Summary — Historical Genesis & Eight-Book Plan

1. Pre-Apollonian Conics vs. the Apollonian Synthesis

Feature	Pre-Apollonian Canon (Menaechmus, Aristaeus, Euclid, Archimedes)	Apollonius’s Conics (c. 200 BCE)
Generating Solid	Three separate right circular cones (right-angled, acute-angled, obtuse-angled)	A single arbitrary oblique (scalene) circular double cone
Cutting Plane	Fixed perpendicular to one slant generator	Arbitrary inclination relative to the axial triangle
Nomenclature	Orthotome, Oxytome, Amblytome	Parabola, Ellipse, Hyperbola
Coordinate Frame	Principal orthogonal axis only	Any oblique diameter PP and vertex tangent (oblique affine frame)
Hyperbola Model	Single branch only	Unified two-branched curve (hai antikeimenai)

2. Textual Survival & Heath’s 1896 Consolidation

• Original Work: 8 Books (~487 propositions attested by Pappus).

• Extant Corpus: 7 Books containing 387 classical propositions: - Books I–IV (226 props.): Extant in Greek via Eutocius of Ascalon's recension (Heiberg 1891–1893). - Books V–VII (161 props.): Extant in the 9th-century Arabic translation of Thābit ibn Qurra commissioned by the Banū Mūsā, published in Latin by Edmond Halley (Halley 1710). - Book VIII: Lost in both Greek and Arabic; reconstructed conjecturally by Ibn al-Haytham and Halley.

• Heath’s Method (1896): Sir Thomas Little Heath condenses repetitive single-branch/double-branch case splits into 147 numbered Propositions (Props. 1–147) while printing every corresponding Greek/Halley bracketed reference directly beneath each heading.