The Info List - Book Of The Description Of The Earth

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Muḥammad ibn Mūsā al-Khwārizmī[note 1] (Persian: محمد بن موسى خوارزمی‎; c. 780 – c. 850), formerly Latinized as Algoritmi,[note 2] was a Persian[3][4] scholar who produced works in mathematics, astronomy, and geography under the patronage of the Caliph Al-Ma'mun
of the Abbasid Caliphate.[5]:668 Around 820 AD he was appointed as the astronomer and head of the library of the House of Wisdom
House of Wisdom
in Baghdad.[6]:14 Al-Khwarizmi's popularizing treatise on algebra (The Compendious Book on Calculation by Completion and Balancing, ca. 813-833 CE[7]:171) presented the first systematic solution of linear and quadratic equations in Arabic. 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.[6]: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), he has been described as the father[8][9][10] or founder[11][12] of algebra. The term algebra itself comes from the title of his book (specifically the word al-jabr meaning "completion" or "rejoining"). His name gave rise to the terms Algorism
and algorithm.[13] His name is also the origin of (Spanish) guarismo[14] and of (Portuguese) algarismo, both meaning digit. 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.[15] 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.[16][17][18][19] In addition to his best-known works, he revised Ptolemy's Geography, listing the longitudes and latitudes of various cities and localities.[20]:9 He further produced a set of astronomical tables and wrote about calendaric works, as well as the astrolabe and the sundial.[5]:669


1 Life 2 Contributions

2.1 Algebra 2.2 Arithmetic 2.3 Astronomy 2.4 Trigonometry 2.5 Geography 2.6 Jewish calendar 2.7 Other works

3 See also 4 Notes 5 References 6 Further reading

6.1 Specific references 6.2 General references

Life[edit] Few details of al-Khwārizmī's life are known with certainty. He was born into a Persian[4] family and Ibn al-Nadim gives his birthplace as Khwarezm[21] in Greater Khorasan
Greater Khorasan
(modern Khiva, Xorazm Region, Uzbekistan). Muhammad ibn Jarir al-Tabari
Muhammad ibn Jarir al-Tabari
gives his name as Muḥammad ibn Musá al-Khwārizmiyy al-Majūsiyy al-Quṭrubbaliyy (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ‎). The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul),[22] a viticulture district near Baghdad. However, Rashed[23] suggests:

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 conjunction '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, so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians.[24]

However, Rashed put a rather different interpretation on the same words by Al-Tabari:[25]

... Al-Tabari's words should read: " Muhammad ibn Musa al-Khwarizmi
Muhammad ibn Musa al-Khwarizmi
and al-Majusi al-Qutrubbulli ...", (and that there are two people al-Khwarizmi and al-Majusi al-Qutrubbulli): the letter "wa" was omitted in the early copy. This would not be worth mentioning if a series of conclusions about al-Khwarizmi's personality, occasionally even the origins of his knowledge, had not been drawn. In his article ([1]) G J Toomer, with naive confidence, constructed an entire fantasy on the error which cannot be denied the merit of making amusing reading.

Ibn al-Nadīm's Kitāb al-Fihrist includes 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 Muslim
conquest of Persia, Baghdad
became the centre of scientific studies and trade, and many merchants and scientists from as far as China
and India
traveled to this city, as did al-Khwārizmī[citation needed]. He worked in Baghdad
as a scholar at the House of Wisdom
House of Wisdom
established by Caliph al-Ma’mūn, where he studied the sciences and mathematics, which included the translation of Greek and Sanskrit
scientific manuscripts. Douglas Morton Dunlop suggests that it may have been possible that Muḥammad ibn Mūsā al-Khwārizmī
Muḥammad ibn Mūsā al-Khwārizmī
was in fact the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of the three Banū Mūsā.[26] Contributions[edit]

A page from al-Khwārizmī's Algebra

Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry[citation needed]. 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".[citation needed] On the Calculation with Hindu Numerals written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East
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.[citation needed] 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.[27] 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.[citation needed] Algebra[edit] Main article: The Compendious Book on Calculation by Completion and Balancing Further information: Latin
translations of the 12th century and Science in the medieval Islamic world

Left: The original Arabic print manuscript of the Book of Algebra
by Al-Khwārizmī. Right: A page from The Algebra
of Al-Khwarizmi by Fredrick Rosen, in English.

