04146nam a22005535i 4500 978-3-031-70916-6 DE-He213 20251030114917.0 cr nn 008mamaa 250102s2024 sz | s |||| 0|eng d 9783031709166 978-3-031-70916-6 10.1007/978-3-031-70916-6 doi BC1-199 HPL bicssc PHI011000 bisacsh QDTL thema Giovannini, Eduardo N. author. aut http://id.loc.gov/vocabulary/relators/aut 90061 The Theory of Plane Area at the Crossroads [electronic resource] : Philosophical, Historical, and Logical Perspectives / by Eduardo N. Giovannini, Edward Hermann Haeusler, Abel Lassalle Casanave. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XXII, 142 p. 78 illus., 5 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 ; 64 Chapter 1. From Euclidean to Hilbertean Practice: The Theory of Plane Area -- Chapter 2. De Zolt's Postulate: The Geometrical Path -- Chapter 3. De Zolt's Postulate: The Abstract Approach -- Chapter 4. De Zolt's Postulate in Three-Dimensions. 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. Logic. 70674 Philosophy History. 70495 Philosophical Logic. 76708 History of Philosophy. 70497 Logic. 70674 Haeusler, Edward Hermann. author. aut http://id.loc.gov/vocabulary/relators/aut 90062 Lassalle Casanave, Abel. author. aut http://id.loc.gov/vocabulary/relators/aut 90063 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031709159 Printed edition: 9783031709173 Printed edition: 9783031709180 Logic, Epistemology, and the Unity of Science, 2214-9783 ; 64 73718 https://doi.org/10.1007/978-3-031-70916-6 ZDB-2-REP ZDB-2-SXPR 66295 66295