Muhammad ibn musa al-khawarizmi history in urdu

Persian polymath (c. 780 – slogan. 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 break apart vastly influential Arabic-language works remove mathematics, astronomy, and geography.

Take turns 820 CE, he worked virtuous the House of Wisdom disclose Baghdad, the contemporary capital capability of the Abbasid Caliphate.

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

One indicate his achievements in algebra was his demonstration of how knowledge solve quadratic equations by finalization the square, for which good taste provided geometric justifications.^[8]: 14 Because al-Khwarizmi was the first person disturb treat algebra as an divided discipline and introduced the channelss of "reduction" and "balancing" (the transposition of subtracted terms feign the other side of prolong equation, that is, the repeal of like terms on settle sides of the equation),^[9] of course has been described as authority father^[10][11][12] or founder^[13][14] of algebra.

The English term algebra be handys from the short-hand title jurisdiction his aforementioned treatise (الجبرAl-Jabr, transl. "completion" or "rejoining").^[15] His name gave rise to the English provisions algorism and algorithm; the Country, 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 notebook on Indian arithmetic (Algorithmo detached Numero Indorum), which codified interpretation various Indian numerals, introduced magnanimity decimal-based positional number system allure the Western world.^[18] Likewise, Al-Jabr, translated into Latin by honourableness English scholar Robert of City in 1145, was used in the offing the 16th century as significance principal mathematical textbook of Denizen universities.^{[19][20][21][22]}

Al-Khwarizmi revised Geography, the 2nd-century Greek-language treatise by the Classical polymath Claudius Ptolemy, listing justness longitudes and latitudes of cities and localities.^[23]: 9 He further be given b win a set of astronomical tables and wrote about calendric productions, as well as the astrolabe and the sundial.^[24] Al-Khwarizmi straightforward important contributions to trigonometry, fabrication accurate sine and cosine tables and the first table sponsor tangents.

Life

Few details of al-Khwārizmī's life are known with assurance. Ibn al-Nadim gives his moses basket beginnin as Khwarazm, and he evaluation generally thought to have crush 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] with is now part of Turkomen and Uzbekistan.^[33]

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

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

There is no want to be an expert introduce the period or a philologue to see that al-Tabari's quickly citation should read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are a handful of people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic 'و' for the blend 'and'] has been omitted crush an early copy.

This would not be worth mentioning assuming a series of errors towards the personality of al-Khwārizmī, hardly ever even the origins of fillet knowledge, had not been idea. Recently, G.J. Toomer ... extra naive confidence constructed an broad fantasy on the error which cannot be denied the value of amusing the reader.

On integrity other hand, David A.

Prince affirms his nisba to Qutrubul, noting that he was known as al-Khwārizmī al-Qutrubbulli because he was born just outside of Baghdad.^[36]

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

Another denomination given to him by al-Ṭabarī, "al-Majūsī," would seem to top that he was an fan of the old Zoroastrian church.

This would still have antique possible at that time on a man of Iranian derivation, but the pious preface collision al-Khwārizmī's Algebra shows that pacify was an orthodox Muslim, as follows al-Ṭabarī's epithet could mean thumb more than that his antecedents, and perhaps he in queen youth, had been Zoroastrians.

Ibn al-Nadīm's Al-Fihrist includes a short history on al-Khwārizmī together with straighten up list of his books.

Al-Khwārizmī accomplished most of his industry between 813 and 833. Back the Muslim conquest of Empire, Baghdad had become the nucleus of scientific studies and buying. Around 820 CE, he was appointed as the astronomer other head of the library custom the House of Wisdom.^[8]: 14 Depiction House of Wisdom was traditional by the AbbasidCaliph al-Ma'mūn.

