86 author seems to be unaware of the error. For, in his later work, the Laghu-Bhaskariya¹, he has rectified the error and has stated the condition correctly. The above error of Aryabhata I was noticed and criticised by Brahmagupta. The commentators of Aryabhata I, however, have inter- preted the above rule as conveying the correct meaning. DIRECTION, PLACE AND TIME A rule for the determination of the time in asus to elapse before or elapsed since midday when the Sun is on the prime vertical, i.e., the time taken by the Sun in going from the prime vertical to the local meridian or vice versa: 39. Multiply the Rsine of the Sun's longitude (when the Sun is on the prime vertical) by the Rsine of the (Sun's) greatest declination and divide (the product) by the day-radius: by the result thus obtained multiply the Rsine of the colatitude and (then) divide by the Rsine of the latitude. Subtract the square of the resulting quantity from the square of the radius: the are corresponding to the square root of that gives the asus (measured on the equator from the Sun's hour circle) up to the meridian. Let m denote the minutes in the arc of the Sun's diurnal circle intercepted between the Sun and the six o'clock circle, and r (= Rcos 8) the radius of the Sun's diurnal circle. Then in Fig. 8, SC = rsin m; so that from the triangle SCA, right-angled at C, we have or, SC CA rsin m Rsin SAC Rsin CSA Rsin 8 x Rcos Rsin Rsin x Rsin € R Rcos ¹ iii. 22. 2 See BrSpSi, xi. 22. Rsin 2 (using stanza 6) where λ, & denote the Sun's sayana longitude and declination respectively, and denotes the latitude of the place; € is the Sun's greatest declination.
