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020 _a9783031522239
_9978-3-031-52223-9
024 7 _a10.1007/978-3-031-52223-9
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
072 7 _aPBX
_2thema
100 1 _aDorrego López, Eduardo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976223
245 1 0 _aIrrationality, Transcendence and the Circle-Squaring Problem
_h[electronic resource] :
_bAn Annotated Translation of J. H. Lambert’s Vorläufige Kenntnisse and Mémoire /
_cby Eduardo Dorrego López, Elías Fuentes Guillén.
250 _a2nd ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXXI, 167 p. 13 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLogic, Epistemology, and the Unity of Science,
_x2214-9783 ;
_v58
505 0 _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 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 _aThis 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.
650 0 _aMathematics.
_965523
650 0 _aHistory.
650 0 _aMathematics
_xPhilosophy.
_969649
650 1 4 _aHistory of Mathematical Sciences.
_966197
650 2 4 _aPhilosophy of Mathematics.
_969650
700 1 _aFuentes Guillén, Elías.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_976224
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031522222
776 0 8 _iPrinted edition:
_z9783031522246
776 0 8 _iPrinted edition:
_z9783031522253
830 0 _aLogic, Epistemology, and the Unity of Science,
_x2214-9783 ;
_v58
_973718
856 4 0 _uhttps://doi.org/10.1007/978-3-031-52223-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59589
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