Euclid’s fifth postulate – the dotted line is the unique line parallel to the line L Illustration: Junaid Mubeen. As it happened, Euclid was never quite able to produce a proof of the fifth ...

Two equivalent versions of Euclid’s fifth postulate are: (i) ‘For every line l and for every point P not lying on l, there exists a unique line m passing through P and parallel to l’.

Nature - Euclid's Parallel Postulate: its Nature, Validity, and Place in Geometrical Systems. Skip to main content. Thank you for visiting nature.com.

THE appearance of this tract is a welcome sign of the growing interest in the foundations of geometry. Those who, greatly daring, first disputed or denied Euclid's fifth postulate were treated, if ...