She ie: 
92 Blake on the Teeth of Cog-Wheels. 
ING POINT; the curve to whose plane the describing 
point is attached, the GeneRaTine cuRVE; that upon whic 
the. generating curve rolls, the BAse cURVE; that part of 
base curve with which the generating curve comes in 
contact, the BASE OF GENERATION. 
Cor.—During the action of isosagistic curves, the veloci- 
ties of ‘heir circles are equal at their point of contact. 
Prop. 3.—Any curve generated by one curve rolling up- 
on another is at every point of it, perpendicular to a line 
drawn from that point to the point in the base, which was 
in contact with the generating curve when that point was 
described. 
Let a }, Fig. 2. be any base curve; c d any generating 
curve rolling upon it; f any point in the plane of cd, and 
gh the curve described by f. Now during the time when 
a small part f of the curve hg is described, the describing 
point revolves about the point e asa centre. Therefore if 
a circle be described from eas a centre with a radius ef, the 
circumference of the circle will coincide at f with the curve 
Ag. But the circumference ofa circle is every where per- 
pendicular to the radii. Therefore the curve hg, which coin- 
cides with the circumference of a circle whose radius is fe, 
is perpendicular to fe. ; 
OROLLARY.—THence it is manifest that no curve on the 
plane ofa circle is susceptible of being generated by anoth- 
er curve, rolling on the circle, unless perpendiculars from 
every successive point of it, commencing at one extreme, 
fall on corresponding successive points of the circle. 
be taken.as the describing point, it will have moved to p 
and described the curve pi on the plane of the circle a 
