 Notes on Euler’s Memoir A Construction Relative to a Problem of Pappus of AlexandriaGuillaume Théret
Chapter Chapter 4 in Spherical Geometry in the Eighteenth Century I, 2026, pp 69-84 from Springer Abstract: Abstract A number of eminent mathematicians have been interested in the “Pappus problem”, a geometrical construction so called by Euler, who gave a solution in his memoir A construction relative to a problem of Pappus of Alexandria translated in Chap. 16 of the present volume. In this chapter, we place this result in a more general context, survey its history, and provide detailed versions, and sometimes proofs, due to several mathematicians, ancient and modern, ranging from Greek Antiquity until modern times. We provide the details of Pappus’ original proof of this problem, and that of a generalized Pappus problem, in the setting of projective geometry, formulated and proved in the modern times. We also give a proof of a related construction of Apollonius of circles tangent to three given objects in the plane. Keywords: Greek mathematics; Pappus problem; Projective geometry; Euclidean geometry; Apollonius problem; Leonhard Euler; 01A50; 01A45; 01A35; 01A20; 51A05; 51N20 (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-12466-1_4 Ordering information: This item can be ordered from DOI: 10.1007/978-3-032-12466-1_4 Access Statistics for this chapter More chapters in Springer Books from Springer |
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