Surya Siddhanta
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मध्यग्रहणतश् चोर्ध्वम् इष्टनाडीर् विशोधयेत्। स्थित्यर्धान् मौक्षिकाच् छेषम् प्राग्वच् च्छेषम् तु मौक्षिके॥
If it be required to know the Koṭi &c. at a given time after the middle of the eclipse, subtract the Ghatikas (between the given time and the end of the eclipse) from the second Sthityardha; from the remainder find the Koṭi &c. as mentioned before. The obscured part found from the second Sthityardha is the portion of the disc yet in obscurity.
english translation
madhyagrahaNataz cordhvam iSTanADIr vizodhayet। sthityardhAn maukSikAc cheSam prAgvac ccheSam tu maukSike॥
hk transliteration by Sanscriptग्राह्यग्राहकयोगार्धाच् छोध्याः स्वच्छन्नलिप्तिकाः। ताद्वर्गात् प्रोज्झ्य तत्कालविक्षेपस्य कृतिम् पदम्॥
Subtract the minutes contained in the given eclipsed part from half the sum of the diameter of that which is covered and that which is the coveror; from the square of the remainder subtract the square of the Moon's latitude at that time.
english translation
grAhyagrAhakayogArdhAc chodhyAH svacchannaliptikAH। tAdvargAt projjhya tatkAlavikSepasya kRtim padam॥
hk transliteration by Sanscriptकोटिलिप्ता रवेः स्पष्टस्थित्यर्धेनाहता हृताः। मध्येन लिप्तास् तन्नाड्यः स्थितिवद् ग्रासनाडिकाः॥
The square-root of the remainder is the Koṭi in minutes (in the lunar eclipse). But in the solar one the remainder (thus found) multiplied by the apparent Sthityardha and divided by the mean Sthityardha gives the Koṭi in minutes. From the Koṭi find the time in Ghatikas in the same way that you found the Sthityardha (from the square-root as mentioned in Śloka 13). At this time (before or after the middle of the eclipse,) the quantity of the eclipsed part is equal to the given one.
english translation
koTiliptA raveH spaSTasthityardhenAhatA hRtAH। madhyena liptAs tannADyaH sthitivad grAsanADikAH॥
hk transliteration by Sanscriptनतज्या +अक्षज्ययाभ्यस्ता त्रिज्याप्ता तस्य कार्मुकम्। वलनाम्शा सौम्ययाम्याः पूर्वापरकपालयोः॥
Find the zenith distance[1] (in the prime vertical of the body which is to be eclipsed), multiply its sine by the sine of the latitude of the place, and divide the product by the radius. Find the arc whose sine is equal to the quotient; the degrees contained in this are called the degrees of the (Áksha or the latitudinal) valana: they are north or south according as the body is in the eastern or western hemisphere of the place. [1.The distance of the circle of position (passing through the body) from the zenith of the place is called the zenith distance in the prime vertical of the body. The rough amount of this can be easily found by the following simple proportion. As half the length of the day of the body : 90. :: the time from noon of the body at a given time : the zenith distance in the prime vertical at the given time. B. D.]
english translation
natajyA +akSajyayAbhyastA trijyAptA tasya kArmukam। valanAmzA saumyayAmyAH pUrvAparakapAlayoH॥
hk transliteration by Sanscriptराशित्रययुताद् ग्राह्यात् क्रान्त्यम्शैर् दिक्समैर् युताः। भेदे +अन्तराज् ज्या वलना सप्तत्यङ्गुलभाजिता॥
From the place of the (said) body increased by 3 signs find the declination, (which is called Áyana or solstitial valaná). Find the sum or difference of the degrees of this declination and those of the latitudinal valaná, when those valanas are of the same name or of contrary names: (the result is called sphuṭa or true valaná). The sine of the true valaná divided by 70 gives the valaná in digits.[2] [2. In the projection of eclipses, after drawing the disc of the body to be eclipsed, the north and south and the east and west lines, which lines will of course represent the circle of position passing through the body (supposed on the ecliptic) and the secondary to that circle at the given place, to find the direction of the line representing the ecliptic in the disc of the body on which the knowledge of the exact directions of the phases of the eclipses depends, it is necessary to know the angle formed by the said secondary and the ecliptic. This angle or that are of a great circle, 90° from the place of the body which is intercepted between the said secondary or the prime vertical and the ecliptic is called the valana or variation (of the ecliptic). And as it is very difficult to find this arc at once, it is divided into two parts of which the one is that portion of the great circle (90° from the place of the body) which is intercepted between the Prime vertical and the Equinoctial and the other is that portion of the same circle which is intercepted between the Equinoctial and the ecliptic; these two portions are called the Áksha valana and the Áyana-valana respectively. The Áksha valana is called the north or south according as the Equinoctial circle meets the great circle (90° from the place of the body) on the north or south of the prime vertical eastward of the body; and it is evident from this that on the northern latitudes when the body is in the eastern or western hemisphere the Áksha valana will be the north or south respectively. And the Áyana-valana is called the north or south according as the ecliptic meets the said great circle on the north or south of the Equinoctial to the east of the body, and hence it is evident that when the declination of the body's place increased by 8 signs is north or south the Áyana-valana will be the north or south respectively. From the sum of these valanas when they are of the same name or from the difference between them when of contrary names the arc which is intercepted between the prime vertical and the ecliptic is found and hence it will be north or south according as the ecliptic meets the said great circle on the north or south of the prime vertical eastward of the body and it is sometimes called the spashta or rectified valana. An image should appear at this position in the text. To use the entire page scan as a placeholder, edit this page and replace "{{missing image}}" with "{{raw image।English translation of the Surya Siddhanta and the Siddhanta Siromani by Sastri, 1861.djvu/56}}". Otherwise, if you are able to provide the image then please do so. For guidance, see Wikisource:Image guidelines and Help:Adding images. Let A {\displaystyle A} be the place of the body; B G C L {\displaystyle BGCL} the great circle 90° from it; B A G {\displaystyle BAG} the eoliptio; D E F {\displaystyle DEF} the Equinoctial; E {\displaystyle E} the Equinoctial point; G H L {\displaystyle GHL} the prime vertical; H {\displaystyle H} the intersecting point of the prime vertical and the Equinoctial, and hence the east or west point of the Horizon and therefore G H {\displaystyle GH} equivalent to the zenith distance in the prime vertical. Then the arc G D {\displaystyle GD} = the Áksha valana, D B {\displaystyle DB} = the Áyana-valana, and G B {\displaystyle GB} = the spashta or rectified valana. These arcs can be found as follows, Let L {\displaystyle L} = latitude of the place, n {\displaystyle n} = the zenith distance in the prime vertical, l {\displaystyle l} = the longitude of the body, e {\displaystyle e} = the obliquity of the eoliptio, d {\displaystyle d} = the declination of the body, x {\displaystyle x} = the Áksha valana, {\displaystyle y} = the Áyana-valana, and z {\displaystyle z} = the rectified valana. Then in the spherical triangle D H G {\displaystyle DHG} sin G D H : sin D H G = sin G H : sin G D {\displaystyle \sin GDH:\sin DHG=\sin GH:\sin GD}: here, sin G D H = sin B D E = cos d {\displaystyle \sin GDH=\sin BDE=\cos d}, sin D H G = sin L {\displaystyle \sin DHG=\sin L}; and sin G H = sin n {\displaystyle \sin GH=\sin n}, ∴ cos d : sin L = sin n : sin x {\displaystyle \therefore \cos d:\sin L=\sin n:\sin x}. ∴ sin x {\displaystyle \therefore \sin x} or the sine of the Áksha valana = sin L sin n cos d {\displaystyle {\frac {\sin L\sin n}{\cos d}}}in which the Radius is used for cos d {\displaystyle \cos d} in the text. This valana is called north or south according as the point D be north or south of the point G. And in the triangle D E B {\displaystyle DEB} sin B D E : sin B E D = sin B E : sin D B {\displaystyle \sin BDE:\sin BED=\sin BE:\sin DB}, or cos d : sin e = cos l : sin y {\displaystyle \cos d:\sin e=\cos l:\sin y} ∴ sin y {\displaystyle \therefore \sin y} or the sine of the Áyana valana = sin e × cos l cos d {\displaystyle {\frac {\sin e\times \cos l}{\cos d}}}in which the Radius is used for cos d {\displaystyle \cos d} in the text. This valana is called north or south; according as the point B be north or south of the point D. And the rectified valana G B = G D + D B {\displaystyle GB=GD+DB}, when the point D lies between the points G and B, but if the point D be beyond them, the rectified valana will be equal to the difference between the Aksha and Ayana valanas. This also is called north or south as the point B be north or south of the point G. To mark the sine of the spashta valana in the projection of the eclipse it is reduced to the circle whose radius is 49 digits in the text. i. e. R : s i n x {\displaystyle R:sinx} = 49: reduced sine of the valana: ∴ reduced sine of the valana = 49 sin x R = 49 sin x 3438 = sin x 70 {\displaystyle {\frac {49\sin x}{R}}={\frac {49\sin x}{3438}}={\frac {\sin x}{70}}} This reduced sine in digits is denominated the valaná in the text. B. D.]
english translation
rAzitrayayutAd grAhyAt krAntyamzair diksamair yutAH। bhede +antarAj jyA valanA saptatyaGgulabhAjitA॥
hk transliteration by Sanscript