Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Homotheties and Shears in Affine Planes

Henryk Oryszczyszyn

Warsaw University, Bialystok

Krzysztof Prazmowski

Warsaw University, Bialystok
Summary.

We study connections between Major Desargues Axiom and
the transitivity of group of homotheties. A formal proof of the theorem
which establishes an equivalence of these two properties of affine
planes is given. We also study connections between trapezium version
of Major Desargues Axiom and the existence of the shears in affine
planes. The article contains investigations on ``Scherungssatz".
Supported by RPBP.III24.C2.
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[2]
[1]
[3]
[5]
[6]
[4]
[7]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
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 [2]
Czeslaw Bylinski.
Partial functions.
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1, 1989.
 [3]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Analytical ordered affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Classical configurations in affine planes.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Ordered affine spaces defined in terms of directed parallelity  part I.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Parallelity and lines in affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Transformations in affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
Received September 21, 1990
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