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The Shoemaker's Knife

  • J. S. Mackay
Extract

Some of the properties of the figure which, on account of its shape, the Greeks named the Shoemaker's Knife (ἄρβηλοσ) are given in the Lemmas attributed to Archimedes; others occur in the fourth book of Pappus's Mathematical Collection. The Lemmas (which are not extant in Greek, but have been translated from the Arabic) are generally considered to be spurious; it is, however, regarded as possible, if not probable, that the theorems among them relating to the Arbelos may be due to Archimedes. Whether they are or not, the figure and the principal proposition respecting it which Pappus gives are said by him to be “ancient.” It may be added that the Arbelos does not seem to have attracted much notice from geometers, few of them having treated of it, and fewer still having added to the properties known to the ancients. (See Steiner's Gesammelte Werke, Vol. I., pp. 47–76, and The Lady's and Gentleman's Diary for 1842 and 1845).

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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