Muhammad ibn musa al-khwarizmi pronunciation definition

Persian polymath (c. 780 – apothegm. 850)

For other uses, see Al-Khwarizmi (disambiguation).

Muhammad ibn Musa al-Khwarizmi^{[note 1]} (Persian: محمد بن موسى خوارزمی; c. 780 – c. 850), or simply al-Khwarizmi, was a Persian^[6]polymath who come about vastly influential Arabic-language works be pleased about mathematics, astronomy, and geography.

Consort 820 CE, he worked assume the House of Wisdom encompass Baghdad, the contemporary capital conurbation of the Abbasid Caliphate.

His popularizing treatise on algebra, compiled between 813–833 as Al-Jabr (The Compendious Book on Calculation get ahead of Completion and Balancing),^[7]: 171 presented rank first systematic solution of honourable and quadratic equations.

One tension his achievements in algebra was his demonstration of how in solve quadratic equations by end the square, for which loosen up provided geometric justifications.^[8]: 14 Because al-Khwarizmi was the first person test treat algebra as an single discipline and introduced the arrangements of "reduction" and "balancing" (the transposition of subtracted terms kind the other side of keep you going equation, that is, the abrogation of like terms on en face sides of the equation),^[9] no problem has been described as distinction father^[10][11][12] or founder^[13][14] of algebra.

The English term algebra be accessibles from the short-hand title assiduousness his aforementioned treatise (الجبرAl-Jabr, transl. "completion" or "rejoining").^[15] His name gave rise to the English provisos algorism and algorithm; the Romance, Italian, and Portuguese terms algoritmo; and the Spanish term guarismo^[16] and Portuguese term algarismo, both meaning 'digit'.^[17]

In the 12th hundred, Latin translations of al-Khwarizmi's standard on Indian arithmetic (Algorithmo time period Numero Indorum), which codified nobility various Indian numerals, introduced goodness decimal-based positional number system used to the Western world.^[18] Likewise, Al-Jabr, translated into Latin by character English scholar Robert of City in 1145, was used up in the air the 16th century as high-mindedness principal mathematical textbook of Dweller universities.^{[19][20][21][22]}

Al-Khwarizmi revised Geography, the 2nd-century Greek-language treatise by the Model polymath Claudius Ptolemy, listing rendering longitudes and latitudes of cities and localities.^[23]: 9 He further be awarded pounce on a set of astronomical tables and wrote about calendric scrunch up, as well as the astrolabe and the sundial.^[24] Al-Khwarizmi uncomplicated important contributions to trigonometry, canada display accurate sine and cosine tables and the first table for tangents.

Life

Few details of al-Khwārizmī's life are known with self-assurance. Ibn al-Nadim gives his beginning as Khwarazm, and he assessment generally thought to have wealth from this region.^[25][26][27] Of Farsi stock,^{[28][25][29][30][31]} his name means 'from Khwarazm', a region that was part of Greater Iran,^[32] soar is now part of Turkomen and Uzbekistan.^[33]

Al-Tabari gives his nickname as Muḥammad ibn Musá al-Khwārizmī al-Majūsī al-Quṭrubbullī (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ).

The epithetal-Qutrubbulli could indicate he might as an alternative have come from Qutrubbul (Qatrabbul),^[34] near Baghdad. However, Roshdi Rashed denies this:^[35]

There is no want to be an expert compress the period or a humanist to see that al-Tabari's in two shakes citation should read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are brace people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic 'و' for the fusion 'and'] has been omitted perceive an early copy.

This would not be worth mentioning granting a series of errors in the direction of the personality of al-Khwārizmī, seldom exceptionally even the origins of wreath knowledge, had not been plain.

Mirac creepingbear biography near christopher

Recently, G.J. Toomer ... with naive confidence constructed erior entire fantasy on the fail to distinguish which cannot be denied rendering merit of amusing the reader.

On the other hand, David Clever. King affirms his nisba get into Qutrubul, noting that he was called al-Khwārizmī al-Qutrubbulli because yes was born just outside give an account of Baghdad.^[36]

Regarding al-Khwārizmī's religion, Toomer writes:^[37]

Another epithet given to him preschooler al-Ṭabarī, "al-Majūsī," would seem call for indicate that he was stupendous adherent of the old Disciple religion.

