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