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

191
Comm. This is clear from fig. 24. If S be the end of
Vṛiṣabha, S' in the figure denotes the end of Karkaṭa
them from the right-angled triangle SAP,
^
sin S'A = sin SA = sin APS × sin PS = sin A'K × cos SK
sin S'A
∴ sin A'K = ————— . But sin S'A = cos S'♈
cos SK
and cos SK = cos δ where δ is the declination at S.
A'K converted into time gives the rising time of AS'
ie. Karkaṭa.
cos S'
∴ the rising time of Karkaṭa = ————
cos δ
In tbe Hindu form, it will be
Karkaṭa-anta-Koṭijyā
Karkaṭa-Rāsi-Udayakāla = ————————————— × R
Karkaṭa-anta-Dyujyā
as stated.
cos ♈S
In modern terms sin A'K = cos ♈K = ————
cos δ
from the formula cos λ = cos α cos δ. Thus, virtually
the formula is a statement of the formula cos λ = cos α
^
cos δ. Aslo the formula sin AS' = sin P sin PS is
parallel to the formula sin δ = sin λ sin ω which we
proved already from Hindu methods.
Verse 57. Still an alternative method.
The H sines of Meṣa etc. being multiplied by
H cos ω divided by their respective H cos δ's and the
arcs thereof being subtracted as before the preceding from
the succeeding we have the rising times of Meṣa etc.
Comm. From figure 24,
^ SN
SN = SL cos LSN and ————— = perpendicular from
cos SK
K on ♈