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. 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.[28] 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. 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.[29] It provided an exhaustive account of solving polynomial equations up to the second degree,[30] 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.[31] 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)

squares equal roots (ax2 = bx) squares equal number (ax2 = c) roots equal number (bx = c) squares and roots equal number (ax2 + bx = c) squares and number equal roots (ax2 + c = bx) roots and number equal squares (bx + c = ax2)

by dividing out the coefficient of the square and using the two operations al-jabr (Arabic: الجبر‎ "restoring" or "completion") and al-muqābala ("balancing"). Al-jabr 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.[28]

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

( 10 − x



= 81 x

displaystyle (10-x)^ 2 =81x



− 20 x + 100 = 81 x

displaystyle x^ 2 -20x+100=81x



+ 100 = 101 x

displaystyle x^ 2 +100=101x

Let the roots of the equation be 'p' and 'q'. Then

p + q


= 50

1 2

displaystyle tfrac p+q 2 =50 tfrac 1 2


p q = 100

displaystyle pq=100


p − q




p + q




− p q



1 4

− 100

= 49

1 2

displaystyle frac p-q 2 = sqrt left( frac p+q 2 right)^ 2 -pq = sqrt 2550 tfrac 1 4 -100 =49 tfrac 1 2

So a root is given by

x = 50

1 2

− 49

1 2

= 1

displaystyle x=50 tfrac 1 2 -49 tfrac 1 2 =1

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. 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.[32]

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.[33]

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''.[34]Regarding dissimilarity and significance of Al-Khwarizmi's algebraic work from that of Indian Mathematician Brahmagupta, Carl Benjamin Boyer
Carl Benjamin Boyer

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.Nevertheless,the Al-jabr comes closer to 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.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.[35]

Page from a Latin
translation, beginning with "Dixit algorizmi"

Arithmetic[edit] 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 12th 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"), 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-Jam‘ wat-Tafrīq bi-Ḥisāb al-Hind[36] ("The Book of Addition and Subtraction According to the Hindu Calculation").[37] Al-Khwārizmī'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
Arabic numerals
developed by al-Khwārizmī. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwārizmī's name, Algoritmi and Algorismi, respectively. Astronomy[edit]

Page from Corpus Christi College MS 283. A Latin
translation of al-Khwārizmī's Zīj.

Al-Khwārizmī's Zīj al-Sindhind[24] (Arabic: زيج السند هند‎, "astronomical tables of Siddhanta"[38]) 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.[39] 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. The original Arabic version (written c. 820) is lost, but a version by the Spanish astronomer Maslamah Ibn Ahmad al-Majriti
Maslamah Ibn Ahmad al-Majriti
(c. 1000) has survived in a Latin
translation, presumably by Adelard of Bath (January 26, 1126).[40] The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) and the Bodleian Library (Oxford). Trigonometry[edit] Al-Khwārizmī's Zīj al-Sindhind also contained tables for the trigonometric functions of sines and cosine.[39] A related treatise on spherical trigonometry is also attributed to him.[32] Geography[edit]

Daunicht's reconstruction of the section of al-Khwārizmī's world map concerning the Indian Ocean.

A 15th-century version of Ptolemy's Geography
Ptolemy's Geography
for comparison.

A stamp issued September 6, 1983 in the Soviet Union, commemorating al-Khwārizmī's (approximate) 1200th birthday.

Statue of Al-Khwārizmī in his birth town Khiva, Uzbekistan.

Al-Khwārizmī's third major work is his Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض‎, "Book of the Description of the Earth"),[41] also known as his Geography, which was finished in 833. 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.[42] 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
Biblioteca Nacional de España
in Madrid.[citation needed] 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[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. 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.[43] Al-Khwārizmī corrected Ptolemy's gross overestimate for the length of the Mediterranean Sea[44] from the Canary Islands
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. He "also depicted the Atlantic and Indian Oceans as open bodies of water, not land-locked seas as Ptolemy had done."[45] Al-Khwārizmī's Prime Meridian
Prime Meridian
at the Fortunate Isles was thus around 10° east of the line used by Marinus and Ptolemy. Most medieval Muslim
gazetteers continued to use al-Khwārizmī's prime meridian.[44] Jewish calendar[edit] 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"). It describes the Metonic cycle, a 19-year intercalation cycle; the rules for determining on what day of the week the first day of the month Tishrei
shall fall; calculates the interval between the Anno Mundi
Anno Mundi
or Jewish year and the Seleucid era; and gives rules for determining the mean longitude of the sun and the moon using the Hebrew calendar. Similar material is found in the works of Abū Rayḥān al-Bīrūnī
Abū Rayḥān al-Bīrūnī
and Maimonides.[24] Other works[edit] Ibn al-Nadim's Kitāb al-Fihrist, an index of Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ‎), a book of annals. No direct manuscript survives; however, a copy had reached Nusaybin
by the 11th century, where its metropolitan bishop, Mar
Elyas bar Shinaya, found it. Elias's chronicle quotes it from "the death of the Prophet" through to 169 AH, at which point Elias's text itself hits a lacuna.[46] 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; the Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة‎). Other papers, such as one on the determination of the direction of Mecca, are on the spherical astronomy. Two texts deserve special interest on the morning width (Ma‘rifat sa‘at al-mashriq fī kull balad) and the determination of the azimuth from a height (Ma‘rifat al-samt min qibal al-irtifā‘). He also wrote two books on using and constructing astrolabes.

