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

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gupta's definition of Karṇa, it will be in this particular
case. √(R² + R²) = R√2 so that the Koṭi will be
√(2 R² — R²) = √R² = R, where the Bhuja also is R
(projection of the line joining the Sun and the Moon on
the north-south line. Though in the verse (11) above one
particular position of the Sun and one of the Moon, are
contemplated, the same argument holds good, says
Bhāskara in the course of the commentary, whatever
positions are occupied by the Sun and the Moon on the
ecliptic. In this case there is only Bhuja existing and
no Koṭi, so that the cusps will be vertical. But in all
these cases, there is Koṭi aecording to Brahmagupta's
definition, so that the ousps will not be vertical according
to him, which is clearly against truth.
Here we have to note that in the example cited by
Bhāskara the Bhuja equal to R is along the north-south
direction, and even though the Koṭi according to Bhās-
karajs definition is conceived to be vertical, the Karṇa
according to Brahmagupta's conception being ES where
E and S are the east and south points, his Koṭi will be
horizontal coinciding with OE, O being the centre of the
horizontal ecliptic. Further according to Brahmagupta,
the join of the ousps will be perpendioular to the Karṇa
whioh does not therefore go against truth. Similarly in
all the cases wherever be the Sun and the Moon on the
horizon, Brahmagupta's Karṇa being a line joining the
centres of the disos of the Sun and the Moon, it will be a
horizontal line and so the ousps could be vertical. It is
not clear whether or not Bhāskara recognized this namely
that the Karṇa and Koṭi of Brahmagupta in the cases
cited above are all horizontal lines so that the cusps could
be vertical even according to Brahmagupta. That is why
he pays homage to Brahmagupta in the last line of (12).
Probably Bhāskara expected that Brahmagupta's Koṭi also
should have been vertical as his. The fact that he
recognized that Brahmagupta's Koṭi will not be vertical