पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४४७

CHAPTER VII MEASUREMENT OF AREAS 251 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 the8e circumstances), of whab 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 (uspended) swing. 208] 209]. The height of one hill is 20 ५byjn8 ; and simi . larly, that of another (bil) is 24 yojionsThe intervening space between them is 22 yojava8 (in length). Two mendicants, who stayed on the top of these two hills, (one on each), and were able to move through the sky, came down, for the purpose of gging 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 bhe 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 quot19nt (so obtained) is multiplied by the number of days spon४ (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 prodnot. 210]. The course contemplatea here is that along the sidea of a right angled riangle. The formula given in the rule, if algebraically represented, is b• +0 x d. where r is the number of days taken to go through the hypotenuse course, 6 and 8the rates of journey of the two menand d the number of days taken in going northwards. This follows from the under mentioned equation which is based on the data given in the problem: 8* d° %° + (x+ %) x =