C 119 1 
greater Circle has a lefs Curvature than a letter Circle > 
and ttnce the Curvature of Circles may be varied inde- 
finitely, by in-larging or diminifhing their Diameters, 
they afford a Scale by which the Curvature of other 
Lines may be meafured. As the Tangent is the right 
Line which touches the Arc fo clofely, that no other 
right Line can be drawn between them ; fo the 
Circle of Curvature is that which touches the Curve 
fo clofely, that no other Circle can be drawn through 
the Point of Contad between them. As the Curve 
is feparated from its Tangent in confequence of its 
Flexure or Curvature, fo it is feparated from the 
Circle of Curvature in confequence of the Variation 
of its Curvature, which is greater or lefs, according 
as its Flexure from that Circle is greater or lefs. 
The Tangent of the Figure being confidered as the 
Bafe, a new Figure is imagined, whofe Ordinate is 
a Third Proportional to the Ordinate and Bafe of the 
Firtt. This new Figure determines the Chord of the 
Circle of Curvature by its Interfedion with the Or- 
dinate at the Point of Contad, and by the Tangent 
of the Angle in which it cuts that Circle, meafures 
the Variation of Curvature. The lefs this Angle is, 
the clofer is the Contad of the Curve and Circle of 
Curvature, of which there may be indefinite Degrees. 
When the Figure propofed is a conic Sedion, the 
new Figure is likewife a conic Sedion 5 and it is a 
right Line when the Firtt Figure is a ‘Parabola , and 
the Ordinates are parallel to the Axis j or when the 
Firtt Figure is an Hyperbola , and the Ordinates are 
parallel to either Afymptote. Hence the Curvature 
and its Variation in a conic Sedion are determined 
by fcveral Conftrudions ,• and, amongft other Thc- 
X x orems, 
