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The Great Contribution of Muslim Scientists

(pg 253) Jared Diamond a world renowned UCLA sociologist, and physiologist won the Pulitzer Prize for his book: "Guns, Germs, and Steel says
"Medieval Islam was technologically advanced and open to innovation. It achieved far higher literacy rates than in contemporary Europe; it assimilated the legacy of classical Greek civilization to such a degree that many classical books are now known to us only through Arabic copies. It invented windmills, trigonometry, lateen sails and made major advances in metallurgy, mechanical and chemical engineering and irrigation methods. In the middle- ages the flow of technology was overwhelmingly from Islam to Europe rather from Europe to Islam . Only after the 1500's did the net direction of flow begin to reverse ."
"Blessed is He Who made Constellations in the skies, And placed therein a Lamp And a Moon giving light." [Al-Qur'aan 25:61]
We are indebted to the Arabic world not only for arithmetic but also for algebra and trigonometry. Logarithms were invented by a mathematician called Al-Khwarizmi in the 7th century. Test tubes, the compass and the first surgical tools were all pioneered by Muslim inventors. A thousand years ago, it is said, Baghdad had 60 hospitals. Did you know why we learnt addition and subtraction sums, set out vertically by reading them from right to left. This is becoz Since Arabic is read from right to left. In Islam, study and the acquisition of knowledge is an obligation for every male and female: the Prophet is quoted as saying: " Go even to China in pursuit of knowledge." This scientific flowering was accompanied by the establishment of the first universities - or madrassahs. In a madrassah, the sheik or professor taught, literally, from a chair. He was assisted by readers. When the west eventually replicated such places of learning, we borrowed such terms. - David Self, http://www.guardian.co.uk/comment/story/0,,1561962,00.html
"And the Sun Runs its course For a period determined For it; that is The decree of (God) The exalted in Might, The All-Knowing." [Al-Qur'aan 36:38]
In the words of Carli Fiorina, former (highly talented and visionary) CEO of Hewlett Packard,
"Its(Islamic) architects designed buildings that defied gravity. Its mathematicians created the algebra and algorithms that would enable the building of computers, and the creation of encryption. Its doctors examined the human body, and found new cures for disease. Its astronomers looked into the heavens, named the stars, and paved the way for space travel and exploration. Its writers created thousands of stories; stories of courage, romance and magic. When other nations were afraid of ideas, this civilization thrived on them, and kept them alive. When censors threatened to wipe out knowledge from past civilizations, this civilization kept the knowledge alive, and passed it on to others. While modern Western civilization shares many of these traits, the civilization I'm talking about was the Islamic world from the year 800 to 1600, which included the Ottoman Empire and the courts of Baghdad, Damascus and Cairo, and enlightened rulers like Suleiman the Magnificent. Although we are often unaware of our indebtedness to this other civilization, its gifts are very much a part of our heritage. The technology industry would not exist without the contributions of Arab mathematicians."
"It is Allah Who sends The Winds, and they raise The Clouds: then does He Spread them in the sky As He wills, and break them Into fragments, until thou seest Raindrops issue from the midst Thereof: then when He has Made them reach such Of His servants as He wills, Behold, they do rejoice!" [Al-Qur'aan 30:48]
"During all the first part of the Middle Ages, no other people made as important a contribution to human progress as did the Arabs, if we take this term to mean all those whose mother-tongue was Arabic, and not merely those living in the Arabian peninsula. For centuries, Arabic was the language of learning, culture and intellectual progress for the whole of the civilized world with the exception of the Far East. From the IXth to the XIIth century there were more philosophical, medical, historical, religiuos, astronomical and geographical works written in Arabic than in any other human tongue."
-Phillip Hitti in 'Short History of the Arabs.'
"It is He Who created The Night and the Day, And the sun and the moon: All (the celestial bodies) Swim along, each in its Rounded course." [Al-Qur'aan 21:33
George Sarton in the "Introduction to the History of Science"
