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Saccheri quadrilaterals. A Saccheri quadrilateral is a quadrilateral with two equal sides perpendicular to the base.It is named after Giovanni Gerolamo Saccheri, who used it extensively in his 1733 book Euclides ab omni naevo vindicatus (Euclid freed of every flaw), an attempt to prove the parallel postulate using the method reductio ad absurdum.
In geometry, a trapezoid (/ ... A Saccheri quadrilateral is similar to a trapezoid in the hyperbolic plane, ... where K is the area of the quadrilateral. ...
Consequently, rectangles exist (a statement equivalent to the parallel postulate) only in Euclidean geometry. A Saccheri quadrilateral is a quadrilateral with two sides of equal length, both perpendicular to a side called the base. The other two angles of a Saccheri quadrilateral are called the summit angles and they have equal measure. The ...
Some believe Saccheri concluded as he did only to avoid the criticism that might come from seemingly-illogical aspects of hyperbolic geometry. One tool that Saccheri developed in his work (now called a Saccheri quadrilateral) has a precedent in the 11th-century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid (Risâla fî ...
Pages in category "Types of quadrilaterals" ... Saccheri quadrilateral; Silver rectangle; Square; T. Tangential quadrilateral; Tangential trapezoid;
English: Diagram of Saccheri quadrilaterals (right, obtuse, acute) Italiano: Quadrilatero di Saccheri (retto, ottuso, acuto)
The theorems of Ibn al-Haytham (Alhazen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Lambert quadrilateral and Saccheri quadrilateral, were part of a line of research on the parallel postulate continued by later European geometers, including Vitello (c. 1230 – c. 1314), Gersonides (1288–1344), Alfonso, John ...
The theorems of Alhacen, Khayyam and al-Tūsī on quadrilaterals, including the Ibn al-Haytham–Lambert quadrilateral and Khayyam–Saccheri quadrilateral, were the first theorems on hyperbolic geometry. Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo ...