In plane kinematics, the knowledge of the location of the instantaneous centre — deriving from the eighteenth century — affords information which is partial and very incomplete. But it is the case that there always exists an enumerable set of$cardinal points$, as they may be named, having the following characteristic: all the properties of the path of any, and every, element or series of elements, fixed in the moving plane, are completely determined by the configuration of this set of cardinal points. In this manner is given a very simple and complete synthesis of the whole realm of plane kinematics.