"The Muslim ideal was, it goes without saying, not visual beauty but God in His plentitude (INFINITENESS OF Almighty); that is God with all his manifestations, the stars and the heavens, the earth and all nature. The Muslim ideal is thus infinite. But in dealing with the infinite as conceived by the Muslims, we cannot limit ourselves to the space alone, but must equally consider time.
"The first mathematical step from the Greek conception of a static universe to the Islamic one of a dynamic universe was made by Al-Khwarizmi (780-850), the founder of modern Algebra. He enhanced the purely arithmetical character of numbers as finite magnitudes by demonstrating their possibilities as elements of infinite manipulations and investigations of properties and relations.
"In Greek mathematics, the numbers could expand only by the laborious process of addition and multiplication. Khwarizmi's algebraic symbols for numbers contain within themselves the potentialities of the infinite..Through their medical investigations they not merely widened the horizons of medicine, but enlarged humanistic concepts generally. And once again they brought this about because of their over riding spiritual convictions. One of the most famous exponents of Muslim universalism and an eminent figure in Islamic learning was Ibn Sina, known in the West as Avicenna (981-1037). They were always eager to put a theory to tests, and they never tired of experimentation http://www.cyberistan.org/islamic/Introl1.html
"It is not permitted To the Sun to catch up The Moon, nor can The Night outstrip the Day: Each (just) swims along In (its own) orbit (According to Law)." [Al-Qur'aan 36:40]
The Earth has been known to be round and not flat at least since the time of Eratosthenes (3rd century BC) by natural philosophers (scientists) at least. However, educated belief long co-existed with popular beliefs that regarded the earth as a flat disc.
From the at least the 9th century, with scholars like Al-Battani , the Muslim World was leading in astronomical knowledge, and the sphericity of the Earth was consequently a well known fact (even in the comparatively primitive astronomy of Europe at the time, belief in a flat Earth was confined to a small minority of theologists). Muslim astronomers calculated the earth's circumference to be 40, 253.4 km (correct to within 200 km). [1]
Ibn Taymiya (died 1328 CE), said: "Celestial bodies are round - as it is the statement of astronomers and mathematicians - it is [likewise] the statement of the scholars of the Muslims; as Abul-Hasan ibn al-Manaadi, Abu Muhammad Ibn Hazm, Abul-Faraj Ibn Al-Jawzi and others have quoted: that the Muslim scholars are in agreement (that all celestial bodies are round). Indeed Allah has said: And He ( i.e., Allah) it is Who created the night and the day, the sun and the moon. They float, each in a Falak. Ibn Abbas says: A Falaka like that of a spinning wheel. The (word) Falak (in the Arabic language) means that which is round." ( Majmu'ul-Fatawa, Vol. 6, pp. 566).
"And We(Almighty) have set on the earth Mountains standing firm, Lest it should shake with them." [Al-Qur'aan 21:31]
George Sarton said ,
"The main task of mankind was accomplished by Muslims. The greatest philosopher, Al-Farabi was a Muslim; the greatest mathematicians Abul Kamil and Ibrahim Ibn Sinan were Muslims; the greatest geographer and encyclopaedist Al-Masudi was a Muslim; the greatest historian, Al-Tabari was still a Muslim."
"He has let free the two bodies Of flowing water, Meeting together: Between them is a Barrier Which they do not transgress." [Al-Qur'aan 55:19-20]
John William Draper in the "Intellectual Development of Europe "
"I have to deplore the systematic manner in which the literature of Europe has continued to put out of sight our obligations to the Muhammadans. Surely they cannot be much longer hidden. Injustice founded on religious rancour and national conceit cannot be perpetuated forever. The Arab has left his intellectual impress on Europe. He has indelibly written it on the heavens as any one may see who reads the names of the stars on a common celestial globe."
"It is He Who has Let free the two bodies Of flowing water: One palatable and sweet, And the other salty and bitter; Yet has He Made a barrier between them, And a partition that is forbidden To be passed." [Al-Qur'aan 25:53]
It is a testament to Ibn Baklarish's reputation "as one of the wisest men of al-Andalus with regard to the practice of medicine", as stated by Ibn Abi Usaybi'ah in the medieval Biographical Dictionary of Physicians.-Medieval script shows Islam's role in learning-JAMES JOHNSTON http://news.scotsman.com/uk.cfm?id=1131512003
"...Is like the depths of darkness In a vast deep ocean, Overwhelmed with billow Topped by billow, Topped by (dark) clouds: Depths of darkness, one Above another: if a man Stretches out his hand, He can hardly see it! For any to whom God Giveth not light, there is no light!" [Al-Qur'aan 24:40]
