Various Speculations on the Area of Spherical Triangles

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

Chapter Chapter 13 in Spherical Geometry in the Eighteenth Century I, 2026, pp 291-308 from Springer

Abstract: Abstract In this memoir, Euler gives several formulae for the area of a spherical triangle in terms of its side lengths. This is an analogue, in spherical geometry, of the Euclidean Heron formula. He then uses these results to solve the problem of finding the locus of the vertices of spherical triangles having a fixed base and the same area.

Keywords: Spherical area; Leonhard Euler; Girard formula; Lexell problem; History of spherical geometry; Mathematics in the eighteenth century; 01A50; 51-03; 53A05; 53A35 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-12466-1_13

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