-30.
  32. ^ Daunicht
  33. ^ a b Edward S. Kennedy, Mathematical Geography, p. 188, in (Rashed & Morelon 1996, pp. 185–201)
  34. ^ Covington, Richard (2007), Saudi Aramco World, May–June 2007: 17–21, http://www.saudiaramcoworld.com/issue/200703/the.third.dimension.htm, retrieved 2008-07-06

Further reading

Biographical
Algebra
Arithmetic
Astronomy
Jewish calendar
Geography

General references

For a more extensive bibliography see: History of mathematics, Mathematics in medieval Islam, and Astronomy in medieval Islam.
Mathematics in medieval Islam
Mathematicians 'Abd al-Hamīd ibn Turk · Abd al-Rahman al-Sufi · Abū al-Hasan ibn Alī al-Qalasādī · Abū al-Wafā' al-Būzjānī · Abū Ishāq Ibrāhīm al-Zarqālī · Abū Ja'far al-Khāzin · Abū Kāmil Shujā ibn Aslam · Abu'l-Hasan al-Uqlidisi · Abu-Mahmud al-Khujandi · Abu Nasr Mansur · Abū Rayhān al-Bīrūnī · Abū Sahl al-Qūhī · Ahmed ibn Yusuf · Al-Abbās ibn Said al-Jawharī · Al-Birjandi · Al-Hajjāj ibn Yūsuf ibn Matar · Al-Jayyani · Al-Karaji · Al-Khazini · Al-Kindi · Al-Mahani · Al-Nayrizi · Al-Saghani · Al-Sijzi · Al-Umawi · Alī ibn Ahmad al-Nasawī · Ali Kuşçu · Avicenna · Banū Mūsā · Brethren of Purity · Hunayn ibn Ishaq · Ibn al-Banna al-Marrakushi · Ibn al-Haytham · Ibn al-Shatir · Ibn Sahl · Ibn Tahir al-Baghdadi · Ibn Yahyā al-Maghribī al-Samaw'al · Ibn Yunus · Ibrahim ibn Sinan · Jamshīd al-Kāshī · Kamāl al-Dīn al-Fārisī · Kushyar ibn Labban · Muhammad Baqir Yazdi · Muhammad ibn Jābir al-Harrānī al-Battānī · Muhammad ibn Mūsā al-Khwārizmī · Muhyi al-Dīn al-Maghribī · Nasīr al-Dīn al-Tūsī · Omar Khayyám · Qāḍī Zāda al-Rūmī · Al-Khalili · Shams al-Dīn al-Samarqandī · Sharaf al-Dīn al-Tūsī · Sinan ibn Thabit · Taqi al-Din · Thābit ibn Qurra · Ulugh Beg · Yusuf al-Mu'taman ibn Hud
Treatises Almanac · Book of Fixed Stars · Book of Optics · De Gradibus · Encyclopedia of the Brethren of Purity · Tables of Toledo · Tabula Rogeriana · The Compendious Book on Calculation by Completion and Balancing · The Book of Healing · Zij · Zij-i Ilkhani · Zij-i-Sultani
Centers Al-Azhar University · Al-Mustansiriya University · House of Knowledge · House of Wisdom · Istanbul observatory of Taqi al-Din · Madrasah · Maktab · Maragheh observatory · University of Al-Karaouine
Influences Babylonian mathematics · Greek mathematics · Indian mathematics
Influenced Byzantine mathematics · European mathematics · Indian mathematics
Astronomy in medieval Islam
Astronomers Abd al-Rahman al-Sufi · Abū al-Wafā' al-Būzjānī · Abū Ishāq Ibrāhīm al-Zarqālī · Abū Ja'far al-Khāzin · Abu-Mahmud al-Khujandi · Abu Nasr Mansur · Abū Rayhān al-Bīrūnī · Abū Sahl al-Qūhī · Ahmed ibn Yusuf · Al-Birjandi · Al-Ghazali · Al-Hajjāj ibn Yūsuf ibn Matar · Al-Khazini · Al-Kindi · Al-Mahani · Al-Nayrizi · Al-Saghani · Al-Sijzi · Ali Kuşçu · Avicenna · Banū Mūsā · Brethren of Purity · Ibn al-Banna al-Marrakushi · Ibn al-Haytham · Ibn al-Shatir · Ibn Yahyā al-Maghribī al-Samaw'al · Ibn Yunus · Ibrahim ibn Sinan · Ja'far al-Sadiq · Jamshīd al-Kāshī · Kamāl al-Dīn al-Fārisī · Kushyar ibn Labban · Muhammad ibn Jābir al-Harrānī al-Battānī · Muhammad ibn Mūsā al-Khwārizmī · Muhyi al-Dīn al-Maghribī · Nasīr al-Dīn al-Tūsī · Omar Khayyám · Qāḍī Zāda al-Rūmī · Shams al-Dīn Abū Abd Allāh al-Khalīlī · Shams al-Dīn al-Samarqandī · Sharaf al-Dīn al-Tūsī · Sinan ibn Thabit · Taqi al-Din · Thābit ibn Qurra · Ulugh Beg · Zakariya al-Qazwini
Works 'Aja'ib al-makhluqat wa-ghara'ib al-mawjudat · Almanac · Arabic star names · Book of Optics · Encyclopedia of the Brethren of Purity · Star chart · Tabula Rogeriana · The Book of Healing · Zij (Astronomical catalog · Book of Fixed Stars · Star catalogue · Tables of Toledo · Trigonometry table · Zij-i Ilkhani · Zij-i-Sultani)
Instruments Alidade · Analog computer · Aperture · Armillary sphere · Astrolabe · Astronomical clock · Celestial globe · Compass · Compass dial · Compass rose · Dioptra · Equatorial ring · Equitorium · Globe · Graph paper · Magnifying glass · Mural instrument · Navigational astrolabe · Nebula · Planisphere · Quadrant · Sextant · Shadow square · Spherical astrolabe · Sundial · Telescope · Triquetrum
Concepts Almucantar · Apogee · Astrophysics · Azimuth · Celestial mechanics · Celestial spheres · Circular orbit · Deferent and epicycle · Earth's rotation · Eccentricity · Ecliptic · Elliptic orbit · Equant · Galaxy · Geocentrism · Gravitational potential energy · Gravity · Heliocentrism · Inertia · Islamic astrology · Moonlight · Obliquity · Parallax · Precession · Qibla · Specific gravity · Spherical Earth · Starlight · Sublunary sphere · Sunlight · Supernova · Temporal finitism · Trepidation · Triangulation · Tusi-couple
Centers Al-Azhar University · House of Knowledge · House of Wisdom · Istanbul observatory of Taqi al-Din · Madrasah · Maragheh observatory · Observatory · Research institute · Samarkand Observatory · Umayyad Mosque · University of Al-Karaouine
Influences

Babylonian astronomy · Hellenistic astronomy · Indian astronomy
Influenced Byzantine astronomy · Chinese astronomy · European astronomy · Indian astronomy

Categories: 8th-century births | 9th-century deaths | Islamic astrology | Persian astrologers | Islamic astronomy | Persian astronomers | Medieval astronomers | Islamic geography | Persian geographers | Islamic mathematics | Persian mathematicians

 

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