174 Journal of the Asiatic Society of Bengal. [N.S., XV, 
and v,’= A, — A,; and consequently 
Uz = Vy — €; and v,'= v,’ — «, /2. 
The calculations according to the Panchasiddhantika 
(ch. xvii) may be expressed in the following form. The later 
texts give rather more complicated but not essentially different 
rules, of which a specimen will be exhibited in due course. 
i. il. | iii. iv. 
| 
a) =e, sin v a =e, sin v)’ | ag=e, sin vy’ | ay=e, sin vg 
| 
b) = e, cos v Rati | by =e, cos v3 
| 
c) = a)? + (rz + 2 es ataa eas | eg ag? + (rq + 04)? 
{ | 
. i ? | ; 
e) =sin-! a) r/c) @=sin-la, | eg=sin-!ag | «=sin~] ayrg/cy 
| 
AHA +e /2 RAE wil 2| Aemed ® 9 | Ag Ag + ey 
| Wi 
Ag HA, [MAB =P 1P. ot twit, 
o 3 
The problem is to calculate « = B, EA,. The line B, M =a is 
perpendicular to HA, while A, M = 6. ‘Now EM? + a? = EB,’ 
a ; 
or (ra + 6)* + a® = EB,* and —~ = sin €; 
EB, 
but 6=r,.cosv and a=r,. sin v, therefore 
Te. Sin Vv 
PIS SONI AS Eee carcino Kee 
a/ 2 2 8 
(ra +7. . cos v)* + 7,2 . sin? y 
é€.sinv 
ee — 
n/1 +2 + 2e. cosv 
A simpler formula is 
(i) sine = 
js 
where e = —. 
Ta 
E Ta + Te COS V 
e. sin v sin v 
=__ lt _—_—_—__—___ 
l+e.cosv§ lje+cosv’ 
