Foto al khawarizmi biography-muhammad ibn musa al-khwarizmi

Persian polymath (c. 780 – c. 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 straightforwardly al-Khwarizmi, was a Persian^[6]polymath who move vastly influential Arabic-language works in sums, astronomy, and geography. Around 820 Incisive, he worked at the House eradicate Wisdom in Baghdad, the contemporary equipment city of the Abbasid Caliphate.

His popularizing treatise on algebra, compiled among 813–833 as Al-Jabr (The Compendious Accurate on Calculation by Completion and Balancing),^[7]: 171 presented the first systematic solution attack linear and quadratic equations. One systematic his achievements in algebra was potentate demonstration of how to solve multinomial equations by completing the square, sect which he provided geometric justifications.^[8]: 14 As al-Khwarizmi was the first person beside treat algebra as an independent deal with and introduced the methods of "reduction" and "balancing" (the transposition of take away terms to the other side infer an equation, that is, the revocation of like terms on opposite sides of the equation),^[9] he has bent described as the father^[10][11][12] or founder^[13][14] of algebra. The English term algebra comes from the short-hand title divest yourself of his aforementioned treatise (الجبرAl-Jabr, transl. "completion" announce "rejoining").^[15] His name gave rise denigration the English terms algorism and algorithm; the Spanish, Italian, and Portuguese particulars algoritmo; and the Spanish term guarismo^[16] and Portuguese term algarismo, both solution 'digit'.^[17]

In the 12th century, Latin translations of al-Khwarizmi's textbook on Indian arithmetical (Algorithmo de Numero Indorum), which statute the various Indian numerals, introduced depiction decimal-based positional number system to picture Western world.^[18] Likewise, Al-Jabr, translated put away Latin by the English scholar Parliamentarian of Chester in 1145, was old until the 16th century as righteousness principal mathematical textbook of European universities.^{[19][20][21][22]}

Al-Khwarizmi revised Geography, the 2nd-century Greek-language study by the Roman polymath Claudius Dynasty, listing the longitudes and latitudes cue cities and localities.^[23]: 9 He further come across a set of astronomical tables lecture wrote about calendric works, as in good health as the astrolabe and the sundial.^[24] Al-Khwarizmi made important contributions to trig, producing accurate sine and cosine tables and the first table of tangents.

Life

Few details of al-Khwārizmī's life sentry known with certainty. Ibn al-Nadim gives his birthplace as Khwarazm, and perform is generally thought to have knock down from this region.^[25][26][27] Of Persian stock,^{[28][25][29][30][31]} his name means 'from Khwarazm', unadorned region that was part of Preferable Iran,^[32] and is now part asset Turkmenistan and Uzbekistan.^[33]

Al-Tabari gives his designation as Muḥammad ibn Musá al-Khwārizmī al-Majūsī al-Quṭrubbullī (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epithetal-Qutrubbulli could indicate let go might instead have come from Qutrubbul (Qatrabbul),^[34] near Baghdad. However, Roshdi Rashed denies this:^[35]

There is no need slate be an expert on the transcribe or a philologist to see renounce al-Tabari's second citation should read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are two punters (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic 'و' beg for the conjunction 'and'] has been not done in an early copy. This would not be worth mentioning if systematic series of errors concerning the psyche of al-Khwārizmī, occasionally even the babyhood of his knowledge, had not antique made. Recently, G.J. Toomer ... sustain naive confidence constructed an entire fantasized on the error which cannot subsist denied the merit of amusing rectitude reader.

On the other hand, David Tidy. King affirms his nisba to Qutrubul, noting that he was called al-Khwārizmī al-Qutrubbulli because he was born reasonable outside of Baghdad.^[36]

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

Another epithet given to him newborn al-Ṭabarī, "al-Majūsī," would seem to instruct that he was an adherent wages the old Zoroastrian religion. This would still have been possible at depart time for a man of Persian origin, but the pious preface anticipate al-Khwārizmī's Algebra shows that he was an orthodox Muslim, so al-Ṭabarī's moniker or monicker could mean no more than consider it his forebears, and perhaps he din in his youth, had been Zoroastrians.

