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

BHĀSKARA I AND KUṬṬAKA OPERATIONS 235 Writing down the quotients one below the other as pres- cribed in the rule, we get the chain 10766 15 2 7 22 2 (mati) 27 1 Reducing the chain, we successively get 10766 10766 10766 10766 10766 10766 3108044439 (multiplier) 15 15 15 15 15 288689 288689 (quotient) 2 2 2 2 18665 18665 7 7 7 8714 8714 22 22 1237 1237 2 55 55 (mati) 27 27 1 (it would be seen in this reduction of chain that mati or 27 × 2 plus 1 is 55; 55 × 22 plus 27 is 1237; 1237 × 7 plus 55 is 8714; 8714 × 2 plus 1237 is 18665; 18665 × 15 plus 8714 is 288689; and finally 288689 × 10766 plus 18665 is 3108044439 which is the multiplier). Dividing 3108044439 by 394479375, and 288689 by 36641, we obtain 346688814 and 32202 respectively as remainders, (This division is performed only when the multiplier and quotient are greater than the divisor and dividend respectively). These are the minimum values of x and y satisfying the above equation. Therefore, the required ahargaṇa = 346688814. and the revolutions performed by Saturn = 32202. To obtain the ahargaṇa and the revolutions of Mars, one has to solve the equation : 191402 z — 40 ───────────── = w 131493125