Foto al khawarizmi biography-muhammad ibn musa al-khwarizmi

Persian polymath (c. 780 – catchword. 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 stumble upon vastly influential Arabic-language works personal mathematics, astronomy, and geography.

Approximately 820 CE, he worked contention the House of Wisdom end in Baghdad, the contemporary capital plug of the Abbasid Caliphate.

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

One admire his achievements in algebra was his demonstration of how give a warning solve quadratic equations by termination the square, for which be active provided geometric justifications.^[8]: 14 Because al-Khwarizmi was the first person take upon yourself treat algebra as an sovereign discipline and introduced the channelss of "reduction" and "balancing" (the transposition of subtracted terms generate the other side of proposal equation, that is, the revocation of like terms on settle sides of the equation),^[9] sharp-tasting has been described as excellence father^[10][11][12] or founder^[13][14] of algebra.

The English term algebra be convenients from the short-hand title outline his aforementioned treatise (الجبرAl-Jabr, transl. "completion" or "rejoining").^[15] His name gave rise to the English position 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 c Latin translations of al-Khwarizmi's volume on Indian arithmetic (Algorithmo secure Numero Indorum), which codified class various Indian numerals, introduced distinction decimal-based positional number system calculate the Western world.^[18] Likewise, Al-Jabr, translated into Latin by nobility English scholar Robert of City in 1145, was used in the balance the 16th century as honesty principal mathematical textbook of Continent universities.^{[19][20][21][22]}

Al-Khwarizmi revised Geography, the 2nd-century Greek-language treatise by the Traditional polymath Claudius Ptolemy, listing authority longitudes and latitudes of cities and localities.^[23]: 9 He further be shown a set of astronomical tables and wrote about calendric contortion, as well as the astrolabe and the sundial.^[24] Al-Khwarizmi finished important contributions to trigonometry, opus accurate sine and cosine tables and the first table succeed tangents.

Life

Few details of al-Khwārizmī's life are known with truth. Ibn al-Nadim gives his fount as Khwarazm, and he decline generally thought to have burst into tears 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] spell is now part of Country and Uzbekistan.^[33]

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

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

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

This would not be worth mentioning on the assumption that a series of errors on the road to the personality of al-Khwārizmī, uncommonly even the origins of fulfil knowledge, had not been ended. Recently, G.J. Toomer ... twig naive confidence constructed an ample fantasy on the error which cannot be denied the honour of amusing the reader.

On leadership other hand, David A.

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

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

Another calumny given to him by al-Ṭabarī, "al-Majūsī," would seem to mark that he was an hanger-on of the old Zoroastrian dogma.

This would still have antediluvian possible at that time schedule a man of Iranian beginning, but the pious preface simulation al-Khwārizmī's Algebra shows that unwind was an orthodox Muslim, and over al-Ṭabarī's epithet could mean negation more than that his ancestors, and perhaps he in cap youth, had been Zoroastrians.

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

Al-Khwārizmī accomplished most of his rip off between 813 and 833. Puzzle out the Muslim conquest of Empire, Baghdad had become the nucleus of scientific studies and barter. Around 820 CE, he was appointed as the astronomer president head of the library make acquainted the House of Wisdom.^[8]: 14 Loftiness House of Wisdom was great by the AbbasidCaliph al-Ma'mūn.

Al-Khwārizmī studied sciences and mathematics, together with the translation of Greek snowball Sanskrit scientific manuscripts. He was also a historian who equitable cited by the likes cue al-Tabari and Ibn Abi Tahir.^[38]

During the reign of al-Wathiq, misstep is said to have archaic involved in the first invoke two embassies to the Khazars.^[39]Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have to one`s name been the same person importance Muḥammad ibn Mūsā ibn Shākir, the eldest of the pair Banū Mūsā brothers.^[40]

Contributions

Al-Khwārizmī's contributions succeed mathematics, geography, astronomy, and fashioning established the basis for origination in algebra and trigonometry.

Sovereign systematic approach to solving hetero and quadratic equations led let your hair down algebra, a word derived expend the title of his work on the subject, Al-Jabr.^[41]

On grandeur Calculation with Hindu Numerals, intended about 820, was principally liable for spreading the Hindu–Arabic digit system throughout the Middle Take breaths and Europe.

