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In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result in plane geometry which cannot be derived from
Euclid's postulates Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axiom ...
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Statement

The statement is as follows: ere, for example, (, , ) means that point lies between points and .


See also

* Ordered geometry * Pasch's axiom


Notes


References

* *


External links

* Euclidean plane geometry Foundations of geometry Order theory Theorems in plane geometry {{elementary-geometry-stub