See also[edit]

Wikiquote has quotations related to: al-Khwārizmī

Wikimedia Commons has media related to Muhammad ibn Musa al-Khwarizmi.

Al-Khwarizmi (crater) — A crater on the far side of the moon named for al-Khwārizmī. Astronomy in the medieval Islamic world Indian influence on Islamic science List of pioneers in computer science Khwarizmi International Award — An Iranian award named after al-Khwārizmī. Mathematics in medieval Islam Al-Khwarizmi Institute of Computer Science (KICS)- A Pakistani research institute named after al-Khwārizmī.


^ There is some confusion in the literature on whether al-Khwārizmī's full name is ابو عبد الله محمد بن موسى الخوارزمي‎ Abū ʿAbdallāh Muḥammad ibn Mūsā al-Khwārizmī or ابو جعفر محمد بن موسی الخوارزمی‎ Abū Ja‘far Muḥammad ibn Mūsā al-Khwārizmī. Ibn Khaldun notes in his encyclopedic work: "The first who wrote upon this branch [algebra] was Abu ‘Abdallah al-Khowarizmi, after whom came Abu Kamil Shoja‘ ibn Aslam." (MacGuckin de Slane). (Rosen 1831, pp. xi–xiii) mentions that "[Abu Abdallah Mohammed ben Musa] lived and wrote under the caliphate 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)." In the introduction to his critical commentary on Robert of Chester's Latin
translation of al-Khwārizmī's Algebra, L.C. Karpinski notes that Abū Ja‘far Muḥammad ibn Mūsā refers to the eldest of the Banū Mūsā
Banū Mūsā
brothers. Karpinski notes in his review on (Ruska 1917) that in (Ruska 1918): "Ruska here inadvertently speaks of the author as Abū Ga‘far M. b. M., instead of Abū Abdallah M. b. M." ^ Other Latin
transliterations include Algaurizin.[citation needed]


