A Construction Relative to a Problem of Pappus of Alexandria

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

Chapter Chapter 15 in Spherical Geometry in the Eighteenth Century I, 2026, pp 337-346 from Springer

Abstract: Abstract In this memoir, Euler solves, in the Euclidean and then in the spherical setting, a problem inspired by a construction of Pappus of Alexandria (Proposition 117 of Book VII of the Collection). The problem is to construct a triangle which is inscribed in a given circle and whose three sides are contained in three lines that are required to pass through three given points. Pappus gives this construction in the Euclidean setting and only in the special case where the three given points are collinear. Euler solves the general case, in the Euclidean and in the spherical settings.

Keywords: Greek mathematics; Pappus problem; Castillon problem; Euclidean geometry; Leonhard Euler; Spherical geometry; 01A50; 01A35; 01A20; 51N20 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-12466-1_15

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