Abstract
We prove that Bachmann’s Lotschnittaxiom, which states that perpendiculars raised on the two legs of a right angle always meet, is equivalent, with respect to Hilbert’s plane absolute geometry, to the statement \(\mathbf{P}\): “For any point P, line l, with P not incident with l, and any line g, there exists a point G on g for which the distance to P exceeds the distance to l”.
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Pambuccian, V. Another equivalent of the Lotschnittaxiom. Beitr Algebra Geom 58, 167–170 (2017). https://doi.org/10.1007/s13366-016-0307-5
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DOI: https://doi.org/10.1007/s13366-016-0307-5