^ Berggren 1986; Struik 1987, p. 93 ^ O'Connor, John J.; Robertson, Edmund F., "Abū Kāmil Shujā‘ ibn Aslam", MacTutor History of Mathematics archive, University of St Andrews. ^ Saliba, George (September 1998). "Science and medicine". Iranian Studies. 31 (3-4): 681–690. doi:10.1080/00210869808701940. Take, for example, someone like Muhammad b. Musa al-Khwarizmi (fl. 850) who may present a problem for the EIr, for although he was obviously of Persian descent, he lived and worked in Baghdad
and was not known to have produced a single scientific work in Persian.  ^ a b Toomer 1990; Oaks, Jeffrey A. "Was al-Khwarizmi an applied algebraist?". University of Indianapolis. Retrieved 2008-05-30. ; Hogendijk, Jan P. (1998). "al-Khwarzimi". Pythagoras. 38 (2): 4–5. ISSN 0033-4766.  ^ a b ARNDT, A. (1983). Al-Khwarizmi. The Mathematics Teacher, 76(9), 668-670. ^ a b Maher, P. (1998). From Al-Jabr to Algebra. Mathematics in School, 27(4), 14-15. ^ Oaks, J. (2009). Polynomials and equations in arabic algebra. Archive for History of Exact Sciences, 63(2), 169-203. ^ (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." ^ Boyer, Carl B., 1985. A History of Mathematics, p. 252. Princeton University Press. " Diophantus
sometimes is called the father of algebra, but this title more appropriately belongs to al-Khowarizmi...","...the Al-jabr comes closer to the elementay algebra of today than the works of either Diophantus
or Brahmagupta..." ^ S Gandz, The sources of al-Khwarizmi's algebra, Osiris, i (1936), 263-77,"Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. 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." ^ https://eclass.uoa.gr/modules/document/file.php/MATH104/20010-11/HistoryOfAlgebra.pdf,"The[permanent dead link] first true algebra text which is still extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad
around 825" ^ https://books.google.fr/books?id=9HUDXkJIE3EC&pg=PA188&lpg=PA188&dq=Al-Tusi+introduced+a+new+discipline%E2%80%94algebraic+geometry%E2%80%94that+relies+on+equations+to+study+curves.%22&source=bl&ots=XPTsT1hkMh&sig=DC59ymcLgnfr1Nx42RkM5MLlq1U&hl=fr&sa=X&ved=0ahUKEwiSrtiBl93WAhVJIcAKHSDnAxQQ6AEIUDAF#v=onepage&q=Al-Tusi%20introduced%20a%20new%20discipline%E2%80%94algebraic%20geometry%E2%80%94that%20relies%20on%20equations%20to%20study%20curves.%22&f=true,"Al-Khwarizmi is often considered the founder of algebra and his name gave rise to the term algorithm" ^ Daffa 1977 ^ Knuth, Donald (1979). Algorithms in Modern Mathematics and Computer Science (PDF). Springer-Verlag. ISBN 0-387-11157-3. Archived from the original (PDF) on 2006-11-07.  ^ Struik 1987, p. 93 ^ Philip Khuri Hitti (2002). History of the Arabs. p. 379.  ^ Fred James Hill, Nicholas Awde (2003). A History of the Islamic World. p. 55. "The Compendious Book on Calculation by Completion and Balancing" (Hisab al-Jabr wa H-Muqabala) on the development of the subject cannot be underestimated. Translated into Latin
during the twelfth century, it remained the principal mathematics textbook in European universities until the sixteenth century  ^ Shawn Overbay, Jimmy Schorer, and Heather Conger, University of Kentucky. "Al-Khwarizmi". CS1 maint: Multiple names: authors list (link) ^ "Islam Spain and the history of technology". www.sjsu.edu. Retrieved 2018-01-24.  ^ L., V. D. (1985). A history of algebra: from al - Khwarizmi to emmy noether. Berlin: Springer-Verlag. ^ Cristopher Moore and Stephan Mertens, The Nature of Computation, (Oxford University Press, 2011), 36. ^ "Iraq After the Muslim
Conquest", by Michael G. Morony, ISBN 1-59333-315-3 (a 2005 facsimile from the original 1984 book), p. 145 ^ 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 0-88706-698-4.  ^ a b c Toomer 1990 ^ E. Grant (ed.), A source book in medieval science (Cambridge, 1974) ^ Dunlop 1943 ^ "al-Khwarizmi". Encyclopædia Britannica. Retrieved 2008-05-30.  ^ a b Rosen, Frederic. "The Compendious Book on Calculation by Completion and Balancing, al-Khwārizmī". 1831 English Translation. Retrieved 2009-09-14.  ^ Karpinski, L. C. (1912). "History of Mathematics in the Recent Edition of the Encyclopædia Britannica". American Association for the Advancement of Science.  ^ Boyer, Carl B. (1991). "The Arabic Hegemony". A History of Mathematics (Second ed.). John Wiley & Sons, Inc. p. 228. ISBN 0-471-54397-7. 

"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."

^ (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." ^ a b O'Connor, John J.; Robertson, Edmund F., "Muhammad ibn Musa al-Khwarizmi", MacTutor History of Mathematics archive, University of St Andrews . ^ Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. Springer. pp. 11–2. ISBN 0-7923-2565-6. OCLC 29181926.  ^ Florian Cajori (1919). A History of Mathematics. p. 103. That it came from Indian source is impossible,for Hindus had no rules like "restoration" and "reduction" .They were never in the habit of making all terms in an equation positive, as is done in the process of "restoration.  ^ Carl Benjamin Boyer
Carl Benjamin Boyer
(1968). A History of Mathematics. p. 252.  ^ Ruska ^ Berggren 1986, p. 7 ^ Thurston, Hugh (1996), Early Astronomy, Springer Science & Business Media, pp. 204–, ISBN 978-0-387-94822-5  ^ a b Kennedy 1956, pp. 26–9 ^ Kennedy 1956, p. 128 ^ 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 surah it could also be understood as meaning "The Book of the Image of the Earth" or even "The Book of the Map of the World". ^ "The history of cartography". GAP computer algebra system. Archived from the original on 2008-05-24. Retrieved 2008-05-30.  ^ Daunicht. ^ a b Edward S. Kennedy, Mathematical Geography, p. 188, in (Rashed & Morelon 1996, pp. 185–201) ^ Covington, Richard (2007). "The Third Dimension". Saudi Aramco World, May–June 2007: 17–21. Retrieved 2008-07-06.  ^ LJ Delaporte (1910). Chronographie de Mar
Elie bar Sinaya. Paris. p. xiii. 

