पृष्ठम्:महाभास्करीयम्.djvu/१२४

TIME-PULVERISER divisor prime to each other. Then by what remains as the (new) divisor multiply the abraded divisor (and also the residue). Thereafter the process for the time-pulveriser is the same as described before (for the ordinary pulveriser). This rule is applicable when the ahargana is not a whole number but a whole number and a fraction. That is to say, when the pulveriser is of the type a(xr/s). b (1) Let a mA, and s = mB, m being the greatest common factor of a and s. Then the equation (1) can be written as AX - Bc Bb (2) where X sx = r. The above rule tells us that whenever we have to solve an equation of the form (1), we must solve it by reducing it to the form (2). If X =d, B is a solution of equation (2), then x = (α Fr)/s, y = B will be a solution of equation (1). where X = Example 1. "The (mean) longitude of the Sun for midnight is found to be 9 signs, 15 degrees, 32 minutes, and 40 seconds. Quickly say the ahargana and the revolutions (performed by the Sun) according to the Āśmakiya." 4x -1. 39 Since the mean longitude of the Sun = 9 signs 15° 32′ 40", therefore, by stanza 46 (ii), the residue of revolutions 166876. We have, therefore, to solve the equation 576 (x1/4) - 166876 210389 = y, (3) where x-1 is the required ahargana and y the revolutions performed by the Sun. As this equation is of the form (1), we reduce it to the form (2) as prescribed in the rule. Thus we get 144X 210389 = 166876 =y, (4) ¹ The "(new) divisor" of the text is the denominator of this fraction. Bhaskara I's example, occurring in his comm, on A, ii, 32-33,