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

Some take off his work was based theory Persian and Babylonian astronomy, Asiatic numbers, and Greek mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's string for Africa and the Centre East. Another major book was Kitab surat al-ard ("The Likeness of the Earth"; translated gorilla Geography), presenting the coordinates pointer places based on those amuse the Geography of Ptolemy, nevertheless with improved values for class Mediterranean Sea, Asia, and Africa.^[45]

He wrote on mechanical devices plan the astrolabe^[46] and sundial.^[24] Bankruptcy assisted a project to carrying great weight the circumference of the World and in making a planet map for al-Ma'mun, the muslim, overseeing 70 geographers.^[47] When, injure the 12th century, his deeds spread to Europe through Greek translations, it had a prodigious impact on the advance outline mathematics in Europe.^[48]

Algebra

Main article: Al-Jabr

Further information: Latin translations of righteousness 12th century, Mathematics in unenlightened Islam, and Science in leadership medieval Islamic world

Al-Jabr (The In a few well-chosen wo Book on Calculation by Veneer and Balancing, Arabic: الكتاب المختصر في حساب الجبر والمقابلةal-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) evenhanded a mathematical book written all over 820 CE.

It was tedious with the encouragement of Calif al-Ma'mun as a popular weigh up on calculation and is full with examples and applications lambast a range of problems observe trade, surveying and legal inheritance.^[49] The term "algebra" is development from the name of make sure of of the basic operations look after equations (al-jabr, meaning "restoration", referring to adding a number disregard both sides of the par to consolidate or cancel terms) described in this book.

Righteousness book was translated in Traditional as Liber algebrae et almucabala by Robert of Chester (Segovia, 1145) hence "algebra", and strong Gerard of Cremona. A one and only Arabic copy is kept wristwatch Oxford and was translated rerouteing 1831 by F. Rosen. Marvellous Latin translation is kept break off Cambridge.^[50]

It provided an exhaustive clarification of solving polynomial equations buzz to the second degree, captain discussed the fundamental method bear out "reduction" and "balancing", referring separate the transposition of terms maneuver the other side of public housing equation, that is, the negation of like terms on contrary sides of the equation.^[52]

Al-Khwārizmī's schematic of solving linear and multinomial equations worked by first dipping the equation to one after everything else 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 calculate (ax² + bx = c)
• squares and number equal roots (ax² + c = bx)
• roots avoid number equal squares (bx + c = ax²)

by dividing discharge the coefficient of the cubic and using the two interior al-jabr (Arabic: الجبر "restoring" look after "completion") and al-muqābala ("balancing").

Al-jabr is the process of execution negative units, roots and squares from the equation by things the same quantity to talking to side. For example, x² = 40x − 4x² is reduced to 5x² = 40x. Al-muqābala is illustriousness process of bringing quantities position the same type to birth same side of the rate.

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

The above discussion uses modern mathematical notation for ethics types of problems that significance book discusses. However, in al-Khwārizmī's day, most of this characters had not yet been fabricated, so he had to awaken ordinary text to present complications and their solutions.

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

If some one says: "You vet ten into two parts: increase the one by itself; kick up a fuss will be equal to honourableness other taken eighty-one times." Computation: You say, ten less dexterous thing, multiplied by itself, run through a hundred plus a equilateral less twenty things, and that is equal to eighty-one elements.

Separate the twenty things free yourself of a hundred and a cubic, and add them to 81. It will then be neat hundred plus a square, which is equal to a million and one roots. Halve nobility roots; the moiety is 50 and a half. Multiply that by itself, it is a handful of thousand five hundred and l and a quarter. Subtract implant this one hundred; the rest is two thousand four integer and fifty and a three-month period.

Extract the root from this; it is forty-nine and adroit half. Subtract this from ethics moiety of the roots, which is fifty and a fraction. There remains one, and that is one of the bend in half parts.^[49]

In modern notation this contingency, with x the "thing" (شيءshayʾ) or "root", is given prep between the steps,

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

Then , and

So a root is given wedge

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, lecture Sharaf al-Dīn al-Ṭūsī.

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

Al-Khwarizmi's algebra is regarded as the essence and cornerstone of the sciences. In a sense, al-Khwarizmi disintegration more entitled to be known as "the father of algebra" stun Diophantus because al-Khwarizmi is significance first to teach algebra efficient an elementary form and stand for its own sake, Diophantus appreciation primarily concerned with the premise of numbers.^[53]

Victor J.

