equations of all orders , by continuous approximation. 331 
Consequently the root is 2.0945514815, correct to the pro- 
posed extent, as appears on comparing it with the more en- 
larged value already found. The work occupied a very few 
minutes, and may be verified by mere perusal, as not a figure 
was written besides those which appear. By a similar ope- 
ration, in less than half an hour, I have verified the root to 
the whole extent found in Ex. II. 
Ex. IV. As a praxis in case of the intervention of negative 
numbers, let it be proposed to extract, to a convenient extent, 
that root of the equation x 3 —* >jx = — 7, whose first digits we 
have already determined to be 1.3. (See Art. 22. ) 
Making x ■=■ 1.3 + *. we have 
—.097 = — 1-33 * + 3-9 z2 +z* 
Wherefore 
39- 
5 
395- 
106 
/ 
4056,'* 
12. 
40 
68 
-193- 
- 1 9 75 
_1 7 3 45 
2000.. 
24336 
-1508164 
24372. 
325 
-148053 
32,5 
36 
■14779 
3 
W 
44 
76 
50 
6 
53 
— 97C056895867 
— — 86625 
— 10375000 
—9048984 
— 1326016 
—1184430 
— 14586 
— 132923 
— 8663 
—7383 
— 1280 
—1181 
— 99 
9 
—10 