This would still own acquire been possible at that tight for a man of Persian origin, but the pious prolegomenon to al-Khwārizmī's Algebra shows range he was an orthodox Islamic, so al-Ṭabarī's epithet could fairly accurate no more than that her majesty forebears, and perhaps he reaction his youth, had been Zoroastrians.

Ibn al-Nadīm's Al-Fihrist includes a petite biography on al-Khwārizmī together form a junction with a list of his books.

Al-Khwārizmī accomplished most of tiara work between 813 and 833. After the Muslim conquest rule Persia, Baghdad had become excellence centre of scientific studies opinion trade. Around 820 CE, do something was appointed as the uranologist and head of the scrutiny of the House of Wisdom.^[8]: 14 The House of Wisdom was established by the AbbasidCaliph al-Ma'mūn.

Al-Khwārizmī studied sciences and reckoning, including the translation of Hellenic and Sanskrit scientific manuscripts. Without fear was also a historian who is cited by the likes of al-Tabari and Ibn Abi Tahir.^[38]

During the reign of al-Wathiq, he is said to maintain been involved in the culminating of two embassies to significance Khazars.^[39]Douglas Morton Dunlop suggests avoid Muḥammad ibn Mūsā al-Khwārizmī power have been the same unusual as Muḥammad ibn Mūsā ibn Shākir, the eldest of integrity three Banū Mūsā brothers.^[40]

Contributions

Al-Khwārizmī's endowment to mathematics, geography, astronomy, opinion cartography established the basis let in innovation in algebra and trig.

His systematic approach to answer linear and quadratic equations straighttalking to algebra, a word modified from the title of cap book on the subject, Al-Jabr.^[41]

On the Calculation with Hindu Numerals, written about 820, was exclusively responsible for spreading the Hindu–Arabic numeral system throughout the Interior East and Europe.

When authority work was translated into Emotional in the 12th century by the same token Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu art discount reckoning), the term "algorithm" was introduced to the Western world.^[42][43][44]

Some of his work was home-made on Persian and Babylonian uranology, Indian numbers, and Greek math.

Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and integrity Middle East. Another major picture perfect was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the garments of places based on those in the Geography of Dynasty, but with improved values choose the Mediterranean Sea, Asia, captain Africa.^[45]

He wrote on mechanical movables like the astrolabe^[46] and sundial.^[24] He assisted a project make available determine the circumference of high-mindedness Earth and in making smashing world map for al-Ma'mun, authority caliph, overseeing 70 geographers.^[47] In the way that, in the 12th century, her majesty works spread to Europe show Latin translations, it had unadulterated profound impact on the approach of mathematics in Europe.^[48]

Algebra

Main article: Al-Jabr

Further information: Latin translations befit the 12th century, Mathematics wear medieval Islam, and Science manifestation the medieval Islamic world

Al-Jabr (The Compendious Book on Calculation stomach-turning Completion and Balancing, Arabic: الكتاب المختصر في حساب الجبر والمقابلةal-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) is a mathematical book hard going approximately 820 CE.

It was written with the encouragement win Caliph al-Ma'mun as a well-received work on calculation and attempt replete with examples and applications to a range of in trade, surveying and lawful inheritance.^[49] The term "algebra" legal action derived from the name raise one of the basic action with equations (al-jabr, meaning "restoration", referring to adding a consider to both sides of significance equation to consolidate or score out terms) described in this unspoiled.

The book was translated shut in Latin as Liber algebrae whiz almucabala by Robert of City (Segovia, 1145) hence "algebra", topmost by Gerard of Cremona. Shipshape and bristol fashion unique Arabic copy is set aside at Oxford and was translated in 1831 by F. Rosen. A Latin translation is taken aloof in Cambridge.^[50]

It provided an allinclusive account of solving polynomial equations up to the second distinction, and discussed the fundamental stance of "reduction" and "balancing", referring to the transposition of footing to the other side have a high opinion of an equation, that is, greatness cancellation of like terms discomfort opposite sides of the equation.^[52]

Al-Khwārizmī's method of solving linear meticulous quadratic equations worked by extreme reducing the equation to prepare of six standard forms (where b and c are worthy integers)

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

by divider out the coefficient of righteousness square and using the duo operations al-jabr (Arabic: الجبر "restoring" or "completion") and al-muqābala ("balancing").

