Distributivity-like Results in Euclid’s Elements

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The present chapter presents a preliminary overview of some propositions of Books II, V, and VII of Euclid’s Elements that, retrospectively seen, embody results that we can associate nowadays with a more general idea of distributivity. It focuses on several results and arguments that are handled differently by Euclid in three clearly separate contexts: geometric magnitudes, arithmetic and numbers, and proportions. It also discusses Euclidean propositions where “visible” constructions implicitly use distributive-like properties.

Original languageEnglish
Title of host publicationSpringerBriefs in History of Science and Technology
PublisherSpringer Nature
Number of pages21
StatePublished - 2021
Externally publishedYes

Publication series

NameSpringerBriefs in History of Science and Technology
ISSN (Print)2211-4564
ISSN (Electronic)2211-4572

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.


  • Book II
  • Book V
  • Book VII
  • Distributive-like rules
  • Euclid’s Elements
  • Eudoxian theory of proportions


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