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

541 When λ approaches 90°, the duration will be very much since cos λ → 0. This is true because the variation in the declination when λ = 90°, is very slow even for the Moon. The above formula holds good so long as λ does not approach 90°. Verse 17. It must be deemed that the declinations will be equal so long as the difference in the declinations is less than r + p numerically. In the case of Vaidhṛti, we are asked to take the sum instead of difference and difference instead of sum in contradistinction. Why? We shall see. We know that Vaidhṛti occurs when the declinotions of the Sun and the Moon are of equal magnitude but of opposite directions subject to the condition that the longitudes are such that their sum is approximately 360°. This condition is stipulated because when the Sun is in the first quadrant and the Moon is in the 3rd quadrant and at the same time their diclinations are equal, the moment does not constitute Vaidhṛti, because the sum of the longitudes is then less than 90° + 270° ie. less than 360°. Hence, for Vaidhṛti one of the two celestial bodies must be in the first quadrant and the other in the fourth quadrant, so that the sum of the longitudes could equal 360° and at the same time the declinations could be equal though of opposite sign. Now compute the declinations of the Sun and the Moon at a particular moment. Suppose they are a and b and both are north. After a few ghatis or days compute again their declinations, say c and d, both again being north. Suppose then c + d < a + b, then Vaidhṛti is going to occur. Construing northern declination to be positive and the southern negative, for Vaidhṛti to occur a + b must be reduced to zero ie. a and b are equal and of opposite direction. Now the argument adduced is "If in time t ghatis or days a̅+̅b̅ has become c̅+̅d̅ (calling a̅+̅b̅ as Ādya and c̅+̅d̅ as Anya) there is a decrease of Ādya - Anya, what time should lapse for a̅+̅b̅ or Adya to reduce to