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

100 PAÑCASIDDHĀNTIKĀ IV. 28 = 120' sin dec × sin lat ÷ {(Cos dec × sin (90° – lat)} = 120' sin dec × sin lat ÷ (day-radius × sin co-latitude) = 240' sin dec × sin lat ÷ (day-diameter × sin co-latitude). From this the arc dE is got. Ed₁ for south declination is got in the same way, from △ s₁E d₁. From dE or Ed₁, the cara-vināḍīs are got thus: For the whole circle of 360° or 21600 minutes of arc, there are 60 × 60 = 3600 vināḍīs. ∴ For the arc of half cara in minutes there are 3600 × arc of half-cara ÷ 21600 = arc of half cara/6 vināḍīs. The whole cara-vināḍīs are twice this, and equal to 2 × minutes of half-cara/6 = minutes of half-cara/3. As we have said, these are added to 30 nāḍikās to find the day-time, when the declination is north, i.e. when the Sun is in six signs from Aries. Those vināḍīs are subtracted when the Sun is in the south, i.e. in the six signs Libra etc. The part of the formula, sin declination × sin-latitude ÷ sin co-latitude, is called ‘Earth sine’, (kṣitijyā), in Hindu astronomical works, which is required to be multiplied by the radius and divided by the day-diameter to get sin half-cara. In certain works the half-cara itself is called cara. [चराद् अक्षानयनम्] चरखण्डः'(ख)पक्षां'शज्याघ्नमद्व्यर्ह्वसमुद्धरेत् 'खजिनै': । द्विः कृत्वा तद्वर्गात् क्रान्तिज्याकृतियुतान्मूलम् ॥ २७ ॥ तेन विभजेत् स्थितज्यां व्यासार्धगुणामवाप्तमक्षज्या । नवतेरक्षोनायाः क्रमशो ज्या लम्बको भवति ॥ २८ ॥ Latitude from Cara 27. Divide the vināḍis of cara by twenty and find the sine of the resulting degrees. Multiply the day-diameter by this, and divide by 240. Put the result in two places. In one place square it and add the square of the sine of declination and find its root. 28. Multiply the result kept in the other place by the radius, and divide by this root. The result is the sine of latitude. Its arc is the latitude. 90' minus latitude is the co-latitude, and its sine, sine co-latitude. The following is the work to be done: i. The vināḍis of cara ÷ 20 = degree of half-cara. Find its sine. ii. Sine half-cara × day-diameter ÷ 240 = sine x. (This is earth-sine or kṣitijyā). 27-28. Quoted by Utpala on BS, 2, p.60. 27b. A. °महस° c. A. व्यावृद्धिं कृत्वा; C. भूजीवां कृत्वा तत् d. A. मूलम् 28a. A. थितिज्यां; C.D. क्षितिज्यां. A. पक्षज्या c. A. नवतेरक्षोसोनाया