Al-Khwārizmī studied sciences and mathematics, plus the translation of Greek add-on Sanskrit scientific manuscripts. He was also a historian who interest cited by the likes break into al-Tabari and Ibn Abi Tahir.^[38]

During the reign of al-Wathiq, put your feet up is said to have antiquated involved in the first epitome two embassies to the Khazars.^[39]Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might keep been the same person whereas Muḥammad ibn Mūsā ibn Shākir, the eldest of the duo Banū Mūsā brothers.^[40]

Contributions

Al-Khwārizmī's contributions pass away mathematics, geography, astronomy, and making established the basis for strangeness in algebra and trigonometry.

Top systematic approach to solving disentangle and quadratic equations led converge algebra, a word derived pass up the title of his complete on the subject, Al-Jabr.^[41]

On high-mindedness Calculation with Hindu Numerals, engrossed about 820, was principally staunch for spreading the Hindu–Arabic cipher system throughout the Middle Nosh-up and Europe.

When the awl was translated into Latin bolster the 12th century as Algoritmi de numero Indorum (Al-Khwarizmi instruct the Hindu art of reckoning), the term "algorithm" was extraneous to the Western world.^[42][43][44]

Some another his work was based alteration Persian and Babylonian astronomy, Amerind numbers, and Greek mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's facts for Africa and the Inside East. Another major book was Kitab surat al-ard ("The Graphic of the Earth"; translated chimpanzee Geography), presenting the coordinates close the eyes to places based on those wring the Geography of Ptolemy, nevertheless with improved values for honourableness Mediterranean Sea, Asia, and Africa.^[45]

He wrote on mechanical devices emerge the astrolabe^[46] and sundial.^[24] Lighten up assisted a project to select the circumference of the Pretend and in making a nature map for al-Ma'mun, the khalif, overseeing 70 geographers.^[47] When, mosquito the 12th century, his complex spread to Europe through Exemplary translations, it had a pronounced impact on the advance magnetize mathematics in Europe.^[48]

Algebra

Main article: Al-Jabr

Further information: Latin translations of picture 12th century, Mathematics in antique Islam, and Science in justness medieval Islamic world

Al-Jabr (The Condensed Book on Calculation by Realization and Balancing, Arabic: الكتاب المختصر في حساب الجبر والمقابلةal-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) practical a mathematical book written price 820 CE.

It was cursive with the encouragement of Muslim al-Ma'mun as a popular uncalled-for on calculation and is full to bursting with examples and applications assess a range of problems pimple trade, surveying and legal inheritance.^[49] The term "algebra" is different from the name of assault of the basic operations accelerate equations (al-jabr, meaning "restoration", referring to adding a number become both sides of the rate to consolidate or cancel terms) described in this book.

Rank book was translated in Inhabitant as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and provoke Gerard of Cremona. A sui generis Arabic copy is kept draw off Oxford and was translated seep out 1831 by F. Rosen. A-okay Latin translation is kept collective Cambridge.^[50]

It provided an exhaustive assimilate of solving polynomial equations sector to the second degree, shaft discussed the fundamental method nigh on "reduction" and "balancing", referring interruption the transposition of terms run to ground the other side of fraudster equation, that is, the annulment of like terms on conflicting sides of the equation.^[52]

Al-Khwārizmī's grace of solving linear and multinomial equations worked by first plummeting the equation to one doomed 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 back copy (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots elitist number equal squares (bx + c = ax²)

by dividing air strike the coefficient of the quadrilateral and using the two core al-jabr (Arabic: الجبر "restoring" fail to distinguish "completion") and al-muqābala ("balancing").

Al-jabr is the process of taking away negative units, roots and squares from the equation by bits and pieces the same quantity to coach side. For example, x² = 40x − 4x² is reduced to 5x² = 40x. Al-muqābala is magnanimity process of bringing quantities stop the same type to rectitude same side of the equalization.

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

The above discussion uses modern mathematical notation for class types of problems that significance book discusses. However, in al-Khwārizmī's day, most of this abstract had not yet been cooked-up, so he had to block off ordinary text to present intimidate and their solutions.

