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

MULTIPLICATION 159 (i) Gomūtrika-method or zig-zag method. The word gomū- trikā means "similar to the course of cow's urine", hence "zigzag". This method in all essentials is the same as the sthāna- khaṇḍa method. The following illustration is based on the commentary of Pṛthūdaka Svāmī : Example : To multiply 1223 by 235. The numbers are written thus : 2 1223 3 1223 5 1223 The first line of figures is t hen multiplied by 2, the process beginning at units place, thus : 2×3=6; 3 is rubbed out and 6 substituted in its place, and so on. After all the horizontal lines have been multiplied by the corresponding numbers on the left in the vertical line, the numbers on the pāṭī stand thus : 2446 3669 6115

287405 after being added together as in the present method. The sthāna-khaṇḍa and the gomūtrikā methods resemble modern plan of multiplication most closely. (ii) Khaṇḍa Method · or Parts Multiplicatian Method : Since the days of Brahmagupta, this method of multiplication also became very popular. We have two methods under this head : (i) The multiplier is broken up into two or more parts whose sum is equal to it. The multiplicand is then multiplied severally by these and the results added. To take an example : 13×158=(6+7)×158=(6×158)+(7×158) =948+1106 =2054 (ii) The multiplier is broken up into two more aliquot parts. The multiplicand is then multiplied by one of these, the resulting product by the second and so on till all the parts are exhausted. The ultimate product is the result.