Let 
be the orders of singular points on a curve (Coolidge 1959, p. 56). Harnack's
first theorem states that a real irreducible curve of order 
cannot have more than
 |
circuits (Coolidge 1959, p. 57).
Harnack's second theorem states that there exists a curve of every order with the maximum number of circuits compatible with that order and with a certain number of double points, provided that number is not permissible for a curve of lower order (Coolidge 1959, p. 61).
