Giovanni Gerolamo Saccheri

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

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

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In 1733, shortly before his death, Saccheri published what is now considered the second work in non-Euclidean geometry, Euclides ab omni noevo vindicatus (Euclid Freed of Every Flaw) after the work of the Persian mathematician Omar Khayy?m. The book languished in obscurity until it was rediscovered by Eugenio Beltrami. Saccheri borrowed many ideas from Khayyam's Ris?la f? sharh m? ashkala min mus?dar?t Kit?b 'Ugl?dis http://www.math.cornell.edu/~dwh/books/eg00/00EG-biblio/, a fact deliberatly ignored in most of the Western references. Despite the fact that Omar Khayyam outlined, introduced and calculated his quadrilateral in his work 700 years earlier than Saccheri, the Western sources insist on referring to this quadrilateral as "the Saccheri quadrilateral".

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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.

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