( *55 ) 
fpedtVely over the fixed Right Lines A a, B b, 
Hb, K k, the Point P in the mean time will defcribe 
a Conick Section, or a Right Line. The Locus of P 
is a Right Line when C P and S P coincide toge- 
ther With the Line-C S. All thefe things are demon- 
ftrated geometrically. 
V. After this, Angles are fubftituted in place of 
Right Lines revolving about thefe Poles ; and it is 
ftilldemenfbated geometrically, that the Locus ofP 
is a Conick Section or Right Line. 
Suppofe that there are four Poles C, S, D and E, a- 
bout which the invariable Angles P C Q, PSR, 
RDM, M E revolve ; and that Q, M and R, 
the Interfedions of the Legs C Q,and E Q, of E M 
and D M, and of D R and S R, are carried over the 
fixed Right Lines A a, B 6, and G g refpedively, 
then the Locus of P is a Conick Sedion, when C P 
and S P do not coincide at once with the Line C S, 
but is a Right Line when C P and S P coincide at the 
fame time with C S, and never a Curve of a higher 
Order. 
VI. Having demonftrated this which leems a re- 
markable Property of the Conick Sedions or Lines 
of the Second Order ; I proceed to fubftitute Curve 
Lines in place of Right Lines in thefe Defcriptions, 
(as I always do in the Treatife concerning the De- 
fcription 
