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

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of the Sun and the Moon. Herein Bhāskara defines the
Koti as the sum of the Saṅkus of the Sun and the Moon
which is the vertical distance between the points on the
armillary sphere which represent the Sun and the Moon.
Bhāskara says 'I deem' to signify that he differs
from Brahmagupta in this, who defines the chord joining
the Sun and Moon on the armillary sphere which is equal
to 2 Hsine of the SM on the sphere as the Karṇa. Brahma-
gupta defines the Bhuja and Karṇa from which he deduces
the Koti as √(Karṇa² — Bhuja²). Bhāskara argues that since
the Karṇa defined by Brahmagupta is not in the vertical
plane, since the Sun and the Moon are not in the same
vertical plane, so, the Koti defined by him throught he Karṇa
will not be in the vertical plane. The Karṇa defined by
Bhāskara is not on the other hand the chord joining the
Sun and the Moon but lies in the vertical plane in which
the perpendicular from the Moon's position on the armil-
lary sphere, on the horizontal plane containing the Sun's
position on that sphere. Also the Bhuja defined both by
Brahmagupta and Bhāskara is the projection on the north-
south line of the join of the Sun's position on the sphere and
the foot of the perpendicular from the Moon's position on
the horizontal plane through the Sun's position and it is
not actually the above join.
Bhāskara is evidently
guided by the right angled
triangle SMN' which is not
strictly a spherical triangle
as per its modern definition
as the arc SN is not that
of a great circle. This
figure guided him to take
the Bhuja horizontal and
the Koti vertical so that
his Karṇa is also in a
Fig. 115
vertical plane. Bhāskara's