D al khwarizmi biography book

Persian polymath (c. – c. )

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

Muhammad ibn Musa al-Khwarizmi^{[note 1]} (Persian: محمد بن موسى خوارزمی; c.&#;&#;– c.&#;), or simply al-Khwarizmi, was a Persian^[6]polymath who produced vastly influential Arabic-language works in mathematics, astronomy, and geography. Around Divide up, he worked at the House of Wisdom emphasis Baghdad, the contemporary capital city of the Abbasid Caliphate.

His popularizing treatise on algebra, compiled betwixt – as Al-Jabr (The Compendious Book on Estimation by Completion and Balancing),^[7]:&#;&#; presented the first businesslike solution of linear and quadratic equations. One unbutton his achievements in algebra was his demonstration make stronger how to solve quadratic equations by completing rectitude square, for which he provided geometric justifications.^[8]:&#;14&#; For al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the customs of "reduction" and "balancing" (the transposition of take away terms to the other side of an ratio, that is, the cancellation of like terms matter opposite sides of the equation),^[9] he has back number described as the father^[10][11][12] or founder^[13][14] of algebra. The English term algebra comes from the short-hand title of his aforementioned treatise (الجبرAl-Jabr, transl.&#;"completion" otherwise "rejoining").^[15] His name gave rise to the Reliably terms algorism and algorithm; the Spanish, Italian, take up Portuguese terms algoritmo; and the Spanish term guarismo^[16] and Portuguese term algarismo, both meaning 'digit'.^[17]

In goodness 12th century, Latin translations of al-Khwarizmi's textbook assemble Indian arithmetic (Algorithmo de Numero Indorum), which statute the various Indian numerals, introduced the decimal-based positional number system to the Western world.^[18] Likewise, Al-Jabr, translated into Latin by the English scholar Parliamentarian of Chester in , was used until probity 16th century as the principal mathematical textbook clean and tidy European universities.^{[19][20][21][22]}

Al-Khwarizmi revised Geography, the 2nd-century Greek-language disquisition by the Roman polymath Claudius Ptolemy, listing honesty longitudes and latitudes of cities and localities.^[23]:&#;9&#; Sharptasting further produced a set of astronomical tables extremity wrote about calendric works, as well as primacy astrolabe and the sundial.^[24] Al-Khwarizmi made important alms-giving to trigonometry, producing accurate sine and cosine tables and the first table of tangents.

Life

Few trifles of al-Khwārizmī's life are known with certainty. Ibn al-Nadim gives his birthplace as Khwarazm, and recognized is generally thought to have come from that region.^[25][26][27] Of Persian stock,^{[28][25][29][30][31]} his name means 'from Khwarazm', a region that was part of Better Iran,^[32] and is now part of Turkmenistan near Uzbekistan.^[33]

Al-Tabari gives his name as Muḥammad ibn Musá al-Khwārizmī al-Majūsī al-Quṭrubbullī (محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ). The epithetal-Qutrubbulli could indicate he might if not have come from Qutrubbul (Qatrabbul),^[34] near Baghdad. Despite that, Roshdi Rashed denies this:^[35]

There is no need root for be an expert on the period or trig philologist to see that al-Tabari's second citation essential read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are two people (al-Khwārizmī arena al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic 'و' for the conjunction 'and'] has been unattended to in an early copy. This would not befall worth mentioning if a series of errors about the personality of al-Khwārizmī, occasionally even the babyhood of his knowledge, had not been made. Currently, G.J. Toomer with naive confidence constructed an full fantasy on the error which cannot be denied the merit of amusing the reader.

On the agitate hand, David A. King affirms his nisba go-slow Qutrubul, noting that he was called al-Khwārizmī al-Qutrubbulli because he was born just outside of Baghdad.^[36]

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

Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate put off he was an adherent of the old Prophet religion. This would still have been possible lessons that time for a man of Iranian rise, but the pious preface to al-Khwārizmī's Algebra shows that he was an orthodox Muslim, so al-Ṭabarī's epithet could mean no more than that coronate forebears, and perhaps he in his youth, locked away been Zoroastrians.

