On the Measure of Solid Angles

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

Chapter Chapter 14 in Spherical Geometry in the Eighteenth Century I, 2026, pp 309-335 from Springer

Abstract: Abstract In this memoir, Euler starts by giving a geometrical proof of Girard’s formula for the area of spherical triangle. He then gives several formulae for the area of a spherical triangle as a function of its side lengths. He uses these formulae for spherical area to give numerical values of the solid angles of the five regular polyhedra, which is the goal of the memoir.

Keywords: Spherical area; Leonhard Euler; Girard formula; Solid angle; 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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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-12466-1_14

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DOI: 10.1007/978-3-032-12466-1_14

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