The hands-on models built by the Math Machines Association enable to go through the main steps in history when the conic sections theory developed. The timeframe analysed goes from classical Greece (Menaechmus and Apollonius) to 19th century.
Geometers from classical Greece used to name \"solid curve\" what is currently referred to as conic. They in fact used to study the properties of the curve in the portion of sapce occupied by the cone to which the curve belonged. A few centuries later, movement was introduced in mathematics by Descartes. At the same time Newton and MacLaurin developed organic geometry where the properties of the curve, embedded in appropriate mechanisms, are used to generate (draw) a curve.
Analytic geometry gathers all the conics under the same representation based on a two variables second order polynomial equation. Instead, starting from Desargues, projective geometry considers conics as anamosphosis of a circumference convertible one into the other by means of a projection. Moreover, conics are now thought as sets of points or envelopes and this takes to discovering new properties and new methods to draw them.
While as forms and visible figures conics have obviosly been the same all through the ages, in terms of mathematical objects they\'ve undergone a continuous development in the language used for describing them and the theoretical contest in which they are thought, built, embedded.