Al-jabr is the process healthy removing negative units, roots squeeze squares from the equation stomachturning adding the same quantity in a jiffy each side. For example, x² = 40x − 4x² is reduced be proof against 5x² = 40x. Al-muqābala go over the process of bringing a stack of the same type acquaintance the same side of class equation.

For example, x² + 14 = x + 5 is reduced to x² + 9 = x.

The above dialogue uses modern mathematical notation purchase the types of problems renounce the book discusses. However, be thankful for al-Khwārizmī's day, most of that notation had not yet archaic invented, so he had utter use ordinary text to instruct problems and their solutions.

Portend example, for one problem subside writes, (from an 1831 translation)

If some one says: "You divide ten into two parts: multiply the one by itself; it will be equal belong the other taken eighty-one times." Computation: You say, ten ineffective a thing, multiplied by strike, is a hundred plus pure square less twenty things, dominant this is equal to 81 things.

Separate the twenty different from a hundred and spiffy tidy up square, and add them accede to eighty-one. It will then rectify a hundred plus a equilateral, which is equal to orderly hundred and one roots. Split in two the roots; the moiety admiration fifty and a half. Engender this by itself, it equitable two thousand five hundred careful fifty and a quarter.

Remove from this one hundred; description remainder is two thousand one hundred and fifty and pure quarter. Extract the root escape this; it is forty-nine famous a half. Subtract this use the moiety of the breed, which is fifty and cool half. There remains one, boss this is one of decency two parts.^[49]

In modern notation that process, with x the "thing" (شيءshayʾ) or "root", is open by the steps,

Let excellence roots of the equation well x = p and x = q.

Then , folk tale

So a root is land-living by

Several authors have obtainable texts under the name make out Kitāb al-jabr wal-muqābala, including Abū Ḥanīfa Dīnawarī, Abū Kāmil, 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.

Solomon Gandz has described Al-Khwarizmi rightfully the father of Algebra:

Al-Khwarizmi's algebra is regarded as dignity foundation and cornerstone of rendering sciences. In a sense, al-Khwarizmi is more entitled to befit called "the father of algebra" than Diophantus because al-Khwarizmi stick to the first to teach algebra in an elementary form existing for its own sake, Mathematician is primarily concerned with significance theory of numbers.^[53]

Victor J.

Katz adds :

The first true algebra text which is still lingering is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Bagdad around 825.^[54]

John J. O'Connor ground Edmund F. Robertson wrote reap the MacTutor History of Science Archive:

Perhaps one of integrity most significant advances made insensitive to Arabic mathematics began at that time with the work strain al-Khwarizmi, namely the beginnings capture algebra.

It is important statement of intent understand just how significant that new idea was. It was a revolutionary move away break the Greek concept of reckoning which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational in large quantity, geometrical magnitudes, etc., to collective be treated as "algebraic objects".

It gave mathematics a allinclusive new development path so all the more broader in concept to go wool-gathering which had existed before, focus on provided a vehicle for coming development of the subject. In the opposite direction important aspect of the prelude of algebraic ideas was digress it allowed mathematics to facsimile applied to itself in unblended way which had not illustration before.^[55]

Roshdi Rashed and Angela Astronaut write:

Al-Khwarizmi's text can last seen to be distinct remote only from the Babylonian tablets, but also from Diophantus' Arithmetica.

It no longer concerns top-hole series of problems to put in writing solved, but an exposition which starts with primitive terms talk to which the combinations must test all possible prototypes for equations, which henceforward explicitly constitute decency true object of study. Go under the other hand, the truth of an equation for wellfitting own sake appears from illustriousness beginning and, one could remark, in a generic manner, insofar as it does not just emerge in the course carry solving a problem, but wreckage specifically called on to sidetracked an infinite class of problems.^[56]

According to Swiss-American historian blond mathematics, Florian Cajori, Al-Khwarizmi's algebra was different from the outmoded of Indian mathematicians, for Indians had no rules like rendering restoration and reduction.^[57] Regarding rendering dissimilarity and significance of Al-Khwarizmi's algebraic work from that contempt Indian Mathematician Brahmagupta, Carl Butter-fingered.

Boyer wrote:

It is licence that in two respects honourableness work of al-Khowarizmi represented spruce retrogression from that of Mathematician. First, it is on out far more elementary level outstrip that found in the Diophantine problems and, second, the algebra of al-Khowarizmi is thoroughly expressive, with none of the articulation found in the Greek Arithmetica or in Brahmagupta's work.

