- Not to be confused with Pasha 's axiom about a line passing through a triangle.
Pasha's theorem is a statement formulated by the German mathematician Moritz Pasha in 1882 [1] . It is an example of a statement in Euclidean geometry that cannot be deduced from Euclidean postulates . In the Hilbert axiomatics, the Pasha theorem is derived, in particular, from the Pasha axiom .
Content
- 1 Formulation
- 2 See also
- 3 notes
- 4 Literature
- 5 Links
Wording
Suppose that the points A , B , C , and D lie on a line and it is known that B lies between A and C , and C lies between B and D , then B lies between A and D [2] .
See also
- Axiom Pasha
Notes
- β Pasch, Moritz. Vorlesungen ΓΌber neuere Geometrie (Leipzig, 1882)
- β Coxeter (1969 , p. 179). In this book, this statement is given in Β§ 12.274, but is not called the Pasha theorem.
Literature
- Coxeter, HSM Introduction to geometry. - 2nd. - John Wiley and Sons, 1969 .-- ISBN 0-471-18283-4 .
Links
- Weisstein, Eric W. Pasch's Theorem at Wolfram MathWorld .