Surya Siddhanta
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प्राक्पश्चिमाश्रिता रेखा प्रोच्यते सममण्डले । उनण्डले च विषुवन्मण्डले परिकीर्त्यते ॥
The line representing the Prime Vertical, the six o'clock line or the equinoctial, passes through the east and west points of the Horizon.
english translation
prAkpazcimAzritA rekhA procyate samamaNDale । unaNDale ca viSuvanmaNDale parikIrtyate ॥
hk transliteration by Sanscriptरेखा प्राच्यपरा साध्या विषुवद्भाग्रगा तथा । इष्टच्छायाविषुवतोर् मध्यम् अग्राभिधीयते ॥
(In the said circle)[1] from the east and west line (to its north) at a distance equal to the equinoctial shadow, draw another line parallel to the former; the distance between the end of the given shadow and the latter line is equal to the sine of amplitude (reduced to the hypothenuse of the given shadow).
english translation
rekhA prAcyaparA sAdhyA viSuvadbhAgragA tathA । iSTacchAyAviSuvator madhyam agrAbhidhIyate ॥
hk transliteration by Sanscriptशङ्कुच्छायाकृतियुतेर् मूलम् कर्णो +अस्य वर्गतः । प्रोज्झ्य शङ्कुकृतिम् मूलम् छाया शङ्कुर् विपर्ययात् ॥
The square-root of the sum of the squares (of the lengths) of the Gnomon and the given shadow is called the hypothenuse of the shadow: from the square of the hypothenuse subtract the square of the Gnomon; the square-root of the remainder will be equal to the shadow; and the length of the Gnomon is to be known (from the shadow) by the inverse calculation.
english translation
zaGkucchAyAkRtiyuter mUlam karNo +asya vargataH । projjhya zaGkukRtim mUlam chAyA zaGkur viparyayAt ॥
hk transliteration by Sanscriptत्रिम्शत्कृत्यो युगे भानाम् चक्रम् प्राक् परिलम्बते । तद्गुणाद् भूदिनैर् भक्ताद् द्युगणाद् यद् अवाप्यते ॥
The circle of Asterisms librates 600 times in a great Yuga (that is to say, all the Asterisms, at first, move westward 27°. Then returning from that limit they reach their former places. Then from those places they move eastward the same number of degrees; and returning thence come again to their own places. Thus they complete one libration or revolution, as it is called. In this way the number of revolutions in a Yuga is 600 which answers to 600,000 in a Kalpa). Multiplying the Ahargaṇa (or the number of elapsed days) by the said revolutions and dividing by the number of terrestrial days in a Kalpa; the quotient is the elapsed revolutions, signs, degrees, &c.
english translation
trimzatkRtyo yuge bhAnAm cakram prAk parilambate । tadguNAd bhUdinair bhaktAd dyugaNAd yad avApyate ॥
hk transliteration by Sanscriptतद्दोस् त्रिघ्ना दशाप्ताम्शा विज्ञेया अयनाभिधाः ॥ ३-१०ख तत्सम्स्कृताद् ग्रहात् क्रान्तिच्छायाचरदलादिकम् ॥
(Rejecting the revolutions), find the Bhuja of the rest (i. e. signs, degrees &c. as mentioned in S'loka 30th of the 2nd Chapter). The Bhuja (just found) multiplied by 3 and divided by 10[1] gives the degrees &c. called the Ayana (this is the same with the amount[2] of the precession of the equinoxes). or a b × h 12 R = the Equinoctial shadow 12 {\displaystyle ab\times {\frac {h}{12R}}={\frac {\text{the Equinoctial shadow}}{12}}}; ∴ a b × h R {\displaystyle ab\times {\frac {h}{R}}} or the reduced Śankutala = the Equinoctial shadow; ∴ The reduced sine of amplitude = the Equinoctial shadow ± the reduced Bhuja; this explains the 7th Śloka. B. D. 1. 27° : 90°. B. D. 2. This is the distance of the Stellar Aries from the vernal equinox. B. D. Add or subtract the amount of the precession of the equinoxes (according as the asterisms are moving eastward or westward at the given time) to or from the place of a planet: from the result (which is equivalent to the longitude of the planet) find the declination, the shadow of the Gnomon, the the ascensional difference &c. This motion of the asterisms (or the precession of the equinoxes) will be verified by the actual observation of the Sun when he is at the equinoctial or the solstitial points.
english translation
taddos trighnA dazAptAmzA vijJeyA ayanAbhidhAH ॥ 3-10kha tatsamskRtAd grahAt krAnticchAyAcaradalAdikam ॥
hk transliteration by Sanscript