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

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of the discs is less than the sum of their angular radii, the
pāta lasts. Extending the meaning of this to Vaidhṛti
also, so long as the numerical difference of the declinations
of the Sun and the Moon ignoring their direction happens
to fall short of the sum of the angular radii, the pāta
lasts.
To obtain this duration of the pāta the argument is
“If the sum or difference of the declinations according as
they are of opposite or the same direction (which was
taken to be Ādya under verses (11) to (14) ) was reduced to
zero in the time computed that time being known as
Spaṣṭaghaṭis, what time will be taken for a difference of
declinations equal to the sum of the angular radii?”
The result is ((r + p) × T) / Ādya where r and p are the
angular radii of the Sun and the Moon, T the time
calculated formerly known as Spaṣṭaghaṭis and Ādya is as
defined above. The above result gives the duration of the
pāta.
Note. An approximate estimate of this duration could
be obtained using differentiation. We have
sin δ = sin λ sin ω so that
cos δ Δδ = sin ω cos λ Δλ
Let Δλ be the motion in longitude of the Moon with
respect to the Sun per nāḍi which will be on the average
12′ approximately.
∴ Δδ = (sin ω cos λ × 12) / cos δ
If in one nāḍi, there be a variation in the declination
equal to the above, what time will be taken for 16′ + 15′
the sum of the angular radii approximately ? The result is
(31 cos δ) / (12 sin ω cos λ)