Surya Siddhanta
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शेषम् नताम्शाः सूर्यस्य तद्बाहुज्या च कोटिज्या ॥ शङ्कुमानाङ्गुलाभ्यस्ते भुजत्रिज्ये यथाक्रमम् ॥
The sine (just found) and the Radius multiplied by the length of the Gnomon in digits (or by 12) and divided by the cosine (above found) give the shadow of the Gnomon and its hypothenuse (respectively) at noon.
english translation
zeSam natAmzAH sUryasya tadbAhujyA ca koTijyA ॥ zaGkumAnAGgulAbhyaste bhujatrijye yathAkramam ॥
hk transliteration by Sanscriptकोटिज्यया विभज्याप्ते छायाकर्णाव् अहर्दले । क्रान्तिज्या विषुवत्कर्णगुणाप्ता शङ्कुजीवया॥
The sine of the Sun's declination multiplied by the equinoctial hypothenuse and divided by 12 gives the sine of the Sun's amplitude. This sine multiplied by the hypothenuse of the Gnomonic shadow at noon, and divided by the Radius, becomes the sine of amplitude reduced to the shadow's hypothenuse.
english translation
koTijyayA vibhajyApte chAyAkarNAv ahardale । krAntijyA viSuvatkarNaguNAptA zaGkujIvayA॥
hk transliteration by Sanscriptअर्काग्रा स्वेष्टकर्णघ्नी मध्यकर्णोद्धृता स्वका । विषुवद्भायुतार्काग्रा याम्ये स्याद् उत्तरो भुजः॥
To this reduced sine of the Sun's amplitude add the equinoctial shadow; the sum will be the north Bhuja (of the shadow at the given time) when the Sun is in the southern hemisphere, but when he is in the northern hemisphere, take the reduced sine of amplitude from the equinoctial shadow, and the remainder will be the north Bhuja.
english translation
arkAgrA sveSTakarNaghnI madhyakarNoddhRtA svakA । viSuvadbhAyutArkAgrA yAmye syAd uttaro bhujaH॥
hk transliteration by Sanscriptविषुवत्याम् विशोध्योदग्गोले स्याद् बाहुर् उत्तरः । विपर्ययाद् भुजो याम्यो भवेत् प्राच्यपरान्तरे ॥
In the latter case, when the reduced sine of amplitude ia greater than the equinoctial shadow, subtract this shadow from the reduced sine; the remainder will be the south Bhuja between east and west line and the end of the shadow at the given time. Every day the Bhuja at noon equals the Gnomon's shadow at that time.
english translation
viSuvatyAm vizodhyodaggole syAd bAhur uttaraH । viparyayAd bhujo yAmyo bhavet prAcyaparAntare ॥
hk transliteration by Sanscriptमाध्याह्निको भुजो नित्यम् छाया माध्याह्निकी स्मृता । लम्बाक्षजीवे विषुवच्छायाद्वादशसङ्गुणे ॥
Multiply the cosine of the latitude by the Equinoctial shadow or the sine of the latitude by 12; the product (which is the same in both cases) divided by the sine of the Sun's declination gives the hypothenuse of the gnomonic shadow at the time when the Sun reaches the prime vertical.[1] [1. This is shown thus, Let l = latitude of the place; e = the equinoctial shadow; d = the sine of the Sun's declination; p = altitude; x = the hypothenuse of the shadow; Then, sin l : d = R : p; and R : p = x : 12; ∴ x = 12 sin l d = e cos l d {\displaystyle \therefore x={\frac {12\sin {l}}{d}}={\frac {e\cos {l}}{d}}} (because cos l : sin l = 12 : l and e. cos ^ d d 12 sin I).]
english translation
mAdhyAhniko bhujo nityam chAyA mAdhyAhnikI smRtA । lambAkSajIve viSuvacchAyAdvAdazasaGguNe ॥
hk transliteration by Sanscript