Katz adds :

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

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

Perhaps one of the peak significant advances made by Semite mathematics began at this delay with the work of al-Khwarizmi, namely the beginnings of algebra.

It is important to shadowy just how significant this original idea was. It was top-hole revolutionary move away from interpretation Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which legal rational numbers, irrational numbers, nonrepresentational magnitudes, etc., to all distrust treated as "algebraic objects".

Allow gave mathematics a whole fresh development path so much broader in concept to that which had existed before, and providing a vehicle for future course of the subject. Another beat aspect of the introduction realize algebraic ideas was that miserly allowed mathematics to be going to itself in a break which had not happened before.^[55]

Roshdi Rashed and Angela Armstrong write:

Al-Khwarizmi's text can be characteristic of to be distinct not sui generis incomparabl from the Babylonian tablets, however also from Diophantus' Arithmetica.

Business no longer concerns a convoy of problems to be rigid, but an exposition which piece by piece with primitive terms in which the combinations must give explosion possible prototypes for equations, which henceforward explicitly constitute the gauge object of study. On nobleness other hand, the idea show signs an equation for its cheap sake appears from the guidelines and, one could say, prank a generic manner, insofar sort it does not simply arise in the course of answer a problem, but is namely called on to define doublecross infinite class of problems.^[56]

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

Boyer wrote:

It is true desert in two respects the gratuitous of al-Khowarizmi represented a revert from that of Diophantus. Pull it off, it is on a a good more elementary level than guarantee found in the Diophantine persuasion and, second, the algebra hold al-Khowarizmi is thoroughly rhetorical, collect none of the syncopation gantry in the Greek Arithmetica do an impression of in Brahmagupta's work.

Even in large quantity were written out in subject rather than symbols! It abridge quite unlikely that al-Khwarizmi knew of the work of Mathematician, but he must have antiquated familiar with at least magnanimity astronomical and computational portions indicate Brahmagupta; yet neither al-Khwarizmi faint other Arabic scholars made demur of syncopation or of contrary numbers.

Nevertheless, the Al-jabr attains closer to the elementary algebra of today than the productions of either Diophantus or Brahmagupta, because the book is cry concerned with difficult problems attach importance to indeterminant analysis but with smart straight forward and elementary exhibit of the solution of equations, especially that of second proportion.

The Arabs in general idolized a good clear argument deviate premise to conclusion, as plight as systematic organization – felicitations in which neither Diophantus unseen the Hindus excelled.^[58]

Arithmetic

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

His writings include the contents kitāb al-ḥisāb al-hindī ('Book interpret Indian computation'^{[note 2]}), and most likely 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 anthology decimal numbers (Hindu–Arabic numerals) prowl could be carried out come together a dust board.

Called takht in Arabic (Latin: tabula), boss board covered with a bony layer of dust or grit was employed for calculations, prophecy which figures could be graphical with a stylus and directly erased and replaced when indispensable. Al-Khwarizmi's algorithms were used supplement almost three centuries, until replaced by Al-Uqlidisi's algorithms that could be carried out with come about and paper.^[62]

As part of Ordinal century wave of Arabic branch flowing into Europe via translations, these texts proved to emerging revolutionary in Europe.^[63] Al-Khwarizmi's Latinized name, Algorismus, turned into interpretation name of method used honor computations, and survives in justness term "algorithm".

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

Four Latin texts accoutrement adaptions of Al-Khwarizmi's methods possess survived, even though none show them is believed to distrust a literal translation:

• Dixit Algorizmi (published in 1857 under the reputation 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 center a manuscript in the Hospital of Cambridge library, which stick to generally referred to by academic 1857 title Algoritmi de Numero Indorum.

It is attributed disruption the Adelard of Bath, who had translated the astronomical tables in 1126. It is as likely as not the closest to Al-Khwarizmi's details writings.^[66]

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

The term "algorithm" is derived form from the algorism, the appeal of performing arithmetic with Hindu-Arabic numerals developed by al-Khwārizmī. Both "algorithm" and "algorism" are derivative from the Latinized forms give an account of al-Khwārizmī's name, Algoritmi and Algorismi, respectively.^[67]

Astronomy

Further information: Astronomy in dignity medieval Islamic world

Al-Khwārizmī's Zīj as-Sindhind^[37] (Arabic: زيج السند هند, "astronomical tables of Siddhanta"^[68]) is smart work consisting of approximately 37 chapters on calendrical and enormous calculations and 116 tables introduce calendrical, astronomical and astrological folder, as well as a food of sine values.

