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

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1. Bhaskara has given that 1593300000 Adhika- māsās occur in a Kalpa of 4320000000 Solar years, which means that 15933 Adhikamāsās occur in 43200 Solar years ie. 5311 Adhikamāsas in 14400 solar months. Converting 14400 / 5311 into a continued fraction, we have 2 + 1/(1+) 1/(2+) 1/(2+) 1/(6+) 1/(1+) 1/(1+) 1/(7+) 1/(3+) 1/2. The successive convergents are 2/1 3/1 8/3 19/7 122/45 141/52. Let us see what these convergents signify. (a) The convergent 19/7 means that on an average there are 7 Adhikamāsās per 19 years. This ratio was adopted in the Romaka Siddhānta of Panchasiddhāntika. It means that 19 × 12 = 228 Solar months are equal to 235 lunations. The Metonic cycle described in modern astronomy is based upon this equivalence. The recurrence of Moon's phases in 19 years ie correspondence of the Moon's phases or tithis with the dates of the English year and Meton's formula are based on this equivalence. Recurrence of phase means recurrence of the relative positions of the Sun and the Moon, which again means recurrence of the Suddhi, for Suddhi is no other than the interval between the New Moon and Saṁkrānti. In the next verse Bhāskara says that a Kshayamāsa recurs after a lapse of either 19 years or 122 years or 141 years. The numerators of the last three convergents are 19, 122 and 141 which are the numbers of Solar years that effect recurrence of the same Suddhi and as is going to be mentioned shortly a Suddhi of 21 tithis is likely to bring in a Kshayamāsa. Hence a Kshayamāsa recurs either in 19 years or 121 years or 141 years.
2. Mention of the occurence of a Kshayamāsa was made by Sripati first and not by the preceding astro- nomers. However, mention of it is there in the Vedic