Definition: Points, Straight Lines, and Planes

Let $\mathcal P$ be an arbitrary non-empty set. The elements $A,B,C\ldots \in \mathcal P$ are called points.

Let $\mathcal L$ be an arbitrary non-empty set. We call the elements $a,b,c \ldots \in \mathcal L$ lines.

Let $\Pi$ be an arbitrary non-empty set. We call the elements $\alpha,\beta,\gamma \ldots \in \Pi$ planes.

Notes

Axioms: 1 2
Definitions: 3
Proofs: 4 5 6 7
Propositions: 8 9 10 11
Sections: 12


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References

Bibliography

  1. Lee, John M.: "Axiomatic Geometry", AMC, 2013
  2. Berchtold, Florian: "Geometrie", Springer Spektrum, 2017
  3. Klotzek, B.: "Geometrie", Studienb├╝cherei, 1971
  4. Hilbert, David: "Grundlagen der Geometrie", Leipzig, B.G. Teubner, 1903