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

गणितसारसंग्रह ७५
of these to the school down in South India, which produced this
notable treatise of Mahāvīrācārya ? 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 inscrip-
tions, those at Nānā Ghāt, using the first three Chinese numerals,
and another of about the same period using the later forms of Mesopo-
tamia, 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 Chiushang, Li Yeh, 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 treatises 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 Brahma-
gupta, Mahāvīrācārya, and Bhāskara may be described as similar
in spirit but entirely different in detail. For example, all of these
writers treat of the areas of polygones, but Mahāvīrācārya is the
only one to make any point of those that are re-entrant. All of them
touch upon the area of a segment of a circle, but all give different
rules. The so-called janya operation (page 209) is akin to work
found in Brahmagupta, and yet none of the problems is the same.
The shadow problems, primitive cases of trigonometry and gnomo-
nics, 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 Bhāskara, and no questions are duplicated.
In the way of similarity, both Brahmagupta and Mahāvīrācārya
give the formula for the area of a quadrilateral,
√((s - a)(s - b)(s - c)(s - d))
—but neither one observes that it holds only for a cyclic
figure. A few problems also show some similarity such as that
of the broken tree, the one about the anchorites, and the