पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

IV. 25 IV. THREE PROBLEMS 97 NPCSPQ is the stellar sphere, with centre E, CQ is the celestial equator, SC is the declination of the Sun S, SEC = degrees of declination, SB is the diurnal circle, with the straight line SB as its dia- meter, and SA as its radius. Suppose the sphere is cut into equal halves, with the cross section NP C SP Q E exposed to view and the axis NP E SP forming a diameter. SE is the radius, and SD (= AE) = sin declination. Then, SA = √(SE² − SD²). But SA = half day-diameter. ∴ day-diameter = 2 SA = 2 √(radius² − sin² declination). अजवृषमिथुनापक्रमजीवाः (षड्घ्नाः स्यु) 'वेद-मुनि-वसवः' | त्र्यष्ट'तिथि' षट्का(ष्टक)विकलाऽभ्यधिका [:] परिज्ञेयाः || २४ || 24. The sines of declinations of the points of the ecliptic ending Aries, Taurus and Gemini are 24' 24", 42' 15", and 48' 48". We shall show these to be correct by computing them. The sine declination of the end of Aries, i.e. rā. 1-0-0 has been derived in example 7(b) to be 24' 24". The sine of declination of the end of Gemini, i.e. rāśi 3-0-0, has been shown to be 48' 48", (the maximum) in the example above. So we shall derive here only sine declination of the end of Taurus, i.e. rāśi 2-0-0. Sine rāśi. 2-0-0 = 103' 55" (from tables). The sine of its declination by IV.16 is, 103' 55" × (60 + 1)/150 = 41' 34" + 41" 34''' = 42' 15"34'''. Here, though 34''' is greater than half a second, the author has omitted it and given 42' 15", to the nearest quarter minute. [पञ्चत्रिंशत्] त्र्यष्टकस्वरूपधृ[तिसंयु]ता क्रमाद् द्विशति | पञ्चाष्टक'तिथि'विकलाधिकौ वृषा(न्यौ) दिनव्यासः || २५ || 25. The respective day-diameters are, in the minutes parts: 200 + 35, 200 + 24, and 200 + 19, with 40" and 15" added to the second and third, (i.e. the day- diameters are, 235', 204' 40" and 219' 15"). Of these, the day-diameter of the end of Aries has been worked out in Example 7 (b). We shall derive the other two. The day-diameter for the Sun at the end of Taurus = 2 √(120² − sin² declination of the end of Taurus), = 2 √(120² − 42' 15"²) = 224' 38". 24b. A.C.D. षड्घ्नास्तु 25a. A. om पञ्चत्रिंशत् c. A. षट्काष्ट्; D. षट्काष्ट[क]विकला b. A. ॰धृता क्रमा. C.D. द्विशती d. A. ॰धिका प d. A. ॰धिको. A. वृषांत्यौ