Hello, Garas!
Construct the line segment which is a geometric mean of two given line segments. Code:
S * * *
* *
*  *
*  x *

*  M *
**+*
P a Q b R
Measure $\displaystyle a=PQ$ and $\displaystyle b=QR$ consecutively on a line.
Bisect the line and locate its midpoint $\displaystyle M$.
Use the $\displaystyle M$ as center and $\displaystyle PM$ as radius,
. . and draw a semicircle.
At $\displaystyle Q$, erect a perpendicular $\displaystyle x$ meeting the semicircle at $\displaystyle S.$
Then $\displaystyle x$ is the geometric mean of $\displaystyle a$ and $\displaystyle b\!:\;\;x \:=\:\sqrt{ab.}$
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Why would we need such a construction?
Suppose we have an $\displaystyle a\times b$ rectangle
. . and we need a square with the same area.
Code:
**
**  
    x
b    
   
** **
a x
Then: .$\displaystyle x^2 \:=\:ab \quad\Rightarrow\quad x \:=\:\sqrt{ab}$
Edit: too slow (again) . . . *sigh*
.