BRAHMAGUPTA'S RULES OF ANALYSIS 237. Brahmagupta further observes: Such is the process when the quotients (of mutual division) are even in number. But if they be odd, what has been stated before as negative should be made as positive. or as positive should be made negative.¹ Regarding the direction for dividing the divisor corres ponding to the greater number by the divisor corresponding to the smaller remainder, Prthudaka Svami (860A.D.) observes that it is not absolute, rather optional; so that the process may be conducted in the same way by starting with the division of the divisor corresponding to the smaller remainder by the divisor corresponding to the greater remainder. But in this case of in- version of the process, he continues, the difference of the remain- ders, must be negative. That is to say, the equation by-ax+c can be solved by transforming it first to the form ax-by-c so that we shall have to start with the division of b by a, For the details of the "Theory of the pulveriser" as applied to the problems in Astronomy, the reader is referred to the writ- ings of Bhaṭṭa Govind, translated by K.S. Shukla, and given as an Appendix to the edition of the Laghu-Bhaskariya. For the rationale of the rules in relation to kuttaka or the pulveriser operation, one may also refer to the chapters by Datta and Singh in the History of Hindu Mathematics: Algebra. Solution of by-ax ±1. This simple indeterminate equation has a special use in astronomical calculations and therefore, Indian algebraists have paid special attention to it. In fact, this equation is solved exactly in the same way as the equation by ax c; it is a parti- 1. एवं समेषु विषमेष्वणं धनं धनमुखं यदुक्त तत् । ऋणधनयोयंस्तत्वं गुरुय प्रक्षोपयोः कार्यम् || -BrSpS:. XVIII, 13.
