quadratic, cubic, quadrato-cuhic, and higher Surds, 37 
— ^qz" —q^z — e* 
3 I’] *• 
+ 292 " —jq‘^+ + w' 
?* 
— 4^ 
5’ , * 
9"- ^ 3 — +9 • ^2 
+ _j, 
—r* = — r’ 
> 
— 4s. 
-d-q*. ——5* 
3 Y =0. 
-4«- 4. 
3 
— r* 
This cubic equation gives, z 
fqs + ir^ + j 
v/- T <z‘^ + T + T 
O 17 4 
i2gr^ + “ ^ 
6+ 
3 
+ 
7 ?* + ¥'■'— 7 n /" — 7 ?*^' + jq^r + 
11 
3 
— i^qr^s + ^ 
Then by hypothesis and solution of quadratics, x =2 — y ^ ± 
Vi — f’ or, X = ^ e ± Vx — g ; and, by substitution, 
x= — y^±y\/^ — 
2q 
-|- 2 _ ^ _j_ X z — \ q 
T^ + 
:, or X 
= 2 ^ ± i —^e^—2q^ 
= ±1%/* 
±i \/— Z — ^q — 
2r 
V.- 
Let now the equation consisting of 3 surds of the 11th 
power be, "3/u + "Vb + ° ! then 
(2;) a + Z) + 11 "Va"b + 55 'Va’6' + 165 "VaV -f 330 
"Vti'b* + 462 ‘Va‘6’ 4b'2 'Va’6“ + 330 "Va'b' + 165 
"Va^b" + 55 "Va‘b'‘ + 1 1 "Vab" — - c. 
