A follow-up to When did Liouville come up with the first transcendental numbers?
In 1909, Thue showed that if $\alpha\in\mathbb R$ is algebraic of degree $n$ and $s>\frac12n+1$, and if $c$ is any constant, then $$0<\left|\alpha-\frac pq\right|<\frac c{q^s}$$ has only finitely many solutions. Über Annäherungswerte algebraischer Zahlen, Journal für die reine und angewandte Mathematik, 135 (1909), 284–305.
I would like to know if he proved this in 1908. There are references to "Om en generel i store hele tal uløsbar ligning. Skrifter udgivne af Videnskabs-Selskabet i Christiania; 1908" but I have not been able to access a copy.
There is also "Bemerkungen über gewisse Näherungsbrüche algebraischer Zahlen. Skrifter udgivne af Videnskabs-Selskabet i Christiania; 1908" but according to Mahler this only deals with the case when $\alpha$ is an $n$th root of a rational number. Regarding the "Om en general" and "Über Annäherungswerte" papers, Mahler brackets them together and is tantalisingly unclear as to whether the earlier one is a preliminary paper or actually a proof of the full theorem. Mahler in German, in English translation.
All the papers mentioned in the question are found in Selected Mathematical Papers of Axel Thue from 1977.
Thue's theorem, as described in the question, is not contained in Om en generel i store hele tal uløsbar ligning from 1908. In this paper Thue proves the following theorem (with slightly modernized notation):
Theorem. If $F(x)\in {\Bbb Z}[x]$ is an irreducible polynomial of degree $r>2$, and $c\in \Bbb Z$, then the equation $$q^r F\Bigl({p\over q}\Bigr)=c$$ has only finitely many solutions in integers $p$ and $q$.
There is an addendum to the 1908 paper, apparently added in proof, where Thue states that he has thus proved what seems to be Erster Hilfssatz (first preliminary result) in Über Näherungswerte... from 1909. The addendum ends with the following remark, pointing towards the 1909 paper:
How we by this theorem, through the above argument, considerably can generalize our main result and by this obtain the limit for the denominators in the continued fraction for $\rho$, we shall show in another disertation.