CHAPTER VII-MEASUREMENT OF AREAS. through the sky and) met in the city there (between the hills); and it turned out that they had travelled (along the sky) over equal distances. (Under these circumstances), of what numerical value were the segments (of the basal line between the two hills)? Of what value, O you who know calculation, is the numerical measure of the equal distance travelled in this (area) representable by a (suspended) swing. 251 P 208-209. The height of one hill is 20 yojanas; and simi- larly, that of another (hill) is 24 yojanas. The intervening space between them is 22 yojanas (in length). Two mendicants, who stayed on the tops of these two hills, (one on each), and were able to move through the sky, came down, for the purpose of begging their food, to the city situated between those (two hills), and were found to have travelled (along the sky) over equal distances. What is the measure (of the length) of the intervening space between that (city) in the middle and the hills (on either side). ★ The rule for arriving at the value of the number of days required for the meeting together of two persons moving with unequal speed along a course representable by (the boundary of) a triangle consisting of (three) unequal sides :- 210. The sum of the squares (of the numerical values) of the daily speeds (of the two men) is divided by the difference between the squares of the values of (those same) daily speeds.. The quotient (so obtained) is multiplied by the number of days spent (by ne of the men) in travelling northwards (before tra- velling to the south-east to meet the other man). The meeting together of (these) two men takes place at the end of the number of days measured by this product. x= 210. The course contemplated here is that along the sides of a right angled triangle. The formula given in the rule, if algebraically represented, is 6² +² x d₂ where is the number of days taken to go through the hypotenuse course, a and b the rates of journey of the two men, and d the number of days taken in going northwards. This follows from the under mentioned equation which 18 based on the data given in the problem b²x²d²b² + (x+d)² x a²
