Al-Mansur, the founder of Baghdad, sent one of his Jewish courtier to the city of Ujjain (now in Madhya Pradesh) to bring one Indian mathematician to his court. In those days Ujjain was the center of mathematics in India. The visit of the Hindu delegation from India to the court of as-Mansur was a turning point in Arab intellectual history. The Indian delegation brought with them, according to the widely travelled geographer Al-Masudi, the document that contained all Hindu knowledge of the spheres, the stars, mathematics, and other sciences. The Indian mathematicians placedheavy reliance on sine function. No doubt it was an invaluable contribution of Hindus but it was refined further by the Arabs. By the ninth century, all six trigonometric functions - sine,and consine, tangent and cotangent, secant and cosecant were vry much in use. Only the first one was from India and all the other five were Arab discoveries.
It was a custom with India that mathematical and astronomical and other works of knowledge were written in verse form for the ease of memorization. The Arab scholars and translators had to grapple with the Sanskrit verses to pick out the core content of knowledge. It helped the Arab scholars to be acquainted with the fundamental science instead of being the mere imitators. Mohammad ibn Musa al-Khwarizmi, born around 783, took advantage of this confluence of knowledge.
The transmission of Hindu knowledge did not take place in a vacuum but it was a systematic synthesis Hindi and Arab classical knowledge. Khwarizimi produced a successful book on the use of new system of numbers. The famous book is know is known as 'The Book of Addition and Subtraction According to the Hindu Calculation'. It was the first book know on the subject. This book is lost but it survives in 12th century Latin translation. It was the book that introduced the present numerals to the West.
Khwarzimi's second book 'Kitab al-jabr wa'l-muqabala'. This book is famous in English as 'The Book of Restoring and Balancing'. It is from the title if this book the modern science derived the term 'algebra'. This book of Khwarzimi was dedicated to his patron Caliph al-Mamun. In his dedication, he writes about the practical utility of this book. He writes,
The fondness for science by which God had distinguished Imam al-Mamun.....has encouraged me to compose a short work .....confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, law-suits and trade, and in their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation and other objects of various sorts and kinds are concerned.
*******
ALGORITHM
The word algorism(Algorithm, which is the base of computer logical structure, and computer programming) comes from the name al-Khwarizmi ("the one from Khwarizm") of an early 9th century Persian mathematician, possibly from what is now Khiva in western Uzbekistan. In English, it was first used about 1230 and then by Chaucer in 1391[1]. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus:
Al-Khwarizmi:
Al-Khwarizmi (Mohammad ebne M?s? Khw?razm? ???? ?? ???? ???????) was a Persian mathematician, astronomer, astrologer and geographer. He was born around 780 in Khw?rizm, then part of the Persian Empire (now Khiva, Uzbekistan) and died around 850. He worked most of his life as a scholar in the House of Wisdom in Baghdad.
His Algebra was the first book on the systematic solution of linear and quadratic equations. Consequently he is considered by many to be the father of algebra, a title some scholars assign to Diophantus. Latin translations of his Arithmetic, on the Indian numerals, introduced the decimal positional number system to the Western world in the twelfth century. He revised and updated Ptolemy's Geography as well as writing several works on astronomy and astrology.
His contributions not only made a great impact on mathematics, but on language as well. The word algebra is derived from al-jabr, one of the two operations used to solve quadratic equations, as described in his book.
Contributions:
His major contributions to mathematics, astronomy, astrology, geography and cartography provided foundations for later and even more widespread innovation in algebra, trigonometry, and his other areas of interest. His systematic and logical approach to solving linear and quadratic equations gave shape to the discipline of algebra, a word that is derived from the name of his 830 book on the subject, al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala (Arabic ?????? ??????? ?? ???? ????? ?????????) or: "The Compendious Book on Calculation by Completion and Balancing". The book was first translated into Latin in the twelfth century.
His book On the Calculation with Hindu Numerals written about 825, was principally responsible for the diffusion of the Indian system of numeration in the Middle-East and then Europe. This book also translated into Latin in the twelfth century, as Algoritmi de numero Indorum. From the name of the author, rendered in Latin as algoritmi, originated the term algorithm.
Some of his contributions were based on earlier Persian and Babylonian Astronomy, Indian numbers, and Greek sources.
Al-Khw?rizm? systematized and corrected Ptolemy's data in geography as regards to Africa and the Middle east. Another major book was his Kitab surat al-ard ("The Image of the Earth"; translated as Geography), which presented the coordinates of localities in the known world based, ultimately, on those in the Geography of Ptolemy but with improved values for the length of the Mediterranean Sea and the location of cities in Asia and Africa.
He also assisted in the construction of a world map for the caliph al-Ma'mun and participated in a project to determine the circumference of the Earth, supervising the work of 70 geographers to create the map of the then "known world".
When his work was copied and transferred to Europe through Latin translations, it had a profound impact on the advancement of basic mathematics in Europe. He also wrote on mechanical devices like the astrolabe and sundial.
