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The Philosophy of Mathematical Practice$
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Paolo Mancosu

Print publication date: 2008

Print ISBN-13: 9780199296453

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199296453.001.0001

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The Euclidean Diagram (1995)

The Euclidean Diagram (1995)

Chapter:
(p.80) 4 The Euclidean Diagram (1995)
Source:
The Philosophy of Mathematical Practice
Author(s):

Kenneth Manders

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199296453.003.0005

This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary for this to work. Case-branching occurs when a construction renders a diagram un-representative. The roles of diagrams in reductio arguments, and of objection in probing a demonstration, are discussed.

Keywords:   diagram attribution, diagram-based reasoning, case-branching, diagram control, Euclid, exact, co-exact, geometrical diagram, geometric practice, objection

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