This note could find use as enrichment material in a course on the classical geometries; its preliminary results could also be used in an advanced calculus course. It is proved that if a , b and c are positive real numbers such that a[squared] + b[squared] = c[squared] , then cosh ( a ) cosh ( b ) greater than cosh ( c ). The proof of this result uses an inequality involving combinatorial symbols and properties of absolutely convergent infinite series. As a corollary, it follows that if a neutral geometry G contains at least one right triangle which satisfies the conclusion of the Pythagorean Theorem, then G is (isomorphic to) Euclidean geometry and, hence, satisfies Playfair's form of the parallel postulate.