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Similarly, the fact that several commentaries on the Aryabhatiya have come from Kerala has been used to suggest that it was Aryabhata's main place of life and activity; however, many commentaries have come from outside Kerala, and the Aryasiddhanta was completely unknown in Kerala.) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well.Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost.It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara I.Aryabhata discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord". When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba.However, in Arabic writings, vowels are omitted, and it was abbreviated as jb.A third text, which may have survived in the Arabic translation, is Al ntf or Al-nanf.It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known.
The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c.Later writers substituted it with jaib, meaning "pocket" or "fold (in a garment)".(In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremona translated these writings from Arabic into Latin, he replaced the Arabic jaib with its Latin counterpart, sinus, which means "cove" or "bay"; thence comes the English word sine.His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times.The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry.