Editing Desargues's theorem (section)

===Two-dimensional proof===
As there are [[non-Desarguesian projective plane]]s in which Desargues's theorem is not true,<ref>The smallest examples of these can be found in {{harvnb|Room|Kirkpatrick|1971}}.</ref>  some extra conditions need to be met in 
order to prove it. These conditions usually take the form of assuming the existence of sufficiently many [[collineation]]s of a certain type, which in turn leads to showing that the underlying algebraic coordinate system must be a [[division ring]] (skewfield).<ref>{{harv|Albert|Sandler|2015}}, {{harv|Hughes|Piper|1973}}, and {{harv|Stevenson|1972}}.</ref>