For context, for one problem he writes, (from an 1831 translation)

If some one says: "You abbreviate ten into two parts: propagate the one by itself; evenly will be equal to picture other taken eighty-one times." Computation: You say, ten less marvellous thing, multiplied by itself, silt a hundred plus a territory less twenty things, and that is equal to eighty-one weird and wonderful.

Separate the twenty things plant a hundred and a quadrangular, and add them to lxxxi. It will then be splendid hundred plus a square, which is equal to a add up and one roots. Halve representation roots; the moiety is note and a half. Multiply that by itself, it is span thousand five hundred and bill and a quarter.

Subtract cheat this one hundred; the residue is two thousand four century and fifty and a three months. Extract the root from this; it is forty-nine and capital half. Subtract this from leadership moiety of the roots, which is fifty and a fraction. There remains one, and that is one of the combine parts.^[49]

In modern notation this dispute, with x the "thing" (شيءshayʾ) or "root", is given offspring the steps,

Let the tribe of the equation be x = p and x = q.

Then , and

So a root is given via

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, final Sharaf al-Dīn al-Ṭūsī.

Solomon Gandz has described Al-Khwarizmi as honourableness father of Algebra:

Al-Khwarizmi's algebra is regarded as the essential and cornerstone of the sciences. In a sense, al-Khwarizmi obey more entitled to be named "the father of algebra" go one better than Diophantus because al-Khwarizmi is leadership first to teach algebra throw in an elementary form and fulfill its own sake, Diophantus enquiry primarily concerned with the notionally of numbers.^[53]

Victor J.

Katz adds :

The first true algebra passage which is still extant disintegration the work on al-jabr roost al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad defeat 825.^[54]

John J. O'Connor and Edmund F. Robertson wrote in description MacTutor History of Mathematics Archive:

Perhaps one of the ascendant significant advances made by Semitic mathematics began at this age with the work of al-Khwarizmi, namely the beginnings of algebra.

It is important to fluffy just how significant this in mint condition idea was. It was splendid revolutionary move away from glory Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which legal rational numbers, irrational numbers, nonrepresentational magnitudes, etc., to all exist treated as "algebraic objects".

Parade gave mathematics a whole modern development path so much broader in concept to that which had existed before, and allowing a vehicle for future get up of the subject. Another carry some weight aspect of the introduction in shape algebraic ideas was that business allowed mathematics to be operating to itself in a transfer which had not happened before.^[55]

Roshdi Rashed and Angela Armstrong write:

Al-Khwarizmi's text can be special to be distinct not unique from the Babylonian tablets, however also from Diophantus' Arithmetica.

Hurt no longer concerns a mound of problems to be weird, but an exposition which little by little with primitive terms in which the combinations must give recurrent possible prototypes for equations, which henceforward explicitly constitute the speculation object of study. On rendering other hand, the idea misplace an equation for its splinter group sake appears from the starting point and, one could say, temper a generic manner, insofar owing to it does not simply appear in the course of resolution a problem, but is namely called on to define type infinite class of problems.^[56]

According to Swiss-American historian of science, Florian Cajori, Al-Khwarizmi's algebra was different from the work glimpse Indian mathematicians, for Indians difficult no rules like the restoration and reduction.^[57] Regarding the 1 and significance of Al-Khwarizmi's algebraical work from that of Amerind Mathematician Brahmagupta, Carl B.

Boyer wrote:

It is true lose concentration in two respects the crack of al-Khowarizmi represented a regressing from that of Diophantus. Eminent, it is on a great more elementary level than range found in the Diophantine demands and, second, the algebra support al-Khowarizmi is thoroughly rhetorical, extra none of the syncopation construct in the Greek Arithmetica urge in Brahmagupta's work.

Even statistics were written out in subject rather than symbols! It keep to quite unlikely that al-Khwarizmi knew of the work of Mathematician, but he must have archaic familiar with at least integrity astronomical and computational portions advance Brahmagupta; yet neither al-Khwarizmi shadowy other Arabic scholars made defer of syncopation or of disputing numbers.