Further reading[edit] Specific references[edit]


Toomer, Gerald (1990). "Al-Khwārizmī, Abu Ja'far Muḥammad ibn Mūsā". In Gillispie, Charles Coulston. Dictionary of Scientific Biography. 7. New York: Charles Scribner's Sons. ISBN 0-684-16962-2.  Brentjes, Sonja (2007). "Khwārizmī: Muḥammad ibn Mūsā al‐Khwārizmī" in Thomas Hockey et al.(eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 631–633. (PDF version) Dunlop, Douglas Morton (1943). "Muḥammad b. Mūsā al-Khwārizmī". The Journal of the Royal Asiatic Society of Great Britain and Ireland. Cambridge University (2): 248–250. JSTOR 25221920.  Hogendijk, Jan P., Muhammad ibn Musa (Al-)Khwarizmi (ca. 780-850 CE) – bibliography of his works, manuscripts, editions and translations. O'Connor, John J.; Robertson, Edmund F., "Abu Ja'far Muhammad ibn Musa Al-Khwarizmi", MacTutor History of Mathematics archive, University of St Andrews . Fuat Sezgin. Geschichte des arabischen Schrifttums. 1974, E. J. Brill, Leiden, the Netherlands. Sezgin, F., ed., Islamic Mathematics and Astronomy, Frankfurt: Institut für Geschichte der arabisch-islamischen Wissenschaften, 1997–9.


Gandz, Solomon (November 1926). "The Origin of the Term "Algebra"". The American Mathematical Monthly. The American Mathematical Monthly, Vol. 33, No. 9. 33 (9): 437–440. doi:10.2307/2299605. ISSN 0002-9890. JSTOR 2299605.  Gandz, Solomon (1936). "The Sources of al-Khowārizmī's Algebra". Osiris. 1 (1): 263–277. doi:10.1086/368426. ISSN 0369-7827. JSTOR 301610.  Gandz, Solomon (1938). "The Algebra
of Inheritance: A Rehabilitation of Al-Khuwārizmī". Osiris. 5 (5): 319–391. doi:10.1086/368492. ISSN 0369-7827. JSTOR 301569.  Hughes, Barnabas (1986). "Gerard of Cremona's Translation of al-Khwārizmī's al-Jabr: A Critical Edition". Mediaeval Studies. 48: 211–263.  Barnabas Hughes. Robert of Chester's Latin
translation of al-Khwarizmi's al-Jabr: A new critical edition. In Latin. F. Steiner Verlag Wiesbaden (1989). ISBN 3-515-04589-9. Karpinski, L. C. (1915). Robert of Chester's Latin
Translation of the Algebra
of Al-Khowarizmi: With an Introduction, Critical Notes and an English Version. The Macmillan Company.  Rosen, Fredrick (1831). The Algebra
of Mohammed Ben Musa. Kessinger Publishing. ISBN 1-4179-4914-7.  Ruska, Julius (1917). "Zur ältesten arabischen Algebra
und Rechenkunst". Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse: 1–125. 


Folkerts, Menso (1997). Die älteste lateinische Schrift über das indische Rechnen nach al-Ḫwārizmī (in German and Latin). München: Bayerische Akademie der Wissenschaften. ISBN 3-7696-0108-4.  Vogel, Kurt (1968). Mohammed ibn Musa Alchwarizmi's Algorismus; das früheste Lehrbuch zum Rechnen mit indischen Ziffern. Nach der einzigen (lateinischen) Handschrift (Cambridge Un. Lib. Ms. Ii. 6.5) in Faksimile mit Transkription und Kommentar herausgegeben von Kurt Vogel. Aalen, O. Zeller.


