Bijaganita
Encyclopedia
Bijaganita was Indian mathematician Bhāskara II's treatise on algebra
. It is the second volume of his main work Siddhānta Shiromani
, Sanskrit
for "Crown of treatises," alongside Lilāvati
, Grahaganita and Golādhyāya.
In Bijaganita Bhāskara II refined Jayadeva
's way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as chakravala method
or cyclic method. Bijaganita is the first text to recognize that a positive number has two square roots
Two notable Scholars from Varanasi Sudhakar Dvivedi
and Bapudeva Sastri
studied Bijaganita in the nineteenth century.
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
. It is the second volume of his main work Siddhānta Shiromani
Siddhānta Shiromani
Siddhānta Shiromani is the major work of Indian mathematician Bhāskara II.Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years old. This is a mammoth work containing about 1450 verses.-Lilavati:...
, Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
for "Crown of treatises," alongside Lilāvati
Lilavati
Lilavati was Indian mathematician Bhāskara II's treatise on mathematics. It is the first volume of his main work Siddhānta Shiromani, Sanskrit for "Crown of treatises," alongside Bijaganita, Grahaganita and Golādhyāya.- Name :The name comes from his daughter Līlāvatī...
, Grahaganita and Golādhyāya.
Contents
The book is divided into six parts, mainly indeterminate equations, quadratic equations, simple equations, surds. The contents are:- Introduction
- On Simple Equations
- On Quadratic Equations
- On Equations involving indeterminate Questions of the 1st Degree
- On Equations involving indeterminate Questions of the 2nd Degree
- On Equations involving Rectangles
In Bijaganita Bhāskara II refined Jayadeva
Jayadeva
Jayadeva was a Sanskrit poet circa 1200 AD. He is most known for his composition, the epic poem Gita Govinda, which depicts the divine love of Krishna-an avatar of Vishnu and his consort, Radha, and it is mentioned that Radha is greater than Hari, and is considered an important text in the...
's way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as chakravala method
Chakravala method
The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly attributed to Bhāskara II, although some attribute it to Jayadeva...
or cyclic method. Bijaganita is the first text to recognize that a positive number has two square roots
Translations
The translations or editions of the Lilavati into English include:- 1817. Henry Thomas ColebrookeHenry Thomas ColebrookeHenry Thomas Colebrooke was an English orientalist.-Biography:Henry Thomas Colebrooke, third son of Sir George Colebrooke, 2nd Baronet, was born in London. He was educated at home; and when only fifteen he had made considerable attainments in classics and mathematics...
, Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara - 1813. Ata Allah ibn Ahmad Nadir Rashidi; Samuel Davis
- 1813. Strachey, Edward, Sir, 1812–1901
- Bhaskaracharya's Bijaganita and its English and Marathi Translation by Prof. S. K. Abhyankar
Two notable Scholars from Varanasi Sudhakar Dvivedi
Sudhakar Dvivedi
Sudhakar Dvivedi was an Indian scholar in Sanskrit and mathematics.He was born in 1855 in Khajuri, a village near Varanasi. At an early age he was attracted to mathematics, which he studied under Pandit Devakrsna...
and Bapudeva Sastri
Bapudeva Sastri
Bapudeva Sastri was a Brahman pandit who became the first professor of both Indian and western astronomy. He was born on November 1, 1821, to a Brahmin family of Maharashtra. He received his early education in western arithmetic and algebra at the Marathi school in Nagpur...
studied Bijaganita in the nineteenth century.