Digital Rare Book:
Brahmagupta's BRAHMA-SPHUTA SIDDHANTA
Edited by Acharyavara Ram Swarup Sharma
Published by Indian Institute of Astronomical and Sanskrit Research, New Delhi - 1965
In Four Volumes
In 628 ca. Indian mathematician and astronomer of Bhinmal, a town in the Jalore District of Rajasthan, India, Brahmagupta wrote Brahmasphutasiddhanta.
"It contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both negative and positive, a method for computing aquare roots, methods of solving linear and some quadratic equations, and rules for summing series, Brahamgupta's identity, and the Brahmagupta's theorem."
By this time a base 10 numeral system with nine symbols was widely used in India, and the concept of zero (represented by a dot) was known.
The book was written completely in verse and does not contain any kind of mathematical notation. Nevertheless, it contained the first clear description of the quadratic formula (the solution of the quadratic equation).
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Brahmagupta (Sanskrit: ???????????; About this sound listen (help·info)) (598–c.670 CE) was an Indian mathematician and astronomer who wrote two works on Mathematics and Astronomy: the Br?hmasphu?asiddh?nta (Extensive Treatise of Brahma) (628), a theoretical treatise, and the Kha??akh?dyaka, a more practical text. There are reasons to believe that Brahmagupta originated from Bhinmal.
Brahmagupta was the first to give rules to compute with zero. The texts composed by Brahmagupta were composed in elliptic verse, as was common practice in Indian mathematics, and consequently have a poetic ring to them. As no proofs are given, it is not known how Brahmagupta's mathematics was derived.