August Adler worked in Vienna.
In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
In 1906 Adler applied the theory of inversion to solve Mascheroni's construction problems. Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses.
However Adler did not simplify Mascheroni's
proof. On the contrary, his new methods were not as elegant, either in
simplicity or length, as the original proof by Mascheroni.