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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 quadrilateralt hat 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 Aryabhata 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 algebraio taste, the purpose, and the method were all distinot in the
| SR No. | 090174 |
| Book Title | Ganitsara Sangrah |
| Original Sutra Author | Mahaviracharya |
| Author | A N Upadhye, Hiralal Jain, L C Jain |
| Publisher | Jain Sanskriti Samrakshak Sangh |
| Publication Year | 1963 |
| Total Pages | 426 |
| Language | Hindi |
| Classification | Book_Devnagari, Mathematics, & Maths |
| File Size | 35 MB |