While the barbarians smashed and burned in western Europe, the Arabs and Persians used the libraries of Alexandria and Asia Minor, translated the scrolls and took them to Baghdad and far beyond. In distant Bukhara on the Silk Road to China, a teenager called Abu Ali Ibn Sina was engrossed in Aristotle's Metaphysics at the age of 17. The year was AD997 and the text - central to the subsequent development of philosophy - had long been lost and unknown in western Europe....Without the work of a 500-year succession of Islamic sages, we would have lost the essence of Aristotle, much of Plato and scores of other ancients- Martin Wainwright , Our Debt to Islam
"Do not the those who(Scientists) see that the heavens and the earth were joined together (as one Unit of Creation), before We clove them asunder? We made from water every living thing. Will they not then believe?"
Arnold and Guillaume in "Lagacy of Islam" on Islamic science and medicine "Looking back we may say that Islamic medicine and science reflected the light of the Hellenic sun, when its day had fled, and that they shone like a moon, illuminating the darkest night of the European middle Ages; that some bright stars lent their own light, and that moon and stars alike faded at the dawn of a new day - the Renaissance. Since they had their share in the direction and introduction of that great movement, it may reasonably be claimed that they are with us yet."
"It is He Who has Created man from water: Then has He established Relationships of lineage And marriage: for thy Lord Has power (over all things)." [Al-Qur'aan 25:54]
Keith L. Moore Professor Emeritus , Department of Anatomy and Cell Biology, University of Toronto. Distinguished embryologist and author of The Developing Human says
"Although I was aware of the glorious history of Muslim scientists in the 10th century AD, and some of their contributions to Medicine, I knew nothing about the religious facts and beliefs contained in the Qur'an and Sunnah."
"Glory to Allah, Who created In pairs all things that The earth produces, as well as Their own (human) kind And (other) things of which They have no knowledge." [Al-Qur'aan 36:36
Under Inventions and Discoveries, the site informs us: that al-Farisi was the first to give an accurate description of the formation of rainbow; that Ibn Nafis was first to describe the pulmonary circulation of the blood 400 years before William Harvey; Ibn al-Haytham was the first to give a correct description of vision; Umar Khayyam was the first mathematician to solve the equations of third degree and above; Al-Farabi was the originator of the theory of mutual renunciation of rights in political philosophy, which was credited to the English philosopher Thomas Hobbes who appeared seven centuries later.
How many of us know that the name Algebra derives from the Arabic word 'aljabr' found in the title of the great book on mathematics 'al jabr wal muqabla' written by Al-Khwarizmi, and that algorithm originates from his name 'al-Khwarizmi'.
But then came the destruction of Baghdad by Mongol armies in 1258 and the final loss of Spain with the surrender of Granada in 1492. This left something of a power vacuum in the Muslim world. Over the next 100 years, it was filled by the "ulama" or religious scholars. Gradually they began to annex the concept of knowledge, and narrow its scope.
"Do they not look at The birds, held poised In the midst of (the air And) the sky? Nothing Holds them up but (the power Of) God. Verily in this Are Signs for those who believe." [Al-Qur'aan 16:79
Did you know the origin of the word astrolabe comes from the Arabic astrulab.
Abbas ibn Firnas was the first person to make a real attempt to construct a flying machine and fly.
Caliph al-Ma'mun, who ruled Baghdad from 813 to 833 CE, gave astronomy the patronage and impetus it needed to become a major science.
He built the first observatory in Islam, and arguably the first observatory in the world or in history.
Many of the traits on which Europe prides itself came to it from Muslim Spain.
"And verily in cattle there is A lesson for you. We(God) give you to drink Of what is inside their bodies, Coming from a conjunction Between the contents of the Intestine and the blood, A milk pure and pleasant for Those who drink it." [Al-Qur'aan 16:66]
Muslim scientists from the 8th to the 14th century CE:
This is a partial list of some of the leading Muslims. Major Muslim contributions continued beyond the fifteenth century. Contributions of more than one hundred other major Muslim personalities can be found in several famous publications by Western historians. Biographies are available in the Islamic Civilization E-book .
Jabir Ibn Haiyan (Geber)
Chemistry (Father of Chemistry) Died 803 C.E.
