# Abu Abdullah Mohammad Ibn Musa al-Khawarizmi

Abu Abdullah Mohammad Ibn Musa al-Khawarizmi was born at Khawarizm (Kheva), south of Aral sea. Very little is known about his early life, except for the fact that his parents had migrated to a place south of Baghdad. The exact dates of his birth and death are also not known, but it is established that he flourished under Al- Mamun at Baghdad through 813-833 and probably died around 840 C.E. Khawarizmi was a mathematician, astronomer and geographer. He was perhaps one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics. In the words of Phillip Hitti, he influenced mathematical thought to a greater extent than any other medieval writer

His work on algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra. The very name Algebra has been derived from his famous book Al-Jabr wa-al-Muqabilah. His arithmetic synthesised Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeral of fundamental importance developed by the Arabs. Similarly, he developed the decimal system so that the overall system of numerals, ?algorithm? or ?algorizm? is named after him. In addition to introducting the Indian system of numerals (now generally known as Arabic numerals), he developed at length several arithmetical procedures, including operations on fractions. It was through his work that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages. He developed in detail trigonometric tables containing the sine functions, which were probably extrapolated to tangent functions by Maslama. He also perfected the geometric representation of conic sections and developed the calculus of two errors, which practically led him to the concept of differentiation. He is also reported to have collaborated in the degree measurements ordered by Mamun al-Rashid were aimed at measuring of volume and circumference of the earth. The development of astronomical tables by him was a significant contribution to the science of astronomy, on which he also wrote a book. The contribution of Khawarizmi to geography is also outstanding, in that not only did he revise Ptolemy?s views on geography, but also corrected them in detail as well as his map of the world. His other contributions include original work related to clocks, sundials and astrolabes. Several of his books were translated into Latin in the early 12th century. In fact, his book on arithmetic, Kitab al-Jam?a wal- Tafreeq bil Hisab al-Hindi, was lost in Arabic but survived in a Latin translation. His book on algebra, Al-Maqala fi Hisab-al Jabr wa-al- Muqabilah, was also translated into Latin in the 12th century, and it was this translation which introduced this new science to the West ?completely unknown till then?. He astronomical tables were also translated into European languages and, later, into Chinese. His geography captioned Kitab Surat-al-Ard, together with its maps, was also translated. In addition, he wrote a book on the Jewish calendar Istikhraj Tarikh al-Yahud, and two books on the astrolabe. He also wrote Kitab al-Tarikh and his book on sun-dials was captioned Kitab al-Rukhmat, but both of them have been lost. [image]The influence of Khawarizmi on the growth of science, in general, and mathematics, astronomy and geography in particular, is well established in history. Several of his books were readily translated into a number of other languages, and, in fact, constituted the university textbooks till the 16th century. His approach was systematic and logical, and not only did he bring together the then prevailing knowledge on various branches of science, particularly mathematics, but also enriched it through his original contribution. No doubt he has been held in high repute throughout the centuries since then. abu abdullah AL-battani ======= (868-929 C.E.) -?????- Abu Abdallah Muhammad Ibn Jabir Ibn Sinan al-Battani al-Harrani was born around 858 C.E. in Harran, and according to one account, in Battan, a State of Harran. Battani was first educated by his father Jabir Ibn San?an al-Battani, who was also a well-known scientist. He then moved to Raqqa, situated on the bank of the Euphrates, where he received advanced education and later on flourished as a scholar. At the beginning of the 9th century, he migrated to Samarra, where he worked till the end of his life in 929 C.E. He was of Sabian origin, but was himself a Muslim. Battani was a famous astronomer, mathematician and astrologer. He has been held as one of the greatest astronomists of Islam. He is responsible for a number of important discoveries in astronomy, which was the result of a long career of 42 years of research beginning at Raqqa when he was young. His well-known discovery is the remarkably accurate determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds, which is very close to the latest estimates. He found that the longitude of the sun?s apogee had increased by 16? , 47? since Ptolemy. This implied the important discovery of the motion of the solar apsides and of a slow variation in the equation of time. He did not believe in the trapidation of the equinoxes, although Copernicus held it. Al-Battani determined with remarkable accuracy the obliquity of the ecliptic, the length of the seasons and the true and mean orbit of the sun. He proved, in sharp contrast to Ptolemy, the variation of the apparent angular diameter of the sun and the possibility of annular eclipses. He rectified several orbits of the moon and the planets and propounded a new and very ingenious theory to determine the conditions of visibility of the new moon. His excellent observations of lunar and solar eclipses were used by Dunthorne in 1749 to determine the secular acceleration of motion of the moon. He also provided very neat solutions by means of orthographic projection for some problems of spherical trigonometry. [image]In mathematics, he was the first to replace the use of Greek chords by sines, with a clear understanding of their superiority.He also developed the concept of cotangent and furnished their table in degrees. He wrote a number of books on astronomy and trigonometry. His most famous book was his astronomical treatise with tables, which was translated into Latin in the 12th century and flourished as De scienta stellerum ? De numeris stellerum et motibus. An old translation of this is available of the Vatican. His Zij was, in fact, more accurate than all others written by that time. His treatise on astronomy was extremely influential in Europe till the Renaissance, with translations available in several languages. His original discoveries both in astronomy and trigonometry were of great consequence in the development of these sciences.

Abu Abdullah Mohammad Ibn Musa al-Khawarizmi
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