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Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 1 · Basics and Panchanga
ज्योतिषमूलं पञ्चाङ्गं च
क्रांत्योः समत्वे पातोऽथ प्रक्षिप्तांशोनिते विधौ ।हीनेऽर्द्धरात्रिकाघातो भावी तात्कालिकेऽधिका ॥ १८२ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 54, verse 182.
When the declinations are equal, that is the point. Now take the Moon less the degrees that were added. If it is less than the Moon at midnight, the point has passed. If it is more, the point is to come.
Simple meaning: When the declinations match, the point is reached. Compare with the midnight Moon to see if it passed.
स्थिरीकृतार्द्धरात्रार्द्धौ द्वयोर्विवरलिप्तकाः ।
The gap between the fixed Moon and the midnight Moon gives the time of the point.
रवींद्वोर्मानयोगार्द्धं षष्ट्या संगुण्य भाजयेत् ।
Half the sum of the Sun's and Moon's sizes, times 60, divided by the difference in motion, gives the half-duration.
पातकालः स्फुटो मध्यः सोऽपि स्थित्यर्द्धवर्जितः ।
The mid-time less the half-duration is the start. Plus the half-duration is the end.