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

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We saw before that Agrā = Śaṅku-tala + Śaṅku-
bhuja. So, in the first place as a first approximation,
Agrā is taken as Śaṅku-bhuja. Since, when z = 45° the
perpendiculars from the celestial body on the planes of
the prime-vertical as well as meridian are equal, and since
the perpendicular on the plane of the prime-vertical is
called Śaṅku-bhuja = b (say) 2b² = H sin² z. This is so
because H sin² z = Sum of the squares of the perpendiculars
on the planes of the meridian and prime-vertical. But
H sin² z = R² − H ocs² z. ∴ R² − 2b'² = H cos² z. So, taking
Agrā as the bhuja b as a first approximation, √R² − 2b²
gives us H cos z. From this using formula III under
latitudinal triangles namely H cos z × s/12 = Śaṅku-tala,
obtain the approximate Śaṅku-tala, from the approximate
H cos z got above. Now using the formula Agrā =
Śaṅku-tala + Śaṅku-bhuja obtain Śaṅku-bhuja as Agrā ⩲
Śaṅku-tala, where the +ve sign is taken when the Sun
has a southern declination, and the difference sign when
the declination is north. Taking this Śaṅku-bhuja, b',
Koṇa-Śaṅku is now √R² − 2b'². In the first place we
took the Agrā itself as the bhuja; but here we have a
better approximation for the Śaṅku-bhuja. From this
Koṇa-Śaṅku again, obtain a still better approximation for
Śaṅku-bhuja and proceeding thus till a constant value is
obtained, we have the required Koṇa-Śaṅku. This is a
beautiful example where the method of successive approxi-
mation was used by the Hindu Astronomers to a good
advantage. It will be noted here that the Śaṅku-tala is
always treated as extending south ie. the Śaṅku-tala will be
south of the Śaṅku since India's latitudes are all north.
Also it is said that when the Sun has southern declination,
A + S = B and when northern A − S = B when A =
Śaṅku-Agrā or simply Agrā (in contradistinction to
Karṇāgrā reduced to a circle of radius K the chayākarṇa)
S = Śaṅku-tala and B = Śaṅku-bhuja. This convention