Giovanni Girolamo Saccheri
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Giovanni Girolamo 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. He taught philosophy at Turin from 1694 to 1697, and philosophy, theology, and mathematics at Pavia from 1697 until his death. He was a protege 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 precedent in the 11th Century Persian polymath Omar Khayyam'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 this work in translation, or 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 this he assumed that the parallel postulate was false, and attempted to derive a contradiction. In fact he was unable to derive a logical contradiction, and instead derived many unlikely results such as the existence of triangles whose angles add up to more than 180°. His results thus instead formed theorems of hyperbolic geometry.
External links
- John J. O'Connor and Edmund F. Robertson. [] at the MacTutor History of Mathematics archive.
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