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

144 GREEK AND INDIAN METHODS
It is almost needless to say that neither in the method nor
in the rules is there any agreement between the Indian and
Greek spherical astronomy in the solution of this problem.
Kaye’s view¹
As to Kaye, it appears that he has not been able to find a
method in the translation of the Sūyrasiddhānta by Burgess. The
figures of his paper referred to before do not show the “Akṣakṣet-
ras” even in their projections on the meridian place. He refers
to Braunmühl’s History of Trigonometry but does not appear to
have been able to follow him in his “Methode der indischen
Trigonometrie.” Kaye, however, is not slow in belittling Indian
trigonometry when he says :—The Indian astronomers employed
the sine function principally and the versed sine occasionally ;
they never employed the tangent function; and generally, but not
always, preferred to employ the sine of the complementary angle
rather than the cosine functions.’’
It is evident that Kaye
never understood the meaning
of the Indian functions of
‘sine’ and ‘cosine.’ These
functions are fully explained
by Bhāskara² when he
says :—
“Of that point the dis-
tance from the east-west line
is the sine and the distance of
the point from the north-south
line is the “cosine”.
[Fig. 14: Circle with points N, S, E, W; P₁, P₂, P₃, P₄; N₁, N₂, N₃, N₄; M₁, M₂, M₃, M₄, A]
Fig. 14
In (Fig. 14), of the arc AP₁, P₁M₁ is the “sine”
and P₁N₁ is the “cosine” of AP₂, P₂M₂ is the “sine” and P₂N₂
is the “cosine”; of AP₃, P₃M₃ is the “sine” and P₃N₃ is the
“cosine”; etc. It is evident that a better definition of these fun-
ctions was never given.
We have thus seen that some of the solutions of Āryabhaṭa

1. J. A. S. B., N. S., XV, p. 154.
2. तस्य बिन्दोः प्राच्य-परायाश्च यदन्तरं सादोर्ज्या ।
   बिन्दोर्याम्योत्तरायाश्च यदन्तरं सा कोटिज्या ॥
   —(Bhāskara, Grahagaṇita, commentary. II. 88-21)