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Muhammad Ibn Mūsā al-Khuwārizmī (arabe: محمد بن موسى الخوارزمي), généralement appelé Al-Khwârismî (latinisé en Algoritmi ou Algorizmi ), né dans les années 780, probablement à Khiva dans la région du Khwarezm (d'où il prend son nom), dans l'actuel Ouzbékistan , mort vers 850 à Bagdad, est un mathématicien, géographe, astrologue et astronome persan , membre de la Maison de la sagesse de Bagdad. [35], Al-Khwārizmī produced accurate sine and cosine tables, and the first table of tangents. Archive for History of Exact Sciences, 63(2), 169–203. = He then does the same for the rivers and towns. 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. There is very little information about his early life, but it is clear that he was one of the brilliant students in Baghdad, Iraq. Get an answer to your question “Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi?Check all that apply. It will then be a hundred plus a square, which is equal to a hundred and one roots. algebra decimal fraction perfect ...” in Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions. Voyage en Mathématique - Ahmed Djebbar - Professeur émérite d'histoire des mathématiques à l'université des sciences et technologies de Lille. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, "The Compendious Book on Calculation by Completion and Balancing". A picture is worth a thousand words. example, for one problem he writes, (from an 1831 translation), If some one says: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." He was born into a Persian family[6] and Ibn al-Nadim gives his birthplace as Khwarezm in Central Asia. ", CS1 maint: multiple names: authors list (. For example, x2 + 14 = x + 5 is reduced to x2 + 9 = x. L., V.D. 1 0. help4u. 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A history of algebra: from al – Khwarizmi to emmy noether. He completed most of his works in the period between 813 and 833, and died around 850. Recently, G.J. q 2 The book was written with the encouragement of 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. Al-Khwārizmī's Zīj al-Sindhind[47] (Arabic: زيج السند هند‎, "astronomical tables of Siddhanta"[48]) 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. Enciclopedia Universal. En plus d'innovations en trigonométrie (avec l'usage du sinus) ou dans la résolution d'équations du second degré. 1 0. Al-Khwārizmī accomplished most of his work between 813 and 833. Most medieval Muslim gazetteers continued to use al-Khwārizmī's prime meridian. Mohammed ibn Musa Alchwarizmi's Algorismus; das früheste Lehrbuch zum Rechnen mit indischen Ziffern. Daunicht read the latitudes and longitudes of the coastal points in the manuscript, or deduces them from the context where they were not legible. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, c. 813–833 CE[8]:171) presented the first systematic solution of linear and quadratic equations. 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. Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle East. 1 0. Should Turkey stop importing them? Cu timpul, lucrările lui al-Khwarizmi au fost traduse în latină. Several authors have also published texts under the name of Kitāb al-jabr wal-muqābala, including Abū Ḥanīfa Dīnawarī, Abū Kāmil Shujāʿ ibn Aslam, Abū Muḥammad al-‘Adlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk, Sind ibn ‘Alī, Sahl ibn Bišr, and Sharaf al-Dīn al-Ṭūsī. Al-Khwarizmi was also known as Abu Ja'far Muhammad ibn Musa al-Khwarizmi. and. [30], 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. The Latinized version of his name gave us the term "algorithm," and the title of his most famous and important work gave us the word "algebra." [17] The Compendious Book on Calculation by Completion and Balancing, translated into Latin by Robert of Chester in 1145, was used until the sixteenth century as the principal mathematical text-book of European universities.[18][19][20][21]. Source(s): Khwarizmi's algorithmic equations were based on the decimal system he made with the mix of Arabic and Indian letters. Berlin: Springer-Verlag. Follow us on Instagram. (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. From Al-Jabr to Algebra. 1 decade ago. [54], There is only one surviving copy of Kitāb Ṣūrat al-Arḍ, which is kept at the Strasbourg University Library. Subtract this from the moiety of the roots, which is fifty and a half. It is attributed to the Adelard of Bath, who had also translated the astronomical tables in 1126. He not only participated in this, but he revised and corrected Ptolemy’s view by systemising and correcting his data for Africa and the Middle East, and as a result, produced the first map of the known world in 830 CE along with other geographers. 