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[HM] Re: Playfair's axiom
Posted:
Sep 1, 2003 4:26 AM
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I believe that the original question dealt with who was the first
to posit the "parallel to a line through a point" form of Euclid's
postulate. Although some have claimed that Proclus hints at it in his
discussion of Euclid I.31, I don't believe it is that explicit.
Calinger claims that Playfair writes :
" Given a line l and a point P not on l, there exists
one and only one line m containing P and no points of l."
It is contained in section 11.1 of Elements of Geometry written in
1795.
I have a copy of Davies Legendre dated 1844 which gives the
following axiom on page 13 :
" 12. Through the same point, only one straight line
can be drawn which shall be parallel to a given
line."
Considering that Legendre published his Elements de Geometrie in
1794, is it possible that the first explicit modern statement is
his? Did he lose credit for a discovery once again?
Jim Kiernan
Brooklyn College
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