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

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in modern astronomy also the phase is measured through
the elongation. But the maximum phase in modern
astronomy is taken to be unity as could be seen from the
formula, for, when EPŜ = 180°, the phase = 1. Thus
the phase multiplied by 15 gives approximately the tithi.
We shall have occasion to deal with this topic later.
(3) Suppose ☾ − ☉ = E°. The number of the
tithis elapsed is equal to the quotient in E / 12. Take the
remainder r°. It means during the current tithi which
has a duration of 12°, r° have elapsed. Let the daily
motions of the Moon and the Sun be m and s so that the
Moon overtakes the Sun by m − s (expressed in minutes
for convenience) during 60 nādīs. The elapsed time of
the current tithi in nādīs is given by (r × 60 × 60) / (m − s). But
r × 60 × 60 = Seconds of arc of the remainder so that
it is said “गतैष्यविलिप्तिकाः”. If it be required to find how
many nādīs the next tithi lasts, (12−r)° or (12−r) × 60′
is to be gained by the Moon over the Sun. So the time in
Nādīs = ((12 − r) × 60 × 60) / (m − s) = एष्यविलिप्तिकाः / (m − s) .
(4) A lunation is again divided into 60 Karaṇas
and so 6° of increase in elongation correspond to a Karaṇa.
These Karaṇas are eleven in number, out of which 4 are
fixed to occur during the latter half of Kṛṣṇa Chautùrdasī,
during the two halves of Amāvāsyā and the first half of
the Sukla pratipat. Their names are Sakuni, Chatuṣpāt,
Nāgava, and Kimstughna. So there remain 56 halves of
tithis during the lunation during which the remaining
seven Karaṇas, Known as Bava, Bālava etc. rotate eight
times. Thus the first half of the duration of any tithi is
covered by one Karaṇa and the latter by another. The
computations of Karaṇas proceeds as with respect to tithis