The twofold role of diagrams in Euclid's plane geometry.
Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid's geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing...
| Published in: | Synthese Vol. 186; no. 1; pp. 55 - 103 |
|---|---|
| Main Author: | |
| Format: | Article |
| Published: |
Springer Nature
May2012
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=76459500&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 76459500 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: May2012 vid: 186 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 76459500 10.1007/s11229-012-0074-2 ppf: 55 ppct: 48 formats: fmt: @attributes: type: P size: 1.1MB tig: atl: The twofold role of diagrams in Euclid's plane geometry. aug: au: Panza, Marco affil: CNRS, IHPST (UMR 8590 of CNRS, University of Paris 1, and ENS Paris), Paris France su: Plane geometry Charts, diagrams, etc. Euclidean algorithm Graphic methods Scholars sug: subj: Plane geometry Charts, diagrams, etc. Euclidean algorithm Graphic methods Scholars keyword: Diagrams Euclid ab: Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid's geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid's plane geometry (EPG). Euclid's arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: ( i) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; ( ii) EPG objects inherit some properties and relations from these diagrams. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2012. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2012 holdings: @attributes: islocal: N |
|---|