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

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“The north and the south with respect to the Equator
and Ecliptic (ie. the north-pole and south-pole) are differ-
ent at the points ♈ and ♎, being at a distance of ω from
each other. Hence the Āyana Valanajyā at those points
is equal to H sin 24° (ω taken to be equal to 24°). But at
the solstices, the north and south will be the same (mean-
ing thereby that the angle subtended by PK at the solstices
is zero, or what is the same, the directions to the respective
poles (of the Equator and the Ecliptic) at the solstitial
points are the same so that the East will be the same for
both the circles at those points. Thus there is no Valana
at the solstices ie. P ⌒ K = 0 where ♋ = cancer. In between
♈ and ♋, the Valana is found in proportion to
H sin (90 + λ) where λ is the longitude of the point and
in inverse proportion to H cos δ, where δ is the decli-
nation. Hence H sin θ = [H sin (90 + λ) / H cos δ] × H sin ω, where
θ is the Āyana Valana. Similarly at the points of inter-
section of the Equator and prime-vertical namely E and W,
the Unmandala (the Equatorial horizon) decides the
north-south direction with respect to the Equator, whereas
the horizon decides the same with respect to the prime-
vertical. These north-south directions with respect to
those two great circles namely the Equator and the prime-
vertical differ by the angle between the Unmandala and
the horizon which is equal PN = ϕ, the latitude of the
place. Hence at the East and West points the Ākṣa
Valanajya or the H sine of Ākṣa-Valana is equal to
H sin ϕ. But at the zenith, the north-south directions
of the Equator and prime-vertical coincide so that there
is no Ākṣa Valana at the zenith. Thus H sine of the
Valana is proportional to H sin ϕ in between the points
on the prime-vertical between the zenith and the East and
West points. (Roughly speaking) H sin ξ =
(H sin ϕ H sin z) / (H cos δ) where ξ = Ākṣa Valana, z = Sama-Vritta-