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Bücher Englische Bücher Wissen & Bildung Geisteswissenschaft, Kunst, Musik Philosophie Allg. & Lexika The Theory of Plane Area at the Crossroads
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The Theory of Plane Area at the Crossroads
Eduardo N. Giovannini, Edward Hermann Haeusler, Abel Lassalle Casanave (Gebundene Ausgabe, Englisch)
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Beschreibung
This book explores a cluster of philosophical, historical, and logical problems concerning the foundations of the theory of plane area in elementary geometry. The motivation of this study is a notable geometrical proposition known as De Zolt’s postulate, which asserts that a polygon cannot be equal in area to a proper polygonal part. The book is the first systematic investigation of the… philosophical and foundational significance of this proposition, which can also be described as the “fundamental theorem” of the theory of plane area. This volume provides a comparative study of Euclid’s development of the theory of area in the Elements and its modern reinterpretation in Hilbert’s classical monograph Foundations of Geometry. It connects the historical reflections on De Zolt’s postulate with the nineteenth-century program of providing a purely geometrical foundation for Euclidean geometry, uncovering a rich array of intertwined conceptual problems. It also shifts the perspective and provides a logical analysis of this geometrical postulate within an original development of the abstract theory of magnitudes, called compatible magnitudes. Finally, it extends the previous formal treatment of De Zolt’s postulate to the case of three-dimensional geometry by producing a type system for polyhedral geometrical mereology. The innovative combination of philosophical, historical, and logical perspectives results in a novel discussion of a fascinating problem at the crossroads of (late) nineteenth-century geometry. This volume will interest readers in the fields of history and philosophy of mathematics, logic, and formal philosophy. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.01.2025
Sprache
Englisch
EAN
9783031709159
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Logic, Epistemology, and the Unity of Science
Sonderedition
Nein
Autor
Eduardo N. Giovannini, Edward Hermann Haeusler, Abel Lassalle Casanave
Seitenanzahl
142
Einbandart
Gebundene Ausgabe
Buch Untertitel
Philosophical, Historical, and Logical Perspectives
Schlagwörter
De Zolt's postulate in theory of plane area, Euclid's theory of area in the Elements, David Hilbert's Foundations of Geometry, Abstract theory of magnitudes, Purity of Method in geometrical reasoning, David Hilbert's axiomatization of Euclidean geometry, Euclid's Common Notion 5, Mereology in Euclid's Elements, Geometrical paradox and 'The whole is greater than the part', A type system of rules for solid geometry
Thema-Inhalt
QDTL - Philosophie: Logik
QDH - Philosophische Traditionen und Denkschulen
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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