C IV ] 
Point is equal to the angular Motion of the Tangent 
of the Curve j as the angular Motion of the Radius 
of a Circle about its Centre is always equal to the 
angular Motion of the Tangent of the Circle. Thus 
the various Properties of the Circle fuggeft various 
Theorems for determining the Centre of the Cur- 
vature. 
Becaufe Figures are often fuppofed to be defcribed 
by the Interfe&ions of right Lines revolving about 
given Poles, Three Theorems are given in Prop. 18. 
26. and 35. for determining the Tangents, Afym- 
ptotes, and Curvature of fuch Lines, from the Dcfcrip- 
tion, which are illuftrated by Examples. A new Pro- 
perty of Lines of the Third Order is fubjoined to 
Prop. 3 5* The Evolution of Lines is confidered in 
Prop. 3 6 . . The Tangents of the E'voluta are the 
Rays of Curvature of the Line which is defcribed by 
its Evolutions and the Variation of Curvature in the 
latter is meafured by the Ratio of the Ray of Cur- 
vature of the former to the Ray of Curvature of the 
latter. 
Sir Ifaac Newton , in a Treatife lately publilhedf 
meafures the Variation of the Curvature by the Ratio 
of the Fluxion of the Ray of Curvature to the Fluxion 
of the Curvej and is followed by the Author, to 
avoid the Perplexity which a Difference in Defini- 
tions occafions to Readers, though he hints (in Art. 
3 86 .) that this Ratio gives rather the Variation of the 
Ray of Curvature, and that it might have been pro- 
per to have meafured the Variation of Curvature 
rather by the Ratio of the Fluxion of the Curvature 
itfelf to the Fluxion of the Curve } fo that the Cur- 
vature being inverfely as the Ray of Curvature, and 
X x 2 Con- 
