o>ooco34^i^4>3nd 
C'diz) 
1 I z — o, ^8 o, 0000692,2 2^8 
434^944^19 
. , ^ / z O, 50 
oooi5'939i 39, and i + =1,000159- 
59139. Whence for the fir ft approximation we have 
ly — 
— = I — v' I, 00C15939139 = — o, 00007969247, 
z 
and V = — o, 000 15 54003 and y = z -}- v ~ 
1,94984459968. Which fs true to eleven places, and 
may eafily be -correded by the . Terms — ;■ which I 
3 
leave to the Readers curiofity. 
Being upon the Subjed of Approximations, it may 
not be amifs to fet down here-two Approximations I have 
formerly hit upon. The one is a Series of Terms for 
exprefting the Root of any Qoadratick Equation: and 
the other is a particular Method of Approximating in the 
invention of Logarithms, which has no occafion for any 
of the Tranfcendental Methods, and is expeditious e- 
nough for making the Tables without much trouble. 
gensrd Series for expeffing the Root of any ^adrM'ick 
Equation. 
Any Quadratick Equation being reduced to this Form 
XX — mqx-]-my=.o, the Root a; will ^ be «xpreft by 
this Series of Terms. ^ 
X = — -f A X — 1 B X C X TT~ 
q ‘ mq^ ‘ h" — % 
0,5^ 
+ D X 
&c. Which muft be thus interpreted. 
c — 2, 
I. The Capital Letters A, B, C, (jrc. ftand for the 
whole Terms with their Signs, preceding thofe where- 
