PHYSICAL anp LITERARY. 139 
Join SG; draw BE perpendicular to 
| CD meeting CD in EF, and draw CF pa- 
rallel to SD meeting DF, a tangent to the 
circle at D, in F. 
Because BE is the fine of the angle | 
BCD, and DF the tangent of the angle 
DGF, that is, of the angle SDC; BE will 
be to DF as the excefs of the arc BD above 
BE to the arc DG; therefore [ Prop. 5.] 
the fector ASG is equal to the fector 
ACB ; therefore the angle ACG is the a- 
nomaly of the excentric. 
THE computation is as follows: In the 
triangle BCS, as the fum of the fides BC, 
. CS, is to the difference of the fides BC, 
CS, fo is the tangent of half the angle 
_ ACB to the tangent of half the difference 
a 
iy 
Cs 
a 
of the angles CSB, CBS; therefore the 
angles CSB, CBS will be given ; that is, 
the angles, ACD, DCB, will be given. A- 
gain, in the triangle CSD, the fum of the 
fides CD, CS, is to the difference of the 
fides CD, CS, as the tangent of half the 
angle ACD to the tangent of half the dif- 
| ference of the angles CSD, CDS; there- 
ie the angle CDS will be given. Again, 
becaude 
