Elementary Variants of Affine Configurational Theorems

Krzysztof Prazmowski

Warsaw University, Bialystok

Krzysztof Radziszewski

Gdansk University

Summary.

We present elementary versions of Pappus, Major Desargues and Minor Desargues Axioms (i.e. statements formulated entirely in the language of points and parallelity of segments). Evidently they are consequences of appropriate configurational axioms introduced in the article [2]. In particular it follows that there exists an affine plane satisfying all of them.

Supported by RPBP.III-24.C2.

MML Identifier: PARDEPAP

Contents (PDF format)

Bibliography

[1] Henryk Oryszczyszyn and Krzysztof Prazmowski. Analytical ordered affine spaces. Journal of Formalized Mathematics, 2, 1990.

[2] Henryk Oryszczyszyn and Krzysztof Prazmowski. Classical configurations in affine planes. Journal of Formalized Mathematics, 2, 1990.

[3] Henryk Oryszczyszyn and Krzysztof Prazmowski. Ordered affine spaces defined in terms of directed parallelity --- part I. Journal of Formalized Mathematics, 2, 1990.

[4] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.