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.