( <5ti ) 
' and zhc ^ part of j, and x be formed of z and tlie 
‘known Quantities, in the fame manner as the Expreffion 
made equal to nothing is formed of y ; and let jf'be equal 
'toz~^V‘. the dilFerence v will be found by Extrat^ing 
xv X 
"the Root of this exprelEon -1- \ 
I I .X I . X . 3 
‘ -]- ^c. r= G. For in this Gale z being become z-\-v =j, 
xv^ 
AT, which is now become x xv -\ (jrc. 
z 
' muft become equal to nothing. 
xvxv^'ic 
The Root V in the Equation x-\ 1 
I I . X 1 . X . 9 
^ (^c. = o, is to be found upon the Suppofition of its 
being very fmall with refped: to z, fas it muft be, if 
z be taken tolerably exadl} by which means the Terms 
jf X 
■. \- may be negleded, upon ac- 
1.1.3 i.x.3.4 
count of their fmallnels with refped to the other Terms, 
^ xv xv"^ 
fo as to leave the Equation x -\ -P- =o, for 
I 1 .X 
finding the firft approximation of v, 
- By extracting the Root of this Equation, we have 
x“ ZX X 
That is, 
X X 
^ je“ IX 
X . 
X V 
Firft, ~ — 
-rr, \i X xV 
• = o. 
^ X X 
X 
X 
X* 2 X 
X . 
xv^ 
Sec. *r- ^ r — 
if — X XV 
— O. 
x"; X 
X 
2 i 
Thirdly 
I 
I 
t ^ 
