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

CHAPTER VII
Greek and Hindu
Methods in Spherical Astronomy
Here we shall reproduce from Sengupta's paper a compa-
rative account of the Greek and ancient Indian methods in
Spherical Astronomy and to bring out the independence of the
Indian Astronomers on this subject. The views on this subject
would necessarily differ from those of many European scholars
such as Colebrooke and Bentley (early 19th century) to Kaye
(early 20th century). Kaye wrote as follows in the Journal of
Asiatic Society of Bengal 1919, No. 3.
The methods by which (the rules) were obtained are
buried in obscurity. Braunmühl¹ has stated "that the
Indians were the first to utilise the method of projec-
tion in the Analemma of Ptolemy." It is intended to
present the Hindu methods as clearly as possible and
to show that Braunmühl has not done sufficient justice
to the Indian astronomers.
As to Kaye, we shall show that his remark quoted above
is due to the fact that he had to rely mostly on the English tran-
slation of the Sūryasiddhānta of Burgess, and perhaps he had no
access to the works of Bhāskara II (1150 A.D.), who was the first
to explain the ancient Indian methods clearly.
Greek and Hindu Methods in Spherical Astronomy
Of the Greek methods in Spherical Astronomy, the
history begins with elementary principles only from Euclid (300
B.C.). Even in Theodosius' Sphaerica² (about 153 B. C.) "there
is nothing that can be called trigonometrical." Heath again says,

1. Heath, Greek Mathematics, Vol. II, p. 291. Braunmuhl, Geschichte der
   Trigonometrie, pp. 38-42.
2. Heath, Greek Mathematics, Vol. II, p. 250.