Method of correfpondent Values , See. 177 
From thefe different feriefes may be formed, by adding two or 
more terms of the given feries together for a term of the re- 
quired feries; which method has been applied to converging 
feries in general in the Meditationes. 
13. The method of correfpondent values eafily affords a refo- 
lution of the problems contained in Mr. Brigg’s or Sir Isaac 
Newton’s method of differences. 
Ex. 1. .Let the quantity be of the formula a 4 bx 4* cx z -f dx 3 
+ &c. . . x n ~y, and n + 1 correfpondent values of x and y be 
given, viz. p 9 y, r, s , See . of x ; S/, Sj', Sr, S s 9 Sec. of y ; then 
... x — q.x — r . x — s . Se c. . x — p.x — r.x — s. See. 0 
VVllljym^^ ■= -= — X =.-=rr=~- — X Sc[ -f 
p—q . p — r . p — s . Sec. 
q—p . q — r . q — s . Sec. 
. Sec. 
x — p . x — a . x —s . .Sec. 0 . x-p.x — q.x — 
=r x or + • — V — - 
T — p . r — q . r — s . Sic. s — p . $ — q . i — r . &c. 
x Sj'-p&c. 
The truth of this problem very eafily appears- by writing 
p, q y r, s, &c. for x in the given feries. 
All the preceding examples may be applied to this cafe, by 
writing x for m in the given feries ; hence the refolutions of 
feveral cafes of equi-diftant ordinates by eafy and not inelegant 
feriefes, amongft which are included the two cafes commonly 
given on this fubje£t. 
14. If a quantity be required, which proceeds according to 
the dimenfions of x 9 reduce the above given value of y into a 
quantity proceeding according to the dimenfions of x 9 and 
there refultsjy = 
s p 
p-i ■ P 
+ 
+ 
Sr 
r—p 
r — s . Sec. — C 
r . p — s . Sec.zz A q—p.q—r.q — s.Se c.“ B 
+ -+.&C.) 
■P 
■9 
s — r . & c. — D 
( 
Sp x q + r + s+ Sec. SqXp + r + s + &c - , $ r Xp q + s'+Sec. 
A 
Hr 
B 
+ 
C 
S s xp + q + r-{-&c. 
“ " D 
H-&c.)^^ J 4 ( 
Sp X qr — j— q s -J- r s — }— Sec. 
~~ A 
+ 
