Blake on the Teeth of Cog-Wheeis. 95 
the point o is in a corresponding point of the curve dc. 
And since the equal arcs are by the construction indefinite- 
ly small, the point o is constantly in the curve bc; first at 
6, and lastly at c. Therefore the point o describes the 
curve bc. 
Cor. 1.—Curves are susceptible of being generated by 
two different curves, rolling on different arcs of the circle as 
the base of generation, when their perpendiculars produced 
fall on another part of the circle, in the same order of suc- 
cession. 
_ Cor. 2.—Any curve being given on the plane of a circle, 
itmay be ascertained whether it can be generated. and if 
itcan be generated, its generating curve may be found. 
