Section 1: General expression of an algebraic function: Part 11

Translated by me as:

From all the forgoing  we conclude:
If v is an algebraic function of order μ and degree m, we can always pose:

                                  v =   q₀ +  p ^{1 / n} + q₂  . p ^{2 / n} + ... q _n-1. p ^{( n-1) / n} ; 

where n is a prime number, q_0, q_{2 ...} q _n-1 are algebraic functions of order μ and degree m - 1 and also, p is an algebraic function of order μ - 1 and  p ^{1 / n} cannot be expressed as a rational function of  q_0, q_{2 ...} q _n-1. [original text corrected]

Commentary:
 
This is just a restatement of what has been established up to this point. There is a misprint where q₁ should be replaced by q_2. Abel does not mention it but p is of unrestricted degree.