C 34 ] 
/ / 
be exprefied by Z V -\- Z V, and by the laft proportion- 
t H 
we fhall find CE = 7 — j but (by 
V^ — ^xZV + ZV l v 7 
conics) CE x Ck — CO x C A, whence we 
fhall obtain Ck == V t~ — f ~ xZV + ZV^ . 
PROPOSITION IV. 
Fig. 4. In the two fimilar right angled plane 
triangles HKS, HMN, right angled at K, and M, 
there is given the right lines KS and MS, to find 
the acute angles, fuppofing the given angle hn M to 
be nearly equal to the required angle HNM. Put 
MS — A, K S = r, MN ~ y, the fine of the 
given angle hn M = y, its cofine = q\ the fine 
of HNM = V, its cofine = V, the fine of 
id IM M — hn M = at, and radius = i. Let M L 
be drawn parallel to H K, and M / parallel to S K : 
then in the right angled plane triangles N M /, 
SML, we have as rad. ( 1 ) : MN (y) : : fine H N M 
(V) : M/ (oV ), and as rad. (1) : MS (a) : fin. 
LMS (V) : LS (aV) 3 but M/ + LS =.KSj there- 
/ 
fore yV aV = r, and by the foregoing notation 
/ 
V — q q' x , and V =zq f — qx\ therefore thefe 
values of V and V being wrote in the above equa- 
tion we fhall find x — and from thence 
V = and V = ^~- r . 
jA — q'v fA — yu 
r R O P O- 