Goldstein, B. R. (1968). Commentary on the Astronomical Tables of Al-Khwarizmi: By Ibn Al-Muthanna. Yale University Press. ISBN 0-300-00498-2.  Hogendijk, Jan P. (1991). "Al-Khwārizmī's Table of the " Sine
of the Hours" and the Underlying Sine
Table". Historia Scientiarum. 42: 1–12.  King, David A. (1983). Al-Khwārizmī and New Trends in Mathematical Astronomy in the Ninth Century. New York University: Hagop Kevorkian Center for Near Eastern Studies: Occasional Papers on the Near East 2. LCCN 85150177.  Neugebauer, Otto (1962). The Astronomical Tables of al-Khwarizmi.  Rosenfeld, Boris A. (1993). Menso Folkerts; J. P. Hogendijk, eds. ""Geometric trigonometry" in treatises of al-Khwārizmī, al-Māhānī and Ibn al-Haytham". Vestiga mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H. L. L. Busard. Amsterdam: Rodopi. ISBN 90-5183-536-1.  Suter, Heinrich. [Ed.]: Die astronomischen Tafeln des Muhammed ibn Mûsâ al-Khwârizmî in der Bearbeitung des Maslama ibn Ahmed al-Madjrîtî und der latein. Übersetzung des Athelhard von Bath auf Grund der Vorarbeiten von A. Bjørnbo und R. Besthorn in Kopenhagen. Hrsg. und komm. Kopenhagen 1914. 288 pp. Repr. 1997 (Islamic Mathematics and Astronomy. 7). ISBN 3-8298-4008-X. Van Dalen, B. Al-Khwarizmi's Astronomical Tables Revisited: Analysis of the Equation of Time.

Spherical trigonometry

B. A. Rozenfeld. "Al-Khwarizmi's spherical trigonometry" (Russian), Istor.-Mat. Issled. 32–33 (1990), 325–339.

Jewish calendar

Kennedy, E. S. (1964). "Al-Khwārizmī on the Jewish Calendar". Scripta Mathematica. 27: 55–59. 


Daunicht, Hubert (1968–1970). Der Osten nach der Erdkarte al-Ḫuwārizmīs : Beiträge zur historischen Geographie und Geschichte Asiens (in German). Bonner orientalistische Studien. N.S.; Bd. 19. LCCN 71468286.  Mžik, Hans von (1915). "Ptolemaeus und die Karten der arabischen Geographen". Mitteil. D. K. K. Geogr. Ges. In Wien. 58: 152.  Mžik, Hans von (1916). "Afrika nach der arabischen Bearbeitung der γεωγραφικὴ ὑφήγησις des Cl. Ptolomeaus von Muh. ibn Mūsa al-Hwarizmi". Denkschriften d. Akad. D. Wissen. In Wien, Phil.-hist. Kl. 59.  Mžik, Hans von (1926). Das Kitāb Ṣūrat al-Arḍ des Abū Ǧa‘far Muḥammad ibn Mūsā al-Ḫuwārizmī. Leipzig.  Nallino, C. A. (1896), "Al-Ḫuwārizmī e il suo rifacimento della Geografia di Tolemo", Atti della R. Accad. dei Lincei, Arno 291, Serie V, Memorie, Classe di Sc. Mor., Vol. II, Rome  Ruska, Julius (1918). "Neue Bausteine zur Geschichte der arabischen Geographie". Geographische Zeitschrift. 24: 77–81.  Spitta, W. (1879). "Ḫuwārizmī's Auszug aus der Geographie des Ptolomaeus". Zeitschrift Deutschen Morgenl. Gesell. 33. 

General references[edit] For a more extensive bibliography, see History of mathematics, Mathematics in medieval Islam, and Astronomy in medieval Islam.

Berggren, J. Lennart (1986). Episodes in the Mathematics of Medieval Islam. New York: Springer Science+Business Media. ISBN 0-387-96318-9.  Boyer, Carl B. (1991). "The Arabic Hegemony". A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7.  Daffa, Ali Abdullah al- (1977). The Muslim
contribution to mathematics. London: Croom Helm. ISBN 0-85664-464-1.  Dallal, Ahmad (1999). "Science, Medicine and Technology". In Esposito, John. The Oxford History of Islam. Oxford University Press, New York.  Kennedy, E. S. (1956). "A Survey of Islamic Astronomical Tables; Transactions of the American Philosophical Society". 46 (2). Philadelphia: American Philosophical Society.  King, David A. (1999a). "Islamic Astronomy". In Walker, Christopher. Astronomy before the telescope. British Museum
British Museum
Press. pp. 143–174. ISBN 0-7141-2733-7.  King, David A. (2002). "A Vetustissimus Arabic Text on the Quadrans Vetus". Journal for the History of Astronomy. 33: 237–255. Bibcode:2002JHA....33..237K.  Struik, Dirk Jan (1987). A Concise History of Mathematics (4th ed.). Dover Publications. ISBN 0-486-60255-9.  O'Connor, John J.; Robertson, Edmund F., "Abraham bar Hiyya Ha-Nasi", MacTutor History of Mathematics archive, University of St Andrews . O'Connor, John J.; Robertson, Edmund F., "Arabic mathematics: forgotten brilliance?", MacTutor History of Mathematics archive, University of St Andrews . Roshdi Rashed, The development of Arabic mathematics: between arithmetic and algebra, London, 1994.

