TY - CHAP
T1 - Distributivity-like Results in Euclid’s Elements
AU - Corry, Leo
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Book II
KW - Book V
KW - Book VII
KW - Distributive-like rules
KW - Euclid’s Elements
KW - Eudoxian theory of proportions
UR - http://www.scopus.com/inward/record.url?scp=85120891017&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-79679-2_2
DO - 10.1007/978-3-030-79679-2_2
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AN - SCOPUS:85120891017
T3 - SpringerBriefs in History of Science and Technology
SP - 5
EP - 25
BT - SpringerBriefs in History of Science and Technology
PB - Springer Nature
ER -