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 harmantika 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) árrived 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 value 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 ad led to the karmantika result, it indeed becomes the accurate value (of the required cubical 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. 13. 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 karmantıka cubical measure, of the If a and b be the measures of a side of the top and bottom surfaces respectively of a truncated pyramıd with a square base it can be easily shown that the accurate measure of the cubical contents is equal to 1h (a² + b² + ab), where his the height of the truncated pyramid. The formula given in the rule for the accurate measure of the cabical contents may be verified to be the same as this with the help of the following values for the Karmântska and Aundra results given in the rule:-- = (a + b )² K= A = x h. Similar verifications may be arrived at in the case of truncated pyramids having an equilateral triangle or a rectangle for the base, and also in the case of truncated cones. +b 2 x h;
