# On the relationship between geometric objects and figures in Euclidean geometry

Bacelar Valente, Mario (2021) On the relationship between geometric objects and figures in Euclidean geometry. [Preprint]

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## Abstract

In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric objects and figures. Geometric objects are defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. This relation, existing between objects and figures, is what enables figures to have a role in pure and applied geometry. That is, we can use a figure or diagram as a representation of geometric objects or composite geometric objects because the relation of idealization corresponds to a resemblance-like relationship between objects and figures. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry. To show that, we will consider Euclid’s Optics.

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Item Type: Preprint
Creators:
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Bacelar Valente, Mario
Keywords: Euclidean geometry; practical geometry; pure geometry; applied geometry; geometric figure; geometric object; diagrams
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics
Depositing User: mario bacelar valente
Date Deposited: 30 Sep 2021 17:06
Item ID: 19629
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics
Date: 2021
URI: https://philsci-archive.pitt.edu/id/eprint/19629