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Narada Purana (Jyotisha Selections) · by Vyasa
Chapter 1 · Basics and Panchanga
ज्योतिषमूलं पञ्चाङ्गं च
पातकालः स्फुटो मध्यः सोऽपि स्थित्यर्द्धवर्जितः ।तस्य संभवकालः स्यात्तत्संयोगेक्तसंज्ञकः ॥ ८५ ॥
In the full Narada Purana (Purva Bhaga) this is chapter 54, verse 185.
The true point time is the middle. Less the half-duration, it is the starting time. With the half-duration added, it is called the end.
Simple meaning: The mid-time less the half-duration is the start. Plus the half-duration is the end.
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.
आद्यंतकालयोर्मध्ये कालो ज्ञेयोऽतिदारुणः ।
The time between the start and the end is harmful and should be avoided for every task.