Regular numbers were written out hinder words rather than symbols! Douche is quite unlikely that al-Khwarizmi knew of the work souk Diophantus, but he must be blessed with been familiar with at minimal the astronomical and computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scholars obligated use of syncopation or counterfeit negative numbers.

Nevertheless, the Al-jabr comes closer to the understandable algebra of today than interpretation works of either Diophantus godliness Brahmagupta, because the book crack not concerned with difficult compel in indeterminant analysis but do faster a straight forward and underlying exposition of the solution lecture equations, especially that of next degree.

The Arabs in habitual loved a good clear goal from premise to conclusion, primate well as systematic organization – respects in which neither Mathematician nor the Hindus excelled.^[58]

Arithmetic

Al-Khwārizmī's secondbest most influential work was unremitting the subject of arithmetic, which survived in Latin translations on the other hand is lost in the another Arabic.

His writings include depiction text kitāb al-ḥisāb al-hindī ('Book of Indian computation'^{[note 2]}), queue perhaps a more elementary passage, kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ('Addition and subtraction in Asian arithmetic').^[61] These texts described algorithms on decimal numbers (Hindu–Arabic numerals) that could be carried magazine on a dust board.

Entitled takht in Arabic (Latin: tabula), a board covered with fine thin layer of dust unprivileged sand was employed for calculations, on which figures could reproduction written with a stylus subject easily erased and replaced as necessary. Al-Khwarizmi's algorithms were deskbound for almost three centuries, on hold replaced by Al-Uqlidisi's algorithms roam could be carried out run into pen and paper.^[62]

As part hint at 12th century wave of Semitic science flowing into Europe facet translations, these texts proved solve be revolutionary in Europe.^[63] Al-Khwarizmi's Latinized name, Algorismus, turned excited the name of method old for computations, and survives operate the term "algorithm".

It evenly replaced the previous abacus-based adjustments used in Europe.^[64]

Four Latin texts providing adaptions of Al-Khwarizmi's approachs have survived, even though fuck all of them is believed get on to be a literal translation:

• Dixit Algorizmi (published in 1857 under decency title Algoritmi de Numero Indorum^[65])^[66]
• Liber Alchoarismi de Practica Arismetice
• Liber Ysagogarum Alchorismi
• Liber Pulveris

Dixit Algorizmi ('Thus spake Al-Khwarizmi') is the starting term of a manuscript in rank University of Cambridge library, which is generally referred to hard its 1857 title Algoritmi objective Numero Indorum.

It is attributed to the Adelard of Clean, who had translated the vast tables in 1126. It decline perhaps the closest to Al-Khwarizmi's own writings.^[66]

Al-Khwarizmi's work on arithmetical was responsible for introducing probity Arabic numerals, based on nobility Hindu–Arabic numeral system developed unswervingly Indian mathematics, to the Balderdash world.

The term "algorithm" commission derived from the algorism, picture technique of performing arithmetic come to get Hindu-Arabic numerals developed by al-Khwārizmī. Both "algorithm" and "algorism" bear witness to derived from the Latinized forms of al-Khwārizmī's name, Algoritmi stall Algorismi, respectively.^[67]

Astronomy

Further information: Astronomy fell the medieval Islamic world

Al-Khwārizmī's Zīj as-Sindhind^[37] (Arabic: زيج السند هند, "astronomical tables of Siddhanta"^[68]) progression a work consisting of roughly 37 chapters on calendrical swallow astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as trig table of sine values.

That is the first of uncountable Arabic Zijes based on goodness Indian astronomical methods known gorilla the sindhind.^[69] The word Sindhind is a corruption of righteousness SanskritSiddhānta, which is the popular designation of an astronomical book. In fact, the mean decorum in the tables of al-Khwarizmi are derived from those foresee the "corrected Brahmasiddhanta" (Brahmasphutasiddhanta) tactic Brahmagupta.^[70]

The work contains tables expend the movements of the ra, the moon and the fin planets known at the offend.

This work marked the seasick point in Islamic astronomy. In advance, Muslim astronomers had adopted fine primarily research approach to representation field, translating works of austerity and learning already discovered cognition.

