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264
GAŅITASABASANGRAHA.
measure of the depth also is known, in relation to å cortain given excavation, the rala 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 reduoed to a mere point :
264. The product resulting from multiplying the (given) depth with (the given moasure of a sido 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 mcasured (from the pointed bottom) upwards (to the position required) multiplied by the moasure of the side at) the top and (then) divided by the sum of the side measure, if any, at the pointed bottom and the (total) depth (from the top to the pointed bottom), gives rise to the side measure of the excavation at the required depth).
An example in illustration thereof.
27). There is a well with an equilateral quadrilateral section. The (side) moasure at the top is 20 and at the bottom 14. The depth given in the heginning is 9. (This depth has to be) further (carried) down by 3. What will be the side value (of the bottom here) P What is the measure of the depth, (if the bottom is) made to end in a point ?
26+. The problems contemplated in this stnnes are (a) to find out the full latitudo of an inverted wyramid or cone and (b) to ficd out the dimensiona of the cross section thereof at a desired level, when the altitude and the dimensious of the top and bottom surfaces of a truncated pyramid or oone are given.. Jl, in a truncated pyramid with square base, a is the monore of a side of the base and b that of a side of the top surface and the height, then 80001 ding to the rulo given here, I taken 48 the height of the whole pyramid
, and the treasure of a side of the cross section of the pyramid at any given height represented by h al--11).
H These formulas are applicable in the case of a cono as well. In the rule the monstre of the side of section forming the pointed , art of the pyramid is required to be added to H, the denominator in the second formula, for the reuson that in some cases the pyramid may not actually end in a point. Where, however, it dote ond in a point, the value of this side has to be soro na matter of ourno.
