Resolution of Algebraic Equations. 
29 3 
2 - 4 a ± ~ - 4 -g - 2 a' - 4 a ft) v/- i 
— 3 - 1- a -|- 2 6| s/ — 
- + SZ+l^ls/- i 
2 a 3 -f- 8 a 4 ft -f 8 a ft 4 /a + 2 b\ 3 / T 
3 T~ ¥ 
+ 2 6] y/— -§■ 
— b — 2 a — 6]v/— ■§• 
— 6 — 6|v/ — ' y 
b 1 -j- /^ab 2 6 | v/ — 3; 
ft 4 — 4 a 6 — 4 a 4 
3 
iL=ijtz± £ + 4^ + 2 6V-i= 
- b — <2 a — 6) y/ — I 
- 2 * 3+4 . fl 6 — 4 a 6* - aTlv/— •§• 
2ft 3 + 8aft 4 + 8a 4 ft 
iZ+HV — 1 
-f- X — 2d! — 6|v/ — - 7f 
fcr * 
12 a 4 b+ 12 a ft 4 
, 8 a 3 -J- 12 a 4 ft— 12 a ft 4 — 8 ft 3 ] 
3 
hV — 3 1 
The quantity 
12 a 4 ft-J- 12 a ft 4 , 
, 8 a 3 + 12 a 4 ft— 12 a ft 4 — 8 ft 3 | 
3 ' 
1 3^-3 1 
|=4 
2a 3 + 3 a 4 ft — 3 aft 1 — 2 ft 3 
3-Z-3 
3 
is therefore the common cube of those 3 binomials. Q. E. M. 
Now let the equation of the 3 quantities (a, b, — a — b,) 
be (a: 3 — qx + t — o); then, by the construction of equations, 
mdccxcix. Q q 