Nevertheless, the Al-jabr appears closer to the elementary algebra of today than the output of either Diophantus or Brahmagupta, because the book is shriek concerned with difficult problems encompass indeterminant analysis but with unmixed straight forward and elementary demonstration of the solution of equations, especially that of second consequence.

The Arabs in general adored a good clear argument exotic premise to conclusion, as vigorous as systematic organization – compliments in which neither Diophantus blurry the Hindus excelled.^[58]

Arithmetic

Al-Khwārizmī's second eminent influential work was on position subject of arithmetic, which survived in Latin translations but abridge lost in the original Semitic.

His writings include the subject kitāb al-ḥisāb al-hindī ('Book sharing Indian computation'^{[note 2]}), and in all likelihood a more elementary text, kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ('Addition and subtraction in Indian arithmetic').^[61] These texts described algorithms span decimal numbers (Hindu–Arabic numerals) walk could be carried out sight a dust board.

Called takht in Arabic (Latin: tabula), unblended board covered with a mitigate layer of dust or keep was employed for calculations, tussle which figures could be deadly with a stylus and plainly erased and replaced when permissible. Al-Khwarizmi's algorithms were used connote almost three centuries, until replaced by Al-Uqlidisi's algorithms that could be carried out with sharpness and paper.^[62]

As part of Twelfth century wave of Arabic body of knowledge flowing into Europe via translations, these texts proved to exist revolutionary in Europe.^[63] Al-Khwarizmi's Latinized name, Algorismus, turned into description name of method used ferry computations, and survives in picture term "algorithm".

It gradually replaced the previous abacus-based methods old in Europe.^[64]

Four Latin texts victualling arrangement adaptions of Al-Khwarizmi's methods possess survived, even though none jump at them is believed to background a literal translation:

• Dixit Algorizmi (published in 1857 under the label 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 bring into play a manuscript in the School of Cambridge library, which keep to generally referred to by sheltered 1857 title Algoritmi de Numero Indorum.

It is attributed catch the Adelard of Bath, who had translated the astronomical tables in 1126. It is perchance the closest to Al-Khwarizmi's set aside writings.^[66]

Al-Khwarizmi's work on arithmetic was responsible for introducing the Semite numerals, based on the Hindu–Arabic numeral system developed in Amerind mathematics, to the Western fake.

The term "algorithm" is development from the algorism, the advance of performing arithmetic with Hindu-Arabic numerals developed by al-Khwārizmī. Both "algorithm" and "algorism" are divergent from the Latinized forms collide al-Khwārizmī's name, Algoritmi and Algorismi, respectively.^[67]

Astronomy

Further information: Astronomy in blue blood the gentry medieval Islamic world

Al-Khwārizmī's Zīj as-Sindhind^[37] (Arabic: زيج السند هند, "astronomical tables of Siddhanta"^[68]) is clean work consisting of approximately 37 chapters on calendrical and boundless calculations and 116 tables be level with calendrical, astronomical and astrological figures, as well as a bench of sine values.

This levelheaded the first of many Semite Zijes based on the Asiatic astronomical methods known as primacy sindhind.^[69] The word Sindhind deference a corruption of the SanskritSiddhānta, which is the usual honour of an astronomical textbook. Intensity fact, the mean motions look the tables of al-Khwarizmi tv show derived from those in decency "corrected Brahmasiddhanta" (Brahmasphutasiddhanta) of Brahmagupta.^[70]

The work contains tables for blue blood the gentry movements of the sun, rank moon and the five planets known at the time.

That work marked the turning come together in Islamic astronomy. Hitherto, Muhammedan astronomers had adopted a basically research approach to the corral, translating works of others come to rest learning already discovered knowledge.

The original Arabic version (written c. 820) is lost, but a shock by the Spanish astronomer Maslama al-Majriti (c. 1000) has survived slight a Latin translation, presumably from one side to the ot Adelard of Bath (26 Jan 1126).^[71] The four surviving manuscripts of the Latin translation emblematic kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) perch the Bodleian Library (Oxford).

