1919. ] Ancient Hindu Spherical Astronomy. 175 
but i Hindus, like the Greeks, did not employ the tangent 
func 
The maximum value of « occurs when EB is a tangent to 
the pe that is when AB is at ey angles to HB; and 
then sin « = r,/rg = e, and v = 90° 
19. "The following calculation for the equation of the 
centre 7 Venus is based upon the later Surya Siddhanta 
elemen 
The equation of the centre for Venus. 
Given mean longitude B18? 13", 
Longitude of conjunction.. 10* 21° 50’: anomaly v = 2° 3° 37’. 
Longitude of apsis 2 19° 52’: anomaly v’ = 5* 18° 35’. 
Epicycle of conjunction 
Epicycle of apsis 
. E- varies from 260° to 262° 
Redu 
ced 
. Ea varies fro 
ee a = se 
Differe: 
Difference A HE, = 2°. 
sai nptiagt 
Ak= = a”; 
AE. anv deseo f. 
Reduced pair vig (Ba 
For ae of | For ouneliots of | For ae of | For a of 
conjunction. apsis. apsis. conjunction. 
Longitude Aon 8° 18°13" | ay oe 9 1°17" | ag =O 1°28" | Age 8? 18° 30’ 
Anomaly vy = 2° 3°37 | vy)’ = 5° 18°35’ | 1’ = 5°18° 24’ | vg 2" 3°14’ 
sin v sin v = 3080’ | sin vy;’= 689’ | sin v2 = 691’ sin v3 = 3069’ 
cos v cos v = 1527’ | cos vy’ = 3369’ | cos v2’ = 3368’ | cos vg = 1548’ 
Corrected epicycle ¢ | = °723 €g = 0328 €a = 0328 €e = “723 
a@=esinv = 2226’ @y = 22°3’ ag = 22°6’ ay = 2218’ 
b=ecosv = by, = 1104’ bz = 110’ bs = 11074’ bg = 1119’ 
c= /at+(r + bp ec) = 5058’ Cg = 3548’ cg = 3458" Cy = 5067’ 
sin-] ar/e=e« ; ag €2 = 0° 22’ €; = 0° 23’ €, = 25° 59’ 
Corrected longitude | a +5 = = 9°1° Th « + 9 1°28’, + 3 = 8* 18° 36’ As + eg = 9° 14° 35’ 
, is the same as that of the Pafichasiddhantika except 
ced. 
The be see 
that vested a aeyeles have eon introdu 
* Since v = 90 + « we have 
e 
tan ‘ae 
l—esine 
of which a solution is sin «= e. 
+ See J.A.0.8., 1858, 213/. 
or sin e =e (1 —sin*e) / (1 — e sin e) 
