Treatise on the Sun

12 Thirty Radius • Thirty Colatitude --- Equinoctial shadow Added to the direction By the squares of the equinoctial shadow Divided = 7 South-east and South-west Intermediate directions = 5 The intended state and having established the proximity = 1

Equinoctial shadow 12
Radius and Sine of Declination in the calculation

Desired Calculation and Its Resolution

When the sine of the colatitude lambajyā; the cosine of the local latitude is used, and the equinoctial shadow viṣuvacchāyā; the shadow cast at noon on the equinox is twelve digits, the hypotenuse karṇa is obtained by dividing through the sine of the declination krāntijyā when the sun is positioned in the prime vertical samamaṇḍala; the great circle passing exactly East and West through the zenith 26. Following this, the calculation of the prime vertical’s hypotenuse in the western orientation is performed. The declination krānti is the lord of the day in the North. The result produced at midday is multiplied by the equinoctial shadow and divided by the sine of the amplitude agra; the distance of the rising sun from the East point 27.

Again, to find the solar position: the sine of its own declination is multiplied by the radius trijyā and divided by the sine of the colatitude to find the sine of the amplitude. When this is multiplied by the desired hypotenuse and divided by the radius, the result is the amplitude in digits 28. Now, taking the sine of the sun's altitude arka-jyā, we proceed to the calculation of the shadow of the gnomon in the intermediate directions koṇa-śaṅku; shadows cast toward the NE, NW, SE, or SW. This is derived from the square of the radius, reduced by the square of the sine of amplitude and multiplied by twelve 29.

In the two Northern intermediate directions: North-east and North-west = 5

Furthermore, the result obtained by the wise for the North-east and other directions is added to the square of the gnomon śaṅku; the vertical pillar used to cast the shadow (72) and divided by the square of the equinoctial shadow 30. Of that The result is known as the karṇī a specific square-root term in Vedic geometry; the wise should set this aside separately. The equinoctial shadow, multiplied by the sun and diminished by the sine of amplitude 31, is divided by the square of the result. It is then added to or subtracted from the karṇī depending on whether the sun is in the Southern or Northern celestial hemisphere dakṣiṇottara gola 32.

The gnomon thus moves through the Southern intermediate directions, and likewise through the Northern ones 33. By taking the difference of those squares from the square of the radius, the square root provides the sine of the zenith distance dṛgjyā. By dividing that by its own gnomon and multiplying by twelve 34, the hypotenuse is found by the wise for their own specific location and time 35.

For the calculation of the shadow at a desired hour iṣṭanāḍī: the radius is increased by the sine of the ascensional difference, and decreased by the southern distance... The text here becomes highly technical, describing the adjustment of the 'Antyā' or last sine in the daily motion multiplied by the radius of the diurnal circle 36. Divided by the radius, this becomes the divisor. When multiplied by the sine of the colatitude and divided by the radius, it becomes the gnomon. Subtract the square of that 37 from the square of the radius to find the sine of the zenith distance, from which the shadow and its hypotenuse are derived.

For the three ratios: Sun, colatitude, equinoctial shadow 22 Radius, middle, 12 Middle, hypotenuse, equinoctial shadow --- The sun in the Southern and Northern hemispheres. "Moves through" = 5 When it moves all around the horizon above itself, the gnomon of the intermediate directions is calculated from the gnomon. Thus the method for the desired gnomon is stated, as it is also said in the Essence Commentary original: "Sāra-bhāṣye" = 5