Centripetal Forces . 
A Hume the three equations before given in Prop. 4. viz. 
** PH r , PH' r , 
C MF M'P X *^ 
P PF' 
— X S 77 : 
M"P J 
P h 
&c .^ = ™x/Vl£ x /-_ 
C' MP •'““M'P 
M' 
- x f 'ztz&cc. and - vi) = x /i±=£^L x y f 
p ^ Vmp j m'p j 
// 
Vk p^' r . • 
^ c * = x */— wpp XJ =±=&c.) X A, from the two former may be 
deduced the equations vv = uf+ Qf' +Ju +/ 7 /3 + y, and vv~ 
* 'j + fcj' 'ft + y , where a. = 
C xPH 
2MP~’ 
/3 = =t 
CxPH' 
1 m? 
7 V M"P — m 7/, p — <xc v » a — 2MP > 
c' x P// /_ , , n/ fYh"xf" Vh"'xf"' 0 \ 
W’ ^ ~- jC M"'F — &c -). whence may 
be derived the two equations uf+@j / +fu+f'@ + y = c/f-t- 
J' +/* +J / fi / + y =7rf=^pf'+<r, where tt= - X 
A P=r -^ ^ = ZlWA 
9 P \ M'P M'P J x 9 \ M"P X ^ M'"P x * 
=t&c. = &c.) x A . 
Reduce thefe two equations to one, fo that f 7 , f'\ &c. and 
their fluxions, may be exterminated, and there refults a 
M • 
fluxional equation of the formula H/’ -f Kf -f L/ + M = o, 
where H, K, L, and M, are functions of one of the before 
mentioned variable quantities (for example, MP = W) which 
may be fuppofed to flow uniformly, and its fluxion. 
PROP. VII. 
1. Fig. 6 . Given the force tending to any point S, the velo- 
city and dire&ion of the body ; to find the curve defcribed. 
Let the body a£ted on by a force f tending to S, at the dis- 
tance D' from S be proje&ed in the dire&ion P'Y 7 , with a 
7 velo~ 
