Spherical Geometry in the Eighteenth Century I - Euler, Lagrange and Lambert - Preface and Chronologies

Aug 2, 2026

Spherical geometry develops from Ancient Greek foundational treatises through advances by Arab mathematicians in spherical trigonometry, then reaches renewed momentum in the eighteenth century through Euler, Lagrange, and Lambert. The volume presents their complete works translated into English from Latin, French, and German, enriched with explanatory footnotes and synthetic essays that place memoirs within mathematical, historical, and philosophical context. Editorial materials also include biographies and chronologies linking Euler’s major life events with publication dates of works referenced in the collection.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages449

Reading Time18 h 51 min

AccessFree to download

Preface

Chronologies

Renzo Caddeo Athanase Papadopoulos Editors Spherical Geometry in the Eighteenth Century I Euler, Lagrange and Lambert Spherical Geometry in the Eighteenth Century I Renzo Caddeo • Athanase Papadopoulos Editors Spherical Geometry in the Eighteenth Century I Euler, Lagrange and Lambert Editors Renzo Caddeo Dipartimento di Matematica e Informatica, Palazzo Delle Scienze Università degli Studi di Cagliari Cagliari, Italy Athanase Papadopoulos Institut de Recherche Mathématique Avancée Université de Strasbourg et CNRS Strasbourg, France ISBN 978-3-032-12465-4 ISBN 978-3-032-12466-1 (eBook) [https://doi.org/10.1007/978-3-032-12466-1](https://doi.org/10.1007/978-3-032-12466-1) Mathematics Subject Classiﬁcation: 01A30, 01A50, 00A30, 01A20, 03A05 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors orthe editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional afﬁliations. Cover illustration: The Astronomer, by Johannes Vermeer (1668) . Musée du Louvre, Paris. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland If disposing of this product, please recycle the paper. [. . . ] With silent worship of the Great of old,– The dead, but sceptred, Sovereigns, who still rule Our spirits from their urns. Lord Byron (Manfred, act 3, scene 4 .) Preface Spherical geometry, as a mathematical ﬁeld, started in Ancient Greece where several fundamental treatises were written on this subject. Among these works, we mention, in historical order, the Moving sphere by Autolycus of Pitane (fourth century BC), the Spherics by Theodosius of Tripoli (ﬁrst century BC), and the Spherics by Menelaus of Alexandria (ﬁrst–second centuries AD) . The next major developmentsin this domain are due to the Arab mathematicians between the tenth and the thirteenth century, and one has to mention here their important work on spherical trigonometry. The Arabs made the connection between the Greek world and the Renaissance in Europe, as far as mathematics is concerned. The next signiﬁcant progress took place in the eighteenth century and it is due to a large extent to Leonhard Euler, Joseph-Louis Lagrange, and Johann Heinrich Lambert, in the works that are presented in the present volume. Spherical geometry received renewed attention in the nineteenth century by Nikolai Ivanovich Lobachevsky, who lectured intensively on this topic and who realized important analogies between the formulae of spherical trigonometry and those of the new geometry he discovered, which he called “imaginary geometry.” As a matter of fact, Lobachevsky used spherical geometry in his foundational work on hyperbolic geometry. In

FAQs

What historical development does the preface describe for spherical geometry?

It traces spherical geometry from Ancient Greece, through Arab mathematicians’ work on spherical trigonometry, to major progress in the eighteenth century by Euler, Lagrange, and Lambert, and later renewed study in the nineteenth and twentieth centuries.

Which mathematicians’ works are included in the volume?

The volume contains the complete works on spherical geometry by Euler, Lagrange, and Lambert.

How are the translations and supporting materials organized?

Memoirs are translated into English and accompanied by explanatory footnotes and synthetic essays that provide mathematical, historical, and philosophical background, highlighting relationships among the original works.

Aug 2, 2026

Upload by Genevieve