LEADER 04690nam 22006735 450 001 9910682599603321 005 20240313112255.0 010 $a3-031-24363-3 024 7 $a10.1007/978-3-031-24363-9 035 $a(MiAaPQ)EBC7211154 035 $a(Au-PeEL)EBL7211154 035 $a(CKB)26240860400041 035 $a(DE-He213)978-3-031-24363-9 035 $a(PPN)26909301X 035 $a(EXLCZ)9926240860400041 100 $a20230307d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIrrationality, Transcendence and the Circle-Squaring Problem $eAn Annotated Translation of J. H. Lambert?s Vorläufige Kenntnisse and Mémoire /$fby Eduardo Dorrego López, Elías Fuentes Guillén 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (178 pages) 225 1 $aLogic, Epistemology, and the Unity of Science,$x2214-9783 ;$v58 311 08$aPrint version: Dorrego López, Eduardo Irrationality, Transcendence and the Circle-Squaring Problem Cham : Springer International Publishing AG,c2023 9783031243622 320 $aIncludes bibliographical references and index. 327 $aPart 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 annotated translation of Lambert's Mémoire (1761/1768) -- Chapter 6. Outine of Lambert's Vorläufige Kenntnisse (1766/1770) -- Chapter 6. An annotated 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. 330 $aThis publication includes an unabridged and annotated translation of two works by Johann Heinrich Lambert (1728?1777) written in the 1760s: Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen and Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques. The translations are accompanied by a contextualised study of each of these works and provide an overview of Lambert?s contributions, showing both the background and the influence of his work. In addition, by adopting a biographical approach, it allows readers to better get to know the scientist himself. Lambert was a highly relevant scientist and polymath in his time, admired by the likes of Kant, who despite having made a wide variety of contributions to different branches of knowledge, later faded into an undeserved secondary place with respect to other scientists of the eighteenth century. In mathematics, in particular, he is famous for his research on non-Euclidean geometries, although he is likely best known for having been the first who proved the irrationality of pi. In his Mémoire, he conducted one of the first studies on hyperbolic functions, offered a surprisingly rigorous proof of the irrationality of pi, established for the first time the modern distinction between algebraic and transcendental numbers, and based on such distinction, he conjectured the transcendence of pi and therefore the impossibility of squaring the circle. 410 0$aLogic, Epistemology, and the Unity of Science,$x2214-9783 ;$v58 606 $aMathematics 606 $aHistory 606 $aMathematics$xPhilosophy 606 $aHistory of Mathematical Sciences 606 $aPhilosophy of Mathematics 606 $aFilosofia de la matemàtica$2thub 606 $aIrracionalisme (Filosofia)$2thub 606 $aTranscendència (Filosofia)$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics. 615 0$aHistory. 615 0$aMathematics$xPhilosophy. 615 14$aHistory of Mathematical Sciences. 615 24$aPhilosophy of Mathematics. 615 7$aFilosofia de la matemàtica 615 7$aIrracionalisme (Filosofia) 615 7$aTranscendència (Filosofia) 676 $a128 676 $a128 700 $aDorrego Lo?pez$b Eduardo$01346448 702 $aFuentes Guille?n$b Eli?as 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910682599603321 996 $aIrrationality, Transcendence and the Circle-Squaring Problem$93074377 997 $aUNINA