Planetary hours of the Prague astronomical clock and the trisection of the angle. (Q2856954)

Planetary hours divide each day into 12 equal parts and also each night into 12 equal parts. On astronomical dials of ancient astrolabes (including the Prague horologe) they are represented by curved arcs which seem to be circular. For instance, the horizon, which corresponds to the 0th and 12th planetary hour, is a circle due to properties of the stereographical projection of the celestial sphere onto the astronomical dial. Nevertheless, the author proved the following statement:NEWLINENEWLINEIf the arc of planetary hours were circular, then an arbitrary angle could be trisected by ruler and compass. Since this is impossible, the arcs of planetary hours are not circular except for the horizon.