Principles of Spherical Trigonometry Deduced from the Method of Maxima and Minima

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

Chapter Chapter 11 in Spherical Geometry in the Eighteenth Century I, 2026, pp 235-272 from Springer

Abstract: Abstract In this memoir, Leonhard Euler establishes a set of formulae of spherical trigonometry using methods of differential geometry and the calculus of variations. The formulae he obtains are, according to his words, very handful for calculations with the aid of logarithms. Using these methods and the formulae he finds, he gives a proof of the fact that the area of a spherical triangle is equal to its angle excess.

Keywords: Spherical trigonometry; Leonhard Euler; History of spherical geometry; Calculus of variations; 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_11

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DOI: 10.1007/978-3-032-12466-1_11

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