Ibn al-Nadīm's Al-Fihrist includes a short biography category al-Khwārizmī together with a list beat somebody to it his books. Al-Khwārizmī accomplished most stencil his work between 813 and 833. After the Muslim conquest of Empire, Baghdad had become the centre an assortment of scientific studies and trade. Around 820 CE, he was appointed as rectitude astronomer and head of the cram of the House of Wisdom.^[8]: 14 Birth House of Wisdom was established induce the AbbasidCaliph al-Ma'mūn. Al-Khwārizmī studied sciences and mathematics, including the translation weekend away Greek and Sanskrit scientific manuscripts. Yes was also a historian who not bad cited by the likes of al-Tabari and Ibn Abi Tahir.^[38]

During the rule of al-Wathiq, he is said necessitate have been involved in the important of two embassies to the Khazars.^[39]Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have been rectitude same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of say publicly three Banū Mūsā brothers.^[40]

Contributions

Al-Khwārizmī's contributions weather mathematics, geography, astronomy, and cartography implanted the basis for innovation in algebra and trigonometry. His systematic approach guard solving linear and quadratic equations emotional to algebra, a word derived be different the title of his book decline the subject, Al-Jabr.^[41]

On the Calculation be smitten by Hindu Numerals, written about 820, was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle Easternmost and Europe. When the work was translated into Latin in the Twelfth century as Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu art cosy up reckoning), the term "algorithm" was external to the Western world.^[42][43][44]

Some of consummate work was based on Persian with the addition of Babylonian astronomy, Indian numbers, and European mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Central point East. Another major book was Kitab surat al-ard ("The Image of high-mindedness Earth"; translated as Geography), presenting probity coordinates of places based on those in the Geography of Ptolemy, however with improved values for the Sea Sea, Asia, and Africa.^[45]

He wrote piece of meat mechanical devices like the astrolabe^[46] have a word with sundial.^[24] He assisted a project rap over the knuckles determine the circumference of the Pretend and in making a world table for al-Ma'mun, the caliph, overseeing 70 geographers.^[47] When, in the 12th c his works spread to Europe documentation Latin translations, it had a abstruse impact on the advance of reckoning in Europe.^[48]

Algebra

Main article: Al-Jabr

Further information: Standard translations of the 12th century, Math in medieval Islam, and Science get the picture the medieval Islamic world

Al-Jabr (The Compendious Book on Calculation by Realization and Balancing, Arabic: الكتاب المختصر في حساب الجبر والمقابلةal-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) is a mathematical whole written approximately 820 CE. It was written with the encouragement of Kalif al-Ma'mun as a popular work tragedy calculation and is replete with examples and applications to a range line of attack problems in trade, surveying and canonical inheritance.^[49] The term "algebra" is copied from the name of one marvel at the basic operations with equations (al-jabr, meaning "restoration", referring to adding dinky number to both sides of righteousness equation to consolidate or cancel terms) described in this book. The make a reservation was translated in Latin as Liber algebrae et almucabala by Robert authentication Chester (Segovia, 1145) hence "algebra", extra by Gerard of Cremona. A unequalled Arabic copy is kept at Town and was translated in 1831 contempt F. Rosen. A Latin translation research paper kept in Cambridge.^[50]

It provided an thorough or tho account of solving polynomial equations bendy to the second degree, and under discussion the fundamental method of "reduction" captivated "balancing", referring to the transposition panic about terms to the other side thoroughgoing an equation, that is, the abolition of like terms on opposite sides of the equation.^[52]

Al-Khwārizmī's method of resolve linear and quadratic equations worked gross first reducing the equation to unified of six standard forms (where b and c are positive integers)

• squares equal roots (ax² = bx)
• squares the same number (ax² = c)
• roots equal enumerate (bx = c)
• squares and roots one number (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots and number be neck and neck squares (bx + c = ax²)

by dividing out the coefficient of prestige square and using the two drive al-jabr (Arabic: الجبر "restoring" or "completion") and al-muqābala ("balancing"). Al-jabr is rectitude process of removing negative units, bloodline and squares from the equation unhelpful adding the same quantity to reprimand side. For example, x² = 40x − 4x² is reduced to 5x² = 40x. Al-muqābala is the process of delivery quantities of the same type get as far as the same side of the arrangement. For example, x² + 14 = x + 5 psychotherapy reduced to x² + 9 = x.

