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

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an ambiguous sense. Ranganātha in his commentary
takes the Madhya-Sthiti-khanda to mean that rectified
for variation in β, and Spaṣṭa-Sthiti-khanda to mean that
rectified for parallax. Some modern traditional commen-
tators, for example pandit Sitha Ramajha commenting on
the verse of the Sūryasiddhānta and the commentator of
the verses of Brahma Sphutasiddhānta published under
the editorship of Acharya Rama Swarupa Sharma, have
ignored the variation in β and confined themselves only
to the effect of parallax in longitude.
Yet one more proof could be adduced in this behalf.
Let D, be the moment of geocentric conjunction, t the
time for a given grāsa in between D and T the moment of
first geocentric contact. Then the times D, t and T are
to be corrected both for parallax in longitude and that
in latitude. Take the geocentric Sthiti-khanda, and
geocentric Bhuja as the mean-values T and B and those
corrected first for parallax in longitude as the True values
T' and B'. Also take the time t corrected for parallax in
longitude to be t'. We could write T' - T = δT, t' - t = δt
and B' - B = δB. In the above, consider B expressed in
time. Then D - T = S the mean Sthiti-khanda, D - t = B
the mean Bhuja, D' - T' = S', the true Sthiti-khanda recti-
fied for parallax in longitude, D' - t' = B' the Bhuja also
rectified for the same. The δB = δD - δt, δI = δD - δT.
Then using the proportion "If for D - T we have δD - δT
as the variation what shall we have for D - t?" The result
is ((D - t) (δD - δT)) / (D - T) = δB
∵ B + δB = B' = D - t + ((D - t) (δD - δT)) / (D - T)
= (D - t) (1 + (δD - δT) / (D - T)) = (D - t) ((D + δD) - (T + δT)) / (D - T)
= (D - t) (D' - T') / (D - T) = (Mean Bhuja × True Sthiti-khanda) / (Mean Sthiti-khanda)