Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Shear Theorems and Their Role in Affine Geometry

Jolanta Swierzynska

Warsaw University, Bialystok

Bogdan Swierzynski

Warsaw University, Bialystok
Summary.

Investigations on affine shear theorems, major and
minor, direct and indirect. We prove logical relationships which hold
between these statements and between them and other classical affine
configurational axioms (eg. minor and major Pappus Axiom, Desargues Axioms
et al.). For the shear, Desargues, and Pappus Axioms formulated in terms of
metric affine spaces we prove they are equivalent to corresponding statements
formulated in terms of affine reduct of the given space.
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[2]
[4]
[5]
[1]
[3]
[6]
[7]
Contents (PDF format)
Bibliography
 [1]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Analytical metric affine spaces and planes.
Journal of Formalized Mathematics,
2, 1990.
 [2]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Analytical ordered affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [3]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Classical configurations in affine planes.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Ordered affine spaces defined in terms of directed parallelity  part I.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Henryk Oryszczyszyn and Krzysztof Prazmowski.
Parallelity and lines in affine spaces.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Jolanta Swierzynska and Bogdan Swierzynski.
Metricaffine configurations in metric affine planes  part I.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Jolanta Swierzynska and Bogdan Swierzynski.
Metricaffine configurations in metric affine planes  part II.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received April 19, 1991
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