Giovanni Girolamo Saccheri

Giovanni Girolamo Saccheri (Italian pronunciation: [dʒoˈvanni dʒiˈrɔlamo sakˈkɛri]; 5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician.

Saccheri was born in Sanremo. He entered the Jesuit order in 1685 and was ordained as a priest in 1694. He taught philosophy at Turin from 1694 to 1697 and philosophy, theology and mathematics at Pavia from 1697 until his death. He was a protégé of the mathematician Tommaso Ceva and published several works including Quaesita geometrica (1693), Logica demonstrativa (1697), and Neo-statica (1708).

He is primarily known today for his last publication, in 1733 shortly before his death. Now considered the second work in non-Euclidean geometry, Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw) languished in obscurity until it was rediscovered by Eugenio Beltrami, in the mid-19th century.

Many of Saccheri's ideas have a precedent in the 11th-century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis), a fact ignored in most Western sources until recently.

It is unclear whether Saccheri had access to that work in translation or he developed his ideas independently. The Saccheri quadrilateral is now sometimes referred to as the Khayyam-Saccheri quadrilateral.

The intent of Saccheri's work was ostensibly to establish the validity of Euclid by means of a reductio ad absurdum proof of any alternative to Euclid's parallel postulate. To do so, he assumed that the parallel postulate was false and attempted to derive a contradiction.

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