Saccheri

Some articles on saccheri:

Giordano Vitale - Work
... Giordano is most noted nowadays for a theorem on Saccheri quadrilaterals that he proved in his 1668 book Euclide restituo (named after Borelli's Euclides Restitutus of 1658) ... So using a figure he found in Clavius, now called a Saccheri quadrilateral, Giordano tried to come up with his own proof of the assumption, in the course of which he proved If ABCD is a Saccheri quadrilateral (an ...
Saccheri Quadrilateral - History
... Saccheri quadrilaterals were first considered by Omar Khayyam (1048-1131) in the late 11th century in Book I of Explanations of the Difficulties in the Postulates of Euclid ... Unlike many commentators on Euclid before and after him (including of course Saccheri), Khayyam was not trying to prove the parallel postulate as such but to derive it from an equivalent postulate he formulated from "the ... considered the three cases right, obtuse, and acute that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he (correctly) refuted the obtuse and acute ...
Saccheri Quadrilateral - Properties
... Let ABCD be a Saccheri quadrilateral having AB as base, CA and DB the equal sides that are perpendicular to the base and CD the summit ... The following properties are valid in any Saccheri quadrilateral in hyperbolic geometry ... the midpoint of the base and the midpoint of the summit divides the Saccheri quadrilateral into two Lambert quadrilaterals ...
Hyperbolic Geometry - History
... Omar Khayyám, Nasir al-Din al-Tusi, Witelo, Gersonides, Alfonso, and later Giovanni Gerolamo Saccheri, John Wallis, Johann Heinrich Lambert, and ... al-Tusi on quadrilaterals, including the Ibn al-Haytham–Lambert quadrilateral and Khayyam–Saccheri quadrilateral, were the first theorems on hyperbolic ... among later European geometers, including Witelo, Gersonides, Alfonso, John Wallis and Saccheri ...
Giovanni Girolamo Saccheri
... Giovanni Girolamo Saccheri (September 5, 1667, Sanremo – October 25, 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician ... Saccheri entered the Jesuit order in 1685, and was ordained as a priest in 1694 ... 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 ...