Elements

Before you start

Assumes

nothing but a straight edge, a compass, and the willingness to be shown rather than told

FreeIntermediatelink checked 17 Sept 2026

Groundwork for

Works in the library that name this one as a prerequisite.

• Non-Euclidean Geometry: A Critical and Historical Study of its DevelopmentRoberto Bonola, 1912Traces two thousand years of failed attempts to prove the parallel postulate and shows that the failures were the discovery: the postulate is independent, so consistent geometries exist without it.
• Projective GeometryOswald Veblen and John Wesley Young, 1910Rebuilds projective geometry from explicit axioms of incidence alone, demonstrating that a geometry can be developed with no notion of distance or angle anywhere in it.
• Geometrical Researches on the Theory of ParallelsNikolai Lobachevsky, 1840Develops a self-consistent geometry in which Euclid's parallel postulate fails, giving the first worked demonstration that a non-Euclidean geometry is logically possible.