Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

Page 51

(ii)
The principle of construction for the purpose of demonstration or proof had been assumed to hold true, for finding the volume of the tetrahedrons.
(iii)
The formula de
first term Sum= Common ratio when the common ratio is less than unity for the geometric progression Sum = first term + (first term) (common ratio)
I + (first term) (common ratio)2
+ ... had been assumed.
For the purpose of finding the value of the volume cf the above solids, a was assumed to be 35.
(iv)
:)
If D is the diameter of the lower base and d the diameter of the upper base of the frustum, and h its height, the volume can be obtained by finding the sum of the following series :78
+(- Ded
. Did)
h D-d 222
-
23
This type of infinite process has been denoted an innumerate type of process by Virsena.79' It comprises of sequence of construction which is innumerate and the sum of an infinite series is practically applied. It is not known what was the justification for making use of such infinite processes, which due to end in exhaustion could be denominated as innumerate.
78. Cf. Mathematics of Tiloypaņņatti, p. 15, op. cit. 79. Cf. Satkhandāgama, book 4, p. 15.