Editing Line (geometry) (section)

=== In axiomatic systems ===
In [[synthetic geometry]], the concept of a line is often considered as a [[primitive notion]],<ref name=":0" />{{Rp|page=95}} meaning it is not being defined by using other concepts, but  it is defined by the properties, called  [[axiom]]s, that it must satisfy.<ref>{{citation |last=Coxeter |first=H.S.M |title=Introduction to Geometry |url=https://archive.org/details/introductiontoge0002coxe |page=4 |year=1969 |edition=2nd |place=New York |publisher=John Wiley & Sons |isbn=0-471-18283-4 |url-access=registration}}</ref> 

However, the [[axiomatic]] definition of a line does not explain the relevance of the concept and is often too abstract for beginners. So, the definition is often replaced or completed by a ''mental image'' or ''intuitive description'' that allows understanding what is a line. Such descriptions are sometimes referred to as definitions, but are not true definitions since they cannot used in [[mathematical proof]]s. The "definition" of line in [[Euclid's Elements]] falls into this category;<ref name=":0" />{{Rp|page=95}} and is never used in proofs of theorems.