Surya Siddhanta
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दिग्भेदे मिश्रिताः साम्ये विश्लिष्टाश् चाक्षलिप्तिकाः । ताभ्यो +अक्षज्या च तद्वर्गम् प्रोज्झ्य त्रिज्याकृतेः पदम् ॥
Find the sine of the latitude, (just found); take the square of that sine from that of the Radius; the square root of the remainder is the cosine of the latitude. The sine of the latitude multiplied by 12 and divided by the cosine of the latitude gives the Palabhá or the equinoctial shadow.
english translation
digbhede mizritAH sAmye vizliSTAz cAkSaliptikAH । tAbhyo +akSajyA ca tadvargam projjhya trijyAkRteH padam ॥
hk transliteration by Sanscriptलम्बज्यार्कगुणाक्षज्या विषुवद्भाथ लम्बया । स्वाक्षार्कनतभागानाम् दिक्साम्ये +अन्तरम् अन्यथा ॥
Find the difference between the degrees of the latitude (at a given place) and those of the Sun's zenith distance at noon when they are both of the same name, but when they are of contrary names find the sum of them; the result will be the Sun's declination; multiply its sine by the Radius.
english translation
lambajyArkaguNAkSajyA viSuvadbhAtha lambayA । svAkSArkanatabhAgAnAm diksAmye +antaram anyathA ॥
hk transliteration by Sanscriptदिग्भेदे +अपक्रमः शेषस् तस्य ज्या त्रिज्यया हता । परमापक्रमज्याप्ता चापम् मेषादिगो रविः॥
Divide the product by the sine of the Sun's greatest declination (or 1397): find the arc (in signs &c. whose sine is equal to the quotient, just found); this arc will be the longitude of the Sun when he is in the first quarter of the Ecliptic: but when he is in the second or third quarter, subtract or add the signs &c. (contained in the arc) from or to 6 signs; (the remainder or the sum will be the longitude of the Sun).
english translation
digbhede +apakramaH zeSas tasya jyA trijyayA hatA । paramApakramajyAptA cApam meSAdigo raviH॥
hk transliteration by Sanscriptकर्क्यादौ प्रोज्झ्य चक्रार्धात् तुलादौ भार्धसम्युतात् । मृगादौ प्रोज्झ्य भगणान् मध्याह्ने +अर्कः स्फुटो भवेत्॥
And when the Sun is in the fourth quarter of the Ecliptic subtract the signs &c. (which compose the arc) from 12 signs; the remainder will be the true longitude of the Sun at noon. (To the longitude, just found, apply the amount of the precession of the equinoxes inversely for the Sun's true place.) (In order to find the mean place of the Sun from his true place above found,) find the 1st equation from the true place of the Sun and apply it inversely to the place repeatedly, the result is the mean place of the Sun (that is, assume the true place as his mean place, find the Sun's first equation from it and add this equation to the true place if the equation be subtractive, but if it be additive, subtract it from the true place; the result will be somewhat nearer to the exact mean place of the Sun at the given noon; assuming this result as the Sun's mean place apply the said mode of calculation, and repeat the process until you get the exact mean place of the Sun).
english translation
karkyAdau projjhya cakrArdhAt tulAdau bhArdhasamyutAt । mRgAdau projjhya bhagaNAn madhyAhne +arkaH sphuTo bhavet॥
hk transliteration by Sanscriptतन्मान्दम् असकृद् वामम् फलम् मध्यो दिवाकरः । स्वाक्षार्कापक्रमयुतिर् दिक्साम्ये +अन्तरम् अन्यथा ॥
Find the sum of the latitude of a given place and the Sun's declination when they are of the same name, but when they are of contrary names find the difference between them; the result will be the zenith distance of the Sun (at noon). Find the sine and cosine of the (found) zenith distance.
english translation
tanmAndam asakRd vAmam phalam madhyo divAkaraH । svAkSArkApakramayutir diksAmye +antaram anyathA ॥
hk transliteration by Sanscript