ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

CHAPTER IX Brahmagupta as an Algebraist Ancient Indian name for algebra is Bījagaṇita where bīja means element or analysis and gaṇita stands for the science of calculation. As early as 860 A.D., Pṛthūdaka Svāmī used this epithet for algebra in his commentary. Brahmagupta calls algebra as Kuṭṭakagaṇita or merely kuṭṭaka, a term which was later on used for "pulveriser" which deals with that special sec- tion of algebra which is connected with indeterminate equations of the first degree. Algebra is often also known as avyakta- gaṇita or the calculations with unknowns, in contrast to arith- metic which was known as vyakta-gaṇita or the calculations with knowns. Algebra goes to Europe from India In the history of mathematical sciences, as Colebrooke rightly remarks, it has long been a question to whom the inven- tion of algebraic analysis is due. There is no doubt that Europe got algebra from Arabs mediately or immediately. But the Arabs themselves scarcely pretend to the discovery of algebra. Colebrooke says that they were not in general inventors but scholars during the short period of their successful culture of the sciences; and the germ at least of the algebraic analysis is to be found among the Greeks in an age not precisely determined, but more than probably anterior to the earliest dawn of civilisation among the Arabs; and this science in a more advanced state subsisted among the Hindus prior to the earliest disclosure of it by the Arabians to modern Europe. (Colebrooke: Disserta- tion on the Algebra of the Hindus)¹. Colebrooke based his observations on the texts he could procure for his studies. These were: Bhāskara II's Bījagaṇita or Vījagaṇita (1150 A.D.) and Līlāvatī (1150 A.D.), the Gaṇitādhyāya and Kuṭṭakādhyāya of Brahmagupta in his famous treatise the Brahma Siddhānta or rather the Brāhmasphuṭasiddhānta (628

1. Colebrooke, H. T., Miscellaneous Essays, Vol. II, 1872, p. 418.