The concept of given in Greek mathematics

Nathan Sidoli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work.

Original languageEnglish
Pages (from-to)353-402
Number of pages50
JournalArchive for History of Exact Sciences
Issue number4
Publication statusPublished - 2018 Jul 1

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • History and Philosophy of Science


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