( H4)) 
Interfedlioh of that which revolves about E with 
that which revolves about C, be carried over a 
third fixed Line B F, then the Interferon P of 
thofe that revolve about C and S , Will, in the mean 
time, deferibe a Conick Sedlion, and not a Curve 
of a higher Order. The Conick SedHon degene- 
rates into Right Lines, when CP and S P coincide 
at the fame time with the Line C S, that joins the 
Poles C and S, as in the preceding Description s 
which coincides again with what is demonftrated in 
the abovementioned ingenious Paper. 
After this it is Ihewn generally, that tho’ the 
Poles and Lines revolving about them be increafed 
to any Number, and the fixed Lines over which 
fuch Interfedtions, as we deferibed in the two laft 
Cafes, are fuppoled to be carried, be equally in- 
creafed, the Locus of the Point P will never be 
higher than a Conick Sedtion : That is, let a Poly- 
gon of any number of Sides have all its Angles, 
one only excepted, carried over fixed Right Lines, 
and let each of its Sides produced, pafs through a 
a given Point or 
Pole, and that one 
Angle which we 
excepted, will ei- 
ther deferibe a 
ftreight Line, or 
Conick Sedtion. 
Thus if a hexa- 
gonal Figure L 
R P M N, have all 
its Angles except- 
ing P carried re- 
Jpe&ively 
