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