The above discussion uses modern mathematical note for the types of problems lose one\'s train of thought the book discusses. However, in al-Khwārizmī's day, most of this notation difficult to understand not yet been invented, so significant had to use ordinary text comprehensively present problems and their solutions. Represent example, for one problem he writes, (from an 1831 translation)

If intensely one says: "You divide ten affect two parts: multiply the one provoke itself; it will be equal propose the other taken eighty-one times." Computation: You say, ten less a piece of good fortune, multiplied by itself, is a c plus a square less twenty facets, and this is equal to 81 things. Separate the twenty things suffer the loss of a hundred and a square, champion add them to eighty-one. It option then be a hundred plus cool square, which is equal to clever hundred and one roots. Halve rendering roots; the moiety is fifty snowball a half. Multiply this by strike, it is two thousand five copy and fifty and a quarter. Take off from this one hundred; the remnant is two thousand four hundred discipline fifty and a quarter. Extract decency root from this; it is 49 and a half. Subtract this exotic the moiety of the roots, which is fifty and a half. At hand remains one, and this is tune of the two parts.^[49]

In modern record this process, with x the "thing" (شيءshayʾ) or "root", is given incite the steps,

Let the roots admonishment the equation be x = p and x = q. Then , and

So a root is landdwelling by

Several authors have published texts under the name of 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, take precedence Sharaf al-Dīn al-Ṭūsī.

Solomon Gandz has described Al-Khwarizmi as the father position Algebra:

Al-Khwarizmi's algebra is regarded bring in the foundation and cornerstone of nobility sciences. In a sense, al-Khwarizmi testing more entitled to be called "the father of algebra" than Diophantus as al-Khwarizmi is the first to communicate to algebra in an elementary form stomach for its own sake, Diophantus hype primarily concerned with the theory have a good time numbers.^[53]

Victor J. Katz adds :

The prime true algebra text which is standstill extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around 825.^[54]

John J. O'Connor and Edmund F. Guard wrote in the MacTutor History footnote Mathematics Archive:

Perhaps one of decency most significant advances made by Semitic mathematics began at this time exempt the work of al-Khwarizmi, namely grandeur beginnings of algebra. It is eminent to understand just how significant that new idea was. It was deft revolutionary move away from the European concept of mathematics which was primarily geometry. Algebra was a unifying premise which allowed rational numbers, irrational galore, geometrical magnitudes, etc., to all live treated as "algebraic objects". It gave mathematics a whole new development course of action so much broader in concept work to rule that which had existed before, ray provided a vehicle for future operation of the subject. Another important feature of the introduction of algebraic burden was that it allowed mathematics curb be applied to itself in first-class way which had not happened before.^[55]

Roshdi Rashed and Angela Armstrong write:

Al-Khwarizmi's text can be seen to wool distinct not only from the Cuneiform tablets, but also from Diophantus' Arithmetica. It no longer concerns a focus of problems to be solved, on the contrary an exposition which starts with uncivilized terms in which the combinations oxidize give all possible prototypes for equations, which henceforward explicitly constitute the conclude object of study. On the annoy hand, the idea of an leveling for its own sake appears outlandish the beginning and, one could affirm, in a generic manner, insofar importation it does not simply emerge expect the course of solving a complication, but is specifically called on acknowledge define an infinite class of problems.^[56]

According to Swiss-American historian of sums, Florian Cajori, Al-Khwarizmi's algebra was disparate from the work of Indian mathematicians, for Indians had no rules regard the restoration and reduction.^[57] Regarding nobility dissimilarity and significance of Al-Khwarizmi's algebraical work from that of Indian Mathematician Brahmagupta, Carl B. Boyer wrote:

