Surya Siddhanta
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क्रान्तिज्याप्ते तु तौ कर्णौ सममण्डलगे रवौ । सौम्याक्षोना यदा कान्तिः स्यात् तदा द्युदलश्रवः॥
When the (Sun's) north declination is less than the latitude, the hypothenuse of the shadow at noon multiplied by the equinoctial shadow and divided by the reduced sine of amplitude at noon, gives the (same) hypothenuse[2] (which is found in the preceding Śloka). [2. This is proved thus. Let h = the hypothenuse of the shadow at noon; a = the sine of amplitude reduced to that hyp. ∴ a R h {\displaystyle \therefore {\frac {aR}{h}}} = the sine of amplitude in terms of the radius.]
english translation
krAntijyApte tu tau karNau samamaNDalage ravau । saumyAkSonA yadA kAntiH syAt tadA dyudalazravaH॥
hk transliteration by Sanscriptविषुवच्छाययाभ्यस्तः कर्णो मध्याग्रयोद्धृतः । स्वक्रान्तिज्या त्रिजीवाघ्नी लम्बज्याप्ताग्रमौर्विका ॥
The sine of the declination (of the Sun) multiplied by the radius and divided by the cosine of the latitude becomes the sine of amplitude. Multiply this sine by tbe hypothenuse of the shadow at a given time and divide the product by the radius: the quantity obtained is the sine of amplitude in digits (reduced to the hypothenuse of the shadow at the given time).
english translation
viSuvacchAyayAbhyastaH karNo madhyAgrayoddhRtaH । svakrAntijyA trijIvAghnI lambajyAptAgramaurvikA ॥
hk transliteration by Sanscriptस्वेष्टकर्णहता भक्ता त्रिज्ययाग्राङ्गुलादिका । त्रिज्यावर्गार्धतो +अग्रज्यावर्गोनाद् द्वादशाहतात् ॥
Subtract the square of the sine of amplitude from the half of the square of the radius; multiply circle of which the azimuth remainder by 144: . -
english translation
sveSTakarNahatA bhaktA trijyayAgrAGgulAdikA । trijyAvargArdhato +agrajyAvargonAd dvAdazAhatAt ॥
hk transliteration by Sanscriptपुनर् द्वादशनिघ्नाच् च लभ्यते यत् फलम् बुधैः।शङ्कुवर्गार्धसम्युक्तविषुवद्वर्गभाजितात् ॥
- divide the product by the half of the square of the gnomon (i. e. 72) increased by the square of the equinoctial shadow. Let the name of the result be the Karaṇí. Let the calculator write down this number (for future reference).
english translation
punar dvAdazanighnAc ca labhyate yat phalam budhaiH।zaGkuvargArdhasamyuktaviSuvadvargabhAjitAt ॥
hk transliteration by Sanscriptतदेव करणी नाम ताम् पृथक् स्थापयेद् बुधः। अर्कघ्नी विषुवच्छायाग्रज्यया गुणिता तथा ॥
Multiply twelve times the equinoctial shadow by the sine of amplitude and divide the product by the former divisor (i. e. 72 added to the square of the equinoctial shadow). Let the result be called the Phala; Add the square of the Karaṇí to the Phala and take the square-root of the sum.
english translation
tadeva karaNI nAma tAm pRthak sthApayed budhaH। arkaghnI viSuvacchAyAgrajyayA guNitA tathA ॥
hk transliteration by Sanscript