Ganittilakam Savrtuttikam

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

Page 54

INTRODUCTION
Liit
As regards this ist method for squaring given by S'rīpati, Simhatilaka observes on pp. 8-9 that S'rīpati has adopted a wrong procedure in having used the phrase qui fapt on p. 7 without explaining the term varga, while Bhāskarācārya, the author of Līlāvatī has followed the right procedure, for, he has first explained the term varga and then explained the method for it.
The second method is stated by S'rīpati as under:
The product of the difference and the sum of the number to be squared and the assumed number, when combined with the square of the assumed, gives the square. This may be expressed algebraically as under:
** =(x-a)(x+a.) +a. Here x is the given number and a the assumed one.. The third method is to multiply the number by itself.
While explaining this method, Simhatilaka has referred to a well-known method given in Tris'atī.
The method for extracting square-root given in Ganitatilaka is the same as given by S'rīdhara, Mahāyīrācārya and Aryabhața II, but it slightly differs from one given by Bhāskara II.
For cubing, four methods are given. Out of them, the first is as under:
The cube of the last (digit), the square of this last (digit) multiplied by three and the succeeding (digit), the square of this succeeding (digit) multiplied by the last and three, and the cube of the succeeding (digit), when added, after each is placed one place before the other give us the cube (required).
1 Siddhagena Gani's commentary (p. 258) on Tattvärthādhigamasutra (III, 11) may be consulted. See Datta and Singh, l. c., pp. 171-172.
2 In accordance with this rule, the following 8 steps are necessary beforo we can get the cube of 317:(i)
(iii)
(iv) 1 317
317 317
317 2779 27791
27791 20181
(ii)
317
27
277
8770