A simple version of the Eratosthenes mesolabium that finds square roots. (This will find square roots of numbers between 0 and 1.)
Move point C up and down using the mouse until the length of CH is the desired value. Then use the mouse to move triangle QSH back and forth until point B is on the line from A to C. Then the length of BG will be the square root of the length of BH.
(This is based loosely on pp.184-185 of David Burton, The History of Mathematics: An Introduction, Seventh Edition, 2011, McGraw-Hill.)