4 3 6 
/ T 
jWk Vince’s new Method of 
i — r . mbx*”" 1 x + i-r . 2mx zm h 
X 
i L m i ^■ Lm \ 
a-\-bx + x 
f u 
X 
/ m — i . , zm — t 
I— r . mbx + I — r . 27WV 
hence by tranfpofition 
,7 m . zw \ 
a + bx + x 
^yt 91 • — — — — . 
and division we have / — = xFxj +"bx m + x 2 ^l 
_ j ■ — z , ~r j+ a 
a + bx + x * 
. i m . z m 
a 4- bx + x 
j_ x r ~^— - — * r 
I + A ,7 ?« , i i+A 
J I + A 
W 2W - 
A 1 a; 
, J m . Zni\ 
a^b* + a * 
+ &C, 
+ A 
X 
i — r , mbx x i — r • 1 mx 
a-\‘hx m - 
mbx i+i — r . 2 m/ 
# 4- +++*•' 
of thefe two laft terms are 
i + A 
x a + bx m + x 
Now the fluents 
-r V 
-4— 
i 4* A 
J 1 - 
n*—m . 
X X 
and: 
u 
i + A 
X Cl + 0X m + X‘ 
w 
1 ,-f A 
/ 
n — i -4-i >m . 
X 1 X 
a + bx -\- x~ I J a-\-bx n + x zm \ 
refpe&ively ; hence, by fubftituting thefe for the laft term 
It is manifeft that 
— x a + btf n + x 2m \ l " and =p — - 
i+A i+A 
x a + bx m + x f will be deftroyed by the two laid terms of 
i- x F x a ^ i - x*~] when we fubftitute for F -its value ; 
i+A 
p^-3^+1 Qy »-4-+l ^ 
hence, if we put M — * 
v — zm — i 
72—2772+1 n — JW + I 72—47/2+1 
omitting the two laft terms — T and U, we fhall have 
/ w. , — — I — r -n 
X X I . . *Ri /T » * 1 i t . . ,m 1 T77«i) t -D 
, 7 nt - 2» f 
2? + VX + X j 
/= 
w — «j . 
X 
m . 2 /w 
« + W+* 
1 x M x a + -j- X 1 *-) + 
n—zm . 
~ x r — t — £_-■ + &c. =±= 
+ A J ' 
X 
J + A 
C 
0 + bx 
m . 2ml 
i + x I 
I + A 
V 
i+A 
/ 
