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Chapters III and IV are devoted to elementary operations with fractions, Mahāvīrāchārya has paid considerable a tention to the problem of expression of a unit fraction as the sum of unit fraction. This problem has interested mathematicians from remote antiquity (Abmes Papyrus 1650 B, C.). Here are three relevant problems ( II 75, 77, 78 ) set in modern notation.
(1)] = 3 +
+ 20+
+ 3n
2 +21-23;
(271-231+ 5***** +(2n-1)2n-+ 2mg (3)==n(n't enjtentan) n+84 +87) ****
(n + a + ag + *** + 2,-2) (n + a, +2, + *** + ar-1)
ar * a, ( n + a2 + a, + *** + a,) Problem IV 4: One third of a herd of elephants and three times the square root of the remaining part of the herd) were seen on the mountain slope; and in a lake was seen a male elephant along with three female elephants. How many were the elephants there?
Here is a sample of monkish humour ! Chapter V treats 'Rule of Three' and its generalised forms.
Chapter VI. Having created the arithmetical apparatus in the earlier chapters, in this long chapter, Mahāvīrāchārya applies it to solving many problems which one encounters in life such as money. lending, number of combinations of given things, indeterminate equations of first degree, etc.
Problem (VI 1281): In relation to twelve (numerically equal ) heaps of pomegranates which having been put together and combined with five of those same fruits) were distributed equally among 19 travellers. Give out the numerical measure of any one heap.
Problem (VI 218 ): The number of combinations of n different things taken r at a time is n(n-1)(n-2) (n-r+1) 12 3. •••••
r! (n-r)!
lor
n!
