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

275
Taking this to be the equinoctial shadow
H sin L = Rs / √(12² + s²) = R itself (Dealing this way
with Kha-hara Rās'is is prohibited in modern mathematics
but Bhāskara adds at the end of the commentary that
dealing with them cautiously does not effect computations
which is of course true, for when the equinoctial shadow is
infinity φ = 90° so that H sin φ = R as got). Hence
L = 90° and 180° - 90° = 90° = L'. Then H sin D =
(R × 780) / (1322 - 18) = same as Sama-S'anku obtained in I = H cos z
so that D = 90 - z. Now from the equation z + δ = φ,
z = φ - δ = L' - D = 90° - (90 - z) where z is the
zenith-distance when the Sun is on the prime-vertical.
∴ The zenith-distance is again the same z. In other
words, the second zenith-distance is also that when the
Sun is on the prime-vertical. Bhāskara has given this
example just to obtain the second shadow as well and he
has chosen the event of the Sun being on the prime-
vertical to show that the procedure indicated by him may
be verified to hold good.
Verses 49, 50. Alternate method to find the shadow.
Let R² s² + H sin² a × 12² = prathama where s =
equinoctial shadow and a the Hindu azimuth. Let Anya
= RsA where A is the Agrā. Divide the prathama and
Anya by (H sin² a - A²) and still call them prathama and
Anya. Then
K = √(Adya + Anya²) ± Anya where K is the Chayā-
Karṇa.
Comm. Let K be the required Chayā-Karṇa.
Then Karnāgrā = KA / R = s + b where b is the bhuja.