# 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

• Points $\mathcal P$ constitute the elements of linear geometry.
• Points $\mathcal P$ and straight lines $\mathcal L$ constitute the elements of plane geometry.
• Points $\mathcal P$, straight lines $\mathcal L$, and planes $\Pi$ constitute the elements of spacial geometry.

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", Studienbücherei, 1971
4. Hilbert, David: "Grundlagen der Geometrie", Leipzig, B.G. Teubner, 1903