( M9 ) 
upon given Lines. Their Afymptotes are alio de- 
termined by more fimple Conftru&ions than thofe 
which are fubjoined to their Defcriptions in that 
Treatife. Of thele we fhall give one Inftance 
here. 
Suppofe the invariable Angles {Fig. i and ^ ) 
F CG, K S H, to revolve about the fixed Foints or 
Poles, C and S. Suppofe the Interfe&ion of the 
two Sides C F, S K, to be carried over the Curve 
BQ^M, whofe Tangent at the Point CL is fup- 
pofed to be the Right Line A E ; and let it be re- 
quired to draw a Tangent at P to the Curve Line 
deferibed by P the Interfe&ion of the other two 
Sides C G and S H. 
Conjlruttion . Draw Q_T eonftituting the Angle 
SQT, equal to C QA,on theoppofite Side ofSQ> 
that A is from C Qj and let (^T meet C S (pro- 
duced if neceffary) in T. Join PT, and confti'tute 
the Angle CPN equal to S PT, on the oppofite 
Side of C P, that P T is from S P, and the Right 
Line PN fhall be a Tangent at P, to the Curve de- 
feribed by the Motion of P, which is always fup- 
pofed to be tbe Interfe&ion of C G and S H. 
x The 
