Surya Siddhanta
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विक्षेपाग्राल् लिखेद् वृत्तम् ग्राहकार्धेन तेन यत् । ग्राह्यवृत्तम् समाक्रान्तम् तद्ग्रस्तम् तमसा भवेत् ॥
From the extremity of the latitude describe a circle with a radius equal to half the measure of the eclipsing body : whatever of the disk of the eclipsed body is enclosed within that circle, so much is swallowed up by the darkness (tamas). [The phraseology of the text in this passage is somewhat intricate and obscure; it is fully explained by the commentary, as, indeed, its meaning is also deducible with sufficient clearness from the conditions of the problem sought to be solved. It is required to represent the deflection of the ecliptic from an east and west line at the moment of greatest obscuration, and to fix the position of the centre of the eclipsing body at that moment. The deflection is this time to be determined by a secondary to the ecliptic, drawn from near the north or south point of the. figure. The first question is, from which of these two points shall the deflection be laid off, and the line to the centre drawn. Now since, according to verse 10, the latitude itself is to be measured upon the line of deflection, the latter must be drawn southward or northward according to the direction in which the latituda is to be laid off. And this is the meaning of the last part of verse 8; " in accordance," namely, with the direction in which, according to the previous part of the verse, the latitude is to be drawn. But again, in which direction from the north or south point, as thus determined, shall the deflection be measured? This must, of course, be determined by the direction of the deflection itself: if south, it must obviously be measured east from the north point and west from the south point; if north, the contrary. The rules of the text are in accordance with this, although the determining circumstance is made to be the agreement or non-agreement, in respect to direction, of the deflection with the moon's latitude—the latter being this time reckoned in its own proper direction, and not, in a lunar eclipse, reversed. Thus, in the case for which the figure is drawn, as the moon's latitude is south, and must be laid off northward from M, the deflection, t)"w", is measured from the north point; as deflection and latitude are both south, it is measured east from N. In an eclipse of the sun, on the other hand, the moon's latitude would, if north, be laid off northward, as in the figure, and hence also, the deflection would be measured from the north point : but it would be measured eastward, if its own direction were south, or disagreed with that of the latitude. The line of deflection, which is Mv" in the figure, being drawn, and having the direction of a perpendicular to the ecliptic at the momemt of opposition, the moon's latitude for that moment, Ml", is laid off directly upon it. The point I" is, accordingly, the position of the centre of the shadow at the middle of the eclipse, and if from that centre, with a radius equal to the semi-diameter of the eclipsing body, a circle be drawn, it will include so much of the disk of the eclipsed body as is covered when the obscuration is greatest. In the figure thf> eclipse is shown as total, the Hindu calculations making it so, although, in fact, it is only a partial eclipse.]
english translation
vikSepAgrAl likhed vRttam grAhakArdhena tena yat । grAhyavRttam samAkrAntam tadgrastam tamasA bhavet ॥
hk transliteration by Sanscriptछेद्यकम् लिखता भूमौ फलके वा विपश्चिता । विपर्ययो दिशाम् कार्यः पूर्वापरकपालयोः॥
By the wise man who draws the projection (chedyaka), upon the ground or upon a board, a reversal of directions is to be made in the eastern and western hemispheres. [This verse is inserted here in order to remove the objection that, in the eastern hemisphere, indeed, all takes place as stated, but, if the eclipse oc- curs west of the meridian, the stated directions require to be all of them reversed. In order to understand this objection, we must take notice of the origin and literal meaning of the Sanskrit words which designate the cardinal directions. The face of the observer is supposed always to be east- ward: then " east " is prdfic, " forward, toward the front "; " west " is pagcdt, " backward, toward the rear "; " south " is dakshina, " on the right "; " north " is uttara, " upward " (i.e., probably, toward the mountains, or up the course of the rivers in north-western India). These words apply, then, in etymological strictness, only when one is looking eastward and so, in the present case, only when the eclipse is taking place in the eastern hemisphere, and the projector is watching it from the west side of his projection, with the latter before him: if, on the other hand, he re- moves to B, turning his face westward, and comparing the phenomena as they occur in the western hemisphere with his delineation of them, then " forward " (prdftc) is no longer east, but west; " right " (dakshina) is no longer south, but north, etc. It is unnecessary to point out that this objection is one of the most frivolous and hair-splitting character, and its removal by the text a waste of trouble: the terms in question have fully acquired in the language an absoluto meaning, as indicating directions in space, without regard to the position of the observer.]
english translation
chedyakam likhatA bhUmau phalake vA vipazcitA । viparyayo dizAm kAryaH pUrvAparakapAlayoH॥
hk transliteration by Sanscriptस्वच्छत्वाद् द्वादशाम्शो +अपि ग्रस्तश् चन्द्रस्य दृश्यते । लिप्तात्रयम् अपि ग्रस्तम् तीक्ष्णत्वान् न विवस्वतः॥
Owing to her clearness, even the twelfth part of the moon, when eclipsed (gmsta), is observable; but, owing to his piercing brilliancy, even three minutes of the sun, when eclipsed, are not observable. [The commentator regards the negative which is expressed in the latter half of this verse as also implied in the former, the meaning being that an obscuration of the moon's disk extending over only the twelfth part of it does not make itself apparent. We have preferred the interpre- tation given above, as being better accordant both with the plain and simple construction of the text and with fact.]
english translation
svacchatvAd dvAdazAmzo +api grastaz candrasya dRzyate । liptAtrayam api grastam tIkSNatvAn na vivasvataH॥
hk transliteration by Sanscriptस्वसम्ज्ञितास् त्रयः कार्या विक्षेपाग्रेषु बिन्दवः। तत्र प्राङ्मध्ययोर् मध्ये तथा मौक्षिकमध्ययोः॥
At the extremities of the latitudes make three points of corresponding names; then, between that of the contact and that of the middle, and likewise between that of the separation and that of the middle.
english translation
svasamjJitAs trayaH kAryA vikSepAgreSu bindavaH। tatra prAGmadhyayor madhye tathA maukSikamadhyayoH॥
hk transliteration by Sanscriptलिखेन् मत्स्यौ तयोर् मध्यान् मुखपुच्छविनिःसृतम् । प्रसार्य सूत्रद्वितयम् तयोर् यत्र युतिर् भवेत्॥
Describe two fish-figures (matsya) : from the middle of these having drawn out two lines projecting through the mouth pnd tail, wherever their intersection takes place.
english translation
likhen matsyau tayor madhyAn mukhapucchaviniHsRtam । prasArya sUtradvitayam tayor yatra yutir bhavet॥
hk transliteration by Sanscript