This volume is the first English edition, with commentaries and introductory material, of the writings on spherical geometry by Leonhard Euler, Joseph-Louis Lagrange and Johann Heinrich Lambert. The book is divided into two parts. The first part contains essays related the works by Euler, Lagrange and Lambert on spherical geometry. The goal of these essays is to include these works in the appropriate mathematical, historical and philosophical contexts. The second part of the volume is devoted to the English translations of the original memoirs, originally written in Latin, French and German. These translations are new and they are done by mathematicians who are involved in the subjects of the memoirs. Footnotes by the editors and the translators are appended to the translations. The book is addressed to students and researchers in geometry. It constitutes an invaluable reference in mathematics, and also in the history and philosophy of mathematics.
1 Introduction by Renzo Caddeo and Athanase Papadopoulos.- Part
I: Essays.- 2 Eulers work on spherical geometry: An overview with comments
by Athanase Papadopoulos and Vladimir Turaev.- 3 An introduction to spherical
geometry based on fundamental works of Euler and Lagrange by Charalampos
Charitos.- 4 On Eulers memoir A construction relative to a problem of Pappus
of Alexandria by Guillaume Théret.- 5 Notes on angles and solid angles, in
relation with Eulers memoir De mensura angulorum solidorum by Stelios
Negrepontis and Athanase Papadopoulos.- 6 On the life and work of Johann
Heinrich Lambert by Athanase Papadopoulos.- 7 A review of Johann Heinrich
Lamberts memoir Theorie der Parallellinien by Athanase Papadopoulos and
Guillaume Théret.- 8 The pentagramma mirificum from Napier to Lambert: Notes
on Lamberts memoir on spherical trigonometry by Annette ACampo-Neuen.-
9 Spherical trigonometry before the modern era: The treatise of Nar al-Dn
al-s by Athanase Papadopoulos.- 10 The polar triangle, from Ibn Irq to
Euler and Lagrange by Athanase Papadopoulos.- Part II: Sources.-
11 Principles of spherical trigonometry deduced from the method of maxima and
minima by Leonhard Euler. Translated from the French by Athanase Papadopoulos
and Alena Zhukova.- 12 General spherical trigonometry, deduced from
fundamental principles in a brief and clear
manner by Leonhard Euler. Translated from the Latin by Renzo
Caddeo.- 13 Various speculations on the area of spherical triangles by
Leonhard Euler. Translated from the Latin by Renzo Caddeo.- 14 On the measure
of solid angles by Leonhard Euler. Translated from the Latin by Renzo
Caddeo.- 16 A construction relative to a problem of Pappus of Alexandria by
Leonhard Euler. Translated from the Latin by Renzo Caddeo.- 17 Algebraic
solution of a problem in geometry
by Joseph-Louis Lagrange. Translated from the French by Athanase
Papadopoulos.- 18 Solution of some problems relative to spherical triangles
with a complete analysis of these triangles by Joseph-Louis Lagrange.
Translated from the French by Vincent Alberge and Athanase Papadopoulos.-
19 Notes and Comments on Trigonometry by Johann-Heinrich Lambert. Translated
from the German by Annette ACampo Neuen.- 15 Some questions of the geometry
of the plane and of the sphere by Leonhard Euler. Translated from the Latin
by Renzo Caddeo.
Renzo Caddeo, born in Sardinia, is a retired professor of geometry and former director of the Department of Mathematics at the University of Cagliari, where he was the organizer of a Masters course dedicated to the visualization of mathematical objects. Before teaching at Cagliari, he studied in Romania and France. His research interests are in differential geometry, in particular in biharmonic maps between Riemannian manifolds and in the surfaces of certain remarkable three-dimensional spaces. He collaborated with Alfred Gray to realize the extended Italian version of the book Modern Differential Geometry of Curves and Surfaces and with Athanase Papadopoulos on the two-volume work Leonhard Euler, Écrits Sur la Musique and the book Christiaan Huygens, Écrits Sur la Musique et le Son. Athanase Papadopoulos (born 1957) is Directeur de Recherche at the French Centre National de la Recherche Scientifique. His main fields of interest are geometry and topology, the history and philosophy of mathematics, and mathematics and music. He has held visiting positions at the Institute for Advanced Study, Princeton (19841985 and 19931894), USC (19981999), CUNY (Ada Peluso Professor, 2014), Brown University (Distinguished visiting professor, 2017), Tsinghua University, Beijing (2018), and the State University of Saint Petersburg (as the Lamé Chair) (2019), and has had several long visits to the Max-Plank Institute for mathematics (Bonn), the Erwin Schrödinger Institute (Vienna), the Graduate Center of CUNY (New York), the Tata Institute (Bombay), Galatasaray University (Istanbul), the University of Florence (Italy), Fudan University (Shanghai), Gakushuin University (Tokyo) and Presidency University (Calcutta) and Banaras Hindu University. He is the author of more than 220 published articles and 50 monographs and edited books.