1 However, Rashed denies this:[26]. Ibn al-Nadīm's Kitāb al-Fihrist includes a short biography on al-Khwārizmī together with a list his books. Muhammad ibn Musa al-Khwarizmi gave the West all of the Hindu digits and much more besides. While great human innovations such as flight and high-speed transportation are premised on algebraic equations, the modern world does not much care about its origins. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and Greek mathematics. Muḥammad ibn Mūsā al-Khwārizmī (Persian: محمد بن موسی خوارزمی‎‎, Arabic: محمد بن موسى الخوارزمی‎‎; c. 780 – c. 850) (Arabic pronunciation: [ælxɑːræzmiː]), formerly Latinized as Algoritmi, was a Persian mathematician, astronomer, and geographer during the Abbasid Caliphate, a scholar in the House of Wisdom in Baghdad. [55], Al-Khwārizmī corrected Ptolemy's gross overestimate for the length of the Mediterranean Sea[56] from the Canary Islands to the eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of longitude, while al-Khwārizmī almost correctly estimated it at nearly 50 degrees of longitude. It is from the title of his work, Hisab Al-Jabr wal Muqabalah (Book of Calculations, Restoration and Reduction), that Algebra (Al-Jabr) derived its name. Muhammad ibn Musa al-Khwarizmi was a Persian mathematician, astronomer, astrologer geographer and a scholar in the House of Wisdom in Baghdad. {\displaystyle pq=100} 1 2 3. 1 decade ago. Born in 780, his full name was Abu Abdallah Muhammad ibn Musa Al-Khwarizmi. [14] His name gave rise to the terms algorism and algorithm,[15] as well as Spanish and Portuguese terms algoritmo, and Spanish guarismo[16] and Portuguese algarismo meaning "digit". Later, with translations of Al-Khwarizmis work into Latin by Adelard of Bath and others in the 12th Century, and with the influence of … [49] A related treatise on spherical trigonometry is also attributed to him. 100 [23]:669 He also made important contributions to trigonometry, producing accurate sine and cosine tables, and the first table of tangents. For example, x2 = 40x − 4x2 is reduced to 5x2 = 40x. Extract the root from this; it is forty-nine and a half. It is perhaps the closest to Al-Khwarizmi's own writings.[46]. Then Al-Khwarizmi had used the Arabic word for root to denote the first degree term of a quadratic equation. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. [22]:9 He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial. The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul),[25] a viticulture district near Baghdad. Maher, P. (1998). Al-Khwarizmi, Muslim mathematician and astronomer whose major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics. [32], It provided an exhaustive account of solving polynomial equations up to the second degree,[33] and discussed the fundamental methods of "reduction" and "balancing", referring to the transposition of terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. Al Mamum assigned him as the court astronomer. Called takht in Arabic (Latin: tabula), a board covered with a thin layer of dust or sand was employed for calculations, on which figures could be written with a stylus and easily erased and replaced when necessary. Today we have the Arabic … Muḥammad ibn Mūsā al-Khwārizmī[note 1] (Persian: Muḥammad Khwārizmī محمد بن موسی خوارزمی‎; c. 780 – c. 850), Arabized as al-Khwarizmi and formerly Latinized as Algorithmi, was a Persian[4][5][6] polymath who produced vastly influential works in mathematics, astronomy, and geography. Al-Khwarizmi, Mahommed ibn Musa. Khwarizmi was also quick to develop trigonometric tables in detail including the sine functions, which were most likely extrapolated to tangent functions by Maslama, an Arab-Muslim astronomer. Le mathématicien et astronome al-Khwarizmi(début du IXe siècle) est bien connu comme étant le fondateur de l’algèbre. Vous avez sans nul doute entendu parlé de la ville de Bagdad, capitale de l’Irak. [38], Al-Khwārizmī's second most influential work was on the subject of arithmetic, which survived in Latin translations but lost in the original Arabic. 1 decade ago. The above discussion uses modern mathematical notation for the types of problems that the book discusses. In his book, The Arabs: A Short History, Philip Khuri, a Lebanese-American professor at Princeton and Harvard University, described Khwarizmi as "one of the greatest scientific minds of Islam and the man who influenced mathematical thought to a greater extent than any other mediaeval writer.”. In the 12th century, Latin translations of his textbook on arithmetic (Algorithmo de Numero Indorum) which codified the various Indian numerals, introduced the decimal positional number system to the Western world. They contained the first Muslim tables and contained not simply the sine function, but also the tangent. 