Brahma-sphuta-siddhanta

work by Brahmagupta

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July 23, 2026

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The Brahma-sphuta-siddhanta is a seminal work by the ancient Indian astronomer and mathematician Brahmagupta, written around 628 CE. This treatise, meaning "Correctly Established Doctrine of Brahma," significantly influenced Islamic and Byzantine astronomy and mathematics.12

Within the Brahma-sphuta-siddhanta, Brahmagupta laid foundations for Indian mathematics, particularly in arithmetic (pati-ganita) and algebra (bija-ganita). He defined zero as the result of subtracting a number from itself and established rules for arithmetic operations involving negative numbers. He also provided solutions to certain indeterminate equations and a formula for the area of a cyclic quadrilateral. The work was translated into Arabic and had a profound impact on the development of Islamic mathematical astronomy.132

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Brahmagupta
…Brahmagupta devoted several chapters of Brahma-sphuta-siddhanta to mathematics. In chapters 12 and 18 in particular, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations), which roughly correspond to arithmetic (including mensuration) and algebra, respectively.…
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…Brahmagupta devoted several chapters of Brahma-sphuta-siddhanta to mathematics. In chapters 12 and 18 in particular, he laid the foundations of the two major fields of Indian mathematics, pati-ganita (“mathematics of procedures,” or algorithms) and bija-ganita (“mathematics of seeds,” or equations), which roughly correspond to arithmetic (including mensuration) and algebra, respectively.…
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Indian mathematics
The role of astronomy and astrology
500 ce) and the Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”) of Brahmagupta. Little is known of these authors. Aryabhata lived in Kusumapura (near modern Patna), and Brahmagupta is said to have been from Bhillamala (modern Bhinmal), which was the capital of the Gurjara-Pratihara dynasty. The “schools” that grew…
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500 ce) and the Brahma-sphuta-siddhanta (628; “Correctly Established Doctrine of Brahma”) of Brahmagupta. Little is known of these authors. Aryabhata lived in Kusumapura (near modern Patna), and Brahmagupta is said to have been from Bhillamala (modern Bhinmal), which was the capital of the Gurjara-Pratihara dynasty. The “schools” that grew…
Read More