Abstract
ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context.
Publisher
Cambridge University Press (CUP)
Subject
History and Philosophy of Science,General Social Sciences
Reference18 articles.
1. XENARCHUS, ALEXANDER, AND SIMPLICIUS ON SIMPLE MOTIONS, BODIES AND MAGNITUDES
2. Tannery Paul . 1883–4. “Pour l'histoire des lignes et surfaces courbes dans l'antiquité.” Bulletin des Sciences mathématiques 2e série, VII:278–291 and VIII:19–30, 101–112, reprinted in Idem, Mémoires scientifiques II:1–47.
3. Les premières classifications des courbes;Rashed;Physis,2005
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献