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

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Let us consider the case of Vyatipāta. Suppose at
the moment concerned, the declinations are of opposite
direction. Find the sum of their numerical magnitudes.
Suppose they are of the same direction; find their differ-
ence. This sum or difference of the declinations gives the
distance between the planes of the diurnal paths of the
Sun and the Moon. This distance is to vanish in order
that the diurnal paths may coincide. So we are asked first
to find the above distance. Suppose we understand that
the Vyatipātha has elapsed by noting the deolinations.
This may be known easily by the criteria given previ-
ously. Supposing 𝑥 and 𝑦 to be the declinatious of the
Moon and the Sun and supposing that 𝑥 is on the decrease
and approaching 𝑦, then the Vyatipātha is to occur. But
suppose 𝑥 < 𝑦 and 𝑥 is on the decrease, then the Vyatipāta
has taken place. Thus knowing whether the Vyatipātha
has elapsed or is to occur, after an arbitrary time 𝑡, com-
pute the declinations of the Sun and Moon and form their
difference or sum as the case may be which gives the
distance between the diurnal paths. Let the first distance
found be called Ādya and the second distance the Anya.
Then the Anya will be less than the Ādya because we have
taken a time towards the occurrence of Vyatipāta when
the distance is to get nullified. Find the difference of the
Ādya and Anya. Then by the proportion “ If in time ‘𝑡’
taken in between the moments of the Ādya and Anya,
the distance between the diurnal paths is reduced by
Ādya — Anya, what time will be taken for the distance
Ādya to vanish ?” we have the result
T = (Ādya × 𝑡) / (Ādya — Anya) which gives approximately the time
that has to elapse for the occurrence of the pāta. This will
be approximate. After a lapse of time T from the Ādya
moment concerned, again compute the declinations and
repeat the procsss. We arrive at a particular point of
time, which gives the moment of occurrence of the pāta.
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