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The Jaina Antiquary
I Vol. XVII before through the middle points of the sides prwidac's eight tetrahedrons and four bodies like DDH . These four being placed together produce a recta pai n wiros: volume is one-fourth the volun.e of th previo a ona, i, «. ? volane of this is k. Continuing the process we go! successively volume: as below :
KKK......... whose sum is
K(i+1+as+as+.....)
= 4K
As K is known to be equal to labi, therefore,
+ = ' n (a - b) h=the voluine of the two tetralied1013. Continued construction is above reduces the volume of 17 tetrahedrons, so that they are reduced to punts under the construie tion is continued indefinitely. The tetrahedions, as has lieen rightly remarked by the author of the Dhavala are reduced to points and so oontribute nothing to the volume. The volume of each of the tetrahedrons ABCD and ABCD is therefore
. (a - b).h = n(a -!») (a - is,
= . area of buse, heigh!. The main points to be noted in the are :
(i) the actual use of an infinit. 9.32 of mediation and (ii) the actual use of the formula for this siin on mullimit oppima.
We shali perhaps never know how the ance natyrmaticing 3 of India justified the use of infinire processes. We content ourselyme by stating th: the Hindu mathematicians chid use infinite Prov.X as early as the Btia or 9th century A. D.
THE VALUE OF The problem of 'squaring the circle' or wiut was more funcio mental in lodia from the point of view of religiwly requirements, the problein of 'circling the square' originated and acquired special
