Notes on Angles and Solid Angles, in Relation with Euler’s Memoir De Mensura Angulorum Solidorum

Stelios Negrepontis () and Athanase Papadopoulos ()
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Stelios Negrepontis: Mathematics Department, Panepistimioupolis, National and Kapodistrian University of Athens
Athanase Papadopoulos: Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée

Chapter Chapter 5 in Spherical Geometry in the Eighteenth Century I, 2026, pp 85-120 from Springer

Abstract: Abstract We provide some historical context to the study of solid angles carried out by Euler in his memoir De mensura angulorum solidorum (On the measure of solid angles). We extend our study to the general notion of angle (not only solid). While doing so, we explore some works by Ancient Greek mathematicians and others by Arabs mathematicians of the Middle-Ages as well as some later Western authors from the Renaissance. In particular, we review the Pythagorean anthyphairetical perspective on angles which establishes the basis of the important relation between the mathematical notion of angle and the philosophical concept of finitization of the Infinite. In doing so, we shall show that questions addressed by Euler lead us to questions raised about 2500 years ago. At the same time, we highlight the fact that mathematics in those times is also today’s mathematics. The reader can meditate in this study on the intermingling between mathematics and philosophy.

Keywords: Leonhard Euler; Angle; Solid angle; Greek mathematics; Euclid; Proclus; Pythagorean mathematics; Plato; Anthyphairesis; Foundations of mathematics; Finitization of the Infinite; History of angles; History of solid angles; Arabic mathematics; Eighteenth century; Philosophy of mathematics; Eudoxus of Cnidus; 01A20; 01A30; 01A50; 00A30; 03A05 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-12466-1_5

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