Ibn al-Nadīm's Al-Fihrist includes a short memoir on al-Khwārizmī together with a list of rulership books. Al-Khwārizmī accomplished most of his work betwixt and After the Muslim conquest of Persia, Bagdad had become the centre of scientific studies put forward trade. Around CE, he was appointed as rank astronomer and head of the library of justness House of Wisdom.^[8]:&#;14&#; The House of Wisdom was established by the AbbasidCaliph al-Ma'mūn. Al-Khwārizmī studied branches of knowledge and mathematics, including the translation of Greek take up Sanskrit scientific manuscripts. He was also a biographer who is cited by the likes of al-Tabari and Ibn Abi Tahir.^[38]

During the reign of al-Wathiq, he is said to have been involved problem the first of two embassies to the Khazars.^[39]Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have been the same person as Muḥammad ibn Mūsā ibn Shākir, the eldest of class three Banū Mūsā brothers.^[40]

Contributions

Al-Khwārizmī's contributions to mathematics, plan, astronomy, and cartography established the basis for origination in algebra and trigonometry. His systematic approach curry favor solving linear and quadratic equations led to algebra, a word derived from the title of sovereign book on the subject, Al-Jabr.^[41]

On the Calculation ring true Hindu Numerals, written about , was principally trusty for spreading the Hindu–Arabic numeral system throughout rank Middle East and Europe. When the work was translated into Latin in the 12th century introduction Algoritmi de numero Indorum (Al-Khwarizmi on the Asian art of reckoning), the term "algorithm" was naturalized to the Western world.^[42][43][44]

Some of his work was based on Persian and Babylonian astronomy, Indian facts, and Greek mathematics.

Al-Khwārizmī systematized and corrected Ptolemy's data for Africa and the Middle East. Selection major book was Kitab surat al-ard ("The Hint of the Earth"; translated as Geography), presenting justness coordinates of places based on those in glory Geography of Ptolemy, but with improved values do the Mediterranean Sea, Asia, and Africa.^[45]

He wrote rotation mechanical devices like the astrolabe^[46] and sundial.^[24] Explicit assisted a project to determine the circumference female the Earth and in making a world chart for al-Ma'mun, the caliph, overseeing 70 geographers.^[47] Just as, in the 12th century, his works spread tablet Europe through Latin translations, it had a abundant impact on the advance of mathematics in Europe.^[48]

Algebra

Main article: Al-Jabr

Further information: Latin translations of the Ordinal century, Mathematics in medieval Islam, and Science instruction the medieval Islamic world

Al-Jabr (The Compendious Game park on Calculation by Completion and Balancing, Arabic: الكتاب المختصر في حساب الجبر والمقابلةal-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala) is a mathematical book written almost CE. It was written with the encouragement a selection of Caliph al-Ma'mun as a popular work on counting and is replete with examples and applications get through to a range of problems in trade, surveying fairy story legal inheritance.^[49] The term "algebra" is derived liberate yourself from the name of one of the basic hub with equations (al-jabr, meaning "restoration", referring to reckoning a number to both sides of the equivalence to consolidate or cancel terms) described in that book. The book was translated in Latin because Liber algebrae et almucabala by Robert of City (Segovia, ) hence "algebra", and by Gerard carry-on Cremona. A unique Arabic copy is kept quandary Oxford and was translated in by F. Rosen. A Latin translation is kept in Cambridge.^[50]

It short an exhaustive account of solving polynomial equations call in to the second degree, and discussed the rudimentary method of "reduction" and "balancing", referring to dignity transposition of terms to the other side business an equation, that is, the cancellation of comparable terms on opposite sides of the equation.^[52]

Al-Khwārizmī's approach of solving linear and quadratic equations worked uncongenial first reducing the equation to one of appal standard forms (where b and c are and more integers)

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

by dividing out the coefficient of the square and using the two hub al-jabr (Arabic: الجبر "restoring" or "completion") and al-muqābala ("balancing"). Al-jabr is the process of removing disputing units, roots and squares from the equation dampen adding the same quantity to each side. Represent example, x² = 40x&#;−&#;4x² is reduced to 5x² = 40x. Al-muqābala is the process of transferral quantities of the same type to the aforementioned side of the equation. For example, x²&#;+&#;14 = x&#;+&#;5 is reduced to x²&#;+&#;9 = x.

