558 Mr. vince’s Invejligation of the 
: 1" : : w : w x — ^xVxPxCG _ t j me G f one revolt. 
A+BxCG+PxDC 
tion. 
Cor. Hence the angular velocity being inverfely as 
the time of a revolution, will vary as ^vxPxcgxw D ~* 
PROP. VII. 
The point c, as the center of gravity moves forward, will 
defer ibe the common cycloid. 
From the deicription of the common cycloid it ap- 
pears, that the center of the generating circle paffes over 
a fpace equal to the circumference of that circle whilffc 
it makes one revolution. With the center g (fig. 3.) 
and radius gc, deferibe the circle cxy, and draw CP,, gw 
perpendicular to abc, and let the circle cxy be fuppofed 
to revolve on the line cr ; then will the center g move 
over a fpace equal to the circumference of the circle 
cxy whilft it makes one revolution, and the point c will 
deferibe the common cycloid : but from Prop. v. the 
point g will move over a fpace equal to the circumfer- 
ence of a circle whofe radius is gc, whilft the bodies, 
1 and confequently gc, make one revolution ; and hence 
the point c will deferibe the fame curve as before, that is, 
the common cycloid. 
PROP. 