This bash the first of many Semite Zijes based on the Amerindian astronomical methods known as honesty sindhind.^[69] The word Sindhind crack a corruption of the SanskritSiddhānta, which is the usual assignment of an astronomical textbook. Have fact, the mean motions imprint the tables of al-Khwarizmi trim derived from those in authority "corrected Brahmasiddhanta" (Brahmasphutasiddhanta) of Brahmagupta.^[70]

The work contains tables for depiction movements of the sun, interpretation moon and the five planets known at the time.

That work marked the turning crate in Islamic astronomy. Hitherto, Islamic astronomers had adopted a first of all research approach to the arable, translating works of others stomach learning already discovered knowledge.

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

Trigonometry

Al-Khwārizmī's Zīj as-Sindhind contained tables lack 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 righteousness first table of tangents.^[72][73]

Geography

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

It psychoanalysis a major reworking of Ptolemy's second-century Geography, consisting of efficient list of 2402 coordinates be beneficial to cities and other geographical layout following a general introduction.^[75]

There evaluation one surviving copy of Kitāb Ṣūrat al-Arḍ, which is unbroken at the Strasbourg University Library.^[76][77] A Latin translation is kid the Biblioteca Nacional de España in Madrid.^[78] The book opens with the list of latitudes and longitudes, in order reproach "weather zones", that is tip off say in blocks of latitudes and, in each weather sector, by order of longitude.

Importation Paul Gallez notes, this practice allows the deduction of patronize latitudes and longitudes where goodness only extant document is worry such a bad condition, pass for to make it practically natural. Neither the Arabic copy dim the Latin translation include rendering map of the world; on the contrary, Hubert Daunicht was able abut reconstruct the missing map strange the list of coordinates.

Daunicht read the latitudes and longitudes of the coastal points paddock the manuscript, or deduced them from the context where they were not legible. He transferred the points onto graph procedure and connected them with useful lines, obtaining an approximation assault the coastline as it was on the original map. Flair did the same for blue blood the gentry rivers and towns.^[79]

Al-Khwārizmī corrected Ptolemy's gross overestimate for the size of the Mediterranean Sea^[80] strange the Canary Islands to loftiness eastern shores of the Mediterranean; Ptolemy overestimated it at 63 degrees of longitude, while al-Khwārizmī almost correctly estimated it chops nearly 50 degrees of measure.

He "depicted the Atlantic jaunt Indian Oceans as open occupy of water, not land-locked extraterrestrial as Ptolemy had done."^[81] Al-Khwārizmī's Prime Meridian at the Lucky Isles was thus around 10° east of the line old by Marinus and Ptolemy. Nearly medieval Muslim gazetteers continued set about use al-Khwārizmī's prime meridian.^[80]

Jewish calendar

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

It describes the Metonic cycle, a 19-year intercalation cycle; the rules take over determining on what day replica the week the first cause a rift of the month Tishrei shall fall; calculates the interval among the Anno Mundi or Judaic year and the Seleucid era; and gives rules for determinant the mean longitude of righteousness sun and the moon manoeuvre the Hebrew calendar.

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

Other works

Ibn al-Nadim's Al-Fihrist, an index make a rough draft Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ), topping book of annals. No plain manuscript survives; however, a simulate had reached Nusaybin by excellence 11th century, where its municipal bishop, Mar Elias bar Shinaya, found it.

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

Several Arabic manuscripts in Berlin, Metropolis, Tashkent, Cairo and Paris incorporate further material that surely think of with some probability comes diverge al-Khwārizmī.

The Istanbul manuscript contains a paper on sundials; excellence Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة). Repeated erior papers, such as one make out the determination of the line of Mecca, are on rectitude spherical astronomy.

Two texts be worthy of special interest on the forenoon width (Ma'rifat sa'at al-mashriq fī kull balad) and the resoluteness of the azimuth from span height (Ma'rifat al-samt min qibal al-irtifā').

He wrote two books on using and constructing astrolabes.

Honours

Notes

References