Zoology, Botany, Animal Husbandry. 740 - 828
Al-Khwarizmi (Algorizm)
Mathematics, Astronomy, Geography. (Algorithm, Algebra, calculus) 770 - 840
'Amr ibn Bahr Al-Jahiz
Zoology, Arabic Grammar, Rhetoric, Lexicography 776 - 868
Ibn Ishaq Al-Kindi (Alkindus)
Philosophy, Physics, Optics, Medicine, Mathematics, Metallurgy. 800 - 873
Thabit Ibn Qurrah (Thebit)
Astronomy, Mechanics, Geometry, Anatomy. 836 - 901
'Abbas Ibn Firnas
Mechanics of Flight, Planetarium, Artificial Crystals. Died 888
Ali Ibn Rabban Al-Tabari
Medicine, Mathematics, Caligraphy, Literature. 838 - 870
Al-Battani (Albategnius)
Astronomy, mathematics, Trigonometry. 858 - 929
Al-Farghani (Al-Fraganus) Astronomy, Civil Engineering. C. 860
Al-Razi (Rhazes)
Medicine, Ophthalmology, Smallpox, Chemistry, Astronomy. 864 - 930
Al-Farabi (Al-Pharabius)
Sociology, Logic, Philosophy, Political Science, Music. 870 - 950
Abul Hasan Ali Al-Masu'di Geography, History. Died 957
Al-Sufi (Azophi)
Astronomy 903 - 986
Abu Al-Qasim Al-Zahravi (Albucasis)
Surgery, Medicine. (Father of Modern Surgery) 936 - 1013
Muhammad Al-Buzjani Mathematics, Astronomy, Geometry, Trigonometry. 940 - 997
Ibn Al-Haitham (Alhazen)
Physics, Optics, Mathematics. 965 - 1040
Al-Mawardi (Alboacen)
Political Science, Sociology, Jurisprudence, Ethics. 972 - 1058
Abu Raihan Al-Biruni
Astronomy, Mathematics. (Determined Earth's Circumference) 973-1048
Ibn Sina (Avicenna)
Medicine, Philosophy, Mathematics, Astronomy. 981 - 1037
Al-Zarqali (Arzachel)
Astronomy (Invented Astrolabe). 1028 - 1087
Omar Al-Khayyam
Mathematics, Poetry. 1044 - 1123
Al-Ghazali (Algazel)
Sociology, Theology, Philosophy. 1058 - 1111
Fall of Muslim Toledo (1085), Corsica and Malta (1090), Provence (1050), Sicily (1091) and Jerusalem (1099). Several Crusades. First wave of devastation of Muslim resources, lives, properties, institutions, and infrastructure over a period of one hundred years. Refer to Muslim History. Translators of Scientific Knowledge in the Middle Ages
Abu Bakr Muhammad Ibn Yahya (Ibn Bajjah) Philosophy, Medicine, Mathematics, Astronomy, Poetry, Music. 1106 - 1138
Ibn Zuhr (Avenzoar)
Surgery, Medicine. 1091 - 1161
Al-Idrisi (Dreses)
Geography (World Map, First Globe). 1099 - 1166
Ibn Tufayl, Abdubacer Philosophy, Medicine, Poetry. 1110 - 1185
Ibn Rushd (Averroes)
Philosophy, Law, Medicine, Astronomy, Theology. 1128 - 1198
Al-Bitruji (Alpetragius)
Astronomy Died 1204
Second wave of devastation of Muslim resources, lives, properties, institutions, and infrastructure over a period of one hundred and twelve years. Crusader invasions (1217-1291) and Mongol invasions (1219-1329). Crusaders active throughout the Mediterranean from Jerusalem and west to Muslim Spain. Fall of Muslim Cordoba (1236), Valencia (1238) and Seville (1248). Mongols devastation from the eastern most Muslim frontier, Central and Western Asia, India, Persia to Arab heartland. Fall of Baghdad (1258) and the end of Abbasid Caliphate. Two million Muslims massacred in Baghdad. Major scientific institutions, laboratories, and infrastructure destroyed in leading Muslim centers of civilization. Refer to "A Chronology of Muslim History Parts III, IV."
Ibn Al-Baitar
Pharmacy, Botany Died 1248
Nasir Al-Din Al-Tusi
Astronomy, Non-Euclidean Geometry. 1201 - 1274
Jalal Al-Din Rumi Sociology 1207 - 1273
Ibn Al-Nafis Damishqui
Anatomy 1213 - 1288
Al-Fida (Abdulfeda) Astronomy, Geography, Histrory. 1273 - 1331
Muhammad Ibn Abdullah (Ibn Battuta) World Traveler. 75,000 mile voyage from Morocco to China and back. 1304 - 1369
Ibn Khaldun
Sociology, Philosophy of History, Political Science. 1332 - 1395
Ulugh Beg
Astronomy 1393 - 1449
Third wave of devastation of Muslim resources, lives, properties, institutions, and infrastructure. End of Muslim rule in Spain (1492). More than one million volumes of Muslim works on science, arts, philosophy and culture was burnt in the public square of Vivarrambla in Granada. Colonization began in Africa, Asia, and the Americas. Refer to "A Chronology of Muslim History Parts IV, V (e.g., 1455, 1494, 1500, 1510, 1524, and 1538)"
Two hundred years before a comparable development elsewhere, Turkish scientist Hazarfen Ahmet Celebi took off from Galata tower and flew over the Bosphorus. Logari Hasan Celebi, another member of the Celebi family, sent the first manned rocket, using 150 okka (about 300 pounds) of gunpowder as the firing fuel.
Tipu, Sultan of Mysore [1783-1799] in the south of India, was the innovator of the world's first war rocket. Two of his rockets, captured by the British at Srirangapatana, are displayed in the Woolwich Museum Artillery in London. The rocket motor casing was made of steel with multiple nozzles. The rocket, 50mm in diameter and 250mm long, had a range performance of 900 meters to 1.5 km.

