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Article ID: CBB000931526

Book XVI: A Mediaeval Arabic Addendum to Euclid's Elements (2008)

De Young, Gregg (Author)

Sciamvs: Sources and Commentaries in Exact Sciences
Volume: 9
Pages: 133--210

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Geometry Transmission of texts Mathematics Translations Arab/Islamic world, civilization and culture 9th century Archimedes Euclid

Euclid's Elements has been transmitted into many languages since it was first composed in Greek and has provoked extensive discussions in many branches of this transmission. The Arabic transmission was no exception. Once it became available in Arabic during the eighth and ninth centuries, Euclid's mathematical classic was corrected, summarized, given addenda, reduced to extracts, commented upon in whole and in part, given alternate demonstrations, paraphrased, and much more. These discussions were not limited to any specific time period, but continued to appear regularly until the nineteenth and twentieth centuries. This paper presents a hitherto unstudied addendum to an edited version of a popular Euclidean treatise. The addendum, entitled Book XVI, comprises nineteen propositions describing techniques for constructing polyhedra within other polyhedra or within spheres. Thus it develops themes related to those of book XV, itself a late Greek addendum to the genuine Euclidean treatise. The contents are, however, in the tradition of Archimedes rather than Euclid. The first part of Book XVI describes construction of semiregular truncated polyhedra inscribed within regular polyhedra (Platonic solids) and within spheres. The addendum ends with what may be the earliest discussion of the construction of a representative example from each of the classes of semiregular polyhedra known today as prisms and antiprisms. Thus, although the editor or copyist who attached this book XVI to the manuscript clearly intended this material as a kind of continuation of the Elements, the intention of the original author is less clearly Euclidean.

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