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. [49] The work contains tables for the movements of the sun, the moon and the five planets known at the time. q Al-Khwarizmi was one of the learned men who worked in the House of Wisdom. Popularizarea cifrelor indo-arabe în Occident îi este atribuită, în general, matematicianului italian Fibonacci (c. 1170-1250), cunoscut şi sub numele de Leonardo din Pisa. What digit did Arab mathematician al-Khwarizmi give to the West around 800 B/B? Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. 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. 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. Sophia L. 1 decade ago. Acces PDF Al Khwarizmi Et L Al Jabr Ac Strasbourg Al Khwarizmi Et L Al Jabr Ac Strasbourg ... écrits, rédigés en langue arabe, ont permis l’introduction de l’algèbre en Europe. Top Answer. Asked by Wiki User. 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. Sa mémoire perdure avec le mot « algorithme », qui est dérivé de son nom. p He "also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done. Al-Khwarizmi – for many this name will not ring a bell – is without a doubt one of the most prominent mathematicians in history. Latinized versions of his name and of his most famous book title live on in the terms algorithm and algebra. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind. Mathematics in School, 27(4), 14–15. 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. "Arabic mathematics: forgotten brilliance? There was a large institute i… Rozenfeld. Separate the twenty things from a hundred and a square, and add them to eighty-one. Regarding al-Khwārizmī's religion, Toomer writes:[27]. [34], 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). "[57] Al-Khwārizmī's Prime Meridian at the Fortunate Isles was thus around 10° east of the line used by Marinus and Ptolemy. His systematic approach to solving linear and quadratic equations led to algebra, a word derived from the title of his book on the subject, "The Compendious Book on Calculation by Completion and Balancing".[29]. Few details of al-Khwārizmī's life are known with certainty. His algebra treatise Hisab al-jabr w'al-muqabala gives us the word algebra and can be considered as the first book to be written on algebra. See Answer. Lib. (1985). What digit did Arab mathematician al-khwarizmi create? Computation: You say, ten less a thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. ", 9th century Persian mathematician, astronomer and geographer, "al-Khwārizmī" redirects here. Exclusive: Mogherini under fire over stink in Lebanon from EU cash, ‘How do you fast in Space?’ and other questions you have about Ramadan 2019, In pictures: Muslims celebrate Eid al Fitr, Europe’s far-right parties make headway amid Covid-19 pandemic, Friends, the virus and the future: a chat with revered Ferzan Ozpetek, No one left outside: Istanbul and Ankara shelter the homeless in hotels, 2020 Human Development Report urgently calls for nature-based development. He was known for writing major works on astronomy and mathematics that introduced Hindu-Arabic numerals and the idea of algebra to European scholars. He gave us the concept of the number zero. Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy. Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi - 15895349 2013-10-30 14:59:06. he created 0-9. Read PDF Al Khwarizmi Et L Al Jabr Ac Strasbourg Khwarizmi. SUMMARY: Abu Abdullah Ibn Musa Al Khwarizmi (780-847), the first great mathematician of the Islamic world, was also the founder of Algebra. Al-Khwārizmī, rendered as (Latin) Algoritmi, led to the term "algorithm". [citation needed], The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة‎ al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) is a mathematical book written approximately 820 CE. Bruce. Arab Mathematician Al-khwarizmi. It is important to understand just how significant this new idea was. His astronomical and trigonometric tables, revised by Maslama Al-Majriti (in the second half of 10th century), were translated into Latin as early as 1126 by Adelard of Bath. Explaining in detail he says: “the following is an example of squares equal to roots, a square is equal to 5 roots. Around 820 CE he was appointed as the astronomer and head of the library of the House of Wisdom in Baghdad.