पृष्ठम्:महाभास्करीयम्.djvu/१५३

68 DIRECTION, PLACE AND TIMÉ It follows that the ascensional difference of Aries, Taurus, and Gemini (taken as a whole) is 128 asus. Subtracting from it the ascen- sional difference of Aries and Taurus, we get 20 asus. This is the ascensional difference of Gemini.¹ The formula for the ascensional difference may now be written as Rşin (asc. diff.) Rsin (asc. diff. for unit equinoctial midday shadow)x (equinoctial midday shadow). [4 x (asc. diff. for unit equinoctial midday shadow)] X (equinoctial midday shadow) or asc. diff. approximately. Hence the above rule. A rule for finding the times of rising of the (sayana) signs at the equator: = 9. (Severally) multiply the Rsines of (one, two, and three) signs by 3141 and divide (each of the products) by the corresponding day-radius. Reduce the resulting Rsines to the corresponding arcs, and then diminish each are by the preceding arc (if any). The residues obtained after subtraction are the times (in asus) of rising of the signs Aries, Taurus, and Gemini at the equator.² ¹ We have taken above the approximate values of the ascensional differences of the last points of Aries, Taurus, and Gemini. Better values are 59-45, 107.77 and 127-4 asus. If these values are taken, then the ascensional differences of Aries, Taurus, and Gemini would come out to be 59.45, 48.32, and 19-63 asus. Four times of these are 238, 193 and 79 asus approx. Hence some astronomers (see Parameśvara's Siddhanta- dipika) give the following reading of the text: वसुत्रिदस्रा (238) गुणरन्ध्रभूमयो (193) नवाद्रव ( 79 ) श्चाभिहताः पलाङ्गुलैः । क्रियगोयमान्तजा- dragin: श्चरासवः स्युः क्रमशस्तु चापिताः || 2 This rule is found also in SüSi, iii. 42-43; BrSpSi, iii. 15; ŠiDVṛ, I, iii. 8; Sise, iv. 15; SiŚi, I, ii. 51.