( ) 
i 6 =:x. Whe nce by taking the Fluxions, 
we have i, and i = 
2 v' ^ X 8 — 4 ^ X i\'^ ^ For finding 
the firft Figures of the Root y, for v' z take f , and we 
have the Equation ih-j-y — 16 = 05 which being 
expanded gives y^ y^ z %z y — 255 = o. 
By this Equation I find that for the firft Tuppofition 
we may take z — %. Therefore in order to find v, let 
us now make 2 = (which is nearer than before) 
and we have x — i\^ z, 16 — 2^ 4. 14 
— 5 ^ — 14= — 4,48 ; x=z 10, 66; it =4,72. Whence 
by the fecond rational Form v = = 
io^66 + 4j-7Jl.><-4>-1L, 
2 X 10, 66 
= o, 38 ; which mufl be too big, becaufe \<s/ z, and 
therefore will require a larger Value of y to exhauft the 
Equation, than where V 2 is exadt. For the fecond fup- 
pofition therefore, let us take z—'i, 3, and make V 2 
= 1, 41421 36, and by help of the Logarithms we fhali 
have z^ 1 1 = 13,47294, whence x = — ^0,22706; 
;cn=; 14, 93429, and x= 5, >84/9. Hence by the zd. 
irrational Formula v ■=. V ^ 4 > 934 i 9 j __ 
5,18419" ‘ 5,^8419 
^5* i^! ~ 9 “ oiyi 6 , which gives y =: z v 
2,31516, which is true to fix Places. If you defire 
it more exadt than to the extent of the Tables of 
Logarithms, taking z. = 2, 31516 for the next fuppo» 
fition, the Calculation muft be repeated by computing of 
zz-\- to a fufficienc number of Places; which, mufl 
be done by the Binomial Series, or by making a Loga- 
B b b b b 2 rithm 
