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

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118 PAÑCASIDDHĀNTIKĀ Rule (ii) is derived from the Great gnomon thus: The radius itself being the Great hypotenuse, and the Great gnomon and the Great shadow (this is 120 cos altitude or 120 sin zenith distance) are the sides of the right angled triangle, we have: Great shadow = √(120² – Great gnomon²) Then the shadow of the 12 digit gnomon is found by the proportion: Great gnomon: Great shadow :: 12 digit gnomon : shadow, and we get the rule (ii), shadow = 12 × √14,400 – Great gnomon² ÷ Great gnomon. In this connection, it may be noted that later authors like Bhāskarācārya II give different terms to different sections of the work. For instance they call sin (degrees of taken time ∓ degrees of half- cara) as Sūtram. Sūtram ± half-cara is called by them Iṣṭāntyā. They call Iṣṭāntyā × day-diameter ÷ 240 as Iṣṭahṛti. Then from Iṣṭahṛti the Śaṅkuliptā is obtained by the proportion: 120: sin colat :: Iṣṭahṛti : Śaṅkuliptā, by the similarity of the akṣākṣetras. [छायातः इष्टकालनाड्यः] [छाया द्वादशकृत्योर्योगान्मूलेन लम्बकघ्नेन ।] 'खखवस्व(श्वि)मुनी(न्दून्') (वि) भज्य लब्धा प्रथमजीवा ॥ ४५ ॥ त(द्युक्रान्ति)ज्याघ्नी विषुवज्ज्या ल(म्ब)कोद्धृता स्थाप्या | प्रथमज्या विश्ले(ष्या) (मे)षाद्ये (ऽन्यत्र) संयु(क्ता) ॥ ४६ ॥ तत्स्थि(त) जीवे गुणिते 'खजिनैर्धु (व्या)सभाजिते चापे । युतवियुतेऽ(ज)तुलादिषु ष(ड्ढृ) तो नाडिका लब्धा ॥ ४७ ॥ Time after sunrise 45. Square the shadow measured in digits, add 144, and get its square root. Multiply this by the sine of co-latitude and by this product divide 1,72,800. The quotient is called the 'First sine'. 46. Now, multiply the sine of declination of the Sun by the sine of latitude and divide by the sine of co-latitude. (Let us call this by its actual name, the Earth-sine.) Place this Earth-sine in two places. In one place, subtract this from or add this to the 'first sine', according as the Sun is in the northern or south- ern hemisphere. 47. This result, and the Earth-sine, are each to be multiplied by 240 and divided by the day-diameter. These are two sines. Find the arcs of each of these. When the Sun is in the northern hemisphere add the two arcs. Other- wise subtract one from the other. Divide the result by 6. The result is the time in nāḍīs after sunrise. 45c. A. वखश्व. A. मुनीन्द्रात्; C. मुनीन्दोः; D. मुनींदु 47a. A. तस्थिति 46a. A. तद्युज्याक्तांत्रीज्याघ्नी b. A. खजिनेधुद्यासभाजिते c. A. विश्लेषा c. A. वियुते च d. A. सेषाद्येनात्र संयुत d. A. षड्ढृतो; C.D. षड्ढृता. A. लब्धा