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The connection between two geometrical axioms of H. N. Gupta

1969
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Proceedings of the American Mathematical Society
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The answer is given here to a problem raised by H. N. Gupta at the end of [l ], namely, if two axioms (E) and (B) are equivalent when added to Euclidean geometry of arbitrary dimension over arbitrary ordered fields. (B) states that, 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 perpendicular drawn from the right angle vertex. (B) holds in the w-dimensional Cartesian space SniS) over an ordered

doi:10.1090/s0002-9939-1969-0246189-1
fatcat:62cla3j4jzajrlstnzkbqcrsfq