Surya Siddhanta
अन्त्या नतोत्क्रमज्योना स्वहोरात्रार्धसङ्गुणा । त्रिज्याभक्ता भवेच् छेदो लम्बज्याघ्नो +अथ भाजितः॥
Divide the product, (thus found), by the radius; the quotient is called the chheda; the chheda multiplied by the cosine of latitude and divided by the radius becomes the Śanku[1] or the sine of the Sun's altitude (at the given time). [1. This will be manifest thus. Let l = {\displaystyle l=} latitude of the place north of the equator; d = {\displaystyle d=} the Sun's declination; a = {\displaystyle a=} the ascensional difference, t = {\displaystyle t=} the time from noon in degrees, and x = {\displaystyle x=} the Sun's altitude. Then we have the equation which is very common; sin x = cos t . cos l . cos d ± R . sin l . sin d . R 2 {\displaystyle \sin {x}={\frac {\cos t.\cos l.\cos d\pm R.\sin l.\sin d.}{R^{2}}}}; = ( cos t . ± tan l . tan d R cos l . cos d R {\displaystyle ={\frac {(\cos t.\pm {\frac {\tan l.\tan d}{R}}\cos l.\cos d}{R}}}; = ( cos t ± sin a ) cos l . cos d R 2 {\displaystyle ={\frac {(\cos t\pm \sin a)\cos l.\cos d}{R^{2}}}}; or = ( R + sin a − vers t ) cos d R . cos d R {\displaystyle ={\frac {(R+\sin a-\operatorname {vers} t)\cos d}{R}}.{\frac {\cos d}{R}}}. It is to be observed here, that when the latitude of the place is north, the sin a {\displaystyle \sin a} becomes plus or minus according as the declination is north or south. B. D.]
english translation
antyA natotkramajyonA svahorAtrArdhasaGguNA । trijyAbhaktA bhavec chedo lambajyAghno +atha bhAjitaH॥
hk transliteration by Sanscript