In 1797 Lorenzo Mascheroni published result that
Every geometric construction that can be carried out by compasses and ruler may be done without ruler.
This theorem named after Lorenzo Mascheroni a Mascheroni theorem. By the way it turned out that Georg Mohr proved this theorem back in 1672 already, but this publication remained unknown, since was written in Latin I guess.
I am looking for elementary proof of the theorem.
We have to prove that the following three constructions can be done with only compasses:
- Points of intersection of two circles given by center and one of the points for each circle
- Points of intersection of a circle (given by center and one of its points) and a straight line (given by two points).
- Point of intersection of two straight lines each of them given by two points.
On this route I found the paper "A short elementery proof of the Mohr-Mascheroni Theorem" by Norbert Hungerbuhler.
But it looks unsatisfactory for me since it uses measurement by means of compasses.
So I believe that there must be some other reference on elementary proof of Mohr-Mascheroni theorem which does not use methods like a measurement by means of compasses.
If anyone knows such a text please inform me to.