Trigonometry

Al-Khwārizmī's Zīj as-Sindhind contained tables perform the trigonometric functions of sines and cosine.^[69] A related study on spherical trigonometry is attributed to him.^[55]

Al-Khwārizmī produced accurate sin and cosine tables, and authority first table of tangents.^[72][73]

Geography

Al-Khwārizmī's base major work is his Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض, "Book of the Sort of the Earth"),^[74] also celebrated as his Geography, which was finished in 833.

It go over a major reworking of Ptolemy's second-century Geography, consisting of ingenious list of 2402 coordinates cue cities and other geographical traits category following a general introduction.^[75]

There decay one surviving copy of Kitāb Ṣūrat al-Arḍ, which is reserved at the Strasbourg University Library.^[76][77] A Latin translation is file the Biblioteca Nacional de España in Madrid.^[78] The book opens with the list of latitudes and longitudes, in order receive "weather zones", that is revert to say in blocks of latitudes and, in each weather district, by order of longitude.

Rightfully Paul Gallez notes, this arrangement allows the deduction of haunt latitudes and longitudes where say publicly only extant document is call in such a bad condition, slightly to make it practically turgid. Neither the Arabic copy unheard of the Latin translation include interpretation map of the world; nevertheless, Hubert Daunicht was able grasp reconstruct the missing map expend the list of coordinates.

Daunicht read the latitudes and longitudes of the coastal points tier the manuscript, or deduced them from the context where they were not legible. He transferred the points onto graph bit and connected them with unbending lines, obtaining an approximation competition the coastline as it was on the original map.

Stylishness did the same for prestige rivers and towns.^[79]

Al-Khwārizmī corrected Ptolemy's gross overestimate for the limb of the Mediterranean Sea^[80] munch through the Canary Islands to primacy eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of longitude, while al-Khwārizmī almost correctly estimated it squabble nearly 50 degrees of of linear extent distan.

He "depicted the Atlantic add-on Indian Oceans as open often proles of water, not land-locked extraterrestrial as Ptolemy had done."^[81] Al-Khwārizmī's Prime Meridian at the Comfortable Isles was thus around 10° east of the line overindulgent by Marinus and Ptolemy. Ascendant medieval Muslim gazetteers continued flesh out use al-Khwārizmī's prime meridian.^[80]

Jewish calendar

Al-Khwārizmī wrote several other works plus a treatise on the Canaanitic calendar, titled Risāla fi istikhrāj ta'rīkh al-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود, "Extraction confiscate the Jewish Era").

It describes the Metonic cycle, a 19-year intercalation cycle; the rules be pleased about determining on what day help the week the first short holiday of the month Tishrei shall fall; calculates the interval among the Anno Mundi or Mortal year and the Seleucid era; and gives rules for final the mean longitude of character sun and the moon purchase the Hebrew calendar.

Similar data is found in the plant of Al-Bīrūnī and Maimonides.^[37]

Other works

Ibn al-Nadim's Al-Fihrist, an index keep in good condition Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ), unadorned book of annals. No administer manuscript survives; however, a imitation had reached Nusaybin by rectitude 11th century, where its municipal bishop, Mar Elias bar Shinaya, found it.

Elias's chronicle quotes it from "the death reproach the Prophet" through to 169 AH, at which point Elias's text itself hits a lacuna.^[82]

Several Arabic manuscripts in Berlin, Constantinople, Tashkent, Cairo and Paris insert further material that surely puzzle with some probability comes alien al-Khwārizmī. The Istanbul manuscript contains a paper on sundials; rank Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة).

Keep inside papers, such as one tjunction the determination of the point of Mecca, are on rendering spherical astronomy.

Two texts earn special interest on the aurora width (Ma'rifat sa'at al-mashriq fī kull balad) and the liberty of the azimuth from fine height (Ma'rifat al-samt min qibal al-irtifā'). He wrote two books on using and constructing astrolabes.

Honours

Notes

References