Surya Siddhanta
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त्रिभज्यया भवेच् छङ्कुस् तद्वर्गम् परिशोधयेत् । त्रिज्यावर्गात् पदम् दृग्ज्या छायाकर्णौ तु पूर्ववत्॥
Subtract the square of the Śanku from that of the radius; the square root of the remainder is drịg-jyá or the sine of the zenith distance (at the given time). (From the śanku and the drịg-jyá) find the shadow and its hypothenuse as mentioned before (in Śloka 32). Multiply the radius by the given shadow (of the gnomon) and divide the product by the shadow's hypothenuse.
english translation
tribhajyayA bhavec chaGkus tadvargam parizodhayet । trijyAvargAt padam dRgjyA chAyAkarNau tu pUrvavat॥
hk transliteration by Sanscriptअभीष्टच्छाययाभ्यस्ता त्रिज्या तत्कर्णभाजिता । दृग्ज्या तद्वर्गसम्शुद्धात् त्रिज्यावर्गाच् च यत् पदम् ॥
The quotient is the drịg-jyá; the square-root of the square of the radius diminished by that of the drịg-jyá (just found), is the śanku; multiply it by the radius and divide the product by the cosine of latitude (of the place).
english translation
abhISTacchAyayAbhyastA trijyA tatkarNabhAjitA । dRgjyA tadvargasamzuddhAt trijyAvargAc ca yat padam ॥
hk transliteration by Sanscriptशङ्कुः स त्रिभजीवाघ्नः स्वलम्बज्याविभाजितः । छेदः स त्रिज्ययाभ्यस्तः स्वाहोरात्रार्धभाजितः॥
The result (thus found) is the chheda; multiply the chheda by the radius; divide the product by the cosine of the declination. Subtract the quotient from the Antyá and take the remainder. From the versed sines (given in ślokas 23—27 of the second chapter) find the arc whose versed sine equals the remainder:
english translation
zaGkuH sa tribhajIvAghnaH svalambajyAvibhAjitaH । chedaH sa trijyayAbhyastaH svAhorAtrArdhabhAjitaH॥
hk transliteration by Sanscriptउन्नतज्या तया हीना स्वान्त्या शेषस्य कार्मुकम् । उत्क्रमज्याभिर् एवम् स्युः प्राक्पश्चार्धन॥
The minutes contained in the arc are the Práṇas in the time before or after noon.[1] Multiply the cosine of latitude by the given reduced sine of amplitude and divide the prodnct by the given shadow's hypothenuse (at a given time). [1. This Rule is the converse of the preceding one. B. D.]
english translation
unnatajyA tayA hInA svAntyA zeSasya kArmukam । utkramajyAbhir evam syuH prAkpazcArdhana॥
hk transliteration by Sanscriptइष्टाग्राघ्नी तु लम्बज्या स्वकर्णाङ्गुलभाजिता । क्रान्तिज्या सा त्रिजीवाघ्नी परमापक्रमोद्धृता॥
The quotient, (thus found), is the sine of the Sun's declination; multiply it by the radius and divide the product by the sine of the greatest declination; find the arc in signs, degrees, &c.; from this arc and that quarter of the ecliptic in which the Sun is situated at the given time the Sun's longitude can be determined (as mentioned before in Ślokas 18 and 19 of this Chapter).
english translation
iSTAgrAghnI tu lambajyA svakarNAGgulabhAjitA । krAntijyA sA trijIvAghnI paramApakramoddhRtA॥
hk transliteration by Sanscript