Surya Siddhanta
भक्ता फलाख्यम् तद्वर्गसम्युक्तकरणीपदम् । फलेन हीनसम्युक्तम् दक्षिणोत्तरगोलयोः॥
The square-root, (just found), diminished or increased by the Phala according as the Sun is south or north of the equinoctial, becomes the Koṇa-śanku[1] or the sine of altitude of the Sun when situated at an intermediate vertical (intersecting the Horizon at the N. E. and S. W. or N. W. and S. E. points). Then a R h : p {\displaystyle {\frac {aR}{h}}:p} (the sine of the Sun's altitude when he is at the prime vertical) = cos l : sin l {\displaystyle \cos l:\sin l} = e {\displaystyle e} (equinoctial shadow): 12; ∴ p = 12 a R h e {\displaystyle \therefore p={\frac {12aR}{he}}}; and ∴ p : R = 12 : x {\displaystyle \therefore p:R=12:x} (the hypothenuse of the Sun's shadow when he reaches the prime vertical): ∴ x = 12 R p = 12 R × h e 12 a R = h e a {\displaystyle \therefore x={\frac {12R}{p}}=12R\times {\frac {he}{12aR}}={\frac {he}{a}}}; supposing the Sun's declination to undergo no change during the day. [1. This is demonstrated thus. Let e {\displaystyle e} = the equinoctial shadow, a {\displaystyle a} = the sine of amplitude, k {\displaystyle k} = the Karaṇí f {\displaystyle f} = the Phala, and x {\displaystyle x} = the Koṇa-śanku.]
english translation
bhaktA phalAkhyam tadvargasamyuktakaraNIpadam । phalena hInasamyuktam dakSiNottaragolayoH॥
hk transliteration by Sanscript