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

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position, such differences were tabulated. It was discovered
that these difference almost vanished when the planet was
in conjunction with the Sun and attained a maximum
when the elongation was nearly a right angle from an
analogy from the Manda-Karma i.e. process of obtaining
the Manda-phala. Since the differences attained their maxi-
mum value when the elongations were nearly a right angle
it could be seen that the Sun played the part of the Uccha
in this case. As the Sun has a quicker motion than the
planet and also as at conjunction the planet has the quick-
est motion relative to the Earth while it is farthest from
the Earth the Uccha ie the Sun here, is termed Śīghroccha.
The excess of the longitude of the Sun over that of the
planet is termed accordingly the Śīghra-kendra and the
Śīghra-phala the equation was formulated as will be shown.
Applying this Śīghra-phala to the mean position, the diffe-
rences still found between the position so obtained and the
observed true position were tabulated. The point indicated
by the above position where the difference was found to be
zero, was identified as the Mandoccha, and through the
maximum difference, the Mandaparidhi was formulated.
In the above discourse, we have tried to give an
account of how the originators of Hindu Astronomy
could give us a workable system. We never assumed that
an Āgama gave us the numbers of sidereal revolutions of
the planets or the measures of the epicycles Manda or
Śīghra. But in the explanation given by Bhāskara under
Bhagaṇōpapatti, one will notice that when Bhāskara gave
the proof of the Moon's sidereal revolutions, he said that
having got the true positions of the Moon on two conse-
cutive days, the mean positions were computed from the
true by an inverse process of applying the equation of
centre, and getting the mean daily motion of the Moon
from those mean positions, the number of sidereal revolu-
tions in a Kalpa were obtained. Here the Upapatti or the
proof adduced by Bhāskara was not a proof but only a
verification in as much as (1) he assumed the formulation
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