Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

Page 315

118
GANITASĀRASANGRAHA.
with which the least remainder in the odd position of order (in the above-meutioned process of successive division is to be multiplied; and (then put down) below (this again) this product increased or decreased (as the case may be by the given known number) and then divided by the last divisor in the above mentioned process of successive division. Thus the Vallikä or the creeper-like chain of figures is obtained. In this) the sum obtained by adding (the lowormost number in the chain) to the product obtained by multiplying the number above it with the number (immediately) above (this upper number, this process of addition being in the same way continued till the whole chain is exhausted, this sum, is to be divided by the (originally
Thus wo get the chain or Vallika noted in the first colunin of figures in the
margin. Then we multiply the penaltimate figure below in 1-51
the chain, viz., 1, by 4, which is above it, and add 8, the last 2--38 number in the chain; the resulting 12 is written down so as 1-13
to be in the place corresponding to 4; then multiplying this 4-12 12 by 1 which is the figure above it in the crecper chain, and
adding 1, the figure similarly below it, we got 13 in the place of 1; proceeding in the same manner 38 and 51 are obtained
in the places of 2 and I respectively. This 51 is divided by 23, the divisor in the problem ; and the remainder 5 is seen to be the least number of fruits in a bunch.
The rationale of the rule will be clear from the following algebraical representation :B + b = y (an integer) = 114 + Di, where p =
(B- Aq) + b A : * = Aps —, (where r, = B – Aqi the first remainder)
= pi + P2, where pe = 'P , and q. is the second quotient and r, the second remainder.
Hence, p = "123 + = 9apa + Pa, where pa = *sp + and qo is the third quotient and rs the third remainder.
Similarly, Pa = ": -b = 94 P8 + pa, whero Pa = " P3S;
Tapi -- b
P2 =
P3 P4 + b
P3 =
8 PA + Ps, where P =
Thus we have,
q2 DI + P2; Di=93 P2 + Ps; P 94 Ps + P4; Ps=9804 + Ps.