Authors:
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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Table of contents (5 chapters)
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Front Matter
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Eduardo Dorrego López
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Front Matter
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Eduardo Dorrego López
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Front Matter
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Back Matter
About this book
This publication 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 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.
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
Authors and Affiliations
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IES Afonso X O Sabio, A Coruña, Spain
Eduardo Dorrego López
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Institute of Philosophy of the Czech Academy of Sciences, Prague, Czech Republic
Elías Fuentes Guillén
About the authors
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
DOI: https://doi.org/10.1007/978-3-031-24363-9
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 2023
Hardcover ISBN: 978-3-031-24362-2Published: 08 March 2023
Softcover ISBN: 978-3-031-24365-3Due: 22 March 2024
eBook ISBN: 978-3-031-24363-9Published: 07 March 2023
Series ISSN: 2214-9775
Series E-ISSN: 2214-9783
Edition Number: 1
Number of Pages: XIX, 171
Number of Illustrations: 2 b/w illustrations, 10 illustrations in colour
Topics: History of Mathematical Sciences, Philosophy of Mathematics