Dec 13

Brahmagupta's Brāhmasphutasiddhānta

Correctly Established Doctrine of Brahma

Brahmagupta wrote his Brāhmasphutasiddhānta in 628 CE, in Sanskrit. It contains ideas including a good understanding of the mathematical role of zero, rules for manipulating both negative and positive numbers. It also contains a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series, Brahmagupta's identity, and the Brahmagupta’s theorem. The book was written completely in verse. I have produced a PDF of Brahmagupta's Brāhmasphuṭasiddhānta with commentary (in Sanskrit) by Sudhākara Dvivedin, published in Benares, India, 1902. It can be read online and downloaded from:


I would like to thank the University of Chicago Library for making their microfilm of the book available so I could have it scanned in Chennai India, where it was converted into hundreds of single TIF images.  I then cropped cleaned and edited these images to produce a downloadable PDF version.

After sharing this with Indian mathematics professors who read Sanskrit, and having been helped by them, I have really started to get to appreciate how Brahmagupta intended arithmetic to work!

This book can also be studied with a 1966 edition of Brahmagupta's Brāhmasphutasiddhānta with Hindi commentary at: