Giovanni Gerolamo Saccheri - Definition and Overview

Giovanni Gerolamo Saccheri (September 5, 1667 - October 25, 1733) was an Italian Jesuit priest and mathematician.

Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694.

In 1733, shortly before his death, Saccheri published what is now considered the first work in non-Euclidean geometry, Euclides ab omni noevo vindicatus (Euclid Freed of Every Flaw). The book languished in obscurity until it was rediscovered by Eugenio Beltrami.

The intent of Saccheri's work was to provide a reductio ad absurdum proof of Euclid's parallel postulate. He assumed that the parallel postulate was false, and attempted to derive a contradiction. He derived many unlikely results (such as the existence of triangles whose angles add up to more than 180°), but was unable to derive a logical contradiction. His results are instead theorems of hyperbolic geometry.