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

in between r and ☉,
not shown in the figure
☉ = the Sun. Let rA =
a° = Ayanamsas defined
before so that r☉ = (a + λ).
From the spherical triangle
r☉M, by Napier's rule,
sin δ = (sin λ + a) sin ω
which in Hindu trigono-
metry becomes H sin δ =
[H sin (λ + a) × sin ω] / R
In Hindu Astronomy the
obliquity of the ecliptic was
taken to be 24°. The value
of the obliquity is now 23°–27' approximately and it has
been know that this has been decreasing. At the time
when the Hindu Astronomers observed this, it should
have been greater than 23°–27' so that if it was taken to be
24°, their observations were not far from truth. This
means that the antiquity of Hindu Astronomy might be far
more than what the Moderns estimate it to be.
(2) How the formula I was derived in Hindu tri-
gonometry was as follows. Let ♋ be the summer solstice
♋C, ☉B, the perpendiculars dropped from ♋ and ☉ on
the line of intersection of the Equatorial and Ecliptic
planes namely rBC. Let perpendiculars be dropped from
♋ and ☉ on the plane of the Equator. Let them be ♋N,
☉D, Join NC and DB. Then ☉B̂D = ♋ĈN = the
dihedral angle between the two planes = ω; ♋C = R
since in Hindu trigonometry H sin 90° = R. Also ♋N =
H sin ♋E (in Hindu trigonometry) = H sin ω; ☉D =
H sin ☉M = H sin δ; ☉B = H sin r☉ = H sin (λ + a)
where λ is the Hindu longitude of the Sun and a =
Āyanamśas. It will be seen that ☉D is a segment of the