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

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Karṇa therefore has nothing to do with the arc SM but
only has the virtue of being in a vertical plane. Sripati
adopted Brahmagupta's method. Kamalākara neither
follows Brahmagupta nor Bhāskara but follows a method
of his own. In fact the methods adopted by these ancient
Hindu astronomers are not mathematically correct because
the question of determining the cusps as well as phase of
the Moon is concerned with the actual positions of the
Sun, Moon and the earth in space and not as seen on the
sphere. Hence M. M. Sudhakara Dwivedi has written a
small book by the name Vāstava-Sṛṅgonnati following
modern methods. The modern method which gives the
truth of the matter is depicted in standar modern texts.
Verse 5. The hypotenuse or Karṇa is the square-root
of the sum of the squares of the Bhuja and Koti. The
Bhuja multiplied by 6 and divided by the Karṇa gives
what is known as the Dik-valana of the Moon. The dire-
ction of the Valana has the same direction as the Spasṭa
Bhuja defined before.
Comm. The idea is that taking the radius of the
Moon's disc to be six angulas or units, representing the
Karṇa, the magnitude of the Bhuja on the same scale
gives a measure of what is defined as Valana. Thus Valana
= 6B/K where B and K stand for the Bhuja and Karṇa
defined before. The idea of this Valana will be clarified in
the ensuing verses.
Verse 6. The Hsine of the elongation of the Moon
is to be multiplied by the radius vector of the Moon
measured in Yojanas, and divided by the radius vector of
the Sun, also measured in Yojanas ; the arc of the Hsine
so obtained is to be added to the longitude of the Moon
in the bright half of the lunation and is to be subtracted
from the same in the dark half.
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