पृष्ठम्:महाभास्करीयम्.djvu/१५०

ASCENSIONAL DIFFERENCES OF THE SIGNS Therefore, we have Therefore earthsine Rsin S or earthsine (4) By definition Rsin (asc. diff.) earthsine Rsin (asc. diff.) Rsin Rsin (90⁰- Rsin x Rsin 8 Rsin (90⁰) radius day-radius earthsine x radius day-radius 65 A rule for finding the ascensional differences of the (sayana) signs Aries, Taurus, and Gemini : 8. Twenty-four multiplied by ten (i.e., 240), 192, and 81--these when (successively) multiplied by the angulas of the equinoctial midday shadow and (the products thus obtained) divided by four become the asus of the ascensional differences corresponding to Aries, Taurus, and Gemini respectively. ¹ 1 The numbers 240, 192, and 81 given above are four times the ascensional differences in asus of the signs, Aries, Taurus, and Gemini respectively for a place having one angula for the equinoctial midday shadow. We have seen that the ascensional difference of the Sun is the difference between the times of rising of the Sun on the local and equatorial horizons. The ascensional difference of the sign Aries is the difference between the times that the sign Aries takes in rising above the local and equatorial horizons. Since the first point of Aries rises simultaneously at both the horizons, therefore the ascensional difference of Aries is equal to the ascensional difference of the last point of Aries (for which >=30º). Similarly, the ascensional difference of Aries and Taurus (taken together) is equal to the ascensional difference of the last point of Taurus (for which λ=60⁰). The ascensional difference of Taurus is equal to the ascensional difference of Aries and Taurus minus the ascensional difference of Aries. ¹ Similar rules occur also in PSi, iii. 10; KK (Sengupta), i. 21; KK (Babua Misra), iii. 1; ŚiDVṛ, I, xiii. 9; SiŚi, I, ii. 50-51,