Abstract
This chapter describes the application of harmonic quadruples. It presents the joining of two diagonal points of a complete quadrangle, the points of intersection, and the remaining two sides of the complete quadrangle. The diagonal points of a complete quadrangle are not collinear (Axiom F). There exists an example of a pappian projective plane satisfying axiom. It is chosen to include the pappian condition in the consistency statement as one shall be working, ultimately, with Axiom F in pappian projective planes. The independence of Axiom F from the axioms for a pappian projective plane is immediate if one considers a fanian plane as an independence incidence basis. A set of axioms for a projective plane together with Axiom F is self-dual. The chapter discusses whether some permutation of diagonal points other than those appearing can be harmonic.
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