Homeomeric Lines in Greek Mathematics.

Abstract : The article presents and discusses the ancient documents on the subject of homeomeric lines. On the basis of such documents, it reconstructs both a definition of the notion and a proof of the result, stated but left unproved in the extant sources, that there are only three such lines: the straight line, the circumference, the cylindrical helix. A point about homeomeric lines of particular historiographical interest is that they were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. Exactly for this reason it proved necessary to investigate what lines are homeomeric. The far-reaching connections of mathematical homeomery with key issues in the ancient cosmological debate are extensively discussed; its relevance as a foundational theme is further analysed in a companion paper (Science in Context 23 (2010), 151-186).
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Submitted on : Thursday, April 29, 2010 - 12:24:43 PM
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Fabio Acerbi. Homeomeric Lines in Greek Mathematics.. Science in Context, Cambridge University Press (CUP), 2010, 23 ((1)), pp. 1-37. ⟨10.1017/s0269889709990226⟩. ⟨halshs-00477492⟩



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