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

302
Comm. Ref. fig. 52. I.A. = AN. I.A. - Carajyā =
B.N. Hvers⁻¹ (BN) = arc EN. Arc EN + Caracāpa =
EN + EM = MN. This converted into time is evidently
the Unnatakāla because the arc MN of the equator is the
arc intercepted between the feet of the declination
circles at rising and at the time concerned M being the
foot of the rising declination circle and N the foot of that
at the time in question. The convention of signs is
clear.
Verse 70 and first half of 71. To obtain the Sun's
longitude from the shadow S.
The gnomonic shadow at noon, being multiplied by R
and divided by K, the inverse H sine of the result gives
the meridian zenith-distance. This being decreased or
increased by the latitude gives the Sun's declination
according as the extremity of the shadow is north or
south. From the declination, we have the Sun's longitude
by the formula H sin δ = (H sin λ H sin ω) / R .
Comm. We have from the triangle formed by the
gnomon and the shadow S, S / K = sin z or SR / K = H sin z
∴ H sin⁻¹ (SR / K) = z. Since we are directed to take
the mid-day shadow, we have the meridian zenith-distance
and from the formula z + δ = φ we have δ. If the
extremity of the shadow be north, the Sun is south of
the zenith, and then φ ~ z = δ. The word वियुक्ताः is
used to signify difference which is positive. If z > φ
then the declination is south and vice-versa. If the
extremity of the shadow is on the south, the Sun is on
the north of the zenith. in which case φ + z = δ.
Second half of verse 71. To obtain φ from δ.