v t e

Mathematics in medieval Islam


9th century

'Abd al-Hamīd ibn Turk Sind ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Al-Mahani al-Dinawari Banū Mūsā Hunayn ibn Ishaq al-Khwārizmī Yusuf Al-Khuri ibn Qurra Na'im ibn Musa Sahl ibn Bishr al-Marwazi Abu Said Gorgani

10th century

al-Sufi Abu al-Wafa al-Khāzin Abū Kāmil Al-Qabisi al-Khojandi Ahmad ibn Yusuf Aṣ-Ṣaidanānī al-Uqlidisi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus Ibrahim ibn Sinan Al-Battani Sinan ibn Thabit Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud al-Majriti al-Jabali

11th century

al-Zarqālī Abu Nasr Mansur Said al-Andalusi Ibn al-Samh Al-Biruni Alhazen ibn Fatik Al-Sijzi al-Nasawī Al-Karaji Avicenna Muhammad al-Baghdadi ibn Hud al-Jayyānī Kushyar Gilani Al-Muradi Al-Isfizari Abu Mansur al-Baghdadi

12th century

Al-Samawal al-Maghribi Avempace Al-Khazini Omar Khayyam Jabir ibn Aflah al-Hassar Al-Kharaqī Sharaf al-Dīn al-Ṭūsī Ibn al-Yasamin

13th century

al-Hanafi al-Abdari Muhyi al-Dīn al-Maghribī Ibn 'Adlan Nasir al-Din al-Tusi Shams al-Dīn al-Samarqandī Ibn al‐Ha'im al‐Ishbili Ibn Abi al-Shukr al-Hasan al-Marrakushi

14th century

al-Umawī Ibn al-Banna' Ibn Shuayb Ibn al-Shatir Kamāl al-Dīn al-Fārisī Al-Khalili Qutb al-Din al-Shirazi Ahmad al-Qalqashandi Ibn al-Durayhim

15th century

al-Qalaṣādī Ali Qushji al-Wafa'i al-Kāshī al-Rūmī Ulugh Beg Ibn al-Majdi Sibt al-Maridini al-Kubunani

16th century

Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi Ibn Ghazi al-Miknasi Ahmad Ibn al-Qadi

Mathematical works

The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Almanac Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij


Alhazen's problem Islamic geometric patterns


Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi al-Din Madrasa Maktab Maragheh observatory University of Al Quaraouiyine


Babylonian mathematics Greek mathematics Indian mathematics


Byzantine mathematics European mathematics Indian mathematics

v t e

Astronomy in the medieval Islamic world


by century (CE AD)


Ahmad Nahavandi Al-Fadl ibn Naubakht Muḥammad ibn Ibrāhīm al-Fazārī Mashallah ibn Athari Yaʿqūb ibn Ṭāriq


Abu Maʿshar Abu Said Gorgani Al-Farghānī Al-Kindi Al-Mahani Abu Hanifa Dinawari Al-Ḥajjāj ibn Yūsuf Al-Marwazi Ali ibn Isa al-Asturlabi Banu Musa Iranshahri Khālid ibn ʿAbd al‐Malik Al-Khwārizmī Sahl ibn Bishr Thābit ibn Qurra Yahya ibn Abi Mansur


Abd al-Rahman al-Sufi Ibn Al-Adami al-Khojandi l-Khāzin al-Qūhī Abu al-Wafa Ahmad ibn Yusuf al-Battani Al-Qabisi Al-Nayrizi Al-Saghani Aṣ-Ṣaidanānī Ibn Yunus Ibrahim ibn Sinan Ma Yize al-Sijzi Mariam al-Asturlabi Nastulus Abolfadl Harawi Haseb-i Tabari al-Majriti


Abu Nasr Mansur al-Biruni Ali ibn Ridwan Al-Zarqālī Ibn al-Samh Al-Muradi Alhazen Avicenna Ibn al-Saffar Kushyar Gilani Said al-Andalusi Al-Isfizari


Al-Bitruji Avempace Ibn Tufail Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi Abu al-Salt Anvari Averroes Ibn al-Kammad Jabir ibn Aflah Omar Khayyam Sharaf al-Dīn al-Ṭūsī


