{"id":53661,"date":"2025-02-17T20:18:04","date_gmt":"2025-02-17T20:18:04","guid":{"rendered":"https:\/\/www.roger-pearse.com\/weblog\/?p=53661"},"modified":"2025-02-17T20:18:04","modified_gmt":"2025-02-17T20:18:04","slug":"the-transmission-of-the-works-of-apollonius-of-perge","status":"publish","type":"post","link":"https:\/\/roger-pearse.com\/weblog\/2025\/02\/17\/the-transmission-of-the-works-of-apollonius-of-perge\/","title":{"rendered":"The Transmission of the Works of Apollonius of Perge"},"content":{"rendered":"

Apollonius of Perge (or Perga; Apollonius Pergaeus) was an ancient mathematical writer who lived in the Hellenistic era, ca. 200 BC.\u00a0 His reputation is based upon his Conics<\/em> (or Conic Sections<\/em>), one of the great works of ancient mathematics.\u00a0 The Conic Sections<\/em> deals with the shapes that are seen when a cone is intersected by a plane, i.e., when it is sliced open. You can get one of four shapes when that happens, including a circle, an ellipse, a parabola, or a hyperbola.<\/p>\n

Seven works, including the\u00a0Conics<\/em>, are mentioned by Pappus of Alexandria (fl. A.D. 320) in his Collections<\/em> book 7:1<\/a><\/sup><\/p>\n

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3.\u00a0 The order of the books of the Domain of Analysis alluded to above is this: Euclid, Data, one book; Apollonius, Cutting off of a Ratio<\/em>, two; Cutting off of an Area<\/em>, two<\/span>; <Determinate Section<\/em>>, two; Tangencies<\/em>, two; Euclid, Porisms<\/em>, three; Apollonius, Neuses<\/em>, two; by the same, Plane Loci<\/em>, two; Conics<\/em>, eight<\/span>; Aristaeus, Solid Loci<\/em>, five; Euclid, Loci on Surfaces<\/em>, two; Eratosthenes, On Means<\/em> [two]. These make up 32 books. I have set out epitomes of them, as far as the Conics of Apollonius, for you to study, with the number of the dispositions and diorisms and cases in each book, as well as the lemmas that are wanted in them, and there is nothing wanting for the working through of the books, I believe, that have I left out.2<\/a><\/sup><\/p>\n<\/blockquote>\n

Pappus then goes on to summarise the contents of each work.\u00a0 Listing them:<\/p>\n

    \n
  1. Conic sections <\/em>(\u03c4\u03bf\u03bc\u03b1\u03b9 \u03c4\u1ff6\u03bd<\/em> \u03ba\u03c9\u03bd\u03b9\u03ba\u1ff6\u03bd<\/em>), in 8 books<\/li>\n
  2. Cutting off a ratio (\u03bb\u03cc\u03b3\u03bf\u03c5 \u1f00\u03c0\u03bf\u03c4\u03bf\u03bc\u03ae),<\/em> in 2 books<\/li>\n
  3. Cutting off an area (\u03c7\u03c9\u03c1\u03af\u03bf\u03c5 \u1f00\u03c0\u03bf\u03c4\u03bf\u03bc\u03ae),<\/em> in 2 books<\/li>\n
  4. Determinate section<\/em> (\u03b4\u03b9\u03c9\u03c1\u03c9\u03c3\u03bc\u03ad\u03bd\u03b7 \u03c4\u03bf\u03bc\u03ae<\/em>), in 2 books<\/li>\n
  5. Tangencies<\/em> (\u1f10\u03c0\u03b1\u03c6\u03b1\u03af<\/em>), in 2 books<\/li>\n
  6. Plane Loci<\/em> (\u03c4\u03cc\u03c0\u03bf\u03b9 \u1f10\u03c0\u03af\u03c0\u03b5\u03b4\u03bf\u03b9<\/em>), two books<\/li>\n
  7. Neuseis \/ Inclinations<\/em>\u00a0(\u03bd\u03b5\u03cd\u03c3\u03b5\u03b9\u03c2<\/em>), two books<\/li>\n<\/ol>\n

    Another six works are referenced by other ancient authors, a list of which can be found in the old Encyclopedia Britannica article here<\/a>.<\/p>\n

    The\u00a0Conic Sections<\/em><\/span><\/p>\n

    The only material that has reached us in Greek is the first four books of the Conics<\/em>, although this is not the original text, but as incompetently revised by Eutocius in the 6th century AD. Books 5, 6 and 7 are not preserved in Greek.\u00a0 The fate of book 8 is unclear, but it does not seem to have existed much later than Pappus in the 3rd century AD, if indeed it existed then.<\/p>\n

    In the Heiberg edition of 18913<\/a><\/sup> the manuscripts are listed as:<\/p>\n