Harnack's TheoremsHarnack'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 withthat 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.
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