# WHAT IS ELEMENTARY GEOMETRY ? 17 mentary logic

@inproceedings{TarskiWHATIE, title={WHAT IS ELEMENTARY GEOMETRY ? 17 mentary logic}, author={Alfred Tarski} }

In colloquial language the term elementary geometry is used loosely to refer to the body of notions and theorems which, following the tradition of Euclid's Elements, form the subject matter of geometry courses in secondary schools. Thus the term has no well determined meaning and can be subjected to various interpretations. If we wish to make elementary geometry a topic of metamathematical investigation and to obtain exact results (not within, but) about this discipline, then a choice of a…

## 2 Citations

Axiomatizations of Hyperbolic Geometry: A Comparison Based on Language and Quantifier Type Complexity

- Mathematics, Computer ScienceSynthese
- 2004

The incidence-based formulation of hyperbolic geometry requires some axioms of the quantifier-type \forall\exists\forall, while the axiom system based on congruence and order can beformulated using only \for all\existed-axioms.

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