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

230 PAÑCASIDDHĀNTIKĀ X.4 ∴ E"E = S"S × EU/SE = EU × (S'S - S' S")/SE = EU × (S'S - E'E)/SE. In order to get the angular diameter of the Shadow, we require the radius of the Shadow, UU', = EE' - EE" = EE' - {EU (SS' - EE')/SE} = 18 - Moon's true dist. × (Sun's radius - 18) ÷ Sun's true dist. = 18 - Moon's true dist. × {18 × 5,14,787 ÷ (2 × 18 × 3438) - 18} ÷ Sun's true dist. (Here, 18 is the number obtained by reducing the earth's radius by 43, and given by the author in giving the parallax, see IX.23.) 18 × 5,14,787 ÷ (2 × 18 × 3438) is the Sun's radius, since, of two orbs, the parallax as viewed from one is the angular semi-diameter as viewed from the other. Therefore: Sun's minutes of parallax: Sun's angular semi-diameter in minutes :: 18: Sun's reduced radius. But the Sun's minutes of parallax = 18 × 3438 ÷ the Sun's true distance, and the Sun's semi- diameter in minutes = 5,14,787 ÷ (2 ×the Sun's true distance) = 18 - Moon's true distance × 18 × 284.4 ÷ (90 × Sun's true dist.) Since, sine angular diameter of the Shadow is got by multiplying the radius by 2, and the max. tabular sine and dividing by the Moon's true distance, sine angular diameter of Shadow = {36 - Moon's true dist. × 36 ÷ (90 × Sun's true dist. ÷ 284.4)} × 120 ÷ Moon's true distance, almost the same as the author has given, but with 284.4 instead of 286. If the number had been 17.9 instead of 18 taken as a whole number for convenience, then we shall get 286 itself, as given by the author. We have already shown that the formula can be simplified. The author must have given it in the involved form for indicating the geometrical construction by way of proof. When the numbers occurring are seen to be correct in the way shown by us, it is quite improper for TS to read ṣaḍaṣṭadasra (278) as ṣaḍaśvadasra (276) and to agree with this, making the Sun's reduced diameter as 146, in their proof, instead of the correct 149.73, got by dividing 5,14,787 by 3438. [विमर्दकालः] चन्द्रतमोव्यासयु(तिं) द्वाभ्यां हृत्वा ततो वर्गात् ॥ २ b ॥ विक्षेपवर्गहीनादासन्नपदे 'वियद्विद्विचन्द्र'घ्ने | सूर्येन्दुभुक्तिविवरो(द्धृ)ते स्थिते(र्ना)डिका लब्धाः || ३ || प्रग्रहणे(न्दोः) कृत्वा विक्षेप [म] तोजनया स्थि(ति) र्भवति । एवं भूयो भूयः स्थित्य(वि) शेषः कृतो यावत् ॥ ४ ॥ Duration of the Eclipse 2b-3. Add the angular diameters of the Moon and the Shadow, divide by two, and square it. Subtract the square of the Moon's latitude from this, and find