Ganitasara Sangraha of Mahavira

SR No.: 011112
Original Sutra Author: N/A
Author: Rangacharya
Publisher: Rangacharya
Publication Year: 1912
Total Pages: 531
Language: English
Classification: Book_English
File Size: 24 MB

Page 453

CHAPTER VII-MEASUREMENT OF AREAS.
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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 distaudes. (Under these ciroumstancos), of what numerical value were the segments (of the basal line between the two hills) P Of what value, O you who know oalculation, is the numerical measure of the equal distance travelled in this (arca) representable by a (suspended) swing.
2087-209}. The height of one hill is 20 yojanas; and similarly, that of another (bill) is 24 yojanas. The intervening space between them is 22 yõjanas (in length). Two mendicants, who stayed on the tops of these two hills, (one on cach), and were able to move through the sky, came down, for the purpoee of begging their food, to the city situated betwoon thoso (two hills), and were fonnd 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 reprosentable by the boundary of) a triangle oonsisting of (three) unequal sides :
2104. The sum of the squares (of the numerical valuos) 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 (80 obtainct) is multiplied by the number of days spent (hy ne of the men) in travelling northwards (before travelling to the south-east to meet the other mai). The meeting together of these two men takes place at the end of the number of days measured by this product.
3107. The coure contemplated here is that along the side of a right anglod triangle. The formula given in the role, if algebraically represented, in
b' +'xd.
.ba
where in the number of daye taken to go through tbe hypotonuso course, a and b the rates of journey of the two men, and d the uumber of days taken in going Dorthwards. This follows from the under mentioned equation whiohin bused on the data given in the problem: