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

IV. 51 IV. THREE PROBLEMS 125 (i) ‘First sine’ = 1,72,800 ÷ (110′ 52″ × √(13 11/60 + 12²)) = 87′ 26″. (ii) Earth-sine = 45′ 56″ × 31′ 4″ ÷ 110′ 52″ = 12′ 52″ (iii) Sine I = (87′ 26″ + 12′ 52″) × 240 ÷ 231′ 50″ = 103′ 55″, (since the Moon is in the southern hemisphere). (iv) Sine II = 12′ 52″ × 240′ ÷ 231′ 50″ = 13′ 23″. (v) Arc sine I = 60°. Arc sin II = 6° 24′. The time of shadow after moonrise = (60° − 6° 24′)/6 = 53° 36′/6 = nā. 8-56, (Moon being in the southern hemisphere). This time pertains to the lunar sāvana day, and converted into ordinary (i.e. solar) sāvana, the time after moonrise = 8-56 × 62 ÷ 60 = nā. 9-14. The time from sunrise = nā. 27-18 + nā. 9-14 = nā. 36-32. The time from sunset = nā. 36-32 − nā. 32-24 = nā. 4-8. The result is correct, because in Example 20, we took this same time and got the shadow aṅg. 13-11, which we have used in this example. चरनाडीक्रमविधिना द्युव्यासा (द्य) थामति [च] विक्षे (पात्) अस्तमयोऽप्यध्वविधिः शेषाणां युक्तितश्चिन्त्यम् ॥ ५१ ॥ 51. For the others, (i.e. for the luminaries other than the Sun and the Moon, viz. the star-planets) also, determining the corresponding operations, and using their respective latitude and day-diameter, and getting the cara-nādīs etc. (in terms of their respective sāvana days), (not only the work of finding the shadow for the given time and time for the given shadow as above, but also) their daily risings and settings and reduction to different localities should be thought out and done. The following is the idea. The computation of the rising and setting of the Sun has been given already in this chapter. The Moon’s rising and setting will be given below, in chapter V. Understanding the nature of the operation from these and taking the star-planets corrected to the different longi- tudes and computing their respective sāvana days and cara-vinādīs, using their latitudes to get their true declinations and day-diameters, everything done in connection with the Sun and the Moon should be done in connection with the star-planets also. It is from this that we understand that in the work of computing the Moon’s shadow we have to use the true declination, day-diameter, and time measured in the Moon’s sāvana day, as we have done already. Therefore this verse may also be taken as an extension of the previous verse. Here TS and NP have done a lot of emendations that are unnecessary for, without those emen- dations we get the same idea as they have given, at such pains. 51a. D. चरनाड्य [प] क्रमा [दि] विधिना A.C.D. om च. A.D. विक्षेपम्; C. विक्षेयम् b. A. द्युव्यासाम्यभाति; C. द्युव्यासाप्तक्रमादि; D. द्युव्यासाप्तक्रम c. C. मये पूर्व विधिः; D. मयेऽप्यूर्ध्वविधिः