The paper sets out to examine anew the inception of classical dynamics from a highly specific vantage point, bearing on the works of Galileo, Huygens and Newton. The point it seeks to establish is that the generic trajectories followed by bodies having weight turn out to be conic sections as described by Apollonius, precisely because setting the problem of trajectory specification had involved a prior mathematisation owing to the general first principles implicit in the investigation of the link between cause and effect. Introduction of such presuppositions is indeed implied by any reliance on the Galilean law of motion as foundation for the investigation of the relationship between force and motion, be it a centrifugal force for Huygens, or a centripetal force for Newton. The conceivable trajectories, when investigated with the means available to Huygens and Newton, needs must confirm to a quadratic law.