go Mr. waring on the General 
Be deduced the equation free from radicals which was 
to be found.. 
3. II. Let x=a-</p+h\/p z , then will the correfpondent 
equation free from radicals be x ttt+ ' — 2 n+ 1 b n apx n — 
It 1 — 1 •? , 71— I ® X 71 — I X Tl “I" 2 ly—i f # 7 1' ~ 2 
x 10 cPpx x 2^ + i b a^px 
r 1.2.2.A.C 1 
— — * - 1 X a 1 - 4 X a +_3 x + j Z±l±2 
1.2.3.4.5.6.7 
1. 2. 3. 4.5. 6.7. 8. 9 
T.n+ib” 4 a’ ) px n ~' 
».»*— i.a — 4.* — 9»a — 2 X 2«-i 
1. 2. 3. 4.5.6. 7. 8. 9. ...2?i — 1 
2«+ i ba zn -'px=a™ +l p+b zn+ 'p\ 
This may be derived from the fame principles as the 
preceding. 
3. III. In general let the equation be x-a'iyp+b^'p z t 
then will the equation free from radicals become x m — 
ma m ~ 1 bpx - m. - — - a m ~ A b z px r - m . 
m-\ m — 5 
a b z px z - 
m. 
2 23 
„_5 6 
3 4 2 3 3 4 5 
- See. . = a m p ± b m p z ; if m denotes an even number, it 
will be —b m p\ but if an odd number, it will be +b m p\ 
4. I. Let n denote an odd number, and x — ap/p + 
biyp l y then will x n -p (pa”~ z bx* + n”^ll a n ~~ ( ‘b z x' i + n. 
LlZ. 
2 
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