Principles of progrejfive and rotatory Motion. 553 
what principle it is that the motion of the center of gra- 
vity is preferved in a right line. 
Let a motion perpendicular to the rod he communi- 
cated to a (fig. 2.) and then by Cor. 3. Prop. I. b will 
not be difturbed by fuch an action ; and a will in the 
firft inftant have a tendency to revolve about b as a cen- 
ter, and would actually defcribe the arc ah, if the body 
B were fixed : let the angle abh be luppofed infinitely 
fmall, and let gk be the arc, the center of gravity would 
have defcribed, and draw the tangents af, Qg , to the 
arcs ah, Gg relpedtively.. Now, if a could have moved 
freely, it would (becaufe af— ah) have defcribed af in 
the fame time the arc ah was defcribed, upon fuppofi- 
tion that B was fixed ; for the radius ba being perpen- 
dicular to the circular arc ah, the force of the lever 
could have no efficacy to accelerate or retard the motion 
of a in the arc ah, and therefore the velocity in that 
arc is the fame as it would have. been if it had moved 
freely in the tangent : hence hf is that fpace through 
which the centrifugal force of a would have carried that 
body, could it have moved freely ; but as a is connected 
to b by means of the lever, it . is manifeft that the fame 
force which would have carried a from h to F in the 
direction of the lever, willy when it has both bodies 
* 
to move, carry it over a fpace which is to fh as a : a + b, 
or 
