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CHAPTER VII-MEASUREMENT OF AREAS.
848
the (two equal) sides is 4 x 60. The share parts are (in the proportion of) 3, 8, and 5. (Find out the values of the areas, the bases, and the sides of the required parts).
In the case of two pillars of known hoight, two strings are tied, one to the top of each. Each of these two strings is strotched in the form of a hypotenuso so as to touch the foot of the other pillar, or so as to go beyond the other pillar and touch (the ground). From the point where the two by potonuso strings meet, another string is suspended (perpendioularly) till (it touohos) the ground. The measure of this (lust) string goes by the name antarávalambaka or the inner porpendicular. The line starting on either side from the point where (this) perpendicular string touches (the ground) and going to the points where the (abovementioned) hypotenuse strings touch the ground has the name of âbâdhā, or the segment of the base. The rule for arriving at the values of such inner perpendicular and (such) segments of the base:
1807. The measurement of each of tho pillars is divided by thu muasurement of the baso covering the length between the (foot of the pillar) and the (point of contact of the hypotenuse) string (with the ground). Each of the quotients (80 obtained) is
1804. If a and represent the height of the pillars in the diagram, o the distance between the two pilla r, and m and the respoctive distanoos of the pillars from the point where the string stretched from the top of the other pillor meets the earth, then, scoording to the rule,
* (c + m) + 0(c + )) (c + m + *); whoro e, and C, sto segments of
( m) ( + ) the base us whole; and p a *. , or cg * , whero p in the mentare of the inner perpendioular. From consideration of the similar triangles in the diagram it may be won that "+and
". .
C
+
m
C
+
