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

378
Comm. The word 'Grāsa' at the moment stands
for AB of fig. 77, Karṇa for CM, where CN is the Bhuja
and MN is the Kōti. The 'Grāsa' at the moment of
opposition has the special name Sthagita.
Second half of verse 17 and verse 18.
To obtain the time after the moment of first contact,
knowing 'Grāsa' at the moment.
T — √((P+r —Grāsa)²—β²) / (m₁—s₁) = t; this 't' is to be rectified
by obtaining the β of the moment and again finding t and
repeating the process till an invariable magnitude is got.
Comm. This is the converse of finding the Grāsa
given the time. The method of rectification is also
evident. In the above equation considering β and t as
variables, and differenting,
δt = (1 × —βδβ) / (2 (m₁—s₁) √((P+r—g)²—β²)) = —βδβ / ((T—t) (m₁—s₁)²)
Knowing δβ, δt could be got without taking recourse
to the method of successive approximations.
Verse 19. Certain definitions.
The 'Middle of the eclipse' (or strictly speaking the
moment when the portion eclipsed is a maximum) occurs
at the moment of opposition. Sparsa or Pragraha is at
the moment of first contact and Mokṣa is at the moment
of last contact, separated from the moment of the middle
of the eclipse by times equal to Sparsa-Sthiti-Khanda and
Mokṣa-Sthiti-Khanda respectively before and after.
Similarly Sammilana and Unmilana or the moment of
the commencement of totality and the end thereof occur
before and after the moment of 'the middle of the eclipse'
by times equal to Sammilana-Marda-Khanda and Un-
milana-Marda-Khanda respectively.