Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 440

CHAPTER VIIMEASUREMENT OF AREAS.
243
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 antarāvalambaka 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 (abovementioned) hypotenuse strings touch the ground has the name of ābādhā, or the segment of the base. The rule for arriving at the values of such inner perpendicular and (such) segments of the base :---
1801. 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 diagram, c the distance between the two pilla rs, and m and n the respective distances of the pillars from the point where the string stretched from the top of the other pillar meets the carth, then, according to "he rule,
. 4 (c + m) + b c + n) x (c + m + x); Ca = { 1 mi Lc+n . (c + m) (c + n) a (c + m) + b(c + n) 7
(c + m + n) ; where ci and c, are segments of (c + m) (c + n) * the babe as a whole ; and p=ci x --_-, or cg * - where p is the meas.
* C + m
c + n ure of the inner perpendicular. From a consideration of the similar triangles in the diagram it may be seen that C2 = c+
and and Gi
1 = + m. P