पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२६

When we come to the question of the relation between the different sections of the East, however, we meet with more difficulty. What were the rations, for example, between the school of Pataliputra, where Arvablata wrote, and that of Ujjain, where both Brahmagupta and Bhaskara lived and taught? And what was the relation of each of these to the school down in South India, which produced this notable treatise of Mahavira- carya? And, a still more interesting question is, what can we say of the influence exerted on China by Hindu scholars, or vice versa? When we find one set of early inscriptions, those at Nana Ghät, using the first three Chinese numerals, and another of about the same period using the later forms of Mesopotamia, we feel that both China and the West may have influenced Hindu science. When, on the other hand, we consider the problems of the great trio of Chinese algebraists of the thirteenth century, Ch'in Chiu- shang, Li Ych, and Chu Shih chieh, we feel that Hindu algebra must have had no small influence upon the North of Asia, although it must be said that in point of theory the Chinese of that period naturally surpassed the earlier writers of India. The answer to the questions as to the relation between the schools of India cannot yet be easily given. At first it would seem a simple matter to compare the teratises of the three or four great algebraists and to note the similarities and differences. When this is done, however, the result seems to be that the works of Brahmagupta, Mahāvīrācārya, and Bhaskara may be described as similar in spirit but entirely different in detail. For example, all of these writers treat of the arcas of polygons, but Mahavira- carya is the only one to make any point of those that are re-ent- rant. All of them touch upon the area of a segment of a circle, but all give different rules. The so-callod janya operation (page 209) is akin to work found in Brahinagupta, and yet none of the problems is the same. The shadow problems, primitive cases of trigonometry and gnomonics, suggest a similarity among these three great writers, and yet those of Mahāvīrācārya are much better than the one to be found in either Brahmagupta or Bhaskara, and no questions are duplicated.