पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४४१

CHAPTER VII-MEASUREMENT OF AREAS. 243 ₂7 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 height, two strings are tied, one to the top of each. Each of these two strings is stretched in the form of a hypotenuse 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 hypotenuse strings meet, another string is suspended (perpendicularly) till (it touches) the ground The measure of this (last) string goes by the name antarávalambaka or the inner perpendicular. The line starting on either side from the point where (this) perpendicular string touches (the ground) and going to the points where the (above- mentioned) hypotenuse strings touch the ground has the name of abadhā, or the segment of the base. The rule for arriving at the values of such inner perpendicular and (such) segments of the base:- 180. The measurement of each of the pillars is divided by the measurement of the base 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 (so obtained) is 180. If a and b represent the height of the pillars in the diagiam, c the distance between the two pilla 14, and m and the respective dist- ances of the pillars from the point where the string stretched from the top of the other pillar meets the carth, then, according to the rule, C₁ = a Lc+n a (c + m) + ÷ a (c + m) + b (c + n) (c + m) (c + n) a m C1 P C x (c + m + n), C₂ = C n b c + _b (c + n) ] x (c + m + n) where c₁ and ca are segments of (cm) (c + n) b -, or C₂ X c + m a + n the base as a whole; and p = c₁ X where p is the meas- ure of the inner perpendicular. Fiom a consideration of the similar triangles. in the diagram it may be seen that C c+n c + m. = and C1 P b P a 222