QUADRATIC EQUATIONS be performed all operations conformably to the state- ment of the example and thus should be carefully framed two or more sides and also equations. Equi-clear- ance should be made first between two and two of them and so on to the last: from one side one un- known should be cleared, other unknowns reduced to a common denominator and also the absolute numbers should be cleared from the side opposite. The residue of other unknowns being divided by the residual coefficient of the first unknown will give the value of the first unknown. If there be obtained several such values, then with two and two of them. equations should be for common denominators. Proceeding in this way to the end find out the value of one unknown. If that value be (in terms of) another unknown then the coefficients of those two will be reciprocally the values of the two unknowns. If, however, there be present more un- knowns in that value, the method of the pulveriser should be employed. Arbitrary values may then be assumed for some of the unknowns. after to Datta and Singh have said that the above rule of Brahma- gupta, and also the one indicated in the commentary of Prthudaka Svāmi, embraces the solution of indeterminate as well as the determinate equations. In fact, all the examples given by Brahmagupta in illustration of the rule are of indeterminate character. So far as the determinate simultaneous equations are concerned, Brahmagupta's method for solving them will be easily recognised to be the same as our present one. 213 Quadratic Equations The geometrical solution of a quadratic equation in this country would take us to the Vedic Sulba period. The Bakha- śali Manuscript also contains certain problems which need the solving of quadratic equations. I shall quote one out of the numerous available: A certain person travels s yojana on the first day and b vojana more on each successive day. Another who travels at the uniform rate of S yojana per day, has a start of t days. When will the first man overtake the second ?