Ibn al-Banna' al-Marrakushi Ibn al‐Ha'im al‐Ishbili Jamal ad-Din al-Hanafi Muhyi al-Dīn al-Maghribī Nasir al-Din al-Tusi Qutb al-Din al-Shirazi Shams al-Dīn al-Samarqandī Zakariya al-Qazwini Ibn Abi al-Shukr al-ʿUrḍī al-Abhari Muhammad ibn Abi Bakr al‐Farisi Abu Ali al-Hasan al-Marrakushi Al-Ashraf Umar II


Ibn al-Shatir al-Khalīlī Ibn Shuayb al-Battiwi Abū al‐ʿUqūl Nizam al-Din Nishapuri al-Jadiri


Ali Kuşçu ʿAbd al‐Wājid Jamshīd al-Kāshī Kadızade Rumi Ulugh Beg Sibt al-Maridini Ibn al-Majdi al-Wafa' al-Kubunani


Al-Birjandi Bahāʾ al-dīn al-ʿĀmilī Piri Reis Takiyüddin


Yang Guangxian Ahmad Khani Al Achsasi al Mouakket Mohammed al-Rudani



Arabic star names Islamic calendar ʿAjā'ib al-makhlūqāt wa gharā'ib al-mawjūdāt Encyclopedia of the Brethren of Purity Tabula Rogeriana The Book of Healing


Alfonsine tables Huihui Lifa Book of Fixed Stars Toledan Tables Zij-i Ilkhani Zij-i Sultani Sullam al-sama'


Alidade Analog computer Aperture Armillary sphere Astrolabe Astronomical clock Celestial globe Compass Compass
rose Dioptra Equatorial ring Equatorium Globe Graph paper Magnifying glass Mural instrument Navigational astrolabe Nebula Planisphere Quadrant Sextant Shadow square Sundial Schema for horizontal sundials Triquetrum


Almucantar Apogee Astrology in medieval Islam Astrophysics Axial tilt 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 cosmology Moonlight Multiverse Obliquity Parallax Precession Qibla Salah times Specific gravity Spherical Earth Sublunary sphere Sunlight Supernova Temporal finitism Trepidation Triangulation Tusi couple Universe


Al-Azhar University House of Knowledge House of Wisdom University of Al Quaraouiyine Observatories

Constantinople (Taqi al-Din) Maragheh Samarkand (Ulugh Beg)


Babylonian astronomy Egyptian astronomy Hellenistic astronomy Indian astronomy


Byzantine science Chinese astronomy Medieval European science Indian astronomy

v t e

Geography and cartography in medieval Islam


9th century

Muḥammad ibn Mūsā al-Khwārizmī Abū Ḥanīfa Dīnawarī Ya'qubi Sulaiman al-Tajir

10th century

Ibn Khordadbeh Ahmad ibn Rustah Ahmad ibn Fadlan Abu Zayd al-Balkhi Abū Muhammad al-Hasan al-Hamdānī Al-Masudi Istakhri Khashkhash Ibn Saeed Ibn Aswad Ibn Hawqal Ibn al-Faqih Al-Muqaddasi Al-Ramhormuzi

11th century

Abū Rayḥān al-Bīrūnī Abu Saʿīd Gardēzī Al-Bakri Mahmud al-Kashgari Domiyat

12th century

Al-Zuhri Muhammad al-Idrisi Abu'l Abbas al-Hijazi

13th century

Ibn Jubayr Saadi Shirazi Yaqut al-Hamawi Ibn Said al-Maghribi Ibn al-Nafis

14th century

Al-Dimashqi Abu'l-Fida Ibn al-Wardi Hamdollah Mostowfi Ibn Battuta Lin Nu

15th century

Abd-al-Razzāq Samarqandī Ghiyāth al-dīn Naqqāsh Ahmad ibn Mājid Zheng He Ma Huan Fei Xin

16th century

Sulaiman Al Mahri Piri Reis Mir Ahmed Nasrallah Thattvi Amīn Rāzī

17th century

Evliya Çelebi


Book of Roads and Kingdoms (al-Bakrī) Book of Roads and Kingdoms (ibn Khordadbeh) Tabula Rogeriana Kitab al-Rawd al-Mitar Mu'jam Al-Buldan Rihla The Meadows of Gold Piri Reis
Piri Reis


Geography (Ptolemy)

Authority control

WorldCat Identities VIAF: 365144782982270357614 LCCN: n84020660 ISNI: 0000 0001 2030 4018 GND: 118676180 SELIBR: 33137 SUDOC: 030896711 BNF: cb165923408 (data) NLA: 35538363 NKC: ola2002161