Cyclides were detected and first studied by Ch. Dupin (1784-1873) in  and are since called “Dupin cyclides”. At that time differential geometry was in a very early stage: Only some investigations of L. Euler (1707-1783) and the fundamental work of G. Monge (1746-1818) “L′Application de l′analyse à la géométrie” proceeded but the famous treatise of C.F. Gauss (1777-1855) “Disquisitiones generales circa superficies curvas” appeared only a few years later.
In parallel, after projective geometry was founded by Poncelet (1788-1867), research on algebraic curves and surfaces had a first blossom. Dupin cyclides belong to both of these areas: In differential geometry, they can be defined as ...