The Theory of Plane Area at the Crossroads (Record no. 66295)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04146nam a22005535i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-031-70916-6 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20251030114917.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 250102s2024 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783031709166 |
| -- | 978-3-031-70916-6 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-031-70916-6 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | BC1-199 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | HPL |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PHI011000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | QDTL |
| Source | thema |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Giovannini, Eduardo N. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 90061 |
| 245 14 - TITLE STATEMENT | |
| Title | The Theory of Plane Area at the Crossroads |
| Medium | [electronic resource] : |
| Remainder of title | Philosophical, Historical, and Logical Perspectives / |
| Statement of responsibility, etc. | by Eduardo N. Giovannini, Edward Hermann Haeusler, Abel Lassalle Casanave. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. 2024. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer Nature Switzerland : |
| -- | Imprint: Springer, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2024. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XXII, 142 p. 78 illus., 5 illus. in color. |
| Other physical details | online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Encoding format | |
| Source | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Logic, Epistemology, and the Unity of Science, |
| International Standard Serial Number | 2214-9783 ; |
| Volume/sequential designation | 64 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 70674 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| General subdivision | History. |
| 9 (RLIN) | 70495 |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 76708 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 70497 |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | |
| 9 (RLIN) | 70674 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Haeusler, Edward Hermann. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 90062 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lassalle Casanave, Abel. |
| Relator term | author. |
| Relator code | aut |
| -- | http://id.loc.gov/vocabulary/relators/aut |
| 9 (RLIN) | 90063 |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer Nature eBook |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031709159 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031709173 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Printed edition: |
| International Standard Book Number | 9783031709180 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Logic, Epistemology, and the Unity of Science, |
| International Standard Serial Number | 2214-9783 ; |
| Volume number/sequential designation | 64 |
| 9 (RLIN) | 73718 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1007/978-3-031-70916-6">https://doi.org/10.1007/978-3-031-70916-6</a> |
| 912 ## - | |
| -- | ZDB-2-REP |
| 912 ## - | |
| -- | ZDB-2-SXPR |
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