C 34 ° ] 
orems, it is fhc\Vn, that the Variation of Curvature 
at any Point of a conic Sedion is as the Tangent of 
the Angle contained by the Diameter which paflfes 
through that Point, and by the Perpendicular to the 
Curve. 
When the Ordinate at the Point of Contad is an 
Afymptote to the new Figure, the Curvature is lefs 
than in any Circle ; and this is the Cafe in which it 
is faid to be infinitely little, or the Ray of Curvature 
is faid to be infinitely great. Of this kind is the Cur- 
vature at the Points of contrary Flexure in the Lines 
of the Third Order. When the new Figure pafles 
through the Point of Contad, the Curvature is greater 
than in any Circle, or the Ray of Curvature vanifhes j 
and in this Cafe the Curvature is faid to be infinitely 
great. Of this kind is the Curvature at the Cufpids 
of the Lines of the Third Order. 
As Lines which pafs through the fame Point have 
the fame Tangent when the Firft Fluxions of the Or- 
dinate are equal, fo they have the fame Curvature 
when the Second Fluxions of the Ordinate are like- 
wife equal > and half the Chord of the Circle of 
Curvature that is intercepted between the Points 
wherein it interfeds the Ordinate, is a Third Propor- 
tional to the right Lines that meafure the Second 
Fluxion of the Ordinate and Firft Fluxion of the 
Curve, the Bafe being fuppofed to flow uniformly. 
When a Ray revolving about a given Point, and ter- 
minated by the Curve, becomes perpendicular to It* 
the Firft Fluxion of the Ray vanifhes; and if its Se- 
cond Fluxion vanifhes at the fame time, that Point 
muft be the Centre of Curvature. The fame is to be 
faid when the angular Motion of the Ray about that 
Point 
