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

887
Note. A small circle parallel to the prime-vertical
is called Upa-Vṛtta. Also secondaries drawn to the
Ecliptic, Equator and the prime-vertical are called
Kadamba-Sūtra, Dhruva-Sūtra and Sama-Sūtra. They are
also called occasionally as Kadamba-prota-Vṛtta, Dhruva-
prota-Vṛtta, and Sama-prota-Vṛtta.
Bhāskara proceeds to find the Āyana Valana in a very
ingenious way in verses 69-74. We shall first give it a
modern treatment so that we may better appreciate his
genius. Let (S) be the Sun's disc. (It does not matter
whether we take the Sun or the Moon). EQ is its diameter
along the diurnal circle, and CL along the Ecliptic. LM
is the difference of the declination of L and S. Let
SL = Δ λ and LM = Δ δ. We have
sin δ = sin λ sin ω ;
differentiating cos δ Δ δ = sin ω cos λ Δ λ
∴ Δ δ = (sin ω cos λ / cos δ) × Δ λ ; put Δ λ = b, the angular
radius of the disc
∴ Δ δ = (b × sin ω cos λ / cos δ) = (b H sin ω × H cos λ / R × H cos δ) .
This gives the Valana in the disc of radius b. If that
be so, what will it be on the sphere of radius R? The result
is (b H sin ω × H cos λ / R × H cos δ) × R / b = (H sin ω × H cos λ / H cos δ)
as got before.
Let us hear Bhāskara, " put the disc of the Sun at
the point of intersection of the Ecliptic and the diurnal
circle. The Valana (LM of fig. 84) at the periphery of
the disc is the difference of the declinations of L and S.
To get the value of this let us first get the value. SL in
terms of λ, the longitude of S. It is (b × B / 225) ; so that LM