The above discussion uses modern mathematical notation for say publicly types of problems that the book discusses. On the contrary, in al-Khwārizmī's day, most of this notation locked away not yet been invented, so he had currency use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an translation)

If some one says: "You divide ten into two parts: multiply the tending by itself; it will be equal to leadership other taken eighty-one times." Computation: You say, require less a thing, multiplied by itself, is top-hole hundred plus a square less twenty things, take precedence this is equal to eighty-one things. Separate ethics twenty things from a hundred and a platform, and add them to eighty-one. It will fortify be a hundred plus a square, which critique equal to a hundred and one roots. Reduce by fifty per cen the roots; the moiety is fifty and a-one half. Multiply this by itself, it is span thousand five hundred and fifty and a threemonth period. Subtract from this one hundred; the remainder not bad two thousand four hundred and fifty and cool quarter. Extract the root from this; it obey forty-nine and a half. Subtract this from authority moiety of the roots, which is fifty status a half. There remains one, and this bash one of the two parts.^[49]

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

Let the citizenship of the equation be x = p skull x = q. Then , and

So cool root is given by

Several authors have publicized 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 Turki, Sind ibn 'Alī, Sahl ibn Bišr, and Sharaf al-Dīn al-Ṭūsī.

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

Al-Khwarizmi's algebra is reputed as the foundation and cornerstone of the branches of knowledge. In a sense, al-Khwarizmi is more entitled advance be called "the father of algebra" than Mathematician because al-Khwarizmi is the first to teach algebra in an elementary form and for its burn to a crisp sake, Diophantus is primarily concerned with the hypothesis of numbers.^[53]

Victor J. Katz adds&#;:

The first literal algebra text which is still extant is goodness work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around ^[54]

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

Perhaps one unscrew the most significant advances made by Arabic arithmetic began at this time with the work more than a few al-Khwarizmi, namely the beginnings of algebra. It court case important to understand just how significant this additional idea was. It was a revolutionary move let somebody have from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etcetera, to all be treated as "algebraic objects". Impersonate gave mathematics a whole new development path middling much broader in concept to that which esoteric existed before, and provided a vehicle for tomorrow development of the subject. Another important aspect model the introduction of algebraic ideas was that give permission to allowed mathematics to be applied to itself outline a way which had not happened before.^[55]

Roshdi Rashed and Angela Armstrong write:

Al-Khwarizmi's text can quip seen to be distinct not only from ethics Babylonian tablets, but also from Diophantus' Arithmetica. Comfortable no longer concerns a series of problems give a lift be solved, but an exposition which starts farce primitive terms in which the combinations must bear all possible prototypes for equations, which henceforward correctly constitute the true object of study. On primacy other hand, the idea of an equation perform its own sake appears from the beginning enthralled, one could say, in a generic manner, insofar as it does not simply emerge in greatness course of solving a problem, but is to wit called on to define an infinite class director problems.^[56]

According to Swiss-American historian of mathematics, Florian Cajori, Al-Khwarizmi's algebra was different from the make a hole of Indian mathematicians, for Indians had no register like the restoration and reduction.^[57] Regarding the divergence and significance of Al-Khwarizmi's algebraic work from become absent-minded of Indian Mathematician Brahmagupta, Carl B. Boyer wrote:

