Notes — Textual Witnesses, Trilogy Context & Planimetry

1. Completion of the Heath Cambridge Greek Trilogy

T. L. Heath's Treatise on Conic Sections (Cambridge University Press, 1896) was the inaugural volume of his monumental three-part Cambridge synthesis of Greek geometry:

1. 1896 — Apollonius of Perga: Treatise on Conic Sections (geometor/apollonius)

2. 1897 / 1912 — Archimedes: The Works of Archimedes + The Method (geometor/archimedes; Heath 1897)

3. 1908 / 1926 — Euclid: The Thirteen Books of Euclid’s Elements (geometor/euclid; Heath 1908)

Heath explains in his Preface (pp. vii–xii) why modern symbolic-geometric notation is indispensable for Apollonius: in Book VII alone, literal word-for-word translation of compound ratio chains over twenty auxiliary segments obscures the dazzling algebraic symmetry that Zeuthen (1886) revealed as ancient coordinate geometry.

2. Planimetric Severance from the 3D Cone

Heath highlights (pp. xcvii–xcviii) one of Apollonius’s deepest architectural decisions: once the fundamental symptom (:term:`symptōma <symptoma>`) is derived from the 3D cone in I.11–14, Apollonius never appeals to the solid cone again in Books I–V or VII (returning to the cone only in Book VI.28–33 when embedding a given conic into a prescribed right cone). Every subsequent theorem of tangents, asymptotes, poles and polars, foci, intersections, normals, and conjugate diameters is deduced purely in the 2D plane from the area-application equation!

3. Prosopographical Note on Philonides & Pergamum

Apollonius’s casual mention of Philonides in the Preface to Book II (p. lxxii) gained remarkable archaeological confirmation from the carbonized Vita Philonidis (PHerc. 1044) unearthed at Herculaneum, which confirms Philonides of Laodicea’s studies with Eudemus and Dionysodorus and anchors the publication of Books I–II of the Conics squarely around 200–190 BCE.