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

^ "Brahmagupta | Indian astronomer". Encyclopedia Britannica. 19 July 2024.
^ Bradley, Michael. The Birth of Mathematics: Ancient Times to 1300, p. 86 (Infobase Publishing 2006).
^ Mackenzie, Dana. The Universe in Zero Words: The Story of Mathematics as Told through Equations, p. 61 (Princeton University Press, 2012).
^ Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)
^ 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.
^ 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

[1] "Brahmagupta | Indian astronomer". Encyclopedia Britannica. 19 July 2024.

[Bradley-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)

[Kaplan-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.

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v t e Indian astronomy
Astronomers	Apastamba Aryabhata I Aryabhata II Vainu Bappu Bhāskara I Bhāskara II Baudhayana Brahmagupta Sandip Chakrabarti Radhagobinda Chandra Subrahmanyan Chandrasekhar Amil Kumar Das P. Devadas Gautama Siddha M. K. Das Gupta Jyesthadeva Kamalakara Katyayana Lagadha Lalla Madhava of Sangamagrama Prasanta Chandra Mahalanobis Mahavira Manava Jayant Narlikar Parameshvara Achyuta Pisharati Venkatraman Radhakrishnan J. J. Rawal Megh Nad Saha Jagannatha Samrat Bapudeva Sastri Jai Singh II of Amber Nilakantha Somayaji Sripati Mahendra Suri Govind Swarup Utpala Varahamihira Shankara Variyar Vasistha Yajnavalkya Pathani Samanta
Works	Aryabhatiya Brahmanas Aitareya Brahmana Shatapatha Brahmana Bṛhat Saṃhitā Ganitagannadi Jyotirmimamsa Shulba Sutras Panchangam Khandakhadyaka Mahādevī Makarandasarini Siddhantas Brāhmasphuṭasiddhānta Maha-Siddhanta Pancha-Siddhantika Paulisa Siddhanta Paitamaha Siddhanta Rājamṛgāṅka (astronomy book) Romaka Siddhanta Surya Siddhanta Vasishtha Siddhanta Tantrasangraha Treatise on Astrology of the Kaiyuan Era Vākyakaraṇa Vedanga Jyotisha Vedas Atharvaveda Rigveda Yavanajataka Zij
Instruments	Armillary sphere Astrolabe Celestial globe Compass Cross-staff Dioptra Equatorial ring Equatorial sundial Globe Gnomon Mural instrument Quadrant Sextant Sundial Triquetrum Water clock Yantraraja
Concepts	Axial tilt Azimuth Cardinal direction Celestial equator Celestial sphere Celestial spheres Center of mass Circular orbit Deferent and epicycle Earth's rotation Eccentricity Ecliptic Elliptic orbit Equant Geocentrism Geoheliocentrism Globe Gravity Heliocentrism Hindu units of time Jyotiṣa Kali ahargaṇa Kalpa Karana Manvantara Moonlight Nakshatra Nityayoga Parallax Precession Ritu Spherical Earth Sunlight Tithi Vāra Yuga Zodiacal sign
Centres	Jantar Mantar Jaipur New Delhi Ujjain Varanasi Kerala school of astronomy and mathematics
Other regions	Babylonian astronomy Ancient Greek astronomy Hellenistic astronomy Islamic astronomy Chinese astronomy European astronomy
Months of the Vedic calendar	Chaitra Vaisakha Jyeshta Aashaadha Shraavana Bhadrapada Ashvin Kartik Margashirsha Pausha Maagha Phalguna