INTRODUCTION. XXI Chinese and Japanese mathematical works" made more or less familiar to the West; and the more important Arab treatises are now quite satisfactorily khown. Various editions of Bhaskara have appeared in India; and in general the great treatises of the Orient have begun to be subjected to critical study. It would be strange, therefore, if we were not in a position to weigh up, with more certainty than before, the claims of the Hindu algebra. Certainly the persevering work of Professor Rangācārya has made this more possible than ever before. As to the relation hetween the East and the West, we should now be in a position to say rather definitely that there is no evidence of any considerable influence of Greek algebra upon that of India. The two subjects were radically different. It is true that Diophantus lived about two centuries before the first Aryabhata, that the paths of trade were open from the West to the East, and that the itinerant scholar undoubtedly carried learning from place to place. But the spirit of Diophantus, showing itself in a dawning symbolism and in a peculiar type of equation, is not seen at all in the works of the East. None of his problems, not a trace of his symbolism, and not a bit of his phraseo- logy appear in the works of any Indian writer on algebra. On the contrary, the Hindu works have a style and a rangi topics. peculiarly their own. Their problems lack the cold, clear, geometric precision of the West; they are clothed in that poetic language which distinguishes the East, and they relate to subjects that find no place in the scientific books of the Grecks. With perhaps the single exception of Metrodorus, it is only when we come to the puzzle problems doubtfully attributed to Alcuin that we find anything in the West which resembles, even in a slight degree, the work of Alcuin's Indian contemporary, the author of this treatise. It therefore seems only fair to say that, although some knowl- edge of the scientific work of any one nation would, even in those remote times, naturally have been carried to other peoples by some wandering savant, we have nothing in the writings of the Hindu algebraists to show any direct influence of the West upon their problems or their theories.
