ae 
% = es 
Blake on the Teeth of Cog-Wheels. 83 
and the curve pA on the plane of the circle b. These 
curves are isosagistic. 
For the line pd is constantly the describing radius to 
the successive points of both curves pi, ph. hese curves 
are therefore both constantly perpendicular to the line pd. 
Hence the curves pi, ph are constantly coincident at the 
point p. Consequently the point p is constantly the point 
ofaction. Therefore the curves are constantly perpen- 
dicular at their point of action to the line pd. Wherefore 
(Prop. 2.) they are isosagistic. 
or.1.—Any curve on the plane of a circle which is sus- 
ceptible of being generated by another curve rolling on the 
circle is isosagistic. 
Cor. 2.—The base circles being considered as the pitch 
circles of two wheels, the curves generated are sections of 
the acting faces of fellow isosagistic teeth. 
Cor. 3.—When the base circles and generating curve si- 
multaneously roll together, the describing point and point 
Ol action constantly coincide. 5 : 
cHOLIuM.— When the generating curve is a circle, and 
the describing point its centre, the curves generated are cir- 
cles concentric with their bases. ‘These are manifestly in- 
capable of acting on each other, and therefore, though they 
are rather in than beyond the limits of the principle, they 
will not be considered as included in.the general term, tso- 
Sagistic curves. ; 
