PHYSICAL ann LITERARY. 155 
ellipfe, the fquare of CL is. equal to the 
rectangle ASP, the log. of CL will be equal 
to half the fum of the logs. of AS, SP: 
And, becaufe the tangent of the angle KSH. 
is to the tangent of the angle GSH as HK 
to HG; that is, from the nature of the 
ellipfe, as LC to CA; therefore, if to the 
log. tang. of the angle GSH, the log. of 
CL be added, and from the fum the log. 
of AC be fubtraéted, the remainder will 
be the log. tang. of the angle KSH. 
Acatrn, the fine of the true anomaly is 
to the fine of the anomaly of the excen- 
tric, as the leffer axis of the orbit to the 
diftance of the planet from the fun. 
- Because CL is to HK as C3 to GH, 
that is, as the radius to the fine of the a- 
maly of the excentric, and HK is to 
KS as the fine of the true anomaly to the 
radius ; therefore CL is to KS as the fine 
of the true anomaly to the anomaly of 
the excentric. 
THE place of a planet in an met or- 
bit [granting the quadrature of the el- 
lipfe} may be found at any given time 
within a fmall limit, by tne following 
theorem. 
THEOREM 
