CHAPTER VII-MEASUREMENT OF AREAS. was capable of moving in the sky. This ascetic flew up and then came down to the city taking the hypotenuse course. The other ascetic descended from the summit (vertically) to the foot of the mountain (and walked along) to the city. (It was found that) both of them had travelled over the same distance. (What is) the distance of the city (from the foot of the mountain) and what the height of the flight upwards? 249 In an area representable by a (suspended) swing (and its vertical supports resting on the ground), the measures of the heights of either two pillars or two hill-tops are taken to be the measures of the horizontal sides of two longish quadrilateral figures. Then, (with the aid of these known horizontal sides and) in relation to the base line either between the two hills or between the two pillars, (as the case may be), the values of the two segments (caused by the meeting point of the perpendicular) are arrived at. These two segments are written down in the inverse order. The values of the two segments so written down in the inverse order are taken to be the values of the two perpendicular sides of the two longish quadrilateral figures. And, now, the rule for arriving at the equal numerical value of the diagonals of those (two longish quadrilateral figures) :- 201 203. In relation to a figure representable by a (sus- pended) swing (and its vertical supports resting on the ground), the measures of the heights of either two pillars or two hills are taken to be the measures of the two sides of a triangle. Then, in relation to the value of the base (line) enclosed between those two 2 M C1 C₂ 2011-203. In the two quadıilaterals of the kind contemplated in this iule, let the vertical sides be represented by a, b, b let the base be c, and let C1, C2, be its seg- ments and the length of each of the equal portions of the rope. 32
