Projective Planes

Michal Muzalewski

Warsaw University, Bialystok

Summary.

The line of points $a$, $b$, denoted by $a\cdot b$ and the point of lines $A$, $B$ denoted by $A\cdot B$ are defined. A few basic theorems related to these notions are proved. An inspiration for such approach comes from so called Leibniz program. Let us recall that the Leibniz program is a program of algebraization of geometry using purely geometric notions. Leibniz formulated his program in opposition to algebraization method developed by Descartes.

MML Identifier: PROJPL_1

Contents (PDF format)

1. Projective Spaces
2. Projective Planes
3. Some Useful Propositions

Bibliography

[1] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[2] Wojciech Leonczuk and Krzysztof Prazmowski. Incidence projective spaces. Journal of Formalized Mathematics, 2, 1990.

[3] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[4] Wojciech A. Trybulec. Axioms of incidency. Journal of Formalized Mathematics, 1, 1989.

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