[7]:14. The seventh Abbasid caliph, Al Mamun, ordered polymaths to measure the volume and circumference of the earth - Khwarizmi was among them. Answer Save. According to Swiss-American historian of mathematics, Florian Cajori, Al-Khwarizmi's algebra was different from the work of Indian mathematicians, for Indians had no rules like the ''restoration'' and ''reduction''. For Ses écrits, rédigés en langue arabe, puis traduits en latin à partir du XII siècle, ont permis l'intro… p Halve the roots; the moiety is fifty and a half. This work marked the turning point in Islamic astronomy. His works was brought to Western World through Latin translation that had been conducted in the 12th century. Al-Khwarizmi. 0. In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities. Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he was an adherent of the old Zoroastrian religion. Al-Khwarizmi flourished while working as a member of the House of Wisdom in Baghdad under the leadership of Kalif al-Mamun, the son of the Khalif Harun al-Rashid, who was made famous in the Arabian Nights. There remains one, and this is one of the two parts.[31]. 0 Isn't it great to be given nothing? History. Baghdad was the city of knowledge at the time of the Golden Era of Muslims. 50 [44], Four Latin texts providing adaptions of Al-Khwarizmi's methods have survived, even though none of them is believed to be a literal translation:[40], Dixit Algorizmi ('Thus spake Al-Khwarizmi') is the starting phrase of a manuscript in the University of Cambridge library, which is generally referred to by its 1857 title Algoritmi de Numero Indorum. ... Country Percent of Production Arab or Non-Arab OPEC Member Russia 12.65% Non-Arab … Will Iraq and Turkey develop a security cooperation against the PKK? Al Khwarizmi was a nineteenth century eminent and multi-faceted Persian mathematician, geographer and astronomer. 2012.. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwārizmī's name, Algoritmi and Algorismi, respectively. The Hindu numerals 1 - 9 and 0 - which have since become known as Hindu-Arabic numerals - were soon adopted by the entire Islamic world. Toomer ... with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader. On the Calculation with Hindu Numerals written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe. "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. Khwarizmi is widely credited for compiling the oldest astronomical tables. He was known for writing major works on astronomy and mathematics that introduced Hindu-Arabic numerals and the idea of algebra to European scholars. Nach der einzigen (lateinischen) Handschrift (Cambridge Un. [31] The term "algebra" is derived from the name of one of the basic operations with equations (al-jabr, meaning "restoration", referring to adding a number to both sides of the equation to consolidate or cancel terms) described in this book. [56], Al-Khwārizmī wrote several other works including a treatise on the Hebrew calendar, titled Risāla fi istikhrāj ta’rīkh al-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود‎, "Extraction of the Jewish Era"). The House of Wisd… [43] Al-Khwarizmi's Latinized name, Algorismus, turned into the name of method used for computations, and survives in the modern term "algorithm". (2009). [37] Regarding the dissimilarity and significance of Al-Khwarizmi's algebraic work from that of Indian Mathematician Brahmagupta, Carl Benjamin Boyer wrote: It is true that in two respects the work of al-Khowarizmi represented a retrogression from that of Diophantus. Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. It was the 9th-century polymath, Muhammad al Khwarizmi, who gave a definite form to the art of algebra and algorithm. It no longer concerns a series of problems to be solved, 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. 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. In the House of Wisdom of Baghdad he was a scholar. The term "algorithm" is derived from the algorism, the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwārizmī. The work on Arabic numerals highlights the decimal positional number system. 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.[36]. They could finally count up to 1 million. 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. This site uses cookies. His writings include the text kitāb al-ḥisāb al-hindī ('Book of Indian computation'[note 2]), and perhaps a more elementary text, kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ('Addition and subtraction in Indian arithmetic'). In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, while Diophantus is primarily concerned with the theory of numbers. In modern notation this process, with x the "thing" (شيء‎ shayʾ) or "root", is given by the steps, Let the roots of the equation be x = p and x = q. The term algebra itself comes from the title of his book (the word al-jabr meaning "completion" or "rejoining"). Al-Khwārizmī's Zīj al-Sindhind also contained tables for the trigonometric functions of sines and cosine. The Latinized version of his name gave us the term "algorithm," and the title of his most famous and important work gave us the As Paul Gallez[dubious – discuss] points out, this excellent system allows the deduction of many latitudes and longitudes where the only extant document is in such a bad condition as to make it practically illegible. , Currently it is known as ‘Khiva’, a city in Uzbekistan on the border with Turkmenistan. Lethal A.I. Nevertheless, the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta, because the book is not concerned with difficult problems in indeterminant analysis but with a straight forward and elementary exposition of the solution of equations, especially that of second degree. He developed it after studying the works of the legendary Indian astronomer Brahmagupta. Haterofmany. B.A. First, it is on a far more elementary level than that found in the Diophantine problems and, second, the algebra of al-Khowarizmi is thoroughly rhetorical, with none of the syncopation found in the Greek Arithmetica or in Brahmagupta's work. During the Middle Ages’ Translation Movement, scholars built on the works of Greek, Babylonian and Indian polymaths, introducing path-breaking scientific concepts. /khwahr iz mee /, n. al /al/ (Muhammed ibn Musa al Khwarizmi), A.D. c780 c850, Arab mathematician and astronomer Perhaps his most important contribution to mathematics was his strong advocacy of the Hindu numerical system, which Al-Khwarizmi recognized as having the power and efficiency needed to revolutionize Islamic and Western mathematics. [51][52], Al-Khwārizmī's third major work is his Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض‎, "Book of the Description of the Earth"),[53] also known as his Geography, which was finished in 833. It is quite unlikely that al-Khwarizmi knew of the work of Diophantus, but he must have been familiar with at least the astronomical and computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scholars made use of syncopation or of negative numbers. The word algorithm derives from his name. [citation needed]. 0 0. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers. Khwarizmi's algorithmic equations were based on the decimal system he made with the mix of Arabic … He also wrote on mechanical devices like the astrolabe and sundial. [7]:14 Because he was the first to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (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),[9] he has been described as the father[4][10][11] or founder[12][13] of algebra. Tigre Moins d'un siècle après la mort de Mahomet (+632), et la chute d'Alexandrie (+640), les tribus Page 12/30 It is a major reworking of Ptolemy's 2nd-century Geography, consisting of a list of 2402 coordinates of cities and other geographical features following a general introduction. [28], Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry. 0. ", S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263–277,"Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. The Istanbul manuscript contains a paper on sundials; the Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة‎). He was born in Persia of that time around 780. harv error: multiple targets (2×): CITEREFBoyer1991 (, Jacques Sesiano, "Islamic mathematics", p. 157, in, The full title is "The Book of the Description of the Earth, with its Cities, Mountains, Seas, All the Islands and the Rivers, written by Abu Ja'far Muhammad ibn Musa al-Khwārizmī, according to the Geographical Treatise written by Ptolemy the Claudian", although due to ambiguity in the word, harv error: no target: CITEREFRashedMorelon1996 (, The Compendious Book on Calculation by Completion and Balancing, "STAGES IN THE HISTORY OF ALGEBRA WITH IMPLICATIONSFOR TEACHING", "Islam Spain and the history of technology", "Mathematics Education in Iran From Ancient to Modern", "The Compendious Book on Calculation by Completion and Balancing, al-Khwārizmī", "History of Mathematics in the Recent Edition of the Encyclopædia Britannica", "Al-Khwārizmī, Abu Ja'far Muḥammad ibn Mūsā", Khwārizmī: Muḥammad ibn Mūsā al‐Khwārizmī, The Biographical Encyclopedia of Astronomers, The Journal of the Royal Asiatic Society of Great Britain and Ireland, Muhammad ibn Musa (Al-)Khwarizmi (c. 780–850 CE), "Abu Ja'far Muhammad ibn Musa Al-Khwarizmi", "Zur ältesten arabischen Algebra und Rechenkunst", Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse. Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have been the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā. A Latin translation is kept in Cambridge. Ms. Ii. + No direct manuscript survives; however, a copy had reached Nusaybin by the 11th century, where its metropolitan bishop, Mar Elyas bar Shinaya, found it.

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