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

ANGLE BETWEEN ECLIPTIC AND MERIDIAN 137 graphical method for constructing the Sun's altitude and azimuth from the hour angle when the Sun's declination is zero but such a graphical method is generally complex as compared with the elegant Indian method. An astronomer who constructs and uses an armillary sphere to arrive at his equations in spherical astro- nomy and who has not a well-developed spherical astronomy at his command must have to draw perpendiculars from the positions of the heavenly body, not only on the meridian plane, the hori- zon or on the prime vertical, as the occasion arises, but also on the line of intersection of the diurnal circle with the horizon. Hence Braunmühl's statement that the Indian methods of spheri- cal astronomy have their origin in the 'Analemma's, in spite of his admitting that Indians were first to utilise its methods, is rather far-fetched and tends to take away the honour from the great Indian astronomers, who devised the beautiful methods. The 'Analemma' as it now exists is a Latin translation from an Arabic version of the original Greek¹. We may reasonably doubt that the Arabic version was greatly influenced by the ancient Indian system. We now pass on to the consideration of other allied or similar problems in the two systems of astronomy. Problem V— To find the Angle between the Ecliptic and the Meridian Indian Method² Let ♈SA be thee cliptic, ♈CE the equator, E the east-point of the horizon (Fig 10). Cut off SH=90° and draw the great circle HEAP' cutting the meri- dian P'SCH at the points P' and H. The aim is to find AP' but it is enough to find EA since AP' is the complement of EA'. Both Āryabhaṭa and Brahmagupta were unable to find EA correctly. Let P be the celestial pole and let PAE' be

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1. On the influence of the ancient Indians on Arab mathematics and astronomy; see Alberuni's India, translated by Dr. E. Sachau, Vol. II, p. 304.
2. Āryabhaṭa, Gola, 45; BrSpSi, IV. 17; Sūrya-siddhānta, IV. 25; Bhāskara's Golādhyāya, VIII, 21-74, first example in his own commentary.