In absolute geometry, the Saccheri-Legendre theorem states that the sum of the angles in a triangle is at most 180 degrees. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Source Saccheri-Legendre theorem (Wikipedia)
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Source Saccheri-Legendre theorem (Wikipedia)
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1. Wikipedia: Saccheri-Legendre theorem
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The existence of at least one triangle with angle sum of 180 degrees in absolute geometry implies Euclid's parallel postulate.
2. MacTutor History of Mathematics Archive: Giovanni Saccheri - Biography
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published in 1733
Saccheri-Legendre theorem (Wikipedia)
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In absolute geometry, the Saccheri-Legendre theorem states that the sum of the angles in a triangle is at most 180°. 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.
- In Branch: Geometry, Lead sentence
Proved By: Giovanni Girolamo Saccheri, Lead
It appeared in Saccheri's 1733 book Euclides ab omni naevo vindicatus [Euclid Freed of Every Flaw] but his work fell into obscurity.
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