The Universal System of Astronomy, Part Two

White etc.
10

...one should make another [line] from the established point up to the horizon line ākāśa-rekhā; literally 'the sky-line' or the horizontal boundary on the instrument. Bring the desired degree of the arc original: svara, likely referring to the fractional value or degree to this line from the sky. This follows the previously stated established conclusion siddhānta; a formal astronomical treatise or proven rule.

The appearance of this shadow from the gnomon original: naravara; literally 'best of men', but used here technically to refer to the primary vertical indicator of a sundial is based on its own position. When connected to the calculated parts, the result is established. By using the straight sine ṛju-jyā, the measurement of time and other factors up to the horizon is determined.

By this method, the earth-sine kujyā; the sine of the sun's daily arc from the horizon to the six-o'clock circle and the sine jyā are situated within the circle. Through the inverse application of these sines, the half-chord of the sky is calculated. According to the text of the Compendium original: grantha-saṃhitā, the difference between the sines is found using the radius trijyā and other primary multipliers.

If the ascensional difference cara; the difference between the sun's right and oblique ascension is to be solved for the sun, one must use the inverse process. The sum of the versed sines utkrama-jyā; a trigonometric function used in ancient Indian astronomy allows the earth-sine to be known.

In the Northern hemisphere uttara-gola, the measurement is taken from the horizon toward the outer part... Rama ...whereas in the Southern hemisphere dakṣiṇa-gola, the calculation involves the descent from the horizon. Using the previously mentioned calculation for the versed sine, the observer can determine the exact standing position of the sun.