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Irrationality, transcendence and the...

Dorrego López, Eduardo.

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Irrationality, transcendence and the circle-squaring problem = an annotated translation of J.H. Lambert's Vorläufige Kenntnisse and Mémoire /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Irrationality, transcendence and the circle-squaring problem/ by Eduardo Dorrego López, Elías Fuentes Guillén.
Reminder of title:	an annotated translation of J.H. Lambert's Vorläufige Kenntnisse and Mémoire /
Author:	Dorrego López, Eduardo.
other author:	Fuentes Guillén, Elías.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xix, 171 p. :ill. (chiefly col.), digital ;24 cm.
[NT 15003449]:	Part I: Antecedents -- Chapter 1. From Geometry to Analysis -- Chapter 2. The situation in the first half of the 18th century. Euler and continued fractions -- Part II: Johann Heinrich Lambert (1728-1777) -- Chapter 3. A biographical approach to Johann Heinrich Lambert -- Chapter 4. Outline of Lambert's Mémoire (1761/1768) -- Chapter 5. An anotated translation of Lambert's Mémoire (1761/1768) -- Chapter 6. Outine of Lambert's Vorläufige Kenntnisse (1766/1770) -- Chapter 6. An anotated translation of Lambert's Vorläufige Kenntnisse (1766/1770) -- Part III: The influence of Lambert's work and the development of irrational numbers -- Chapter 8. The state of irrationals until the turn of the century -- Chapter 9. Title to be set up.
Contained By:	Springer Nature eBook
Subject:	Circle-squaring. -
Online resource:	https://doi.org/10.1007/978-3-031-24363-9
ISBN:	9783031243639

Irrationality, transcendence and the circle-squaring problem = an annotated translation of J.H. Lambert's Vorläufige Kenntnisse and Mémoire /
Dorrego López, Eduardo.

Irrationality, transcendence and the circle-squaring probleman annotated translation of J.H. Lambert's Vorläufige Kenntnisse and Mémoire /[electronic resource] :by Eduardo Dorrego López, Elías Fuentes Guillén. - Cham :Springer International Publishing :2023. - xix, 171 p. :ill. (chiefly col.), digital ;24 cm. - Logic, epistemology, and the unity of science,v. 582214-9783 ;. - Logic, epistemology, and the unity of science ;v. 58..

Part I: Antecedents -- Chapter 1. From Geometry to Analysis -- Chapter 2. The situation in the first half of the 18th century. Euler and continued fractions -- Part II: Johann Heinrich Lambert (1728-1777) -- Chapter 3. A biographical approach to Johann Heinrich Lambert -- Chapter 4. Outline of Lambert's Mémoire (1761/1768) -- Chapter 5. An anotated translation of Lambert's Mémoire (1761/1768) -- Chapter 6. Outine of Lambert's Vorläufige Kenntnisse (1766/1770) -- Chapter 6. An anotated translation of Lambert's Vorläufige Kenntnisse (1766/1770) -- Part III: The influence of Lambert's work and the development of irrational numbers -- Chapter 8. The state of irrationals until the turn of the century -- Chapter 9. Title to be set up.

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.

ISBN: 9783031243639

Standard No.: 10.1007/978-3-031-24363-9doiSubjects--Personal Names:

3632295
Lambert, Johann Heinrich,
1728-1777--Translations into English.Subjects--Topical Terms:

3632298
Circle-squaring.

LC Class. No.: QA467

Dewey Class. No.: 516.204

Irrationality, transcendence and the circle-squaring problem = an annotated translation of J.H. Lambert's Vorläufige Kenntnisse and Mémoire /
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490 1 $a Logic, epistemology, and the unity of science, $x 2214-9783 ; $v v. 58
505 0 $a Part I: Antecedents -- Chapter 1. From Geometry to Analysis -- Chapter 2. The situation in the first half of the 18th century. Euler and continued fractions -- Part II: Johann Heinrich Lambert (1728-1777) -- Chapter 3. A biographical approach to Johann Heinrich Lambert -- Chapter 4. Outline of Lambert's Mémoire (1761/1768) -- Chapter 5. An anotated translation of Lambert's Mémoire (1761/1768) -- Chapter 6. Outine of Lambert's Vorläufige Kenntnisse (1766/1770) -- Chapter 6. An anotated translation of Lambert's Vorläufige Kenntnisse (1766/1770) -- Part III: The influence of Lambert's work and the development of irrational numbers -- Chapter 8. The state of irrationals until the turn of the century -- Chapter 9. Title to be set up.
520 $a 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.
600 1 0 $a Lambert, Johann Heinrich, $d 1728-1777 $v Translations into English. $3 3632295
650 0 $a Circle-squaring. $3 3632298
650 0 $a Irrationalism (Philosophy) $3 1090890
650 0 $a Transcendence (Philosophy) $3 815629
650 1 4 $a History of Mathematical Sciences. $3 1530523
650 2 4 $a Philosophy of Mathematics. $3 2192005
700 1 $a Fuentes Guillén, Elías. $3 3632296
710 2 $a SpringerLink (Online service) $3 836513
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830 0 $a Logic, epistemology, and the unity of science ; $v v. 58. $3 3632297
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950 $a Mathematics and Statistics (SpringerNature-11649)