After graduating from high school, Euler studied law in Marburg and then worked in various legal positions from 1936 to 1944.

At the 1949 federal party conference of the FDP in Bremen, he wanted to enforce a commitment to rearmament but failed due to the anti-militarist sentiment of the majority of delegates.

[3] While the first demand was passed with a clear majority because of the KPD's decisive influence on the VVN, the proposal regarding the peace society failed; after all, Harald Abatz [de], an FDP member, was the federal chairman of the DFG.

Both sought to exonerate the so-called main culprits and those accused of all current or impending sanctions at the time.

In 1952, he called for the Baden-Württemberg FDP/DVP, which he described as demi-Marxists, to be excluded from the party after Reinhold Maier entered into a coalition with the SPD in the southwestern state.

In his first electoral term, he was also chairman of the expert committee for the reorganization of the federal territory, in which he represented far-reaching demands for a reduction in the number of German states.

Together with the so-called ministerial wing (including the four previous FDP ministers of the Adenauer II cabinet: Franz Blücher, Fritz Neumayer, Victor-Emanuel Preusker, and Hermann Schäfer), Euler, after whom these 16 MPs were also called the Euler Group, left on December 23rd.

Towards the end of the electoral term, he became chairman of the Bundestag Committee on Nuclear Issues for the DP/FVP parliamentary group.