Plucker aimed at furnishing modern geometry with suitable analytical methods so as to give it an independent analytical development.
Plucker finally (Gergonne Ann., 1828-1829) showed how many points must be taken on a curve of any degree so that curves of the same degree (infinite in number) may be drawn through them, and proved that all the points, beyond the given ones, in which these curves intersect the given one are fixed by the original choice.
In 1833 Plucker left Bonn for Berlin, where he occupied a post in the Friedrich Wilhelm's Gymnasium.
In 1836 Plucker returned to Bonn as ordinary professor of mathematics.
From this time Plucker's geometrical researches practically ceased, only to be resumed towards the end of his life.