Brāhmasphuṭasiddhānta

The Brāhmasphuṭasiddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is the main work of Brahmagupta, written c. 628. Τhis text of mathematical astronomy contains significant mathematical content, including a good understanding of the role of zero, rules for manipulating both negative and positive numbers, a method for computing square roots, methods of solving linear and quadratic equations, and rules for summing series, Brahmagupta's identity, and Brahmagupta’s theorem.

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).

Brāhmasphuṭasiddhānta is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zero. He wrote the following rules:

The last of these rules is notable as the earliest attempt to define division by zero, even though it is not compatible with modern number theory (division by zero is undefined for a field).

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