434 Afr. Vince’s new Method of 
g*=x, and the fluent of - ■ * - is the hyp. log. x + */ 1 4- 
which call O ; hence f - / x = IL — x M x /i + x* + ~ ~ 1 - 
U Vl+x* . zs 
f fpf — 11^ * f _0 + & c .± 5 irixQ. 
V j + #~ Ot. Of„r \/ i A - x u IS 
2 S . 2 J — J 
2i • 2J — 5 
V' I + x l 
If S 
= I, /* • ■ . * - = |n/ i+f x^ - i Qj= 
J i/i+x 2 
,4 
S—2,r -fj==— | v/ 1 + * 2 X 1 - _* + !a+ |Q = iG. 
J Vi+j' 3 
J = 3, Z' = -g-v/i +* 2 x — ■ +* + ri- /3-|«-|o= y . 
V j + * 0 S3 6.3 60 
J = 4, A^= = ^v/j + /x- — + - * + 5-^- y 
v/ ^ s v 7 s ~ 3 8 ..5 ' 8.3 
&c. 
& c. 
&c. 
Ex. 2. To find the fluent of x 1 x>/ z + x, given the fluent 
©f x~ *x fz+x, and s an odd number. 
Here a =2, » = 1, r= - i, s - =ot, m-vnzx - j, 0 r — - v 
ss — \ ; .*. v — bti M =— — p — &c. and the 
fluent (QJ of aT¥x v/ 2 + v is 7r 4* v/ 2# + where tt ~ hyp. 
tog.. + * + v^F; hence J* x~ ics/ 2 + # = — b- x T+xT x 
' '+3 *■ 
L-X—i-X Jlf—'xs/z + x — X — X /v 2 ~ ~ xs/ 2 + ,r 
f 2 J— 2 ^ J+3 J— 4 ^ 
f x-^x 
M 
3 
4-_L_x — X f a; 2 WW™ 
i + 2 i-6 ^ 
3+1 
&c 
lt£. 
2 + 
^+3 
X 2 
If 
