292 Mr. Wilson’s Essay on the 
in pairs, and three of their differences be also taken so as to 
have their sum nothing, (a — ■ b, a 2, b, — 2a - 6) ; if then 
each sum be formed into a binomial, by joining to it its corre- 
spondent difference multiplied by the imaginary surd y/— 
the quantities so formed 
a -f b a — b\s/ — £ 
— a - {- a -f- 2 6^ \/ — £ 
— b — 2 a — 6]v/ — y will have the 
Example 1st, 
O -j- b -j- d — b) y/ — £ 
-f b\ z -f 2/tf + b}x a — b] y/ — £ 
'2 a 3 -f- 8^ 6 4- 2 ft z 
.a-\-b X a — 6\v/ — y= ... J 6) \/ — y) 
a -f- 6 -f o — h s/ — y 
2 fl 3 + ioa*ft + loab 1 -^ 2 ft 3 . j — r\a T\ / . 
X \- 2 .a + b\ xa — 6) >/--■§- 
+ 
+ 6]* X a 
v/-i 
2 tf 3 -f 2 fi z ft+ 2 fl ft a _2 ft 3 
3 
+ ±ii x r=rj\ v /_x 
12 a* 6 4- 12 a b* 
&T * — j * 
« 3 4- 1 2 ft— 12 a ft*— 8 ft 3 
3^-3 
= a + l)\+a — b\\/— i) 
-a + a + 2&|v/— i 
-fl-f-a-f2 6ly/— £ 
a 1 — 2 ^— 4<z6 \/ 
-a 1 — 4 a ft — 46 s 
2 a z — 4 a ft — 4 ft z 
2« 2 — 4 ^ 6 ! y/ — £ = ... — 4 + 0 -j- 2 &J\/ — y| 
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