Spherical Geometry in the Eighteenth Century I : Euler, Lagrange and Lambert

Caddeo, Renzo (EDT)/ Papadopoulos, Athanase (EDT)

Springer Nature Switzerland AG（2026/02発売）

• 製本 Hardcover:ハードカバー版
• 言語 ENG
• 商品コード 9783032124654

Full Description

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.

Contents

1 Introduction by Renzo Caddeo and Athanase Papadopoulos.- Part I: Essays.- 2 Euler's 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 Euler's memoir A construction relative to a problem of Pappus of Alexandria by Guillaume Théret.- 5 Notes on angles and solid angles, in relation with Euler's 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 Lambert's memoir Theorie der Parallellinien by Athanase Papadopoulos and Guillaume Théret.- 8 The pentagramma mirificum from Napier to Lambert: Notes on Lambert's memoir on spherical trigonometry by Annette A'Campo-Neuen.- 9 Spherical trigonometry before the modern era: The treatise of Naṣīr al-Dīn al-Ṭūsī by Athanase Papadopoulos.- 10 The polar triangle, from Ibn ʿIrāq 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 A'Campo Neuen.- 15 Some questions of the geometry of the plane and of the sphere by Leonhard Euler. Translated from the Latin by Renzo Caddeo.