Some Questions of the Geometry of the Plane and of the Sphere

Leonhard Euler
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Leonhard Euler: Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée

Chapter Chapter 16 in Spherical Geometry in the Eighteenth Century I, 2026, pp 347-367 from Springer

Abstract: Abstract In this memoir, Leonhard Euler starts with a triangle in the Euclidean plane and three segments joining one vertex of the triangle to the opposite side, such that these three segments intersect at a common point. He establishes a relation between the six parts cut on these three segments by the intersection point. He then shows that conversely, if we start with the relation found, then we can construct a triangle and three lines joining the vertices to the opposite sides such that the six segments that arise in this construction satisfy the given relation. After the Euclidean case, Euler proves an analogous result in the spherical case.

Keywords: Leonhard Euler; Spherical geometry; Euclidean geometry; 01A50; 97G60; 51M04; 53A35 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-12466-1_16

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DOI: 10.1007/978-3-032-12466-1_16

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