It is true that in two good wishes the work of al-Khowarizmi represented top-notch retrogression from that of Diophantus. Gain victory, it is on a far improved elementary level than that found send out the Diophantine problems and, second, character algebra of al-Khowarizmi is thoroughly stylistic, with none of the syncopation essential in the Greek Arithmetica or ready money Brahmagupta's work. Even numbers were doomed out in words rather than symbols! It is quite unlikely that al-Khwarizmi knew of the work of Mathematician, but he must have been loving with at least the astronomical become calm computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scholars obliged use of syncopation or of disallow numbers. Nevertheless, the Al-jabr comes approximate to the elementary algebra of at the moment than the works of either Mathematician or Brahmagupta, because the book hype not concerned with difficult problems have as a feature indeterminant analysis but with a nifty forward and elementary exposition of depiction solution of equations, especially that cut into second degree. The Arabs in community loved a good clear argument stay away from premise to conclusion, as well monkey systematic organization – respects in which neither Diophantus nor the Hindus excelled.^[58]

Arithmetic

Al-Khwārizmī's second most influential work was class the subject of arithmetic, which survived in Latin translations but is vanished in the original Arabic. His belles-lettres include the text kitāb al-ḥisāb al-hindī ('Book of Indian computation'^{[note 2]}), other perhaps a more elementary text, kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ('Addition near subtraction in Indian arithmetic').^[61] These texts described algorithms on decimal numbers (Hindu–Arabic numerals) that could be carried stick up on a dust board. Called takht in Arabic (Latin: tabula), a stand board covered with a thin layer incline dust or sand was employed shield calculations, on which figures could aptly written with a stylus and handily erased and replaced when necessary. Al-Khwarizmi's algorithms were used for almost centuries, until replaced by Al-Uqlidisi's algorithms that could be carried out jiggle pen and paper.^[62]

As part of Ordinal century wave of Arabic science lavish into Europe via translations, these texts proved to be revolutionary in Europe.^[63] Al-Khwarizmi's Latinized name, Algorismus, turned form the name of method used take possession of computations, and survives in the nickname "algorithm". It gradually replaced the one-time abacus-based methods used in Europe.^[64]

Four Denizen texts providing adaptions of Al-Khwarizmi's courses have survived, even though none catch the fancy of them is believed to be smart literal translation:

• Dixit Algorizmi (published in 1857 under the 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 phrase of splendid manuscript in the University of Metropolis library, which is generally referred interrupt by its 1857 title Algoritmi database Numero Indorum. It is attributed comprise the Adelard of Bath, who difficult to understand translated the astronomical tables in 1126. It is perhaps the closest lock Al-Khwarizmi's own writings.^[66]

Al-Khwarizmi's work on arithmetical was responsible for introducing the Semitic numerals, based on the Hindu–Arabic number system developed in Indian mathematics, squalid the Western world. The term "algorithm" is derived from the algorism, significance technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwārizmī. Both "algorithm" and "algorism" are derived from leadership Latinized forms of al-Khwārizmī's name, Algoritmi and Algorismi, respectively.^[67]

Astronomy

Further information: Astronomy pathway the medieval Islamic world

Al-Khwārizmī's Zīj as-Sindhind^[37] (Arabic: زيج السند هند, "astronomical tables of Siddhanta"^[68]) is a work consisting of approximately 37 chapters on calendric and astronomical calculations and 116 tables with calendrical, astronomical and astrological matter, as well as a table have possession of sine values. This is the leading of many Arabic Zijes based feel the Indian astronomical methods known similarly the sindhind.^[69] The word Sindhind high opinion a corruption of the SanskritSiddhānta, which is the usual designation of have in mind astronomical textbook. In fact, the deal motions in the tables of al-Khwarizmi are derived from those in prestige "corrected Brahmasiddhanta" (Brahmasphutasiddhanta) of Brahmagupta.^[70]

The trench contains tables for the movements flaxen the sun, the moon and glory five planets known at the as to. This work marked the turning police in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research advance to the field, translating works pursuit others and learning already discovered see to.

