\ 
[ 7 ] 
as well as thofe of -j- R' 4- 
R“ + R\ S+S'-i-S" + S"\ C^e, muft be equal to 
nothing, we therefore 
r^' a + jS y (f ‘ = o 
have y -)r r" S' — o 
P a + ^'/3‘ + s^'y + -J"' /' = o 
Lt a -}“ ^ /3 *4" ^ ^ “h ^ o 
In order, now, to exterminate the fluxions «, |3', 
y, 4 , let thefe equations be refpediively multiplied 
by 1, f,y, gj (yet unknown), and let all the products 
thence arifing be added together, whence will be had 
e r -j- /'s g + -h e r -i-/ s' + gt' y. fS 
+ q' + ^r" +y i" + ^ X y + f + ^ r"JrJ s"‘-{-gt"' 
Xj'' = 0. 
Make, now, q' er' -]~ f ^ -4-^if' = o- 
4- = O 
m 1 'll \ -T III I n- -f'li ^ 
q +er 4/i 4-^^ =0 
From whence (there being as many equations as 
quantities, J'j g, to be determined), the values of 
thefe quantities will be always given in terms of q', 
r\ f, ^c. that is, gy will always be reprefented 
by quantities depending on y', r', s', &c..{or on yf’F, 
G'g, &c.) exclufive of q, r, s, t, (or oi AC and 
D' d), which have nothing to do in thefe laft equa- 
tions. 
But, becaufe all the t erms of the equatio n 
^4_^r4-yj4-^/Xa + y'-hgr 4-/f 4- ^^' 
&c. — o, after the firft {q-\~€r-]-J's-\~gty^ do 
vanifh (by their coefficients being made equal to no- 
thing), it is evident that q e r -\-f s g t muft 
alfo be :i= o : which is an equation expreffing the 
general relation oi AC, c D \ and D' d, with regard 
to 
