Pappus axiom
From Encyclopedia of Mathematics
If 
and 
are two distinct straight lines and 
and 
are distinct points on 
and 
, respectively, and if none of these is the point of intersection of 
and 
, then the points of intersection of 
and 
, 
and 
, 
and 
are collinear.
Figure: p071140a
The truth of Pappus' axiom is equivalent to the commutativity of the skew-field of the corresponding projective geometry. The Desargues assumption is a consequence of Pappus' axiom (Hessenberg's theorem), and at the same time Pappus' axiom is a degenerate case of the Pascal theorem. The axiom was proposed by Pappus (3rd century).
Comments
References
| [a1] | O. Veblen, J.W. Young, "Projective geometry" , 1 , Ginn (1910) |
How to Cite This Entry:
Pappus axiom. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pappus_axiom&oldid=12149
Pappus axiom. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pappus_axiom&oldid=12149
This article was adapted from an original article by P.S. ModenovA.S. Parkhomenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article