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

192
∴ (SL cos ω) / (cos δ) = H sin rK. SL = H sin rS
∴ H sin rK = (H sin rS × H cos ω) / (H cos δ)
We proved the above in a modern way. The Hindu
concept is derived from the similarity of SML and ACM′
where C is the centre of the sphere and M′ is the foot of
the perpendicular from A on the plane of the equator
∴ LM / CM′ = SL / CA ∴ LM = (H cos ω × H sin rS) / R
Since LM = SN.
LM divided by H cos δ and multiplied by R gives H sin rK
∴ H sin rK = [(H cos ω × H sin rS) / R] × [R / (H cos δ)] =
= (H cos rS × H cos ω) / (H cos δ)
i.e. H sin α = (H sin λ × H cos ω) / (H cos δ)
Here H cos ω is called Trigṛha-dyu-maurvī because
it is the H cosine of the declination of λ when λ = 90°.
Verses 58, 59. The magnitudes of the rising times.
Those rising times are 1670, 1793, 1937 ; these in the
same and reverse orders diminished or increased by their
respective Chara segments which are also in the same and
reverse orders give the rising times of the Sāyana Rasis
beginning from Meṣa for the locality. The Rasis from
Tulā are in a reverse direction i.e. as the Meṣa is proje-
cting upwards above the horizon, Tulā will be projecting
below the horizon so that, the time taken by Meṣa to
rise is exactly the time taken by Tulā to set.
Comm. We shall compute the rising times of
Sāyana Rasis for Lanka first i.e. for zero latitude using
modern methods from the formula tan α = cos ω tan λ