xi Brahmagupta is calculated to lead to the conclusion that, in all probability, Mahavīrācārya was familiar with the work of Brahmagupta and endeavoured to improve upon it to the extent to which the scope of his Ganita-sara- sangraha permitted such improvement. Mahāvīrācārya's classification of arithmetical operations is simpler, his rules are fuller and he gives a large number of examples for illustration and exercise. Prthüdakas vāinin, the well- known commentator on the Brahmasphuta-siddhānta, could not have been chronologically far removed from Mahāvīrācārya, and the similarity of some of the exam- ples given by the former with some of those of the latter naturally arrests attention. In any case it cannot be wrong to believe, that, at the time, when Mahāvīrācārya wrote his Ganita-sara-sangraha, Brahmagupta must have been widely recognized as a writer of authority in the field of Hindu astronomy and mathematics. Whether Bhaskarācārya was at all acquainted with the Ganita- sara-sangraha of Mahāvīrācārya, it is not quite easy to say. Since neither Bhaskarācārya nor any of his known commentators seem to quote from him or mention him by name, the natural conclusion appears to be that Bhas- karācārya's Siddhanta-siromani, including his Lilāvatī and Bijaganita, was intended to be an improvement in the main upon the Brahmasphuta-siddhanta of Brahmas gupta. The fact that Mahaviräcārya was a Jaina might have prevented Bhaskarācārya from taking note of him; or it may be that the Jaina mathematician's fame had not spread far to the north in the twelfth century of the Christian era. His work, however, seems to have been widely known and appreciated in Southern India. So early as in the course of the eleventh century and perhaps PREFACE.
