The Hero–Apollonius Lemma in Nicomedes and Euclid

Wilbur Richard Knorr
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Wilbur Richard Knorr: Stanford University, Program in the History of Science

Chapter Chapter 2 in Textual Studies in Ancient and Medieval Geometry, 1989, pp 29-40 from Springer

Abstract: Abstract The lemma [f], present in identical wordings in HE and AJ, has been argued in the preceding chapter to be a remnant from the 3rd century B.C. prototype underlying the Hero and Apollonius–Parmenion versions of the cube duplication. It establishes, relative to the accompanying diagram (Fig. 2.1), where DE is perpendicular bisector of BG, the following identity: $$GA \cdot AB+DB^2=DA^2$$ .

Keywords: Geometric Problem; Secant Line; Identical Wording; Ancient Text; Ancient Tradition (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4612-3690-0_3

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