@article{Pambuccian2022OnAS,
title={On a splitting of the parallel postulate},
author={Victor Pambuccian},
journal={Journal of Geometry},
year={2022},
volume={113},
pages={1-13}
}

While the Euclidean parallel postulate P can be replaced with the conjunction of the two axioms, “Given three parallel lines, there is a line that intersects all three of them” ( ML ) and “Given a line a and a point P on a , as well as two intersecting lines m and n , both parallel to a , there exists a line g through P which intersects m but not n ” ( S ) to obtain plane Euclidean geometry based on Hilbert’s plane absolute geometry $${{\mathcal {A}}}$$ A , it is shown if $${{\mathcal {A}}}$$ A… Expand

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