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It is interesting to note that this general formula was discovered in Europe as late as in 1634 by Herigone (Smith's History of Mathematics Vol. II). We may also recall here that the number 7 which occurs in Saptabhangi provides a simple example in the theory of Permutations and Combinations. A layman can verify that he can form seven and only seven different combinations of three distinct objects. Jainas have been using mathematics freely in their sacred literature from very remote antiquity. The above example supports this fact.
Problem ( VI 220 ): 0 friend, tell me quickly how many varieties there may be, owing to variation in combination of a single-string necklace made up of diamonds, supphires, emeralds, corals and pearls ?
Problem (VI 287 ) : What is that quantity which when divided by 7, (then ) multiplied by 3, ( then ) squared, ( then ) increased by 5, (then) divided by 3/5, (then ) halved and ( then ) reduced to its square root, happens to be 59.
Note the sheer devilry of it!
In chapters VII and VIII problems on mensuration are treated, Some of the formulas used are noted here :
(1) The Pythargorean formula for the sides of a right angled
triangle is a: = b + 0% where a is the hypotenuse. (2). Area of A ABC is
Vs (s-a) (8-b) (8-c) where 2 s= a + b + c. (3). The area and the diagonals of a quadrilateral ABCD are : v (s-a ) (8 - b) (8-0) (s-d) where 2 g = a + b +c+d; (ac+bd) (ab+cd). a c+bd) (ad + bc). ad + b c
a b+cd It is unfortunate that both Mahāvīrāchārya and his predecessor Brahmagupta made the common mistake of not mentioning the fact that these formulas hold for oyclic quadrilaterals only.
(4). T = 3 or ✓ 10.
(5). The circumference of an ellipse whose major and minor axes are of lengths 2 a and 2 b is ✓ 24 b2 + 16 ao which reduces to 2 av 1- 2 where e is the eccentricity. It is difficult to imagine.
