Summary — Apollonius’s Six Analytic Treatises in Pappus VII¶
Treatise |
Books |
Survival / Restoration |
Core Geometric Problem & GEOMETOR Link |
|---|---|---|---|
Cutting Off of a Ratio (De Sectione Rationis) |
2 |
Extant in Arabic (Halley 1706) |
Line through O cutting given ratio on two fixed lines ( |
Cutting Off of an Area (De Sectione Spatii) |
2 |
Pappus VII lemmas; restored Halley 1706 |
Line through O cutting given rectangle on two fixed lines ( |
Determinate Section (De Sectione Determinata) |
2 |
Pappus VII (66 lemmas); Snell / Simson |
1D cross-ratio / involution ( |
Tangencies (De Tactionibus, epaphai) |
2 |
Pappus VII; Viète 1600 |
10 contact cases PPP–CCC (up to 8 tangent circles); |
Inclinations (De Inclinationibus, neusis) |
2 |
Pappus VII; Ghetaldi / Horsley |
Plane-constructible verging insertions (rhombus, semicircle, two lines) |
Plane Loci (Loca Plana) |
2 |
Pappus VII; Fermat (1636) / Simson (1749) |
Circle of Apollonius (); |