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

483 Fig. 112 Comm. During the early part of the night or during the latter part thereof, when the Sun is below the horizon, the Sun will be occupying symmetrical positions with respect to the horizon at times which are equally removed from Sunset and the next Sun-rise. This is clear from the figure 112. Let A and B be two such symmetrical positions where AM and BN are the Hsines of the altitudes. Evidently AM = BN, C P̂ A = C P̂ B. Since the rising eastern hour-angle of the Sun equals he setting western hour- angle, and since C P̂ A = C P̂ B, the time elapsed after Sunset when the Sun is at B, will be equal to the time before Sun-rise in the position A. Hence by congruence AM = BN = Hsine of the altitudes in the two symmetric positions. Using the modern formula from the triangle PZS, cos z = sin ϕ sin δ + cos ϕ cos δ cos h, when C P̂ A = C P̂ B = h cos z will be the same in the two positions A and B. Putting z = 90 + θ, cos z = - sin θ will be the same ie. H sin θ will be the same in the two positions ie. the Śaṅkus will be the same. In the formula