सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

305 projections of the rising points of the Sun on the same plane. Let perpendiculars be dropped from S₁, S₂, S₃ on the plane of the horizon. Let o be the centre of the sphere. Let ns be the north-south line. In position S₁, S₁C = Śanku-Bhujā, KA = Śankutala, oA = Agrā, so that A = S + B (1) In the position S₂. S₂D = Śanku-Bhuja, LA = Śanku-tala, oA = Agrā, so that B + A = S; but here B is negative, a the azimuth being south so that writ- ing - B for B, - B + A = S ∴ A = S + B again. In position S₃, OB = A, MB = S, OM = B so that A + S = B; but here A is +ve, δ being south and B is negative a being south; hence writing - A and - B for A and B A + S = - B or A = S + B again. This shows that with the convention cited above A = S + B holds good universally. Now let us consider the situation with respect to the Karnāgrā. Each of the three quantities a, b, s have now opposite directions. If δ be north, the Sun will be on the north of Equator, but the extremity of the shadow will now be on the south of the Equinoctial shadow line (E.S.L.) ie. the line which is parallel to the East-west line at a distance of the equinoctial shadow s, and which is tbe locus of the extremity of the shadow on the equinoctial day; thus when the Agrā is considered to be positive being on the north of the East point, the Karnāgrā, though it is on fhe south will have to be considered positive. Similarly when the azimuth of the Sun a is on the north of the prime-vertical and is so considered to be positive, the extremity of the shadow being on the south of the East-west line and has a negative azimuth, the bhuja is still to be considered positive. Again the Śankutala being always south of the Udayāsta Sūtra being considered south and positive, the corresponding quantity into which it gets converted on the horizontal dial namely the equinoctial shadow s will be north of the East-west line and will be considered 39