पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४६०

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264 GANITASARAGANGRAHA measure of the depth also is know, in relation to a certain given excavation. the rule for arriving at the value of the sides (of the resulting bottom section) at any optionally given depth, and also for arriving at the (resulting) depth (of the excavation) if the bottom is reduced to a mere point 26d. The product resulting from multiplying the (given) depth the given measure of a side at the top, when divided by the difference between the measures of the top side and the bottom side gives rise here to the (required) depth (when the bottom is) made to end in a point. The depth measured (from the pointed bottom) upwards (to the position required) multiplied by (the moasure of the sido at the top and (then) divided by the sum of the side measure, if anyat the pointed bottom and the (total) depth (from the top to the pointed bottom), gives rise to tho side measure (of the excavation at the required depth). An example 1 &(lustration , thereof. 274. There is a well with an equilateral quadrilateral section. The (hide) measure at the top is 0 and at the bottom 14. The depth given in the beginning is . (This depth has to be) further (carried) down by B. What will be the side value (of the bottom here) ? What is the measure of the depth, (if the bottom is) made to end in a point ? 26). The problems contermplated in this stanzs are (c) to find out the full latitude of an inverted pyramid or cone and (b) to find out the dimensions of the cross scotion thereof at a desired level, when the altitude and the dimensions of the top and bottom surfaces of a truncated pyramid or cone are given. If, in a truncated pyramid with square bake, a is the measure of a side of the base and b that of a side of the top surface and h the height, then according to the rule given here, I taken as the height of the whole pyramia a = } and the treasure of a side of the cross section of the pyramid at any -b a (H-CA,) given height represented by } These formula8 are applicable in the case of a none as well. In tho rulo the measure of the side of section forming the pointed । art of the pyramid is required to be added to H, the |eno ator in the second formula, for the reason that in some cases the pyramid may not actually end in a point. Where, however does end in a point, the value of this aide has to be zero as a matter of conrue,