Dr . Waring on the 
i 7 
Sq X pr +ps +rj -f&c. Srx^+^+^ + &c. S* X-pq+pr + qr + &c. f ^ 
¥ --r c + d + occ.J 
/Sp X qrs-t-kc. S qxprs-\~&c, Srxpqs + &tc. Ss Xpqr+&c. 
X ^ ~v A * B ' C + D 
_i_ 
&C.) #*“3 4- &C. 
The law and continuation of this feries is evident to any 
one verfant in thefe matters from infpeftion. 
Thefe fradions may be reduced to a common denominator by 
fubftituting for Sp and A the products Sp x P and AxP, where 
P zzq ~r . q — s . r — s . &c. ; for Sq and B the produfts Sq x Q 
and BxQ, where Q^== p — r . p — s . r — s . &c. ; for Sr and G 
the produfts Sr x R and CxR, where R ~p — q . p — s . q — s . 
&c. ; for S s and D the produdls Sr x S / and C x S', where S' — 
p — q . p — r . q — r . &c. &c. 
The fractions, in particular cafes, will often be reducible to 
lower terms. 
\ 
15. Let y~ax b + hx b+l + cx h + z! + &cc . 9 and the correfpon- 
dent values of x and y be given as before, then will y = 
X h X x‘— q X X — r X x —s X &C. 
p b Xp l — q X p l — r X p'—s X &c. 
r b xr l —p l Xf L — q ~r l —s X &c. 
Sr -p &e. 
x 
S/> + 
<& / J 1 l l l o 
^ Xa — p X x — r xx — s X &c. 
b i .11 l l i „ 
q X q —p Xq—r—q—sX &c. 
h 
x Sq 
1 
1 
xh x x l p lxxi^-qtxx- s* X &cc. x x .*• — x — q X x — r x &c. 
Sr+ 77^-r7x7l7 +& , x 
This feries may in the fame manner as the preceding be 
reduced to terms, proceeding according to the dimenfions of 
* ; and the feriefes given in the examples may ( mutatis mutan- 
dis J be predicated of it. 
16. A more general method of correfpondent values is given 
in the Meditationes, as alio the 
fubfequentjy 
a — q x — . x — s . &c. 
p — q .p — r *p — s . &c. 
X 
