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

157 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.