so Dr, Al'LMAn*s Methods of , clearing Equations of 
Put + -6 + c = : then 
(4;) +^V^ 6 ’ .^x/^z* + v^*~ 7 = — 
— ^i^bc* — n: multiply by then^ \/ b c , 
\/h* . — — . I — ... . .^ 
—7WbcJ\/ b + '^\/c . = — Wbc , Wb + — n . 
^-Vc^ 
V6 Wc\ this quadratic equation, ’When solved, gives 
-Wb + Vc ■ Va = ^ 
i8c—4« .Jv/6 + 43 Jv^ 6 *c* 4 c— 18/; — 4« . 
This equation, when cubed, will-exhibit the quantity or factor 
a, free from the cubic radical sign ; thus, a .^^b + or, 
, -f 3496c +246. —1656. 
+ ga^Vb'c -j- s^Wbc* = ^ —165c. ^\/6v 424c. 
-f36;i — 18«. — 18«. 
-4- ac 
■VZcn 
h. 
i5c. 34/6+49^V^V +c? ^Vc^^^—i^c.^\/b-^/\,SWb^c*-\-c. 24 /c. 
— w. 
— «. 
— 4 «. 
— 186. 
4 c. 
— 4«. 
Restore for 42, transpose, and double: then 
3 
a. ——a. 
L 3 3 
12^2. -4- \%iX* 2o>» 4.6 
46 ^ ^ 
— c. i c. 
3 3 
■35 
4 ac-^ijic. 
-a. 
— ±b. Wb + 45 Wb'c* - Wc, 
3 3 
^,58 
3 3 
This equation squared, transposed, and divided, by be- 
comes 
