Chapter

The Euclidean Diagram (1995)

Kenneth Manders

in The Philosophy of Mathematical Practice

Published in print June 2008 | ISBN: 9780199296453
Published online February 2010 | e-ISBN: 9780191711961 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199296453.003.0005
 The Euclidean Diagram (1995)

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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

Chapter.  22938 words.  Illustrated.

Subjects: Philosophy of Mathematics and Logic

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