Section 2: Properties of algebraic functions which satisfy a given equation: Part 2

Translated by me as: 

Now I say that equation (3) can not take place unless there is separately

r₀  =  0 , r₁ =  0  . . . r_n-1 =  0 .

Indeed otherwise we would have with  p ^{1 / n}  =  z , [original text corrected]  the two equations

z ⁿ  -  p =  0 , and

r₀ +  z ¹  + r₂  . z ²   ...+  r _n-1 . z ^n-1 =  0

Commentary: 

z satisfies an equation of nth order and also an equation of order n-1