पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

IV. THREE PROBLEMS 85 Fig. IV. 3 AK = sine AG (neglecting the first sign) because, EF, HJ, JK, GF, are all equal, as already men- tioned. Therefore, for an arc or angle in the second quadrant, (3 to 6 signs), deduct it from six signs and get the sine of the remainder. For that in the third quadrant, (6 to 9 signs), deduct six signs and find the sine of the remainder. For that in the fourth quadrant, deduct it from twelve signs and find the sine of the remainder. Example 2 (a). Find the sine of the arc or angle equal to 4 signs. It is in the second quadrant. Therefore, sine 4 signs = sine 6 signs − 4 signs = sine 2 signs = 103′ 55″. Example 2 (b). Find the sine of signs 7-11-15. This is in the third quadrant. Therefore sine of sign 7-11-15 = sine (7-11-15 − 6-0-0) = sine 1-11- 15 = 79′ 7″. Example 2 (c). Find the sine of signs 9-15-0. This is in the 4th quadrant. Therefore sine of signs 9-15-0 = sine (12 signs − sign 9-15-0) = sine 2-15-0 = 115′ 55″. Declination From here to the end of the chapter, problems based on the solution of spherical triangles are dealt with, being problems involving position, time and direction. As a preliminary, the declina- tion of the Sun and the Moon are required, which are given first. Stellar sphere (Bhagola) The ancient astronomers speak of three spheres, the Terrestrial sphere or Earth sphere on which we live, the Stellar sphere or the Sphere of the stars, and the Sky sphere or the Sphere of the sky. We shall describe the terrestrial sphere in connection with the Sāura chap. XIII-XV. Of the other two, we shall now describe the stellar sphere, a knowledge of which is immediately required. It is the apparent sphere on which the stars appear to be fixed, and form a frame of reference for