Surya Siddhanta
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तच्चापम् भादिकम् क्षेत्रम् पदैस् तत्र भवो रविः। इष्टे +अह्नि मध्ये प्राक्पश्चाद् धृते बाहुत्रयान्तरे ॥
On any day place a vertical gnomon on an horizontal plane; mark the end of the shadow at three different times on the plane, and describe a circle passing through these points. Then the end of the shadow of that gnomon will revolve in the circumference of this circle through that day.[2] [2. This Rule is refuted by Bháskaráchárya in his Goladhyáya, and he is right, because the end of the gnomonical shadow revolves in an hyperbola in the places between the arctic and antarctic circles. B. D.]
english translation
taccApam bhAdikam kSetram padais tatra bhavo raviH। iSTe +ahni madhye prAkpazcAd dhRte bAhutrayAntare ॥
hk transliteration by Sanscriptमत्स्यद्वयान्तरयुतेस् त्रिस्पृक्सूत्रेण भाभ्रमः। त्रिभद्युकर्णार्धगुणाः स्वाहोरात्रार्धभाजिताः॥
english translation
(In order to find the right ascensions of the ends of the three first signs of the ecliptic i. e. Aries, Taurus and Gemini, find the declinations of the said ends) then multiply the sines of one, two, and three sines by the cosine of the greatest declination of the Sun separately, and divide the products by the cosines of the declinations (above found), respectively: The quotients will be the sines of the arcs; find the arcs in minutes. (These arcs will be the right ascensions of the ends of the three first signs of the ecliptic).
hindi translation
matsyadvayAntarayutes trispRksUtreNa bhAbhramaH। tribhadyukarNArdhaguNAH svAhorAtrArdhabhAjitAH॥
hk transliteration by Sanscriptक्रमाद् एकद्वित्रिभज्यास् तच्चापानि पृथक् पृथक् । स्वाधो +अधः परिशोध्याथ मेषाल् लङ्कोदयासवः॥
The number of minutes contained in the first right ascension, (above found), is the number of Práṇas which Aries takes in its rising at Lanká (or the equator); then take the first right ascension from the second and the second from the third; the remainders in minutes will denote the numbers of Práṇas in which Taurus and Gemini rise at the equator. (The numbers of the Práṇas, thus found, contained in the rising periods of Aries, Taurus and Gemini at the equator are) 1670, 1795 and 1935 (respectively). (In order to find the rising periods of the first three signs of the ecliptic at a given place of N. L., find at first the ascensional differences of the ends of the said signs at that place and subtract the first ascensional difference from the second and the second from the third. The first ascensional difference and these remainders are severally called the Charakhanḍas of the said signs for the given place). Subtract the Charakhanḍas (of the first three signs) for the given place from their rising periods at the equator: the remainders will be the rising periods in Práṇas of the said signs at the given place.
english translation
kramAd ekadvitribhajyAs taccApAni pRthak pRthak । svAdho +adhaH parizodhyAtha meSAl laGkodayAsavaH॥
hk transliteration by Sanscriptखागाष्टयो +अर्थगो +अगैकाः शरत्र्यङ्कहिमाम्शवः । स्वदेशचरखण्डोना भवन्तीष्टोदयासवः॥
The rising periods of the first three signs of the ecliptic at the Equator successively increased by their a contrary order the rising periods of the following three signs (i. e. Cancer, Leo and Vergo). The rising periods of the first 6 signs, thus found, answer in an inverse order to those of the latter six Libra, &c. for the given place.
english translation
khAgASTayo +arthago +agaikAH zaratryaGkahimAmzavaH । svadezacarakhaNDonA bhavantISTodayAsavaH॥
hk transliteration by Sanscriptव्यस्ता व्यस्तैर् युताः स्वैः स्वैः कर्कटाद्यास् ततस् त्रयः। उत्क्रमेण षडेवैते भवन्तीष्टास् तुलादयः॥
From the Sun's longitude ascertained at the given time, find the Bhukta and Bhogya times in Práṇas, (in the following manner. Find the sign in which the Sun is and find the Bhukta degrees or the degrees which the Sun has passed and the Bhogya degrees or those which he has to pass). Multiply the numbers of the Bhukta and Bhogya degrees (separately) by the rising period of the said sign (at the given place) and divide the products by 30. (The first quotient is the Bhukta time in Práṇas in which the Sun has passed the Bhukta degrees, and the latter is the Bhogya time in Práṇas in which he has to pass the Bhogya degrees.)
english translation
vyastA vyastair yutAH svaiH svaiH karkaTAdyAs tatas trayaH। utkrameNa SaDevaite bhavantISTAs tulAdayaH॥
hk transliteration by Sanscript