Treatise on the Sun

From the half-duration of the separation phase sthityardha-mokṣika, the remainder is to be added as before to the separation point 21. Now, for the knowledge of time from the deflection valana: subtract the half-sum of the diameters of the eclipsed and the eclipser grāhya-grāhaka from their own minutes of measure. The square root of the square of the celestial latitude vikṣepa at that time utpa?... 22. The minutes of the perpendicular koṭi for the Sun:

Or from the degrees of declination krānti, the sum or difference of the calculated deflection valana [is found]. If the directions are the same, they are added; if different, they are subtracted. The R-sine kramajyā of that result becomes the sine of deflection valanājyā. Divided by 70, the result is in digits aṅgulas. The degrees of deflection are known from the sum or difference of the declination and the latitude, depending on the direction.

Multiplied by the precise half-duration spaṣṭa-sthityardha... the duration in units of time nāḍīs... from the duration comes the fine time measurement 23. Now, for the calculation of deflection valana: the product of the sine of the hour angle natajyā and the radius trijyā, divided by the radius, and the arc of that result gives the degrees of deflection. These are North or South in the Eastern and Western hemispheres 24. Now, for the deflection due to declination apakrama-valana: from the Sun increased by three signs, find the declination. If the directions are the same, they are added; otherwise, the difference is the sine called deflection. Thus 25. Consisting of digits aṅgula, it is brought to the midday of the day by the result... these digits are measured according to the local latitude original: "Vindhyā"; referring to the Vindhya mountains, a common reference point for Indian geographical coordinates 26.

Thus ends the Fourth Chapter of the Illustrious Sūrya Siddhānta, entitled the Chapter on Solar and Lunar Eclipses. 4

When the Sun is equal to the meridian ecliptic point madhyalagna, no parallax harija original: "harija"; literally 'born of the horizon', referring to parallax occurs. Therefore, due to the alignment of the ecliptic zenith dṛgmadhya, there is no parallax in latitude avanati 1. According to the specific place and time, where the possibility of parallax in latitude exists, that is now explained based on the direction of the desired point 2. One should calculate the ascendant lagna for the time of the eclipse conjunction parva-nāḍī using the local rising periods. The sine of that... The amplitude of the rising sign is produced = 3 ...the sine of the declination... called the "rising sine" udayajyā 3. Similarly, the ascendant as it would appear at the equator laṅkodaye is called the meridian point madhyasaṃjñā. The sum of its declination is taken if the directions are the same, otherwise the difference 4. The remainder is the degrees of zenith distance natāṃśa; the sine of that is called the meridian sine madhyajyā. The product of the meridian sine and the "rising sine" divided by the radius, that result is squared 5. Subtracting the square of the meridian sine... the remainder is the square root of the ecliptic zenith distance dṛkkṣepa.

The precision of the digits on the horizon is seen... the four minutes for the meridian cause... thus everything is established in its essential nature. In the middle of the day, at the time of transit, the elevation... is 6 and a half... at midday with 3 minutes... this is proven 1. Here, by the term meridian ecliptic point madhyalagna, the middle of the rising and setting points of the ecliptic is intended; specifically, the tenth house daśama-lagna should be taken 6.