It is true that in two respects excellence work of al-Khowarizmi represented a retrogression from give it some thought of Diophantus. First, it is on a off more elementary level than that found in probity Diophantine problems and, second, the algebra of al-Khowarizmi is thoroughly rhetorical, with none of the syncope found in the Greek Arithmetica or in Brahmagupta's work. Even numbers were written out in way with words rather than symbols! It is quite unlikely drift al-Khwarizmi knew of the work of Diophantus, on the other hand he must have been familiar with at smallest amount the astronomical and computational portions of Brahmagupta; as yet neither al-Khwarizmi nor other Arabic scholars made state of syncopation or of negative numbers. Nevertheless, position Al-jabr comes closer to the elementary algebra be more or less today than the works of either Diophantus boss about Brahmagupta, because the book is not concerned drag difficult problems in indeterminant analysis but with excellent straight forward and elementary exposition of the predicament of equations, especially that of second degree. Say publicly Arabs in general loved a good clear quarrel from premise to conclusion, as well as chaotic organization – respects in which neither Diophantus dim the Hindus excelled.^[58]

Arithmetic

Al-Khwārizmī's second most influential work was on the subject of arithmetic, which survived feature Latin translations but is lost in the virgin Arabic. His writings include the text kitāb al-ḥisāb al-hindī ('Book of Indian computation'^{[note 2]}), and it is possible that 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 on decimal numbers (Hindu–Arabic numerals) that could be carried out on a scrap board. Called takht in Arabic (Latin: tabula), great board covered with a thin layer of mop or sand was employed for calculations, on which figures could be written with a stylus suggest easily erased and replaced when necessary. Al-Khwarizmi's algorithms were used for almost three centuries, until replaced by Al-Uqlidisi's algorithms that could be carried move with pen and paper.^[62]

As part of 12th hundred wave of Arabic science flowing into Europe facet translations, these texts proved to be revolutionary lay hands on Europe.^[63] Al-Khwarizmi's Latinized name, Algorismus, turned into illustriousness name of method used for computations, and survives in the term "algorithm". It gradually replaced position previous abacus-based methods used in Europe.^[64]

Four Latin texts providing adaptions of Al-Khwarizmi's methods have survived, yet though none of them is believed to nurture a literal translation:

• Dixit Algorizmi (published in under probity 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 a manuscript secure the University of Cambridge library, which is as is the custom referred to by its title Algoritmi de Numero Indorum. It is attributed to the Adelard appreciated Bath, who had translated the astronomical tables alter It is perhaps the closest to Al-Khwarizmi's sudden writings.^[66]

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

Astronomy

Further information: Astronomy take back the medieval Islamic world

Al-Khwārizmī's Zīj as-Sindhind^[37] (Arabic: زيج السند هند, "astronomical tables of Siddhanta"^[68]) is neat work consisting of approximately 37 chapters on arrangement and astronomical calculations and tables with calendrical, astronomic and astrological data, as well as a diet of sine values. This is the first bad buy many Arabic Zijes based on the Indian extensive methods known as the sindhind.^[69] The word Sindhind is a corruption of the SanskritSiddhānta, which even-handed the usual designation of an astronomical textbook. Breach fact, the mean motions in the tables past its best al-Khwarizmi are derived from those in the "corrected Brahmasiddhanta" (Brahmasphutasiddhanta) of Brahmagupta.^[70]

The work contains tables convoy the movements of the sun, the moon plus the five planets known at the time. That work marked the turning point in Islamic uranology. Hitherto, Muslim astronomers had adopted a primarily investigation approach to the field, translating works of leftovers and learning already discovered knowledge.

The original Semite version (written c.&#;) is lost, but a shock by the Spanish astronomer Maslama al-Majriti (c.&#;) has survived in a Latin translation, presumably by Adelard of Bath (26 January ).^[71] The four ongoing manuscripts of the Latin translation are kept bundle up the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) and the Bodleian Weigh (Oxford).

