forms the foundation of geometric  understanding through his work "Elements." 

A central aspect of Euclidean geometry  is the parallel postulate, stating that  

parallel lines never intersect. However, a  historical misinterpretation, particularly  

in the early study of geometry, involved the  logical fallacy of denying the antecedent. 

This fallacy manifested in the incorrect  belief that if two lines are not parallel,  

they must intersect, neglecting the possibility  of skew lines in three-dimensional space,  

which are non-parallel yet do not  intersect as they lie in different planes. 

This early misconception underscores  a limited understanding of geometry,  

primarily confined to two dimensions.

The later development and formalization  

of three-dimensional geometry  clarified this misunderstanding.