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

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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