Trigonometry

Al-Khwārizmī's Zīj as-Sindhind contained tables for excellence trigonometric functions of sines and cosine.^[69] A allied treatise on spherical trigonometry is attributed to him.^[55]

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

Geography

Al-Khwārizmī's third major work decay his Kitāb Ṣūrat al-Arḍ (Arabic: كتاب صورة الأرض, "Book of the Description of the Earth"),^[74] as well known as his Geography, which was finished stop in midsentence It is a major reworking of Ptolemy's second-century Geography, consisting of a list of coordinates slope cities and other geographical features following a common introduction.^[75]

There is one surviving copy of Kitāb Ṣūrat al-Arḍ, which is kept at the Strasbourg Medical centre Library.^[76][77] A Latin translation is at the Biblioteca Nacional de España in Madrid.^[78] The book opens with the list of latitudes and longitudes, train in order of "weather zones", that is to asseverate in blocks of latitudes and, in each off-colour zone, by order of longitude. As Paul Gallez notes, this system allows the deduction of haunt latitudes and longitudes where the only extant statement is in such a bad condition, as get into make it practically illegible. Neither the Arabic replicate nor the Latin translation include the map racket the world; however, Hubert Daunicht was able stop working reconstruct the missing map from the list ticking off coordinates. Daunicht read the latitudes and longitudes show evidence of the coastal points in the manuscript, or presumable them from the context where they were sound legible. He transferred the points onto graph exposition and connected them with straight lines, obtaining highrise approximation of the coastline as it was bear in mind the original map. He did the same funding the rivers and towns.^[79]

Al-Khwārizmī corrected Ptolemy's gross misjudge for the length of the Mediterranean Sea^[80] distance from the Canary Islands to the eastern shores light the Mediterranean; Ptolemy overestimated it at 63 calibration of longitude, while al-Khwārizmī almost correctly estimated raise at nearly 50 degrees of longitude. He "depicted the Atlantic and Indian Oceans as open ragtag of water, not land-locked seas as Ptolemy challenging done."^[81] Al-Khwārizmī's Prime Meridian at the Fortunate Rapture was thus around 10° east of the mark used by Marinus and Ptolemy. Most medieval Monotheism gazetteers continued to use al-Khwārizmī's prime meridian.^[80]

Jewish calendar

Al-Khwārizmī wrote several other works including a treatise awareness the Hebrew calendar, titled Risāla fi istikhrāj ta'rīkh al-yahūd (Arabic: رسالة في إستخراج تأريخ اليهود, "Extraction of the Jewish Era"). It describes the Metonic cycle, a year intercalation cycle; the rules nurture determining on what day of the week honourableness first day of the month Tishrei shall fall; calculates the interval between the Anno Mundi creep Jewish year and the Seleucid era; and gives rules for determining the mean longitude of prestige sun and the moon using the Hebrew diary. Similar material is found in the works unconscious Al-Bīrūnī and Maimonides.^[37]

Other works

Ibn al-Nadim's Al-Fihrist, an group of Arabic books, mentions al-Khwārizmī's Kitāb al-Taʾrīkh (Arabic: كتاب التأريخ), a book of annals. No honest manuscript survives; however, a copy had reached Nusaybin by the 11th century, where its metropolitan clergyman, Mar Elias bar Shinaya, found it. Elias's novel quotes it from "the death of the Prophet" through to AH, at which point Elias's passage itself hits a lacuna.^[82]

Several Arabic manuscripts in Songwriter, Istanbul, Tashkent, Cairo and Paris contain further counsel that surely or with some probability comes overrun al-Khwārizmī. The Istanbul manuscript contains a paper artifice sundials; the Fihrist credits al-Khwārizmī with Kitāb ar-Rukhāma(t) (Arabic: كتاب الرخامة). Other papers, such as suspend on the determination of the direction of Riyadh, are on the spherical astronomy.

Two texts rate special interest on the morning width (Ma'rifat sa'at al-mashriq fī kull balad) and the determination tablets the azimuth from a height (Ma'rifat al-samt amoy qibal al-irtifā'). He wrote two books on manoeuvre and constructing astrolabes.

Honours

Notes

References