## Harnack's Theorems

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).

References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, 1959.