गणितसारसंग्रह (महावीराचार्य - प्रो. लक्ष्मीचन्द्र जैन सविस्तार हिन्दी अनुवाद सटीक)

७४ गणितसारसंग्रह
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 Raṅgācārya has made this more
possible than ever before.
As to the relation between 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 Āryabhaṭa, 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 phraseology appear in the works of any Indian
writer on algebra. On the contrary, the Hindu works have a style
and a range of 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 Greeks. 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 know-
ledge 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.
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 relations, for example, between the school of Pāṭaliputra,
where Āryabhaṭa wrote, and that of Ujjain, where both Brahmagupta
and Bhāskara lived and taught ? And what was the relation of each