ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

ANGLE MADE BY THE VERTICAL 141 SQ = SS' × (R cos S'SQ / R) = (P × R sin ZS / R) × (R cos S'SQ / R) ¹= (P / R) √((R sin ZS)² - (R sin ZN')²) ²= (P / R²) × R sin N'S × R cos ZN', where N' is the nonagesimal. Thus R cos S'SQ is seen to be = (R sin N'S × R cos ZN') / (R sin ZS) The Indian method is fully described by Bhāskara in his 'Golādhyāya. VIII, 12-25. The truth of the Indian rule for R cos S'SQ is easily seen from the spherical triangle ΠZS, where Π is the pole of the ecliptic. Greek Method : ³Ptolemy takes SK and SL=90° each, along the vertical circle ZSEK and the ecliptic N'SA. The great circle through K and L cuts the horizon at R which is the pole of the vertical circle. He takes SKL for the triangle and EAR for the trans- versal, then (sin SE / sin EK) × (sin KR / sin LR) × (sin LA / sin AS) = 1 or sin LR = (cos ZS × cos AS) / (sin ZS × sin AS) or cos S'SQ = cot ZS × cot AS = tan SE × cot AS. The Indian and the Greek rules are altogether different both in form and method. There can, therefore, be no question of any connection between them. Problem VIII :— To convert the Celestial Longitude of a Heavenly Body into its Polar Longitude If σ be the position of a (Fig.13), γK and σK are the celestial longitude and the celestial latitude, respectively ; γM and σM are the polar longitude and polar latitude ; γN and σV are the right ascension and declination of the star. Indian Method : All Indian astronomers attempt at finding MK which, sub-

1. Āryabhaṭa, Gola, 34; Pañcasiddhāntikā, IX, 22 BrSpSi, XI, 23.
2. BrSpSi, V, 4-5; Sūryasiddhānta, V, 7-8 Bhāskara, Grahagaṇita, XII, 4.
3. Manitius, ibid, p. 119.