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

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ness resulting as follows. Let M/N be a fraction to which
m/n is a convergent having small numbers as numerator and
denominator, so that M/N is taken to be equal to m/n (1 + 1/λ).
Thus M/N = m/n (1 + 1/λ) or Mn = Nm (1 + 1/λ)
∴ Mn − Nm = Nm/λ or λ = Nm / (Mn − Nm). In the present
case M is the number of Adhikamāsas, and N the number
of solar months. m/n if taken to be 2/65
− 2 × Solar months
∴ In this case λ = --------------------------------------------------
65 × Adhikamāsas − 2 × Solar months
which is indicated in the commentary by Bhāskara.
In this context, it may be mentioned that a Karaṇa-
grantha named Nārasiṁha based upon Sūryasiddhānta
(A Karaṇagrantha is a manual according which the Hindu
calendar is computed with easy numbers without under-
going the laborious process indicated in the treatises called
Siddhāntas like the present Siddhānta Śiromaṇi. In
these Karaṇagranthas, instead of taking the beginning of
the Kalpa or Mahāyuga or the Yuga, as the epoch, a recent
date ie. the date of the author of the Karaṇagrantha is
taken as the epoch, and processes using approximations
are adopted for the sake of ease. Naturally therefore these
Karaṇas (as they are also called) get easily obsolete
within the course of a few hnudreds of years so that a fresh
Karaṇa is called for preparation, if the calculations were
to accord with the Siddhāntas which those Karaṇas pro-
fess to follow. In fact, the present Karaṇa of Nārasiṁha
written in 1333 Śaka year ie. in 1411 A.D. declares that
a previous Karaṇa named Tithicakra reported to have
been written by one Mallikārjuna Suri grew obsolete and