Section 1. General expression of an algebraic fuunction: Part 6

Translated by me as:

From which it follows, we can say

                                                                   v = f(r', r''...ⁿ√ p)

where p is a function of  μ-1 order but r',r''... are functions of  μ order and at most m-1 degree, and we can always assume it is impossible to express ⁿ√ p as a rational function of these quantities.


Commentary:


Here v is from the previous discussion an algebraic function of order μ and degree m. Abel chooses to emphasize the dependence of v on one particular radical term and express the dependence on all other radical terms by using the quantities  r',r''....