248 GANITASĀRASANGRAHA. (pillar) and the square of that of the base is subtracted. Half (of the resulting remainder) is divided by the difference between (the measures of) the two pillars. The quotient gives rise to the measure of the height (of the standing part) of the broken (pillar). An example in illustration thereof. 197. One pillar is 5 hastas in height; similarly another pillar, which is the taller, is 23 hastas (in height). The (length of the) interveuing space (between the pillars) is 12 hastas. The top of the broken taller (pıllar) falls on to the top of the other (pillar). (Find out the height of the standing part of the broken taller pillar.) Taking two-thirds of the numerical value of the vertical side of a longish quadrilateral as the height of a mountain, the rule for arriving, with the aid of the numerical value of the height of that mountain, at the numerical values of the horizontal side and of the diagonal of that longish quadrilateral 198 Twice the height of the mountain is the measure of the distance between the (foot of the) mountain and the city (there). Half (the height) of the mountain is the measure (of the distance) of the upward flight in the sky. The diagonal is arrived at on adding together half the height of the mountain and the distance (of the city from the foot of the mountain). An example in illustration thereof. 1991-2001. On a mountain having a height of 6 yojanas there were 2 ascetics. One of them went walking on foot. The other B E 1994-2004. If in the marginal figure, a represents the height of the mountain, b the distance of the city from the foot of the mountain, and c the length of the hypotenuse course, then a is, according to the supposition made in the preamble to the rule in 1981, of the side AB. Therefore the height of the flight upwards 2.e., EB, is a I A a - b C As the courses of the two ascetics are equal, c+ a = a + b,.. c = a +b ..c²=a² + b² + ab. ... .... C III But ca²+ b²;. ab = 2a²..b=2a... The three formulas marked I, II and III above are those given in the rule. ... .... II
