Brahmagupta

Brahmagupta was an Indian mathematician and astronomer of the seventh century, the foremost mathematician of his time in India. His father was Jisnugupta, and he wrote the Brahmasphutasiddhanta in 628 in 25 chapters, composing it at Bhillamala, today the city of Bhinmal, then the capital of the lands ruled by the Gurjara dynasty. He later became head of the astronomical observatory at Ujjain, the foremost mathematical centre of ancient India, and wrote a second work, the Khandakhadyaka, in 665. In the first treatise he defined zero as the result of subtracting a number from itself and set out arithmetical rules for fortunes (positive numbers) and debts (negative numbers), and he made a flawed attempt to extend arithmetic to division by zero. He also gave an algorithm for square roots, methods for quadratic and indeterminate equations including solutions of equations of the type a x squared plus c equals y squared, rules for summing series, and formulae for the area and diagonals of a cyclic quadrilateral, alongside long sections on eclipses and planetary positions.