Ibn Sahl’s machines to draw conics continuously

Abstract

The article describes the machines proposed by Ibn Sahl, who lived in the tenth century, to draw continuously the three irreducible conics. These machines are based on the use of a director circle which, just as the directrix of a parabola allows one to draw the conic as a locus, and to find the tangent line at each point. All this is demonstrated with a touchscreen: the visitor may choose a conic and start several animations which show the geometry of the conic and its envelope. The corresponding machine is operated by the visitor who, by moving an on-screen pencil with their finger, can draw the conic, simulating the actual working of the machine.