/ 
analytical and geometrical Methods of Investigation . g t 
quantities, be derived; consequently, if the symbol /is to de- 
signate a reverse operation, I can only know what that reverse 
operation is, by attending to the manner by which the expres- 
sions affected with the symbol / were derived. Henc4 
VI. / = z when x = e*. 
<jr X 
= * when i + x = 6* 
/^== =2 when x = (a*/- 1)— {*✓-» - 
In like manner, 
fx* (i-f- x z )~l=.z, x-{~ s/i+ x z z=z £ ^ or x 
fx- l2X+X*)-l = Z, l+X^\/ox + 
f 2X ' 
J I— 
}• 
* 
X = 6*. 
= ** or * 
— i 
**+I 
/■^§= =*, -£±2f± = 6 . or x/T+T* =.i±!l, 
X v I -J- j 1 Vi 1 * 1—4** 
or «r ~ 
^ * 
2T— 
5 a — £■ 
Again, suppose 
x 
/ 2 — 1 1 l | 1 — g V y\r = »-» s • | s h/~* 
but v' 1— x z =2- 1 , ( S zV'-i^- r - z Y- i I,* consequently ,r==;rv^i~i\ 
= ^7=== : hence, reversely. 
or %■ 
/t=3t = x > x bein s = ( 2 /-!) '• { ^=5 - c--y- } . 
In like manner, 
/v==r = Z, X— 2— . { + r-zV- }. 
f , = *»-£ = ( x— 2~*. | r*'— ■ j—ji/rr, jj. 
* * ta ^ e nQ n °tice, at present, of the arbitrary quantities which may be introduced 
in the integration of these equations. 
Ns 
