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