— GEOMETOR • proclus

Prologue Part I: Mathematical Being & Common Science

Intermediate Being (Metaxy), Limit & Unlimited, