74 Dr. Waring on 
po 1 ■. VO z 
curve at the point P, and aflame — - = 2 C and'-— iQ,' refpec- 
1 Vv T t 1 
tively ; from the given centers of forces M, M', M", M"', 
&c. draw MS, MS', M"S", M 7 "^" &c.; Mr, MY, M 7 V 7 , 
M "V", &c. refpedtively perpendicular to the two planes RPV 
and RPT ; and PL and P / perpendicular to the line PR in the 
fame two planes RPV and RPT ; and alfo SP, ST, S"P, S "P, 
&c ; rP, s' P, s" P, &c. : from the points S, S', S", S'", &c. 
j, /, &c. draw the lines SH, S'H', S"H", &c. 
j/6, s'h\ s"b'\ s'" h'" , & c. refpedtively perpendicular to the 
lines PL and P/; and SK, S'K', S"K", S"'K'", &c. sk, s'k\ 
s "k", s'"k"\ &c. perpendicular to the line RP ; and let the 
forces/"",/ 7 '", &c< tending to all the points M'", M"", &c. 
(except three, M, M', and M") be given ; then from the three 
given equations ^ = ^ x/'^SL x/" ± &c. and £ 
p * x/± !i x /' ± ^ x/"rfc&c. and ^ = ^x/- PK ' 
r 
MP 
PK" 
JV1"P 
lVi P ^ M"P 
'M'"P 
s. r/ , PK r,., g Pi r Pi' r 
— X f X / =±r CCC. = X /-*- X 7- 
"P J — m"p ^ — MP ^ — M'P^*/ 
A\ “MP 
‘M'P 
M'P 
Pi 
// 
M"P 
X/" 
=!= &c. which contain only three unknown quantities, can be 
deduced the forces /, /', and /", required, tending to the 
points M, M', and M". 
PROP. v. 
Let a body a£ed on by forces tending to any given points 
S, S', S", &c. move in a given curve, to find its velocity in 
any point of the curve. 
Find the fluent of the fluxion (f x 5=fc /' x x 
j'" x V £~± &c.) A=/b±/ / D / = t/"D ,, ± &c. = - vv when 
the forces, are all contained in the fame plane ; or the fluent of 
