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020 _a9783031709166
_9978-3-031-70916-6
024 7 _a10.1007/978-3-031-70916-6
_2doi
050 4 _aBC1-199
072 7 _aHPL
_2bicssc
072 7 _aPHI011000
_2bisacsh
072 7 _aQDTL
_2thema
100 1 _aGiovannini, Eduardo N.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_990061
245 1 4 _aThe Theory of Plane Area at the Crossroads
_h[electronic resource] :
_bPhilosophical, Historical, and Logical Perspectives /
_cby Eduardo N. Giovannini, Edward Hermann Haeusler, Abel Lassalle Casanave.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXXII, 142 p. 78 illus., 5 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 ;
_v64
505 0 _aChapter 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.
520 _aThis 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.
650 0 _aLogic.
_970674
650 0 _aPhilosophy
_xHistory.
_970495
650 1 4 _aPhilosophical Logic.
_976708
650 2 4 _aHistory of Philosophy.
_970497
650 2 4 _aLogic.
_970674
700 1 _aHaeusler, Edward Hermann.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_990062
700 1 _aLassalle Casanave, Abel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_990063
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031709159
776 0 8 _iPrinted edition:
_z9783031709173
776 0 8 _iPrinted edition:
_z9783031709180
830 0 _aLogic, Epistemology, and the Unity of Science,
_x2214-9783 ;
_v64
_973718
856 4 0 _uhttps://doi.org/10.1007/978-3-031-70916-6
912 _aZDB-2-REP
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