The Universal System of Astronomy, Part Two

Therefore, from the sine of declination krāntijyā; the angular distance of the Sun north or south of the celestial equator, with the twelve-digit gnomon original: dvādaśa-koṭī; referring to the standard vertical pillar used for shadow measurements acting as the side, the result is the base bhuja; the horizontal side of a right-angled triangle. From that sine of declination, the earth-sine kujyā; the distance between the rising-setting line and the diurnal circle's diameter is produced by the radius trijyā; literally "three-jivas," the radius of the circle used in calculations. He now explains the calculation of the ascensional difference carajyā; the difference between the local and equatorial rising times and the Swan original: haṃsa; likely referring to a specific point or solar parameter in the Siddhānta system...

Twelve is the base the gnomon height and the hand is the hypotenuse karṇa; the diagonal measurement from the gnomon's tip to the shadow's edge. From that, the sine of the zenith distance nata-aṃśa-jyā; the angular distance from the point directly overhead is the gnomon original: śaṅku... base... hypotenuse... radius... This establishes the method of the Swan mentioned previously.

By this, the desired middle... beginning from the East and so on, the South-East original: āgneyī is established. Similarly, by the radius original: triguṇa, as stated in the Chapter on the Three Problems Tri-praśna-adhikāra; a standard section in Indian astronomical texts dealing with time, direction, and place, the ascensional difference... is diminished by the versed sine utkramajyā; a trigonometric function (1 - cosine) of the hour angle natakāla; the time elapsed before or after noon.

From that cause, the remaining sine is positive. Subtracted from the midday original: dinārddha; literally "half-day"... twelve...

He explains the calculation of the sine of declination original: krāntijyā. The sine of declination is multiplied by the radius and divided by the sine of the maximum declination. This should be subtracted... the second Sun... 24 degrees... the sine of the maximum declination original: caturviṃśati-jyā; the sine of 24 degrees, the traditional Indian value for the obliquity of the ecliptic.