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Shri Mahavir Jain Aradhana Kendra
www.kobatirth.org
Acharya Shri Kailassagarsuri Gyanmandir
260
GANITASĀRASANGRAHA.
multiplied with each other (as required by the rules bearing upon the finding out of areas when the values of the sides are known). The area (so arrived at), when multiplied by the depth, gives rise to the cubical measure designated the karmāntika result. In the case of those same figures representing the top sectional area and the bottom sectional area, the value of the area of each of these figures is (separately) arrived at. The area values (so obtained) are added together and then divided by the number of sectional) areas (taken into consideration). The quotient (so obtained) is multiplied by the yalue of the depth. This gives rise to (the cubical measure designated) the aundra result. If one-third of the difference between these two results is added to the karmāntika result, it indeed becomes the accurate value of the required cubica! contents).
Examples in illustration thereof. 12]. There is a well whose (sectional) area happens to be an equilateral quadrilateral. The value (of each of the sides) of the top (sectional area) is 20 (hastas), and that (of each of the sides) of the bottom (sectional area) is only 16 (hastas). The depth is 9 (hastas). O you who know calculation, tell me quickly what the cubical measure here is.
131. There is a well whose (sectional) area happens to be an equilateral triangular figure. The value (of each of the sides) of the top (sectional area) is 20 (hastas), and that (of each of the sides of the bottom (sectional area) is 16; the depth is 9 (hastas). What is the value of the karmāntika cubical measure, of the
If a and I be the measures of a side of the top and bottom surfaces respectively of a truncated pyramid with a square base, it can be easily shown that the acourate measure of the cubical contents is equal to h (a + b 2 + ab), where h is the height of the truncated pyramid. The formula given in the rule for the acourato measure of the cabical contents may be verified to be the same as this with the help of the following values for the Karmantika and Aundra resolts given in the rule:---
La 2 +
2 Similar verifications may be arrived at in the case of troncated pyramids having an equilateral triangle or a rectangle for the base, and also in the case of truncated cones.
Kala + b 2
Ta + b \
x 1;
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