Bibliography & Critical Editions

Primary Public Domain editions, ancient and medieval witnesses, early-modern reconstructions, and GEOMETOR ecosystem references cited via :cite: across the Conics codex.

Apollonius of Perga (ed. Sir Thomas Little Heath) (1896)

  • Citation Key: heath:1896

  • Work: Treatise on Conic Sections, Edited in Modern Notation with Introductions Including an Essay on the Earlier History of the Subject

  • Publication / Locus: Cambridge: At the University Press, 1896 (pp. clxx + 254)

  • Apparatus Note: Primary Public Domain English codex source: 170-page historical and mathematical introduction plus Books I–VII rendered into 147 consolidated propositions mapped to all 387 classical Greek/Arabic numbers.

  • Archival / Ecosystem Link: https://archive.org/details/treatiseonconics00apolrich

Apollonius of Perga (ed. Johan Ludvig Heiberg) (1891)

  • Citation Key: heiberg:1891

  • Work: Apollonii Pergaei quae Graece exstant cum commentariis antiquis, Vol. I

  • Publication / Locus: Leipzig: B. G. Teubner, 1891

  • Apparatus Note: Definitive critical Greek text and Latin translation of Books I–III (and Book IV opening) based on Codex Vaticanus Graecus 206.

  • Archival / Ecosystem Link: https://archive.org/details/apolloniipergaei01apoluoft

Apollonius of Perga (ed. Johan Ludvig Heiberg) (1893)

  • Citation Key: heiberg:1893

  • Work: Apollonii Pergaei quae Graece exstant cum commentariis antiquis, Vol. II

  • Publication / Locus: Leipzig: B. G. Teubner, 1893

  • Apparatus Note: Completion of Book IV, extant Greek fragments, Lemmas of Pappus (Synagoge VII), and Commentaries of Eutocius of Ascalon on Books I–IV.

  • Archival / Ecosystem Link: https://archive.org/details/apolloniipergaei02apoluoft

Apollonius of Perga (ed. Edmond Halley) (1710)

  • Citation Key: halley:1710

  • Work: Apollonii Pergaei Conicorum Libri Octo, et Sereni Antissensis De Sectione Cylindri & Coni Libri Duo

  • Publication / Locus: Oxford: E Theatro Sheldoniano, 1710

  • Apparatus Note: Monumental Oxford folio editio princeps presenting Books I–IV in Greek/Latin, Books V–VII in Latin translated from Thābit ibn Qurra’s Arabic MS Bodleian Marsh 667, and Halley’s conjectural Book VIII.

  • Archival / Ecosystem Link: https://archive.org/details/bub_gb_6N__e_V4xbAC

Apollonius of Perga (ed. Edmond Halley) (1706)

  • Citation Key: halley:1706

  • Work: Apollonii Pergaei De Sectione Rationis Libri Duo ex Arabico MSto Latine Versi; Accedunt Ejusdem De Sectione Spatii Libri Duo Restituti

  • Publication / Locus: Oxford: E Theatro Sheldoniano, 1706

  • Apparatus Note: Halley’s Latin translation from Bodleian Arabic MS Selden Arch. A. 34 of Apollonius’s otherwise lost Cutting Off of a Ratio (Περὶ λόγου ἀποτομῆς), with restoration of Cutting Off of an Area.

  • Archival / Ecosystem Link: https://archive.org/details/apolloniipergaei00apol

Ludwig M. L. Nix (1889)

  • Citation Key: nix:1889

  • Work: Das fünfte Buch der Conica des Apollonius von Perga in der arabischen Übersetzung des Thabit ibn Corrah

  • Publication / Locus: Leipzig: W. Drugulin, 1889

  • Apparatus Note: Arabic text and German translation of the Preface and opening propositions of Book V from Bodleian MS Marsh 667, cited by Heath on p. lxxiv.

Hugo Balsam (1861)

  • Citation Key: balsam:1861

  • Work: Des Apollonius von Perga sieben Bücher über Kegelschnitte nebst dem durch Halley wieder hergestellten achten Buche

  • Publication / Locus: Berlin: Georg Reimer, 1861

  • Apparatus Note: German translation and analytical study of Books I–VII consulted closely by Heath.

Hieronymus Georg Zeuthen (1886)

  • Citation Key: zeuthen:1886

  • Work: Die Lehre von den Kegelschnitten im Altertum

  • Publication / Locus: Copenhagen: Andr. Fred. Höst & Sohn, 1886

  • Apparatus Note: Foundational historical reconstruction of Greek geometric algebra, Apollonian transformation of coordinates, and the synthesis of the Three- and Four-Line Locus.