Persian mathematician al-Mahani (b. 820) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. [ edit]
'Abd al-Hamid ibn Turk 'Abd al-Hamid ibn Turk contributed to the study of quadratic equations . [ edit]

Thabit ibn Qurra
Arab mathematician and geometer Thabit ibn Qurra (b. 836) made many contributions to mathematics, particularly geometry. In his work on number theory, he discovered an important theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other. Amicable numbers later played a large role in Islamic mathematics.
Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. Thabit ibn Qurra studied curves required in the construction of sundials. Thabit ibn Qurra also undertook both theoretical and observational work in astronomy. [ edit]

Abu Kamil
Egyptian mathematician Abu Kamil ibn Aslam (850) forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. He had begun to understand what we would write in symbols as . He also studied algebra using irrational numbers. [ edit]

Arab mathematician and astronomer Abu Abdallah Muhammad ibn Jabir al-Battani (868-929) made accurate astronomical observations which allowed him to improve on Ptolemy's data for the Sun and the Moon. He also produced a number of trigonometrical relationships:
He also solved the equation sin x = a cos x discovering the formula:
and used al-Marwazi's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents , compiling tables of them. [ edit]

Sinan ibn Thabit
Arab scientist Sinan ibn Thabit ibn Qurra (c. 880-943) was the son of Thabit ibn Qurra and the father of Ibrahim ibn Sinan. He wrote the mathematical treatise On the elements of geometry, a commentary on Archimedes ' On triangles, and several other astronomical and political treatises. He studied medicine, the science of Euclid , the Almagest, astronomy, the theories of meteorological phenomena, logic and metaphysics. [ edit]

Ibrahim ibn Sinan
Although Islamic mathematicians are most famed for their work on algebra, number theory and numeral systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy. Ibrahim ibn Sinan ibn Thabit ibn Qurra (b. 908), son of Sinan ibn Thabit and grandson of Thabit ibn Qurra, introduced a method of integration more general than that of Archimedes, and was a leading figure in a revival and continuation of Greek higher geometry in the Islamic world. He studied optics and investigated the optical properties of mirrors made from conic sections .
Ibrahim ibn Sinan, like his grandfather, also studied curves required in the construction of sundials, for the purposes of astronomy, time-keeping and geography, which provided motivations for geometrical and trigonometrical research. [ edit]

Abu'l-Hasan al-Uqlidisi
The Indian methods of arithmetic with the Indo-Arabic numerals were originally used with a dust board similar to a blackboard. Arab mathematician Abu'l-Hasan al-Uqlidisi (b. 920) showed how to modify the Indian methods of arithmetic for pen and paper use. [ edit]

Abul Wafa
Persian mathematician Abu'l-Wafa (940-998) invented the tangent function. The Indo-Arabic system of calculating allowed the extraction of roots by Abu'l-W�fa.
Abu'l-W�fa applied spherical geometry to astronomy and also used formulas involving sine and tangent. [ edit]

Abu Bakr al-Karaji
Algebra was further developed by Persian mathematician Abu Bakr al-Karaji (953-1029) in his treatise al-Fakhri, where he extends the methodology to incorporate integral powers and integral roots of unknown quantities.
Al-Karaji is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials and and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years.
The discovery of the binomial theorem for integer exponents by al-Karaji was a major factor in the development of numerical analysis based on the decimal system. [ edit]

Al-Haytham (b. 965), also known as Alhazen, in his work on number theory, seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form where is prime.
Al-Haytham is also the first person that we know to state Wilson's theorem, namely that if is prime then is divisible by . It is unclear whether he knew how to prove this result. It is called Wilson's theorem because of a comment made by Edward Waring in 1770 that John Wilson had noticed the result. There is no evidence that John Wilson knew how to prove it and most certainly Waring did not. Joseph Louis Lagrange gave the first proof in 1771 and it should be noticed that it is more than 750 years after al-Haytham before number theory surpasses this achievement of Islamic mathematics.
Al-Haytham also studied optics and investigated the optical properties of mirrors made from conic sections. [ edit]

Abu Nasr Mansur
Abu Nasr Mansur ibn Ali ibn Iraq (970-1036) applied spherical geometry to astronomy and also used formulas involving sine and tangent. He is well known for discovering the sine law. [ edit]

Abu Sahl al-Kuhi
Persian mathematician Abu Sahl Waijan ibn Rustam al-Quhi (10th century), also known as Abu Sahl al-Kuhi or just Kuhi, was a leading figure in a revival and continuation of Greek higher geometry in the Islamic world. He studied optics and investigated the optical properties of mirrors made from conic sections. He also did some important work on the centers of gravity. [ edit]

Persian mathematician al-Biruni (b. 973 ) used the sine formula in both astronomy and in the calculation of longitudes and latitudes of many cities. Both astronomy and geography motivated al-Biruni's extensive studies of projecting a hemisphere onto the plane. [ edit]

Arab mathematician al-Baghdadi (b. 980) looked at a slight variant of Thabit ibn Qurra's theorem of amicable numbers. There were three different types of arithmetic used around this period and, by the end of the 10th century, authors such as al-Baghdadi were writing texts comparing the three numeral systems: Finger-reckoning arithmetic (a system derived from counting on the fingers with the numerals written entirely in words), the sexagesimal numeral system (developed by the Babylonians), and the Indo-Arabic numerals. This third system of calculating allowed most of the advances in numerical methods. Al-Baghdadi also contributed to improvements in the Indo-Arabic decimal system. [ edit]

