Brāhmasphuṭasiddhānta

The Brāhma-sphuṭa-siddhānta ("Correctly Established Doctrine of Brahma", abbreviated BSS) is a main work of Brahmagupta, written c. 628.^[1] This text of mathematical astronomy contains significant mathematical content, including the first 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 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).^[2][3]

Positive and negative numbers

Brāhmasphuṭasiddhānta is one of the first books to provide concrete ideas on positive numbers, negative numbers, and zero.^[4] For example, it notes that the sum of a positive number and a negative number is their difference or, if they are equal, zero; that subtracting a negative number is equivalent to adding a positive number; that the product of two negative numbers is positive. Some of the notions of fractions differ from the modern rational number system. For example, Brahmagupta allows division by zero resulting in a fraction with a 0 in the denominator, and defines 0/0 = 0. In modern mathematics, division by zero is undefined for any field.^[5]

Influence

Ashadhara, the son of Rihluka, wrote Graha-jnana with tables based on Brahma-sphuta-siddhanta in 1132. This work is also known by the names Graha-ganita, Brahma-tulyanayana, Bhaumadi-panchagraha-nayana, Kshanika-grahanayana, or simply Ashadhara. Harihara wrote an extended version of the Graha-jnana around 1575 CE.^[6]

References

1. "Brahmagupta | Indian astronomer". Encyclopedia Britannica. 19 July 2024.
2. Bradley, Michael. The Birth of Mathematics: Ancient Times to 1300, p. 86 (Infobase Publishing 2006).
3. Mackenzie, Dana. The Universe in Zero Words: The Story of Mathematics as Told through Equations, p. 61 (Princeton University Press, 2012).
4. Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)
5. Kaplan, Robert (1999). The Nothing that is: A Natural History of Zero. New York: Oxford University Press. pp. 68–75. ISBN 0-19-514237-3.
6. David Pingree, ed. (1970). Census of the Exact Sciences in Sanskrit Series A. Vol. 1. American Philosophical Society. p. 54.

External links

• Brahmasphutasiddhanta at GRETIL (mathematical chapters: 12, 18-20, 21.17-23)
• O'Connor, John J.; Robertson, Edmund F., "Brahmagupta", MacTutor History of Mathematics Archive, University of St Andrews