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

226 BRAHMAGUPTA AS AN ALGEBRAIST der. The residue (and the divisor corresponding to the smaller remainder) being mutually divided, the last resi- due should be multiplied by such an optional integer that the product being added(in case the number of quo- tients of the mutual division is even) or subtracted (in case the number of quotients is odd) by the difference of the remainders (will be exactly divisible by the last but one remainder. Place the quotients of the mutual division successively one below the other in a column; below them the optional multiplier and underneath it the quotient just obtained). Any number below . : . the penultimate) is multiplied by the one just above it and then added by that just below it. Divide the last number (obtained by doing so repeatedly) by the divisor corresponding to the smaller remainder; then multiply the residue by the divisor corresponding to the greater remainder and add the greater remainder. (The result will be) the number corresponding to the two divisors.¹ There is an alternative rendering of this passage also as follows : . Divide the divisor corresponding to the greater remain- der by the divisor corresponding to the smaller remain- der. The residue (and the divisor corresponding to the smaller remainder) being mutually divided (until the remainder becomes zero), the last quotient should be multiplied by an optional integer and then added (in case the number of quotients of the mutual division is even) or subtracted (in case the number of quotients is odd) by the difference of the remainders. (Place the other quotients of mutual division successively one below the other in a column; below them the result just obtained and underneath it the optional integer). Any

1. अधिकाग्रभागहारं छिन्यादूनाग्रभागहारेण । शेषपरस्परभक्तं मतिगुणमग्रान्तरे क्षिप्तम् ॥ अध उपरि गुणितमन्त्ययुगूनाच्छेद भाजिते शेषम् । अधिकाग्रच्छेदगुणं द्विच्छेदाग्रमधिकाग्रयुतम् । —Ārya. II. 32-33