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

132 GREEK AND INDIAN METHODS from the Greek method in this case also. As the triangle KLS is difficult to show in the diagram, it is shown in its projection on the meridian plane in Burgess's translation of the "Sūrya- siddhānta,"(page 232)and also in Wilkinson and Bāpūdeva Śāstrī's translation of the 'Siddhānta Śiromaṇi,' p. 175. This has led Braunmühl to assume that the Indian method of arriving at the equation of ascensional difference and some other equations of spherical astronomy has its origin in the Analemma of Ptolemy. A careful study, however, does not justify the identification of Indian methods with the graphic method of the Analemma, which is deduced from the projections of the position of a heav- enly body on the meridian prime vertical and the horizon. It is being presently shown that what was done out of difficulty in drawing the figures properly has been taken by Braunmühl as a Greek connection. Problem III¹ :— To find the “Time-altitude” Equation If from any point S on the diurnal circle a perpendicular be drawn to the Udyāsta-Sūtra spoken of before, this perpendi- cular is called the cheda or ‘iṣṭahṛti.’ The perpendicular from S on the horizon is called ‘Śaṅku’² the sine of the altitude. The line joining the foot of the ‘Śaṅku’ and that of the perpendicular on the ‘Udayāsta-Sūtra’ goes by the name of ‘Śaṅkutala’ and this Śaṅkutala lies to the south of the ‘Udayāsta-Sūtra’ during the day. In this figure (Fig 8) if AA' be the ‘Udayāsta-Sūtra’ or the intersection of the diurnal circle and the horizon, and S a point on the diurnal circle denoting a position of the Sun, SK, SL perpendiculars on AA' and the horizon respectively; SL is called the ‘Śaṅku,’ SK the ‘cheda’ and LK, the ‘Śaṅkutala’. In this triangle KSL, the angle KSL was recognised to be the latitude of the station. Thus the triangle SKL is not taken in its projection on the meridian plane. The side SK is taken 'as formed of two parts.

1. Āryabhaṭa could not arrive at the true equation. Cf. Gola 28. The correct rules occur in Pañcasiddhāntikā, IV, 42, 44; Brahmasphuṭasiddhānta, III, 36-38, 26-40; Sūryasiddhānta, III, 34-35.
2. Bhāskara says : ग्रहस्थानाल्लम्बः शंकुः । तस्यतलमुदयास्तसूत्राद्दक्षिणतो भवति ॥ “Gola, VIII-39-41, Āryabhaṭa uses the term शङ्क्वग्रम्” Gola, 29.