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  2. Saccheri quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Saccheri_Quadrilateral

    Saccheri quadrilateral. 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.

  3. Saccheri–Legendre theorem - Wikipedia

    en.wikipedia.org/wiki/Saccheri–Legendre_theorem

    Saccheri–Legendre theorem. In absolute geometry, the Saccheri–Legendre theorem states that the sum of the angles in a triangle is at most 180°. [1] Absolute geometry is the geometry obtained from assuming all the axioms that lead to Euclidean geometry with the exception of the axiom that is equivalent to the parallel postulate of Euclid. [a]

  4. Giovanni Girolamo Saccheri - Wikipedia

    en.wikipedia.org/wiki/Giovanni_Girolamo_Saccheri

    University of Turin. University of Pavia. Notable students. Luigi Guido Grandi [1] Giovanni Girolamo Saccheri (Italian pronunciation: [dʒoˈvanni dʒiˈrɔːlamo sakˈkɛːri]; 5 September 1667 – 25 October 1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry ...

  5. Hyperbolic geometry - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_geometry

    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 ...

  6. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    In geometry, a trapezoid (/ ˈtræpəzɔɪd /) in North American English, or trapezium (/ trəˈpiːziəm /) in British English, [ 1 ][ 2 ] is a quadrilateral that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel ...

  7. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    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 ...

  8. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively.

  9. Garfield's proof of the Pythagorean theorem - Wikipedia

    en.wikipedia.org/wiki/Garfield's_proof_of_the...

    Garfield in 1881. Garfield's proof of the Pythagorean theorem is an original proof the Pythagorean theorem invented by James A. Garfield (November 19, 1831 – September 19, 1881), the 20th president of the United States. The proof appeared in print in the New-England Journal of Education (Vol. 3, No.14, April 1, 1876). [1][2] At the time of ...

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