Ganittilakam Savrtuttikam

Author(s): Hiralal R Kapadia
Publisher: Oriental Research Institute Vadodra

Page 53

LII
sandhi, (2) tatstha, (3) rūpavibhāga and (4) sthānavibhāga. Mahavirācārya, too, has mentioned the same four. Aryabhata II records only the common method of kapaṭasandhi. Bhaskara II has however noted five, four of which are the same as noted by Sridhara, and the fifth is the one known as iṣṭagunana. All these five methods given by Bhaskara II occur in S'ripati's Siddhantas'ekhara.1
Now a word about the method of division. It was considered by Indian mathematicians as too elementary to be described, whereas it was looked upon as a tedious and difficult operation by European scholars as late as the 16th century. S'ripati explains the method as follows:
Remove the common factors, if any, from hara (divisor) and bhajya (dividend) and then divide in the pratiloma (inverse) order.
Further details of this process such as dividing the digits of the dividend by the divisor are neither stated by him nor by Simhatilaka.
As regards the three methods of squaring given by S'ripati, the first is as under:
After the last digit is squared, double this last digit should be multiplied by the rest of the digits respectively. Then the remainder left by removing this last digit should be moved, and the procedure should be repeated.*
1 Cf. Datta and Singh, l. c, pp. 135-136.
2 See Datta and Singh, 7. c., p. 150; and Smith, History, p. 132.
3 This is same as multiplying the rest of the digits by twice the last.
4 According to this rule, the following 11 steps are required to square 163:
(i)
163
1
(viii)
3
1266
136
3
INTRODUCTION
(ii)
163
12
(ix)
3
1266
136
3
(iii)
163
126
1
3 12669 136 3
(iv)
63
126
I
and
(v)
63
126
1
(xi)
12669 136 3
(vi)
63
126
136
(vii)
26569
It appears that out of these 11 steps, the steps (vi) to (ix) have been wrongly given in the original MS. by the scribe, and through oversight this mistake has not been corrected by me on p. 9, and that the steps (v), (vi) and (xi) have been omitted in the original MS. by the scribe.
63
1266
136
3
For the explanation of the method in English see Datta and Singh, . c., pp. 157-160.