I was reading practising for Math Olympiads and reading a bit about field extensions with the compass and straightedge constructions and though all steps are straight-forward, one thing bugs me: They all assume a segment of length $1$ already given. Take for example: Exemplary Wikipedia Article - Multiplication, division and square roots all rely on this assumption.
Why is this so and doesn't this violate the principles of compass and straightedge construction? Furthermore, am I allowed to assume a segment of length $1$ as given?