ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

162 BRAHMAGUPTA AND ARITHMETIC The method has been more clearly enunciated by Mahāvīra (850 A.D.) in the Gaṇitasārasaṁgraha : Having squared the last (digit), multiply the rest by the digits by twice the last, (which) is moved forward (by one place). Then moving the remaining digits con- tinue the same operation (process), This gives the square.¹ Brahmagupta's method of squaring is shown by the follow- ing example : To square 125. The number is written down 125 The square of the digit in the last place, i. e., 5²=25 is set over it thus : 25 125 Then, 2 x 5=10 is placed below the other digits, and 5 is rubbed out, thus : 25 12 10 Multiplying by 10 the rest of the digits, i.e., 12 and setting the product over them (the digits), we have. 1225 12 10 Then rubbing out 10 which is not required and moving the rest of the digits, i. e. 12 we, have 1225 12 Thus one round of operations is completed. Again as before, setting the square of 2 above it and 2×2=4 below 1. we have 1625 1 4

1. GSS. P. 12.