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

BHASKARA I AND KUṬṬAKA OPERATION 231 x = q₁y₁ + x₁ ; ∴ q₁y₁ + x₁ = bm + α Thus it is found that the minimum value α of x is equal to the remainder left on dividing its calculated value by b. whence we can calculate the minimum value of N (=aα+R₁). This will explain the rationale of the operations described in the latter portion of the rule of Āryabhaṭa I. Bhāskara I and Kuṭṭaka Operation In Chapter I of the Mahābhāskarīya, Bhāskara I has descri- bed the preliminary operation to be performed on the divisor and dividend of a pulveriser. We shall quote it from the edition of K.S, Shukla : The divisor (which is "the number of civil days in a yuga) and the dividend (which is "the revolution num- ber of the desired planet") become prime to each other on being divided by the (last non-zero) residue of the mutual division of the number of civil days in a yuga and the revolution number of the desired planet. The operations of the pulveriser should be performed on them (i. e. on the abraded divisor and abraded dividend). So has been said.¹ An indeterminate equation of the first degree of the type (ax — c) / a = y (with x and y unknown) is known in Hindu mathematics by the name of "pulveriser"—kuṭṭakāra). In this equation, a is called the "dividend" (bhājya), b the "divisor" (bhāgahāra), c the interpolator (kṣepa), x the "multiplier" (guṇakāra), and y the "quotient" (labdha). In the pulveriser contemplated in the above stanza : a = revolution number of a planet.- b = civil days in a yuga, c = residue of the revolutions of the planet (Śeṣa)

1. भूदिनेष्टगणावन्योन्य भक्तशेषेण भाजितौ हारभाज्यौ दृढौ स्यातां कुट्टाकारं तयोर्विदुः । — MBh. I. 41