i 150 ) 
The Afymptotes of the Curve, deferibed by P, 
are determined thus. Find, as in the abovementioned 
Treatife, when thefe Sides become parallel, whofe 
Interfe&ion is fuppofed to trace the Curve ; which 
always happens when the Angle CQ^S becomes 
equal to the Supplement of the Sum of the invaria- 
ble Angles F C G, K S H, to four Right ones, be- 
caufe the Angle CPS then vanilhes. Suppofe (in 
Fig. 3 and 4,) that when this happens, the Iuter- 
fedtion of the Sides C F, S K is found in Q. 
Conftitute the Angle S Q,T equal to C Q A, as 
before, and let Q_T meet C S in T. Take CN 
equal to S T, the oppofite Way from C that S T 
lies from S. Through N draw D N parallel to C G 
or S H, which are now parallel to each other, and 
D N fhall be an Afymptote of the Curve deferibed 
by the Motion of P. 
If in place of a Curve Line B Q.M,a fixed Right 
Line A E be fubftituted, then the Point P will de- 
icribe a Conick Sedion, whofe Tangents and A- 
lymptotes are determined by thefe Conftrudtions. 
In this Supplement, it is afterwards ihewn how to 
draw the TangentsandAfympotes of all the Curves 
which 
