560 Mr. vince’s Inveftigat'mt of the 
found at a, b and w refpesftively, and awb will be the 
pofition of the lever. Now it is evident, that c is not 
the point about which the bodies begin to revolve, for 
(confidering the lever to be produced to c) that point 
muft have moved over a fpace c c equal to g q, when the 
lever is come into the pofition awb : draw co perpendi- 
cular to cb, and go perpendicular to gw, and o will be 
the center of rotation at the commencement of the mo- 
tion. For conceive co to be a lever, then the lever abc 
has a circular motion about c, whilft that point is mov- 
ing from c to c, and confequently the point o is carried 
forward in a direction parallel to c c by this motion; but 
as the lever co is carried by a circular motion about c 
in a contrary direction, it is evident that that point of 
the lever co muft be at reft where thefe two motions are 
equal, as they are in contrary directions. Now the ve- 
locity of c in the direction c c : velocity of g about c : : 
Gq : Gg : : (by fim. triang.) co : cg, and the velocity of 
the point g about c : velocity of the point o about c : : 
cg : co ; hence ex aquo the velocity of c in the direc- 
tion of cc, or of o in the direction op parallel to c c, is 
equal to the velocity of the fame point o in a contrary 
direction arifing from its rotation about c, and confe- 
quently o being a point at reft, muft be the center of ro- 
tation in iff* motus initio. Alfo, becaufe ma is equal 
and 
