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We study Saccheri`s three hypotheses on a two right-angled isoscelesquadrilateral, with a rectilinear summit side. We claim that in the Hilbert`sfoundation of geometry the euclidean parallelism is a theorem, and in theh-plane the hyperbolic parallelism under a hyperbolic transformation has imagethe euclidean parallelism. We prove that Saccheri`s rectilinear quadrilateralscan be only rectangle. Finally we believe that the independence of theeuclidean parallel postulate is just a matter of philosophy of logic.

Saccheri's Rectilinear Quadrilaterals