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

130 PAÑCASIDDHĀNTIKĀ IV. 54 the radius is the hypotenuse; and in the other Sūryāgrā (i.e. śaṅkutalam) is the base, the Great gnomon is the perpendicular and what is called Taddhṛti is the hypotenuse (Vide Sid. Śiromaṇi, Gola, Tripraśna 49). Therefore, when sin lat, sin colat, and the Great gnomon are known Sūryāgrā can be calculated by the proportion: Sin colat : sin lat :: Great gnomon : Sūryāgrā. Sūryāgrā = Great gnomon × sin lat ÷ sin colat. The Great gnomon can be found from the similarity of the two triangles, in one of which the shadow is the base, the twelve-digit gnomon is the perpendicular and the shadow-hypotenuse is the hypotenuse, and in the other sin zenith distance is the base, the Great gnomon is the perpendicular, and the radius is the hypotenuse. Therefore by the proportion: shadow-hypotenuse : 12 :: radius : Great gnomon, the Great gno- mon = 12 × 120' ÷ shadow-hypotenuse. Hence by substituting we get, Sūryāgrā = 12 × 120' × sin lat ÷ (shadow-hypotenuse × sin colat). Since the celestial sphere is bent southward, Sūryāgrā is really south, permanently, (from the point of view of a man in the northern hemisphere, as we have already said). But here, as we are dealing not with the Sun but with the shadow, which is opposite to the Sun, we have taken the Sūryāgrā as always north. We shall illustrate these things by Fig. 18. We have mentioned that for observers in the northern hemisphere the diurnal circles bend southward, resulting in the 'southing' of the celestial bodies, because of the southward bend of the stellar sphere. As the shadow moves in the direction opposite to the Sun, the tip of the shadow moves in circles bent northwards, like I, II, III, in the Fig. Also, it should be remembered, as we are depicting the shadows in the Fig, the direction of Agrā and Sūryāgrā are reversed. Fig. IV. 18.