Abstract
It is shown that the axiom ‘For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse’, when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom ‘Every line which passes through the interior of a sphere intersects that sphere’.
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Blass, A., Pambuccian, V. On a problem of H. N. Gupta. Geom Dedicata 61, 329–331 (1996). https://doi.org/10.1007/BF00150031
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DOI: https://doi.org/10.1007/BF00150031