Centripetal Forces . y l 
the relation between the diftance SP and SY can be deduced 
an equation exprefling the relation between the diftance S p and 
perpendicular Sy from the point S to the tangent py of a 
curve, whole force and velocity at every equal diftance is the 
fame as in the given curve, but the direction different. 
2. Given an equation K = o exprefling the relation between 
SP = D and SY — P ; to find an equation exprefling the relation 
between SM = x and PM =jy, the abfcils and ordinate of the 
fame curve. 
In the given equation K=0 for D and P write refpeftively 
\/ x z +y z and and there refults a fluxional equation 
L = o of the firft order, of which the fluent expreffes the ge- 
neral relation between x and y. 
Cor. If in the given equation for P be wrote ;-P / , there 
refults the equation K = which exprefles the relation between 
the perpendicular Sy = P and diftance S/> = D / of every curve, 
which at equal diftances has the fame velocity and force tend- 
ing to S; reduce the equations K/rz zo, D = \Zx 2 +y z and 
wP' — YrY- i . into one, fo that D and P' may be exterminated, 
a / .2 , .2 
x +y 
and there will refult the fame fluxional equation of the firft: 
order, exprefling the relation between x , y, and their fluxions, 
whatever may be the value of n, The general fluent of this 
fluxional equation contains the relation between the abicifs and 
ordinates of all curves, which have the fame force and velocity 
at the fame diftance as the force and velocity in the given 
curve. 
PROP 
