Wybrane problemy zadań konstrukcyjnych na płaszczyźnie euklidesowej i wykorzystanie do ich rozwiązywania twierdzeń geometrii rzutowej

Abstract

The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose, the theoretical backgrounds of projective geometry have been used. It has been proved that in the projective approach some constructions on a Euclidean plane become linear constructions. In particular, a linear construction of this type may be the typical operation of inversion in respect of a circle and an arbitrary conic as well as its generalization, which in reference literature is known under the name of Hirst transformation.