Omar Khayyam
The Persian poet Omar Khayyam (b. 1048) was also a mathematician, and wrote Discussions of the Difficulties in Euclid, a book about flaws in Euclid's Elements. He gave a geometric solution to cubic equations, one of the most original discoveries in Islamic mathematics. He was also very influential in calendar reform. He also wrote influential work on Euclid's parallel postulate .
Omar Khayyam gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work:
"If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared. "
The Indo-Arabic system of calculating also allowed the extraction of roots by Omar Khayyam. Omar Khayyam also combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. [ edit]

Moroccan mathematician Al-Samawal (b. 1130) was an important member of al-Karaji's school of algebra. Al-Samawal was the first to give the new topic of algebra a precise description when he wrote that it was concerned " with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known." [ edit]

Sharaf al-Din al-Tusi
Persian mathematician Sharaf al-Din al-Tusi (b. 1135), although almost exactly the same age as al-Samawal, did not follow the general development that came through al-Karaji's school of algebra but rather followed Khayyam's application of algebra to geometry. He wrote a treatise on cubic equations, which represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry. [ edit]

Nasir al-Din al-Tusi
Spherical trigonometry was largely developed by Muslims, and systematized (along with plane trigonometry) by Persian Shi'a mathematician Nasir al-Din al-Tusi (12011274). He also wrote influential work on Euclid's parallel postulate .
Nasir al-Din al-Tusi, like many other Muslim mathematicians, based his theoretical astronomy on Ptolemy's work, but al-Tusi made the most significant development in the Ptolemaic planetary system until the development of the Nicolaus Copernicus. One of these developments is the Tusi-couple, which was later used in the Copernican model. [ edit]

Ibn Al-Banna
Moroccan mathematician ibn al-Banna (b. 1256) used symbols in algebra, though symbols were used by other Islamic mathematicians at least a century before this. [ edit]

Persian mathematician Al-Farisi (b. 1260) gave a new proof of Thabit ibn Qurra's theorem of amicable numbers, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 17,296 and 18,416 which have been attributed to Leonhard Euler, but we know that these were known earlier than al-Farisi, perhaps even by Thabit ibn Qurra himself. Apart from number theory, his other major contribution to mathematics was on light. [ edit]

Ghiyath al-Kashi
Persian mathematician Ghiyath al-Kashi (1380-1429) contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as ð, which he computed to 16 decimal place of accuracy. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Kashi also developed an algorithm for calculating nth roots, which was a special case of the methods given many centuries later by Ruffini and Horner.
Al-Kashi also produced tables of trigonometric functions as part of his studies of astronomy. His sine tables were correct to 4 sexagesimal digits, which corresponds to approximately 8 decimal places of accuracy. The construction of astronomical instruments such as the astrolabe, invented by Mohammad al-Fazari, was also a speciality of Muslim mathematicians. [ edit]

Ulugh Beg
Timurid mathematician Ulugh Beg (1393 or 1394 1449), also ruler of the Timurid Empire, produced tables of trigonometric functions as part of his studies of astronomy. His sine and tangent tables were correct to 8 decimal places of accuracy. [ edit]

Moorish mathematician Abu'l Hasan ibn Ali al Qalasadi (b. 1412) used symbols in algebra, though symbols were used by other Islamic mathematicians much earlier.
In the time of the Ottoman Empire (from 15th century onwards) the development of Islamic mathematics became stagnant. This parallels the stagnation of mathematics when the Romans conquerored the Hellenistic world. [ edit]

Muhammad Baqir Yazdi
In the 17th century, Muhammad Baqir Yazdi gave the pair of amicable numbers 9,363,584 and 9,437,056 many years before Euler's contribution to amicable numbers. [ edit]

Many Arabic texts on Islamic mathematics were translated into Latin and had an important role in the evolution of later European mathematics. A list of translations, from Greek and Sanskrit to Arabic, and from Arabic to Latin, is given below. [ edit]

Greek to Arabic
The following mathematical Greek texts on Hellenistic mathematics were translated into Arabic, and subsequently into Latin:
Euclid's Data, Optics, Phaenomena and On Divisions.

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