Q. & A. 711 to 1707 with solved Papers css 1971 to date

Nasir al-Din al-Tusi (Almuhaqqiq): He accompanied Hulagu Khan
to Baghdad. He was good both in astronomy and astrology. He
persuaded a savage like Hulagu Khan, a man with no taste for such

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Political and Cultural History of Islam

sciences, to build an observatory for him at Maragha and equipped it with sophisticated instruments. From this new study centre, the work of Baghdad and Cairo astronomers found its way into China during the reign of Kublai Khan. He compiled a book al-Zij al-Ilkhani based on his 12 years hard work and observation and also on information gathered from Greek, Indian and Muslim sources. Ulugh Beg: Grandson of Timur, Ulugh Beg is also credited with the accuracy of his observations. In trigonometric functions, his accuracy is more than that of al-Biruni. He is regarded as the last representative of the school of Baghdad. His work published in 1437, gives a comprehensive survey of the contemporary knowledge of astronomy, linking the ancient with that of the modern era, earlier than Kepler. Abdur Rahman II was a great patron of science. Astronomical studies were therefore held in no less esteem in Muslim Spain. Unfortunately all their works were destroyed. Of course, we know that observatories at Toledo and Cordova enjoyed great fame then. One can judge the high quality of this lost work of these Muslim scholars by the numerous contemporary Christian authors who borrowed from them.
Mathematics
Muslim contribution in all branches of mathematics are noteworthy. To start with arithmetic, the style of writing digits from right to left is an evident proof of its Arab origin. For example the figure of five hundred in the English style should be written as 005 and not as 500. Prior to this, numbers were written in alphabets or abjad, then the introduction of the zero sign by Muhammad Ibn Ahmad in 986, was an invention that revolutionized mathematics and was introduced in the West as late as the beginning of the thirteenth century. The Arabs also contributed a great deal to fractions: to the principle of errors, which is employed to solve the algebraic problems arithmetically; to be higher theory of numbers with its problems-on the primitive, perfect and associated numbers. They also solved the famous problem of finding a square, which on addition and subtraction yields another square. Algebra was originated and developed by the Arabs so much in the Course of two centuries, that it touched gigantic proportions.
Al-Khawarizmi: Is credited with the first treatise Hisab al-jabr wal muqabalah, on the subject. This work in Gerard of Cremona’s translation: After being the cornerstone of the mathematical edifice built by the Arabs who came after him, was one day to initiate their
Scientific and Literary Progress under the Abbasids 607
first Western colleagues to the beauty of algebraic calculus and at the same time to that of decimal arithmetic”. Al-Khawarizmi solved algebraic equation of the 1st and 2nd degree and also introduced his geometrical method of solving these equations. He also recognized that quadratic equations have two roots. His work was continued by Thabit Ibn Qurrah, the translator of Ptolemy’s Almagest who developed algebra and first realized its application in geometry. By the llth century, the Arabs had founded, developed and perfected geometrical algebra and could solve equation of 3rd and 4th degree. Cantor confirms the Arabs superiority in algebra by saying- ”At least in science with which we are at present concerned (i.e. algebra) the Arabs of the year 1100 were uncommonly superior to the most learned Europeans”.
Abul Wafa: In 10th century he created and successfully developed a branch of geometry which consists of problems leading to algebraic equations of higher degree than the 2nd . He made many valuable contributions to the theory of poly hedra, which is even now considered, the most difficult subject.