44.8 
Dr. hutton on Cubic Equations’ 
By die i 41 fen e$ 
‘ 3405 1 - lo S- "•5321299 
07082798 
36 
y 35-° 
feries = — 1 739441 - 0*2404097 
■ ;= 4* 0*948 167 
791274 the leaf! root 
By the latter feries 
- 07082798 
\Q$Oji . v log, 1*4872798' 
v'isp - 
feries ~ + •156877$. • 1*195:5596 
X = - *9481669 
— *7912898 the fame root 
Which n early agree with the fame root found in Art. 1 1 3. 
136, But in Art. 6a the fame root was found to be 
hil 7 ! 1 hence then we fhall have thefe fil'd two follow- 
2 
ing equations,, and by means of their fum and differ- 
ence we obtain the other two 4 • . r 
v^ot/7 •frgfr V Vr~ >36 4* y>2 1 p_ 
, I 2 * 
4± + 2,5,8.0.81 
$20 \/ 7 -H 36 — v 20 \/ 7 36 — 1/2 1 4- 3 
> ip/t * "T A" 
72 
— + 
T . 3 >6.902.15.175^ 
2 . 5 . 8: 
- + See. 
>^20 \/ 7 4-3 6— 5/^20 y' 7 — r 3 6 
3 6 
^350 = 4-; 
— + -Aj, 5 /. 81 -!. +' Sic. 
3 3.6.9.175 
. - <■ — . ■ 1 •' . p - . j •*. • 
2. *5.3 1 •• ^ ; j.:~ ^.-8 .-0 r 81^ 
r ,, 
b 
21 — 3 
" 36 V Z T 3 . .6 . 9 . 1 75 ‘ 3.6.9.1205.175’ 
And the laft of thefe agrees with one found in Art: 115:. 
1 37. Ex. 4. In the equation x % 1 5 a; = 22, we have 
ab - 22, and ^* + is* = 5 ; confequently b s 11, and 
r = 5 3 - = 1 25 - 121= 4, which being lefs than <£ 2 or 
1 2 1 , this belongs to the firrt clafs of feries, or that for 
the greateft root. 
Now 
