Giovanni Gerolamo Saccheri (September 5, 1667 – October 25, 1733) was an Italian Jesuit priest and mathematician. Jump to: navigation, search September 5 is the 248th day of the year (249th in leap years). ...
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Jump to: navigation, search October 25 is the 298th day of the year (299th in leap years) in the Gregorian Calendar, with 67 days remaining. ...
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The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ...
Jump to: navigation, search Roman Catholic priest LCDR Allen R. Kuss (USN) aboard USS Enterprise A priest or priestess is a holy man or woman who takes an officiating role in worship of any religion, with the distinguishing characteristic of offering sacrifices. ...
A mathematician is a person whose area of study and research is mathematics. ...
Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694. Events February 6  James Stuart, Duke of York becomes King James II of England and Ireland and King James VII of Scotland. ...
Events February 6  The colony Quilombo dos Palmares is destroyed. ...
In 1733, shortly before his death, Saccheri published what is now considered the second work in nonEuclidean geometry, Euclides ab omni noevo vindicatus (Euclid Freed of Every Flaw) after the work of the Persian mathematician Omar Khayyám. The book languished in obscurity until it was rediscovered by Eugenio Beltrami. Saccheri borrowed many ideas from Khayyam's Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis [1], a fact deliberately 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". Behavior of lines with a common perpendicular in each of the three types of geometry The term nonEuclidean geometry (also spelled: nonEuclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ...
Tomb of Omar KhayyÃ¡m, Neishapur, Iran. ...
Eugenio Beltrami (16 November 1835  18 February 1900) was an Italian mathematician notable for his work on nonEuclidean geometry, electricity, and magnetism. ...
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. Jump to: navigation, search Reductio ad absurdum (Latin for reduction to the absurd, traceable back to the Greek Î·Ì” ÎµÎ¹Ï‚ Î¬Ï„Î¿Ï€Î¿Î½ Î±Ï€Î±Î³Ï‰Î³Î·, reduction to the impossible, often used by Aristotle) is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then conclude...
Jump to: navigation, search Euclid Euclid of Alexandria (Greek: ) (ca. ...
a and b are parallel, the transversal t produces congruent angles. ...
Jump to: navigation, search A triangle is one of the basic shapes of geometry: a twodimensional figure with three vertices and three sides which are straight line segments. ...
Jump to: navigation, search A triangle immersed in a saddleshape plane (an hyperbolic paraboloid), as well as two diverging parallel lines. ...
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