Treatise on the Sun

1. The sine of the zenith distance of the sun = 2 The inner sine multiplied by the sun is 3

The base of the triangle is multiplied and divided by that Referring to the trigonometric ratios derived from the gnomon, results in fourteen. When multiplied by the hypotenuse of its own shadow, in this base, the North-South difference is determined. These are the minutes of the Solar Declination sūrya-krānti 15. When the directions are different, they are combined; when they are the same, they are subtracted to find the latitude. By subtracting the square of that sine from the square of the radius, and taking the square root 16, one finds the sine of the colatitude multiplied by the sun. The sine of the latitude is then added to the equinoctial shadow and the colatitude as it has been stated.

Calculation of the Sun via its Shadow chāyārka-sādhanam

Now, regarding the calculation of the Sun via its shadow: find the difference between the local latitude and the sun's zenith distance if they are in the same direction, or their sum if they are in different directions 17. The remainder is the declination; its sine, multiplied by the radius and divided by the sine of the maximum declination, gives the arc. Starting from Aries, the Sun’s position is determined 18. Subtracting from the end of Gemini or adding to the beginning of Libra or subtracting from the end of Sagittarius, the Sun's true position at midday is revealed 19.

Calculation of the Mean Position madhyamānayanam

Now, the calculation of the mean position: through repeated application of the inverse result, the Sun reaches its mean position. For the calculation of the mean midday shadow, one must find the sum or difference of the local latitude and the sun's declination depending on their directions 20. The remainder

represents the degrees of the Sun's zenith distance. The sine of that is the base, and the cosine is the perpendicular. These are multiplied by the measure of the gnomon in digits śaṅkumānāṅgulābhyaste, respectively 21.

When the base and perpendicular are divided by the radius, the Hypotenuse of the Shadow chāyā-karṇa is produced. Now, for the calculation of the directions and points of the compass 22: The sine of declination is multiplied by the equinoctial hypotenuse and divided by the sine of the colatitude The text uses 'gnomon-sine' to refer to the sine of the colatitude in this context. The Sun's Amplitude arkāgrā is then multiplied by its own hypotenuse and divided by the midday hypotenuse 23. The Sun's amplitude is added to the equinoctial shadow; if it is to the south, the base is southern. In the northern hemisphere, if it is subtracted from the equinoctial shadow, the base is northern 24. If the values are reversed, the base becomes southern. Because of the difference between the two arcs, the midday base and the midday shadow are always established 25.

Calculation of the Hypotenuse of the Prime Vertical samamaṇḍala-karṇanayanam