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

522 by the ancient Hindu astronomers, before the time of Bhāskara, for the reason that the Moon does not exactly move in the ecliptic but in his own orbit whose inclination to the ecliptic was taken to be 4½°. The points of intersec- tion of the ecliptic with the lunar orbit, or what are called Rāhu and Ketu, the nodes of the lunar orbit, have themselves a motion backwards on the ecliptic in 18.59575 solar years as per Bhāskara. This makes the lunar orbit oscillate about the mean position of the ecliptic, so that sometimes the lunar orbit lies between the celestial equator and some-times not between them. This phenomenon makes the computation more difficult, to obtain the declination of the Moon. Bhāskara says that even great Ācāryas like Lalla and Brahmagupta went wrong or got confused in computing the moments of the occurence of a Pāta. Bearing upon Bhāskara’s statement that such Ācāryas also got confused, some second-rate astronomer exclaimed in the following interesting manner “त्रिस्कन्धविद्याकुशलैकमल्लो लल्लोऽपि यत्राऽप्रतिभा बभूव, यातेऽपि किञ्चित् गणिताधिकारे पाताधिकारे मम नाऽधिकारः” ie. “when even an unrivalled scholar like Lalla, who was well-versed in the three branches of Jyotiṣa betrayed his ignorance in this context of Pātādhi- kāra, though I am a bit of a mathematician, I could have no pretensions to any knowledge in this difficult chapter”. In Fig. 124, Vyatīpāta occurs when SL=MN, where S and M are the Sun and the Moon situated respectively in Uttarāyaṇa and Dakṣi- ṇāyana but in the same uttaragola. The positions of S and M could be interchanged ie. S may be in the second quadrant of the ecliptic and M in the first quadrant and if their declinations be equal, then Fig. 124 also Vyatīpāta occurs. Of course in this figure 124, we have taken the Moon also situated on the ecliptic. In