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 329

CHAPTER VI-MIXED PROBLEMS.
127
numbers immediately above it, (till the topmost figure in the chain becomes included in the operation), is to be arrived at. (Thereafter) this resulting sum and the divisor in the problem (give rise), in the shape of two remainders, (to the two values of) the unknown quantity (which is to be multiplied by the given dividend-coefficient in the problem), which (values)are related oither to the known given quantity that is to be added or to the known given quantity that is to be subtracted, according as the number of figure-links in the above-mentioned chain of quotients is even or odd. (Where, however, the given groups, increased or decreased in more than one way, are to be divided or distributed in more than one proportion), the divisor related to the larger group-value, (arrived at as explained above in relation to either of two specified distributions), is to be divided over and over (as above by the divisor
Carry out the required process of continued division 67)59(0
(
59)67(1
59
Below this are next written down 1 and 1, the last equal divisor and remainder. Here also, as in Fallika-huftikara, it is worthy of note that in the last division there can be really no remainder, as 2 is fully divisible by 1. But since the last remainder is 1+13 14 wanted for the chain, it is allowed to occur
by making the last quotient smaller than possible. And to the last number 1 hore, add 13, which is the remainder obtained by dividing 80 y 67; the 14 so obtained in also written down at the bottom of the chain, which now becomes complote.
1
Now, by the continued process of multiplying and adding the figures in this
explained in the note under stanza No. 115,
chain, as already we arrive at 592. This is then divided by 67; and the remainder 57 is one of the values of r, when 80 is taken as negativo owing to the number of figures in the chain being odd. When NO is taken as positive, the value of e is 6757 or 10. If the number of figures in the chain happen to be even, then the value of a firet arrived at is in relation to the positive agra, if this value betracted from the divisor, the value of in relation to a negative agra is arrived at,
8)59(7
56
1
14
3)8(2
C
2)3(1 2
1--382 7-345 2-47
1--16 1-15
After discarding the first quotient, the others are written down in a chain thus:
1)2(1
1
1
7
2
1
1
1
•