04499nam a22005415i 4500 978-3-031-52223-9 DE-He213 20251030112024.0 cr nn 008mamaa 240502s2024 sz | s |||| 0|eng d 9783031522239 978-3-031-52223-9 10.1007/978-3-031-52223-9 doi QA21-27 PBX bicssc MAT015000 bisacsh PBX thema Dorrego López, Eduardo. author. aut http://id.loc.gov/vocabulary/relators/aut 76223 Irrationality, Transcendence and the Circle-Squaring Problem [electronic resource] : An Annotated Translation of J. H. Lambert’s Vorläufige Kenntnisse and Mémoire / by Eduardo Dorrego López, Elías Fuentes Guillén. 2nd ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XXI, 167 p. 13 illus., 7 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Logic, Epistemology, and the Unity of Science, 2214-9783 ; 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, 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. Mathematics. 65523 History. Mathematics Philosophy. 69649 History of Mathematical Sciences. 66197 Philosophy of Mathematics. 69650 Fuentes Guillén, Elías. author. aut http://id.loc.gov/vocabulary/relators/aut 76224 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031522222 Printed edition: 9783031522246 Printed edition: 9783031522253 Logic, Epistemology, and the Unity of Science, 2214-9783 ; 58 73718 https://doi.org/10.1007/978-3-031-52223-9 ZDB-2-SMA ZDB-2-SXMS 59589 59589