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

378 Comm. The word 'Grāsa' at the moment stands for AB of fig. 77, Karṇa for CM, where CN is the Bhuja and MN is the Kōti. The 'Grāsa' at the moment of opposition has the special name Sthagita. Second half of verse 17 and verse 18. To obtain the time after the moment of first contact, knowing 'Grāsa' at the moment. T — √((P+r —Grāsa)²—β²) / (m₁—s₁) = t; this 't' is to be rectified by obtaining the β of the moment and again finding t and repeating the process till an invariable magnitude is got. Comm. This is the converse of finding the Grāsa given the time. The method of rectification is also evident. In the above equation considering β and t as variables, and differenting, δt = (1 × —βδβ) / (2 (m₁—s₁) √((P+r—g)²—β²)) = —βδβ / ((T—t) (m₁—s₁)²) Knowing δβ, δt could be got without taking recourse to the method of successive approximations. Verse 19. Certain definitions. The 'Middle of the eclipse' (or strictly speaking the moment when the portion eclipsed is a maximum) occurs at the moment of opposition. Sparsa or Pragraha is at the moment of first contact and Mokṣa is at the moment of last contact, separated from the moment of the middle of the eclipse by times equal to Sparsa-Sthiti-Khanda and Mokṣa-Sthiti-Khanda respectively before and after. Similarly Sammilana and Unmilana or the moment of the commencement of totality and the end thereof occur before and after the moment of 'the middle of the eclipse' by times equal to Sammilana-Marda-Khanda and Un- milana-Marda-Khanda respectively.