Giovanni Girolamo Saccheri (September 5, 1667 - October 25, 1733) was an Italian Jesuit priest and mathematician. Events 1590 - Alexander Farnese 's army forces Henry IV of France to raise the siege of Paris. Events 1147 - The Portuguese, under Afonso I, and Crusaders from England and Flanders conquer Lisbon after a Year 1733 ( MDCCXXXIII) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Italy (Italia officially the Italian Republic, (Repubblica Italiana is located on the Italian Peninsula in Southern Europe, and on the two largest The Society of Jesus ( Latin: Societas Iesu, SJ and SI or SJ, SI) is a Catholic religious order
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). Tommaso Ceva ( December 20, 1648 &ndash February 3, 1737) was an Italian Jesuit Mathematician from
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. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with Euclidean geometry Eugenio Beltrami ( 16 November, 1835 - 4 June, 1899) was an Italian mathematician notable for his work on Non-Euclidean geometry
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. For the Thoroughbred racehorse see Omar Khayyam (horse Ghiyās od-Dīn Abol-Fath Omār ibn Ebrāhīm Khayyām Neyshābūri (غیاث الدین
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. A Saccheri quadrilateral is a Quadrilateral with two equal sides perpendicular to the base
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. Reductio ad absurdum ( Latin for "reduction to the absurd" also known as an apagogical argument, reductio ad impossibile Euclid ( Greek:.) fl 300 BC also known as Euclid of Alexandria, is often referred to as the Father of Geometry In Geometry, the parallel postulate, also called Euclid 's fifth postulate since it is the fifth postulate in Euclid's ''Elements'', is a distinctive To do this he assumed that the parallel postulate was false, and attempted to derive a contradiction. Since Euclid's postulate is equivalent to the statement that the sum of the internal angles of a triangle is 180°, he considered both the hypothesis that the angles add up to more or less than 180°.
The first led to the conclusion that straight lines are finite, contradicting Euclid's second postulate. So Saccheri correctly rejected it. However, today this principle is accepted as the basis of elliptic geometry, where both the second and fifth postulates are rejected. Elliptic geometry (sometimes known as Riemannian geometry) is a Non-Euclidean geometry, in which given a line L and a point
The second possibility turned out to be harder to refute. In fact he was unable to derive a logical contradiction and instead derived many non-intuitive results; for example that triangles have a maximum finite area and that there is an absolute unit of length. He finally concluded that: "the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines". Today, his results are theorems of hyperbolic geometry. In
References
- Martin Gardner, Non-Euclidean Geometry, Chapter 4 of The Colossal Book of Mathematics, W. Martin Gardner (b October 21, 1914, Tulsa Oklahoma) is a popular American mathematics and science writer specializing in Recreational mathematics W. Norton & Company, 2001, ISBN 0-393-02023-1
- M. J. Greenberg, Euclidean and Non-Euclidean Geometries: Development and History, 3rd edition, W. H. Freeman, 1994.
External links
- O'Connor, John J. & Robertson, Edmund F. , “Giovanni Girolamo Saccheri”, MacTutor History of Mathematics archive
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