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

७६ गणितसारसंग्रह
common one relating to the lotus in the pond, but these prove
only that all writers recognized certain stock problems in
the East, as we generally do to-day in the West. But as already
stated, the similarity is in general that of spirit rather than of
detail, and there is no evidence of any close following of one writer
by another.
When it comes to geometry there is naturally more evidence
of Western influence. India seems never to have independently
developed anything that was specially worthy in this science.
Brahmagupta and Mahāvīrācārya both use the same incorrect rules
for the area of a triangle and quadrilateral† that is found in the
Egyptian treatise of Ahmes. So while they seem to have been
influenced by Western learning, this learning as it reached India
could have been only the simplest. These rules had long since been
shown by Greek scholars to be incorrect, and it seems not unlikely
that a primitive geometry of Mesopotamia reached out both to
Egypt and to India with the result of perpetuating these errors. It
has to be borne in mind, however, that Mahāvīrācārya gives correct
rules also for the area of a triangle as well as of a quadrilateral
without indicating that the quadrilateral has to be cyclic. As to the
ratio of the circumference to the diameter, both Brahmagupta and
Mahāvīrācārya used the old Semitic value 3, both giving also √10
as a closer approximation, and neither one was aware of the works
of Archimedes or of Heron. That Āryabhaṭa gave 3·1416 as the
value of this ratio is well known, although it seems doubtful how
far he used it himself. On the whole the geometry of India seems
rather Babylonian than Greek. This, at any rate, is the inference
that one would draw from the works of the writers thus far known.
As to the relations between the Indian and the Chinese algebra,
it is too early to speak with much certainty. In the matter of
problems there is a similarity in spirit, but we have not yet enough
translations from the Chinese to trace any close resemblance. In
each case the questions proposed are radically different from those
found commonly in the West, and we must conclude that the
algebraic taste, the purpose, and the method were all distinct in the