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

220 PAÑCASIDDHĀNTIKĀ IX.21 The following is the explanation of the rule: See fig. 2. There, n is the nonagesimal, i.e. o.e.p. minus three rāśis. Z is the zenith. n.z is the zenith distance of n, and sine nz, called the 'Sun's dṛk-kṣepa', is wanted here, to get the Moon's parallax in latitude. This Siddhānta takes the spherical triangle Z n M, right angled at n, to be approximately equal to a plane right-angled triangle, with the sines of the arcs as straight lines and finds the dṛk-kṣepa by, (sine zn)² = (sine MZ)² – (sine nM)² = sin² z.d. of m.e.p. – sin² (m.e.p. ~n). (The correct method has already been expounded by us in Chap. VI, when dealing with the solar eclipse according to the Pauliśa.) Sin (z.d. of M.e.p.) has been got already. The other quantity required, viz. sin (M.e.p. ~ n), is got by the well-known formulae relating to spherical right angled triangles, (already given by us), sin (M.e.p. ~ n) = sin (z.d. of M.e.p.) ×sin MZn ÷ 120'. But, MZn = O'ZW = OZE, which is the amplitude of the o.e.p. Its sine, Udayā, given here = the declination of the o.e.p. × 120' ÷ sine colatitude = sin longitude of o.e.p. × 48' 48" ÷ sin colatitude, as given in chap. IV. [शङ्कु:] दृ[क्]क्षेपकृतिं जह्यात् त्रिज्यावर्गात् ततोऽस्य यन्मूलम् । लग्नाऽर्कविवरमौर्व्या गुणितं त्रिज्योद्धृतं शङ्कुः ॥ २१ ॥ Gnomon 21. Subtract from 14,400, the square of sin z.d. of n, (kept unused in the other place in the previous work), and find its square-root. Multiply this by the sine of the distance between the Sun and the o.e.p., and divide by 120'. The result, which is the sine of the Sun's altitude, is called Śaṅku, i.e. the Sun's Śaṅku. ∴ Śaṅku = √ 14,400 – sin² (z.d. of n) × sin (o.e.p. ~ sun) ÷ 120'. [sin² (z.d. of n) has already been got, and kept apart] Example 14. To complete example 10. From Ex. 13, by (i), o.e.p. = rā. 5-27-56, and by (iii), sin² (z.d. of n) = 792.25, from Ex. 10, Sun = rā. 2-0-0. Śaṅku = √ 14,400 – 792.25 × sin (rā. 5-27-26 – rā. 2-0-0) ÷ 120' = 116' 39" × sin (rā. 3-27-26) ÷ 120' = 116' 39" × 106' 7" ÷ 120' = 103' 10". The rule is derived as follows: From fig. 2 it can be seen that the Sun's altitude is 90° – Zs. ∴ Śaṅṅku = Sine Sun's altitude = Cos Zs = Cos ZW × Cos ns ÷ 120' (by the well-known formula, already given) = √ radius² – sin² Zn × sin Os ÷ 120', (∵ ns is os – 90°). sin Zn is sine z.d. of n already found, and its square has already been got and kept apart for use here. ∴ Śaṅku = √ 14,400 – sin² z.d. of n × sin (o.e. P ~ sun) ÷ 120' as given by the author. 21a. A. दृक्षेप; B. दक्षेप. B. कृति A. जह्या c. B.विवरे b. A. वर्गात्रितोस्प. A. °वन्मूलं; B. °पन्मूलं d. B. गुणित. A. त्रिज्योदृवृतं; B. त्रिज्योधृत