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

465
time in between the moment of rising of p and that of q,
the position of the Kṛta-Āyana-Dṛk-Karmakagraha.
When the latitude is very small, an approximate
estimate of this correction is given in asus as
(β' × H sin ξ) / (H cos ϕ) × R / (H cos δ) or (β' × H sin ϕ) / (H cos ϕ) × R / (H cos δ) .
That this formula is (β'=qp) only approximate is seen
from the fact that H sin ξ ≉ H sin ϕ. This second
formula can be proved as follows.
Ākṣavalana in asus = (β' × H sin ϕ) / (H cos ϕ) × R / (H cos δ) where
β' is the Sphuṭa-Vikṣēpa. Taking qpa as a plane triangle
pa = qp tan p̂qa = qp × tan P̂En approximately
= Sphuṭa-Vikṣēpa × (H sin ϕ) / (H cos ϕ) . Hence
AC = (β' × H sin ϕ) / (H cos ϕ) × R / (H cos δ) . With respect to the first
formula ie.
Akṣavalana in asus = (β' × H sin ξ) / (H cos ϕ) × R / (H cos δ) '
pa = qp tan p̂qa = (qp × H sin p̂qa) / (H cos p̂qa) . Here instead
H cos p̂qa which is Yaṣṭi previously defined, H cos PEn
ie. H cos ϕ, an approximate value is substituted, because
the latitude is small. Having obtained the value of pa,
it is then reduced to the Equator by multiplying by R and
dividing by H cos δ. The convention with respect to
the sign is clear. The idea of Kramalagna and Vilōma-
lagna may be elucidated as follows. In fig. 110, q, is on
the horizon rising whereas p had already arisen. So to
· 59