What is the simplest way to find $\frac{n}{7}th$ of a line with mathematical proof? I'd like to know if it is possible to find out the simplest way to get $\frac{1}{7}$, $\frac{2}{7}$, $\frac{3}{7}$, $\frac{4}{7}$, $\frac{5}{7}$ and $\frac{6}{7}$ of a line in 2-dimensional geometry. Straight edge and compass preferred as tools.
I have drawn one example which shows $\frac{1}{7}$, $\frac{6}{7}$, $\frac{3}{7}$ and $\frac{4}{7}$ parts of the line below. Dotted lines are half points of the square. Blue ones are aid lines. The last line from B to G intersects point H, which is giving hoped fractions of seven.

In addition I'm forward to see mathematical proof of the geometry.

From first chapter of "Four pillars of geometry", John Stillwell

