57 6 Mr. vince’s Invejllgatlon of the 
velocity of p, agreeable to what was proved in the laft 
Propofition. 
Cor. a. Hence the point about which p begins its ro- 
tatory motion may eafily be found ; for produce (if ne- 
ceffary) fb and of to meet in a, and a will be the point 
required; and by fim. triang. be ( 
: cf : :fo ( = v ) ■: oa 
zxvxQxGcxFO 
Ox GC x FO + P xjO x DC 
QXGCxFO+Px.eOxDC 
d 
2.XQXGC 
and hence 
_ P XgO X DC - Qx GC x OF 
¥a ~ -XOXGC 
Cor. 3. If, inftead of fuppofing q_ to have been at 
reft, it had been moving forward in a direction parallel 
to that of the body p, with the velocity v t the motion 
of each body after the ftroke may eafily be determined : 
for confidering P asadting upon Q_with the velocity v-u, 
we fliall have by this Propofition (putting 2M = 
oje gc x Foq-Fx^b x b e) v - v * 2M= thc velocit y commu- 
nicated to g, therefore v +y-v x 2M - the velocity of Q_ 
11 ' r p TN 
after the ftroke ; alfo y-vx m x -- = the velocity gained 
vj 
by the point d from fimple impact, and confequently 
the velocity of that point after =v+v-vx mx- , hence 
- PD 
v-u-v— i»xm x - - the velocity loft by p at the point 
v_X 
T from fimple impact, therefore p’s velocity after the 
ftroke = v - v — v - v- v x m x ~ x -Sr. In the fame 
CO r(J 
a 
manner 
