Xii., and gave a further extension and complete account of his theory in his Theorie der algebraischen Curven (1839).
While there he published his System der analytischen Geometrie, auf neue Betrachtungsweisen gegrundet, and insbesondere eine ausfuhrliche Theorie der Curven driller Ordnung enthaltend (Berlin, 1835).
Here he published his Theorie der algebraischen Curven, which formed a continuation of the System der analytischen Geometrie.
We now come to Julius Plucker; his " six equations " were given in a short memoir in Crelle (1842) preceding his great work, the Theorie der algebraischen Curven (1844).
The expression for the number of inflections 3m(rn - 2) for a curve of the order m was obtained analytically by Plucker, but the theory was first given in a complete form by Hesse in the two papers " Uber die Elimination, u.s.w.," and " Uber die Wendepuncte der Curven dritter Ordnung " (Crelle, t.
P. 337), and in part carried out by Hesse in the memoir " Uber Curven dritter Ordnung " (Crelle, t.
Investigations in regard to them are given by Plucker in the Theorie der algebraischen,Curven, and in two memoirs by Hesse and Jacob Steiner (Crelle, t.
The points called foci presented themselves in the theory of the conic, and were well known to the Greek geometers, but the general notion of a focus was first established by Plucker (in the memoir " Uber solche Puncte die bei Curven einer hdheren Ordnung den Brennpuncten der Kegelschnitte entsprechen " (Crelle, t.
Clebsch, " Uber die Singularitaten algebraischer Curven " (Crelle, t.
Connected with this is the paper Vom Kriimmungsschwerpuncte ebener Curven, which contains numerous properties of pedals and roulettes, especially of their areas.