Formal definition of ruler and compass constructions I would see a formal definition of ruler and compass constructions. I have searched in internet but I haven't found a very formal definiton.
Update:
I founded these lectures about my question:
1 - https://www.isibang.ac.in/~jay/MC/Raghavan%201.pdf
2 - https://conf.math.illinois.edu/~rotman/ruler.pdf

You are given a starting set $C_0$ of points, which are declared to be constructed.
Figures (lines and circles) may be drawn. A point that is not in the starting set is a constructed point must be an intersection point of two drawn figures. A line may only  be drawn through 2 constructed points. A drawn circle may only be centered at a constructed point, and a drawn circle's radius must be the distance between 2 constructed points.
A constructed point must be obtained as an intersection point of 2 drawn figures in a finite number of steps:
The set $F_0$ is the empty set. Step $n+1$ ($n\ge 0$) is to draw the set $F_{n+1}$ of all figures that can be drawn using only the set $C_n$ of points and the rules above. 
The set $C_{n+1}$ contains (only) the points of intersection of pairs of members of $F_{n+1}$  and the members of $C_0$.
Unless stated otherwise, it is assumed that $C_0$ contains just 2 points. 
