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

489 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. 62