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.

MML Identifier: CONMETR1

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. Metric-affine configurations in metric affine planes --- part I. Journal of Formalized Mathematics, 2, 1990.
[7] Jolanta Swierzynska and Bogdan Swierzynski. Metric-affine 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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