पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४६६

270 GANITASHRASANGRAHA the measures of the breadth at the bottom are (respectively) 7, 6 and 5, (the same) at the top being 4, 3 and 2 hosta8 ; the length i8 24 ha8ta8. (Find out the number of bricks in the pile1 The rule for arriving, in relation to a given raised platform (part of) which ha8 fallen down, at the number of bricks found (intact) in the infallen (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 8tration there. 58. (In relation to a raised platform, the length is 12 hosta8 the breadth at the bottom is 5 hosta3(the breadth) at the top is 1 host, and the height all through is 10 haatak. (A measure of) 5 hosts (in height) of that (platform) gets broken down and falls. How many are those (unit) bricks there (in bhe broken and the unbroken parts of the platform) { When a (high) font-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 : is plane, the breadth of which is 2 hesta8 at the raisod end and 4 Mostas at the other end. Vide diagram in the margin of page 263. 52. The measure of the top•breadth of the standing par of the platform which is the same as the bottombreadth of the fallen part of the platform b) d algebraically + %; 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 correot by applying the properties of similar triangles The operation referred to in the role as having been already degoribed in what if given in stana 4 above