Pappus of Alexandria (ed. Friedrich Hultsch) (1877)

  • Citation Key: hultsch:1877

  • Work: Pappi Alexandrini Collectionis quae supersunt, Vol. II (Book VII: Domain of Analysis)

  • Publication / Locus: Berlin: Weidmann, 1877

  • Apparatus Note: Critical Greek edition of Pappus Book VII preserving the syllabus, proposition counts, and auxiliary lemmas for Apollonius’s Conics and six lost analytic treatises.

Euclid (trans. Sir Thomas Little Heath) (1908)

  • Citation Key: euclid:heath1908

  • Work: The Thirteen Books of Euclid’s Elements (3 vols.)

  • Publication / Locus: Cambridge: At the University Press, 1908 (2nd ed. 1926); GEOMETOR • euclid

  • Apparatus Note: Third pillar of Heath’s Cambridge Greek Trilogy; Books I.44, II.5–6, II.11, II.14, III.16–18, III.35–37, VI.27–29, and XII.10 underpin Apollonius’s demonstrations.

  • Archival / Ecosystem Link: https://geometor.github.io/euclid

Archimedes (ed. Sir Thomas Little Heath) (1897)

  • Citation Key: archimedes:heath1897

  • Work: The Works of Archimedes, Edited in Modern Notation with Introductory Chapters

  • Publication / Locus: Cambridge: At the University Press, 1897 (Supplement: The Method, 1912); GEOMETOR • archimedes

  • Apparatus Note: Second pillar of Heath’s Cambridge Greek Trilogy, pairing Quadrature of the Parabola and On Conoids and Spheroids directly with Apollonius’s symptom theory.

  • Archival / Ecosystem Link: https://geometor.github.io/archimedes

François Viète (1600)

  • Citation Key: viete:1600

  • Work: Apollonius Gallus, seu Exsuscitata Apollonii Pergaei Περὶ Ἐπαφῶν Geometria

  • Publication / Locus: Paris: David Le Clerc, 1600

  • Apparatus Note: Classical Euclidean reconstruction of Apollonius’s lost On Tangencies culminating in Problem X (CCC: circle tangent to three given circles).

Johannes Kepler (1604)

  • Citation Key: kepler:1604

  • Work: Ad Vitellionem Paralipomena, Quibus Astronomiae Pars Optica Traditur (Cap. IV, §4: De Coni Sectionibus)

  • Publication / Locus: Frankfurt: Claudius Marnius & Heirs of Johann Aubry, 1604

  • Apparatus Note: Introduces the term ‘foci’ for Apollonius’s ‘points arising from the application’ (III.45–52), supplies the parabola focus at finite distance with the second focus at infinity, and formulates projective continuity.

René Descartes (1637)

  • Citation Key: descartes:1637

  • Work: La Géométrie (Books I–II: Problem of Pappus on Three, Four, and Many Lines)

  • Publication / Locus: Leiden: Jan Maire, 1637

  • Apparatus Note: Solves the Apollonius–Pappus Three-Line and Four-Line Locus in symbolic algebraic coordinates, inaugurating modern algebraic geometry.

Clark Kimberling (1998–2026)

  • Citation Key: kimberling:etc

  • Work: Encyclopedia of Triangle Centers (ETC)

  • Publication / Locus: University of Evansville / GEOMETOR • etc

  • Apparatus Note: Catalogues the Isodynamic Points X(15), X(16) (intersections of the three coaxal Apollonius circles of a triangle) and the Apollonius Point X(181) (perspector of the outer Soddy/Apollonius CCC contact triangle).

  • Archival / Ecosystem Link: https://geometor.github.io/etc

Norman J. Wildberger (2005)

  • Citation Key: wildberger:2005

  • Work: Divine Proportions: Rational Trigonometry to Universal Geometry

  • Publication / Locus: Sydney: Wild Egg, 2005; GEOMETOR • wildberger

  • Apparatus Note: Reformulates classical Apollonian conics, focus-directrix quadrances, and projective polarity purely over arbitrary fields without transcendental functions.

  • Archival / Ecosystem Link: https://geometor.github.io/wildberger

Lean Community (mathlib4) (2024–2026)

  • Citation Key: mathlib4:polepolar

  • Work: Mathlib.LinearAlgebra.QuadraticForm.PolePolar / Projective Conic Polarity

  • Publication / Locus: Lean 4 Formal Mathematical Library

  • Apparatus Note: Formalizes bilinear symmetric polarity, self-polar triangles, and harmonic cross-ratio division corresponding directly to Apollonius Conics Book III Props. 30–40.

  • Archival / Ecosystem Link: https://leanprover-community.github.io/mathlib4_docs/