[4i] 
with the conjugate axis, and palling through the 
given point tt taken therein, it is propofed to deter- 
mine the length of the fegments F f> E e y intercepted 
between the circumference of the circle, and the pe- 
rimeter of the ellipfis. 
From the point F, draw the right line F d parallel 
to the tranfverfe axis A B, meeting the conjugate 
GD in the point d y and the circle in c; draw the lines 
C F, CJ] Cr, and let ctc be joined : Then by conics 
we fhall have, as CB:CD tang. F tt D : tang. 
c 7rD, and in the right lined triangle Ctj-c, it will be 
as C c (CD) ! fin. Ctt c : : C n : fin. C ctt, whence 
the angle cCk becomes known ; but as CD : CB :: 
tang, c C : tang. FC?r j therefore FCjr is known ; 
from which taking away the given angley'C tt, there 
remains the angle FCf-, confequently all the angles, 
in the right lined triangle/C F, together with the fide 
C/(CD), are known: we (hall therefore have, in 
the right lined triangle, F J C, as fin. / F C:Cf:: fin. 
f CF :jfF, one of the required fegments, and by a 
fimilar operation, the other fegment E e will be found, 
whence as ef is given, E F will become known. 
COROLLARY I. 
The required fegments Ff y E e y will be found in 
the fame manner, when the given point tt is not taken 
in one of the axes, but any where between ; but in 
that cafe, the point where the line EF interfeds the 
conjugate axis, muft be firfi: determined. 
COROLLARY II. , 
If a perpendicular C n be let fall from C upon the 
line EF, the angle vCn will be given, to which, 
Vol. LV1I. G . adding 
