270 the measures of the breadth at the bottom are (respectively) 7, 6 and 5, (the sa ne) at the top being 4, 3 and 2 hastas; the length is 21 hastas. (Find out the number of bricks in the pile). GANITASĀRASANGRAHA. The rule for arriving, in relation to a given raised platform (part of) which has fallen down, at the number of bricks found (intact) in the unfallen (part) and also at the number of bricks found in the fallen (part) :-- 52 The difference between the top (breadth) and the bottom (breadth) is multiplied by the height of the fallen (portion) and divided by the whole height. (To the resulting quotient) the value of the top (breadth) is added This gives rise to the measure of the basal breadth in relation to the upper (fallen portion) as well as to the top breadth in relation to the lower (intact portion) The remaining operation has been already described. An example in illustration thereof. 53. (In relation to a raised platform), the length is 12 hastas the breadth at the bottom is 5 hastas, (the breadth) at the top is 1 hasta, and the height all through is 10 hastas. (A measure of), 5 hastas (in height) of that (platform) gets broken down and falls. How many are those (unit) bricks there (in the broken and the un broken parts of the platform) ? When a (high) fort-wall is broken down obliquely, the rule for arriving at the number of bricks which remain intact and of the bricks that have fallen down :- plane, the breadth of which is 2 hastas at the raised end and 4 hastas at the other end. Vide diagram in the margin of page 269. 52. The measure of the top-breadth of the standing par of the platform - which is the same as the bottom-breadth of the fallen part of the platform-is (a - b) d algebraically + b, where a is the bottom-breadth, b is the top- breadth, h the total height and d the height of the fallen part of the raised platform. This formula can be easily shown to be correct by applying the properties of similar trianglos. h The operation referred to in the rule as having been already described is what is given in stanza 4 above. ·
