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

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Moon's hourly motion is given in modern almanacs. Since
it is very cumbrous to use the method of successive approxi-
mation to determine the ending moment of every tithi, the
Hindu almanac-makers generally compute the ending
moment of a tithi using the daily motion of the moon
computed for the moment of Sun-rise of the day. Only for
ritual purposes, the method of successive approximation is
used and also in the computation of eclipses.
Verse 39. Computation of the Sīghragatiphala.
δl − [H sin (90−E₂) × δm] / K = δS where δl is the daily
motion of the Sīghrōcca, E₂ = Sīghraphala, δm = daily
motion in the Sīghra mean anomaly, K = Sīghrakarṇa,
and δS the true motion of the planet. If δS is negative the
planet is retrograde.
Comm. This is mathematically an important verse,
and the proof given by Bhāskara really reflects his
genius. Before we attend to his proof, we shall give this a
modern treatment. (Ref. figs. 14, 15). SA and EA' are the
Fig. 14
heliocentric and geocentric directions to Aswini the Hindu
Zero-point of the Zodiac; S = Sun, E = Earth; V = In-
ferior planet Venus or Mercury; J = Superior planet; E =
Sīghra-phala, K = Sīghra Karṇa; M = Sīghra anomaly.