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

ANGLE MADE BY THE VERTICAL 18
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 ASN, where A 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.