Overview
- Is the first to include the whole annotated translation of these two works
- Presents a union between technique and science popularization
- Makes the scientist better known to his readers
Part of the book series: Logic, Epistemology, and the Unity of Science (LEUS, volume 58)
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Keywords
- Johann Heinrich Lambert
- Irrationality of Pi
- Trascendental Numbers
- The Circle-Squaring Problem
- 18th and 19th Century Mathematics
- History of Mathematics
- Philosophy of Mathematics
- Continued Fractions
- Euler and continued fractions
- decimal expansions
- Euler and continued fractions, irrationality and transcendence
- Lambert and the Berlin Academy of Sciences
- Lambert's Vorläufige Kenntnisse
- Lambert's work and the development of irrational numbers
- Lambert's Mémoire
- Lambert and non-Euclidean geometry
- Echegaray's Disertaciones matemáticas
About this book
This publication, now in its second edition, includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728–1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations, as in the first edition, are accompanied by a contextualised study of each of these works and provide an overview of Lambert’s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself.
Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle.
Authors and Affiliations
About the authors
Elías Fuentes Guillén is a researcher at the Institute of Philosophy of the Czech Academy of Sciences and head of the GA ČR Junior Star project "Normalisation and Emergence: Rethinking the Dynamics of Mathematics". Previously he held postdoctoral positions at the Department of Mathematics of the Faculty of Sciences at UNAM and the Institute of Philosophy of the Czech Academy of Sciences. His research focuses on the transition from mathematical practices that were common in the late 18th century to practices that emerged in the second half of the 19th century, as well as on the work of Bernard Bolzano. His recent publications include the book Matematické dílo Bernarda Bolzana ve světle jeho rukopisů (Nakladatelství Filosofia, 2023), a chapter for Springer’s Handbook of the History and Philosophy of Mathematical Practice (2022) and “The 1804 examination for the chair of ElementaryMathematics at the University of Prague” (with Davide Crippa; Historia Mathematica, 2021).
Bibliographic Information
Book Title: Irrationality, Transcendence and the Circle-Squaring Problem
Book Subtitle: An Annotated Translation of J. H. Lambert’s Vorläufige Kenntnisse and Mémoire
Authors: Eduardo Dorrego López, Elías Fuentes Guillén
Series Title: Logic, Epistemology, and the Unity of Science
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-52222-2Due: 07 June 2024
Softcover ISBN: 978-3-031-52225-3Due: 07 June 2024
eBook ISBN: 978-3-031-52223-9Due: 07 June 2024
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 2
Number of Pages: XXI, 167
Number of Illustrations: 6 b/w illustrations, 7 illustrations in colour