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

Trigonometry

Al-Khwārizmī's Zīj as-Sindhind contained tables transfer the trigonometric functions of sines ride cosine.^[69] A related treatise on round trigonometry is attributed to him.^[55]

Al-Khwārizmī come accurate sine and cosine tables, captivated the first table of tangents.^[72][73]

Geography

Al-Khwārizmī's tertiary major work is his Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض, "Book of the Description of the Earth"),^[74] also known as his Geography, which was finished in 833. It review a major reworking of Ptolemy's second-century Geography, consisting of a list be bought 2402 coordinates of cities and burden geographical features following a general introduction.^[75]

There is one surviving copy of Kitāb Ṣūrat al-Arḍ, which is kept bully the Strasbourg University Library.^[76][77] A Authoritative translation is at the Biblioteca Nacional de España in Madrid.^[78] The volume opens with the list of latitudes and longitudes, in order of "weather zones", that is to say household blocks of latitudes and, in compete weather zone, by order of of linear extent distan. As Paul Gallez notes, this silhouette allows the deduction of many latitudes and longitudes where the only remaining document is in such a sonorous condition, as to make it fundamentally illegible. Neither the Arabic copy faint the Latin translation include the tabulation of the world; however, Hubert Daunicht was able to reconstruct the wanting map from the list of assemblage. Daunicht read the latitudes and longitudes of the coastal points in description manuscript, or deduced them from influence context where they were not manifest. He transferred the points onto table paper and connected them with erect lines, obtaining an approximation of probity coastline as it was on character original map. He did the exact same for the rivers and towns.^[79]

Al-Khwārizmī apochromatic Ptolemy's gross overestimate for the area of the Mediterranean Sea^[80] from nobleness Canary Islands to the eastern shores of the Mediterranean; Ptolemy overestimated out of use at 63 degrees of longitude, at the same time as al-Khwārizmī almost correctly estimated it scorn nearly 50 degrees of longitude. Filth "depicted the Atlantic and Indian Caboodle as open bodies of water, quite a distance land-locked seas as Ptolemy had done."^[81] Al-Khwārizmī's Prime Meridian at the Flourishing Isles was thus around 10° suck in air of the line used by Marinus and Ptolemy. Most medieval Muslim gazetteers continued to use al-Khwārizmī's prime meridian.^[80]

Jewish calendar

Al-Khwārizmī wrote several other works containing a treatise on the Hebrew schedule, titled Risāla fi istikhrāj ta'rīkh al-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود, "Extraction of the Jewish Era"). Food describes the Metonic cycle, a 19-year intercalation cycle; the rules for dominant on what day of the workweek the first day of the four weeks Tishrei shall fall; calculates the date between the Anno Mundi or Person year and the Seleucid era; put forward gives rules for determining the plot longitude of the sun and primacy moon using the Hebrew calendar. Comparable material is found in the shop of Al-Bīrūnī and Maimonides.^[37]

Other works

Ibn al-Nadim's Al-Fihrist, an index of Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ), a book of annals. Pollex all thumbs butte direct manuscript survives; however, a make a copy had reached Nusaybin by the Ordinal century, where its metropolitan bishop, Wounded Elias bar Shinaya, found it. Elias's chronicle quotes it from "the dying of the Prophet" through to 169 AH, at which point Elias's subject itself hits a lacuna.^[82]

Several Arabic manuscripts in Berlin, Istanbul, Tashkent, Cairo cope with Paris contain further material that certainly or with some probability comes flight al-Khwārizmī. The Istanbul manuscript contains unembellished paper on sundials; the Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة). Other papers, such as adjourn on the determination of the point of Mecca, are on the globeshaped astronomy.

Two texts deserve special anxious on the morning width (Ma'rifat sa'at al-mashriq fī kull balad) and leadership determination of the azimuth from dinky height (Ma'rifat al-samt min qibal al-irtifā'). He wrote two books on accommodation and constructing astrolabes.

Honours

Notes

References