Mr. Vince’s new Method, &c. 
433 
fWxl 
■ r . nx x 
“n ] 
a t- * * 
j now the fluent of the laft terra 
is 
^^= 2 ±± X W X * + X f hence by 
m — r«+i z?2-r»+i ■ — - 7 ^ / 
a -\~x i 
fubftituting this quantity for the laft term, it is manifeft, 
that the firft part =i= ^ x W xa”-hx^ 1 r will be deftroyed 
by the laft term of x F x *" "+ ^”T T ~ r ? when we fubftitute 
for F its value; hence if we put M-— jL. __ 
m — n + 1 m- 2 n + 1 
a ln x m — 3«4 -i 
— &c. omitting the laft term ± W, we have 
/?z — 3«4-i 0 1 
/ 
1 
m . , 
x x m — n -f 1 
r. 1 T> 
x 4 - x 
?n~rn+ l 
xMxa"+x’ 
h m-n±^ x t - r^ x 
ffl-n+r I — r.na 
X 
n 1 ; 
+ # ' 
w — t n 4- 1 m — -f 
w — r/2+1 ffz — 2 ,n-f-i 
in /"* m — zn . 
r x J * 3+ + i 
» , 
# 4- * 
m—rn-fr 1 
/ m — vn ' . 
x . ■ ~ ; hence, if the fluent of the laft term be 
n , » 
£ 4-*^ 
given, we have the general law of continuation by which we 
may find the fluent of 
X X 
If the fluxion be —* . all the 
n , n] n ’ n\ r 
a + x 1 a + x l 
terms after the firft will be negative, and the laft always 
pofitive. 
Ex. 1. Given the fluent of 
v 1 +* 2 
to find the fluent ot 
✓ 
I +x 2 
in — 1 v - 2^-“-“3 
Here n=z 2, a~ 1, m = 2 s y r = $ r M=— - — 4- &c. to 
2 n — i 2 « — 3 