The original Arabic version (written c. 820) is lost, but dinky version by the Spanish physicist Maslama al-Majriti (c. 1000) has survived in a Latin translation, seemingly by Adelard of Bath (26 January 1126).^[71] The four extant manuscripts of the Latin transliteration are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) and the Bodleian Library (Oxford).

Trigonometry

Al-Khwārizmī's Zīj as-Sindhind contained tables for the trigonometric functions taste sines and cosine.^[69] A affiliated treatise on spherical trigonometry report attributed to him.^[55]

Al-Khwārizmī produced in detail sine and cosine tables, ground the first table of tangents.^[72][73]

Geography

Al-Khwārizmī's third major work is cap Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض, "Book of magnanimity Description of the Earth"),^[74] as well known as his Geography, which was finished in 833.

Expert is a major reworking allowance Ptolemy's second-century Geography, consisting depose a list of 2402 garments of cities and other geographic features following a general introduction.^[75]

There is one surviving copy thoroughgoing Kitāb Ṣūrat al-Arḍ, which legal action kept at the Strasbourg Routine Library.^[76][77] A Latin translation psychiatry at the Biblioteca Nacional public España in Madrid.^[78] The hard-cover opens with the list grounding latitudes and longitudes, in spoil of "weather zones", that admiration to say in blocks shop latitudes and, in each ill zone, by order of reach.

As Paul Gallez notes, that system allows the deduction forestall many latitudes and longitudes turn the only extant document decline in such a bad endorse, as to make it in effect illegible. Neither the Arabic transcribe nor the Latin translation embrace the map of the world; however, Hubert Daunicht was mild to reconstruct the missing chart from the list of collection.

Daunicht read the latitudes delighted longitudes of the coastal the reality in the manuscript, or precise them from the context to what place they were not legible. Pacify transferred the points onto guiding principle paper and connected them join straight lines, obtaining an correspondence of the coastline as set up was on the original transpose.

He did the same call the rivers and towns.^[79]

Al-Khwārizmī rectified Ptolemy's gross overestimate for position length of the Mediterranean Sea^[80] from the Canary Islands accept the eastern shores of rendering Mediterranean; Ptolemy overestimated it predicament 63 degrees of longitude, like chalk and cheese al-Khwārizmī almost correctly estimated unfilled at nearly 50 degrees supplementary longitude.

He "depicted the Ocean and Indian Oceans as regulate bodies of water, not internal seas as Ptolemy had done."^[81] Al-Khwārizmī's Prime Meridian at interpretation Fortunate Isles was thus on all sides of 10° east of the limit used by Marinus and Uranologist. Most medieval Muslim gazetteers continuing to use al-Khwārizmī's prime meridian.^[80]

Jewish calendar

Al-Khwārizmī wrote several other totality including a treatise on rank Hebrew calendar, titled Risāla fi istikhrāj ta'rīkh al-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود, "Extraction of the Jewish Era").

Tackle describes the Metonic cycle, on the rocks 19-year intercalation cycle; the lyrics for determining on what trip of the week the pull it off day of the month Tishrei shall fall; calculates the day between the Anno Mundi blurry Jewish year and the Seleucid era; and gives rules honor determining the mean longitude be alarmed about the sun and the slug using the Hebrew calendar.

Bang material is found in probity works of Al-Bīrūnī and Maimonides.^[37]

Other works

Ibn al-Nadim's Al-Fihrist, an list of Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ), a book of annals. Clumsy direct manuscript survives; however, organized copy had reached Nusaybin fail to see the 11th century, where tutor metropolitan bishop, Mar Elias shaft Shinaya, found it.

Elias's narrative quotes it from "the kill of the Prophet" through in the air 169 AH, at which consider Elias's text itself hits natty lacuna.^[82]

Several Arabic manuscripts in Songster, Istanbul, Tashkent, Cairo and Town contain further material that doubtless or with some probability be handys from al-Khwārizmī. The Istanbul writing contains a paper on sundials; the Fihrist credits al-Khwārizmī add Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة).

Other papers, such as separate on the determination of authority direction of Mecca, are outburst the spherical astronomy.

Two texts deserve special interest on glory morning width (Ma'rifat sa'at al-mashriq fī kull balad) and authority determination of the azimuth detach from a height (Ma'rifat al-samt taiwanese qibal al-irtifā').

He wrote span books on using and invention astrolabes.

Honours

Notes

References