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

ALGEBRA GOES TO EUROPE FROM INDIA 197 posed on the authority of Abulfaraj, to have flourished in the time of the Emperor Julian or about A. D. 360. Colebrooke further says : Admitting the Hindu and Alexandrian authors to be nearly equally ancient, it must be conceded in favour of the Indian algebraist, that he was more advanced in the science; since he appears to have been in possession of the resolution of equations involving several unknowns, which it is not clear, nor fairly presumable, that Diophantus, knew; and a general method of indeterminate problems of at least the first degree, to a knowledge of which the Grecian algebraist had certainly not attained ; though he displays infinite sagacity and ingenuity in particu- lar solutions ; and though a certain routine is indiscer- nible in them. Colebrooke appears to be of the view that Greeks. were the first to discover the solution of equations involving one unknown; and this knowledge was passed to ancient Indians by their Greek instructors in impro- ved astronomy. But "by the ingenuity of the Hindu- scholars, the hint was rendered fruitful and the algeb- raic method was soon ripened from that slender beginn- ing to the advanced state of a well arranged science, as it was taught by Āryabhaṭa, and as it is found in treatises compiled by Brahmagupta and Bhāskara." We do not agree with this analysis in entirety. Indian algebra is entirely of Indian roots. It had its beginning in the times of Saṃhitās and Brāhmaṇas. Some of the equations and problems were solved by geometric methods. It must have had its origin in the Śulba period if not before. Āryabhaṭa undoubtedly was the discoverer of many algebraic solutions of equations of the first and higher order with one and more unkno- wns. It is rather too much to trace the influence of Diophantus on Indian algebra which developed in this country independently. Brahmagupta is one of the most brilliant algebraists we ever had in the entire history of mathematics.