### From Euclid into Chaos

#### Noneuclidean Geometry Chronograph

- 1733, Saccheri (proposes alternatives to Post. 5, only hypothetical)
- 1763, Klugel (suggests Post. 5 cannot be proved as a theorem)
- 1766, Lambert (discovers non-euclidean geometry)
- 1794, Gauss (develops non-euclidean geometry, tries to prove
the world is Euclidean)
- 1826, Lobachevsky (develops hyperbolic geometry)
- 1829, Lobachevsky (publishes hyperbolic geometry)
- 1831, Bolyai (publishes hyperbolic geometry)

Revised 05 February 1996 by Ralph Abraham
<abraham@vmi.vismath.org>