CHAPTER VII-MEASUREMENT OF AREAS. 192. There are 49 hastas in the measurement of the height of a bamboo (as it is growing). It is broken somewhere between (the top and the bottom). The distance (between the fallen top on the floor and the bottom of the bamboo) is 21 hastas. How far away (from the foot) is it broken? 193-195. The height of a certain tree is 20 hastas. A certain man scated on the top (of it) threw down a fruit thereof along a path forming a hypotenuse. Then another man standing at the foot of the tree went towards that fruit taking a path repre- senting the other side (i.e., the base of the triangle in the situation) and received that fruit. The sum of the distances travelled by that fruit and this man turned out to be 50 hastas. What is the numerical value of the hypotenuse representing the path of that fruit? What may be the measure of the other side representing the path of the man who was at the foot of the tree f The numerical value (of the height) of a taller pillar as also the numerical value (of the height) of a shorter pillar is known. The numerical value (of the length) of the intervening space between the two pillars is also known. The taller (of the two pillars) gets broken and falls so that the top thereof rests on the top of the shorter pillar, (the other end of the broken bit of the taller pillar being in contact with the top of the remaining portion thereof). And now the rule for arriving at the numerical value (of the length) of the broken part of the taller pillar as also at the numeri- cal value (of the height) of the remaining part (of the same taller pillar) :- 196. From the square of (the numerical measure of) the taller (pillar), the sum of the square of the measure of the shorter 196. If a represents the height of the taller pillar and b that of the shorter pillar, c the length of the inter- vening space between them, and a, the height of the standing portion of the broken pillar, then, according to the rule, α₁ = 247 a²-(b²+c²). 2 (a - b) a₂ a.- 1 C b
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