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

541
When λ approaches 90°, the duration will be very
much since cos λ → 0. This is true because the variation
in the declination when λ = 90°, is very slow even for the
Moon. The above formula holds good so long as λ does
not approach 90°.
Verse 17. It must be deemed that the declinations
will be equal so long as the difference in the declinations
is less than r + p numerically.
In the case of Vaidhṛti, we are asked to take the sum
instead of difference and difference instead of sum in
contradistinction. Why? We shall see. We know that
Vaidhṛti occurs when the declinotions of the Sun and the
Moon are of equal magnitude but of opposite directions
subject to the condition that the longitudes are such that
their sum is approximately 360°. This condition is
stipulated because when the Sun is in the first quadrant
and the Moon is in the 3rd quadrant and at the same time
their diclinations are equal, the moment does not constitute
Vaidhṛti, because the sum of the longitudes is then less
than 90° + 270° ie. less than 360°. Hence, for Vaidhṛti
one of the two celestial bodies must be in the first quadrant
and the other in the fourth quadrant, so that the sum of
the longitudes could equal 360° and at the same time the
declinations could be equal though of opposite sign. Now
compute the declinations of the Sun and the Moon at a
particular moment. Suppose they are a and b and both
are north. After a few ghatis or days compute again their
declinations, say c and d, both again being north. Suppose
then c + d < a + b, then Vaidhṛti is going to occur.
Construing northern declination to be positive and the
southern negative, for Vaidhṛti to occur a + b must be
reduced to zero ie. a and b are equal and of opposite
direction. Now the argument adduced is "If in time
t ghatis or days a̅+̅b̅ has become c̅+̅d̅ (calling a̅+̅b̅ as
Ādya and c̅+̅d̅ as Anya) there is a decrease of Ādya - Anya,
what time should lapse for a̅+̅b̅ or Adya to reduce to