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Richard Hoche’s Teubner Edition (1866), Martin Luther D’Ooge’s Translation (1926) & Boethius’s Latin Transmission

Primary Textual Witnesses & Public-Domain Provenance

This Digital Scriptorium edition of Nicomachus of Gerasa's Introductio Arithmetica (Ἀριθμητικὴ Εἰσαγωγή) rests on three public-domain pillars documented in resources/introductio_arithmetica/sources_manifest.json:

  1. Greek Critical Edition — Richard Hoche (Teubner, 1866): Richard Hoche, Nicomachi Geraseni Pythagorei Introductionis Arithmeticae Libri II (Leipzig: B. G. Teubner, 1866; hoche:1866). Established from the oldest extant witnesses—notably Codex Cizensis (11th/12th c.), Göttingensis (G), and Monacensis (M)—Hoche’s pagination (pp. 1–72 for Book I, pp. 73–147 for Book II) remains the universal scholarly reference standard. Our Greek -el track stages the SHA-256 verified Open Greek and Latin First1KGreek TEI-XML witness (tlg0358.tlg001.1st1K-grc1.xml) audited directly against 300 DPI scans of Hoche’s 1866 facsimile.

  2. English Translation & Mathematical Studies — D’Ooge, Robbins & Karpinski (Michigan / Macmillan, 1926): Nicomachus of Gerasa: Introduction to Arithmetic, translated into English by Martin Luther D'Ooge, with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski (University of Michigan Studies, Humanistic Series, Vol. XVI, New York: Macmillan, 1926; dooge:1926, public domain in the United States). D’Ooge’s lucid translation (pp. 181–286) and Robbins’s critical footnotes (such as correcting the transmitted exemplars \(4, 7, 8\) and \(3, 5, 6\) in II.28.3–4 to \(4, 6, 7\) and \(4, 6, 9\)) anchor our -en and -notes tracks.

  3. Latin Quadrivium Parallel — Boethius (ed. Friedlein, Teubner, 1867): Around 500 CE, Anicius Manlius Severinus Boethius adapted Nicomachus’s Greek treatise into Latin as De Institutione Arithmetica Libri Duo (boethius:friedlein:1867), coining the enduring Latin noun quadruvium (“fourfold way”) at I.1 (p. 7.25 Friedlein) to translate Nicomachus’s four “bridges” (gephyrai) and “ladders” (klimakes) of I.3.6. Every Codex unit cross-references Boethius’s corresponding chapters alongside Iamblichus (iamblichus:pistelli:1894), John Philoponus (philoponus:hoche:1864), Thomas Aquinas (aquinas:in-boethium-trinitate), Luca Pacioli (pacioli:divina-proportione:1509), and Johannes Kepler.

Archival Folio Pagination Key

  • Hoche 1866 Teubner Facsimile (hoche_1866_teubner.pdf): PDF page = Hoche page + 18 (Book I begins on Hoche p. 1 = PDF p. 19; Book II begins on Hoche p. 73 = PDF p. 91).

  • D’Ooge 1926 Michigan Edition (dooge_1926_michigan.pdf): PDF page = D'Ooge page + 16 (Translation Book I begins on D’Ooge p. 181 = PDF p. 197; Book II begins on D’Ooge p. 230 = PDF p. 246).