''Bijaganita'' (
iːd͡ʒəgəɳit̪ᵊ, -ɪt̪ᵊ IAST
The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Brahmic family, Indic scripts as employed by Sanskrit and related Indic languages. It is based on a scheme that ...
: ') was
treatise
A treatise is a Formality, formal and systematic written discourse on some subject concerned with investigating or exposing the main principles of the subject and its conclusions."mwod:treatise, Treatise." Merriam-Webster Online Dictionary. Acc ...
on
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
by the Indian mathematician
Bhāskara II
Bhāskara II ('; 1114–1185), also known as Bhāskarāchārya (), was an Indian people, Indian polymath, Indian mathematicians, mathematician, astronomer and engineer. From verses in his main work, Siddhānta Śiromaṇi, it can be inferre ...
. It is the second volume of his main work ''
Siddhānta Shiromani (''"Crown of treatises") alongside ''
Lilāvati'', ''Grahaganita'' and ''Golādhyāya''.
Meaning
The title of the work, , which literally translates to "mathematics () using seeds ()", is one of the two main branches of mediaeval Indian mathematics, the other being , or "mathematics using algorithms". derives its name from the fact that "it employs algebraic equations () which are compared to seeds () of plants since they have the potentiality to generate solutions to mathematical problems."
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 (; born ), also spelt Jaideva, was a Sanskrit poet during the 12th century. He is most known for his epic poem ''Gita Govinda'' which concentrates on Krishna's love with the ''gopi'', Radha, in a rite of spring. This poem, which presen ...
's way of generalization of Brahmagupta's approach to solving indeterminate quadratic equations, including Pell's equation which is known as
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, (c. 1114 – 1185 CE)Hoiberg & Ramchandani – Students' Britannica India: Bhask ...
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 Bijaganita into English include:
* 1817.
Henry Thomas Colebrooke
Henry Thomas Colebrooke FRS FRSE FLS (15 June 1765 – 10 March 1837) was an English orientalist and botanist. He has been described as "the first great Sanskrit scholar in Europe".
Biography
Henry Thomas Colebrooke was born on 15 June ...
''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 Dwivedi and
Bapudeva Sastri studied Bijaganita in the nineteenth century.
See also
*
Bījapallava
*
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, ...
*
Kṛṣṇa Daivajña
*
Pātīgaṇita
*
Timeline of algebra and geometry
*
Trairāśika
Trairāśika is the Sanskrit term used by Indian astronomers and mathematicians of the pre-modern era to denote what is known as the " rule of three" in elementary mathematics and algebra. In the contemporary mathematical literature, the term "rule ...
References
Bibliography
*
*
External links
Hindi translation by Durga Prasad
{{Indian mathematics
Indian mathematics
Social history of India
History of science and technology in India
History of algebra
12th-century books
12th-century Sanskrit literature