apollonius

GEOMETOR • apollonius presents the Digital Scriptorium 3-Track Book Codex and cross-corpus concordance of Apollonius of Perga's Treatise on Conic Sections (Κωνικά, Books I–VII, c. 200 BCE), anchored on Sir Thomas Little Heath's landmark 1896 Cambridge University Press edition (Heath 1896), Johan Ludvig Heiberg's Teubner Greek text (1891–1893), and Edmond Halley's 1710 Oxford edition of Thābit ibn Qurra's Arabic Books V–VII (Halley 1710).

I.1–14: Single Oblique Double Cone & Three Sections A B C O E₁ E₂ P H₁ H₂ Ellipse Parabola (∥ AC) Hyperbola (2 branches) I.5: Subcontrary Circular Section A B C K G D E M P ∠AKG = ∠ACB ⇒ PM² = DM·ME = KM·MG

The Apollonian Synthesis: Every circular cone—right or scalene—generates the parabola, ellipse, hyperbola, and opposite branches by varying the inclination of a single cutting plane.

Completing the Heath Cambridge Greek Trilogy

With geometor/apollonius, the GEOMETOR Digital Scriptorium completes Sir Thomas Little Heath’s Cambridge trilogy of classical Greek geometry:

  1. Apollonius (1896) — Treatise on Conic Sections (geometor/apollonius): 387 classical propositions consolidated into 147 propositions across Books I–VII, plus the analytic treasury in Pappus Book VII.

  2. Archimedes (1897 / 1912) — The Works of Archimedes & The Method (geometor/archimedes): Exhaustion, mechanical equilibrium, and quadrature of conic segments and paraboloids.

  3. Euclid (1908 / 1926) — The Thirteen Books of Euclid’s Elements (geometor/euclid): The axiomatic and area-application foundation (G.1–G.601 in geometor/elements).

Explore the Codex

  • Conics (3-Track Book Codex) — Synchronized English, Summary, and Notes tracks across 8 Units (Prefaces & Introduction, Books I–VII, and the Lost Analytic Treasury in Pappus Book VII) illustrated with 12 standalone ``.euclid-graphic`` SVG plates.

  • Mission & Architectural Scope — Exact symbolic conic roadmap, strict content/code separation, and sympy.geometry capability audit.

  • About Apollonius & the Textual Tradition — Life of The Great Geometer, the Heath Trilogy, and the Greek-Arabic manuscript transmission.

  • Python Package & Concordance API — Reference for geometor.apollonius concordance verification, apparatus generation, and CLI utilities.