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

IV. 43 IV. THREE PROBLEMS 115 The sine of amplitude to be used in the formula can be got by measuring the arc of amplitude, or the distance of the point, from the east-west line. Example 15. Sine declination is 42′ 15″. Sine amplitude is 84′ 30″. Find the latitude. From the formula, sin. colat = 120′ × 42′ 15″ ÷ 84′ 30″ = 60′. Colatitude arc of this, i.e. 30°, latitude = 90° − 30° = 60°. [इष्टकालच्छाया] तत्कालचरविनाडीद्विदशांशं द्विष्टमजतुलाद्येषु । [षड्घ्नी] भ्यो नाडीभ्यो जह्यात् संयोजयेच्चाऽपि ॥ ४१ ॥ तज्ज्या स्थितज्यया संयुता विसंयोजिताऽ [जतु] लाद्येषु । अविशोधने (च) जीवा षड्घ्नीनामे [व] कर्तव्या ॥ ४२ ॥ एवं कृत्वा हन्यात् द्युव्यासेनाऽवलम्बकघ्नेन । छिंद्यात् ‘खखाऽष्टवस्वश्विभिः’ फलं शङ्कुलिप्ताख्यम् ॥ ४३ ॥ Shadow at desired time 41. To find the gnomonic shadow caused by the Sun at any time: Take the cara in vināḍis and divide by 20. Degrees of half-cara are obtained. Place the degrees in two places. Convert the time from sunrise in nāḍis into degrees by multiplying by 6. From these degrees, deduct or add the half-cara degrees according as the sun is in the six signs beginning with Meṣa or in the six signs beginning with Tula, respectively. 42. Find the sine of the resulting degrees, and add or subtract this from the sine of the half-cara kept apart in the second place, according as the Sun is in the 6 signs Meṣa etc., or in the six signs Tulā etc. (The result is a sine. If the half-cara degrees cannot be deducted from the time converted into degrees, then simply find the sine of the degrees of sine, and take it for further work.) 43. Multiply this sine by the sine of colatitude and the day-diameter and divide by 28,800. The result is sine altitude of the Sun. 41-44. Quoted by Utpala on BS 2, p.61. 41b. A.सदशांशां दिष्टमज c. A.षघ्नाभ्यो 42a. A.तज्या स्थिज्यया b. A.योजिताद्येषु; C.D. योजिताजतुलाद्येषु c. A.°नेन झीवा; C-D. U.°नेन जीवा d. A.षन्नानामेषकत्र्तव्या (A2. षड्घ्नी) 43a. A.कृत्वा हन्या b. A.द्युव्योमेनाव; U. लम्बघ्नेन A. Haplographical omission of 43 c-d, 44 and 45a-b: लम्बकघ्नेन [... लम्बकघ्नेन] छिंद्यात् Hence they are added here from Utpala's quotaton thereof. 10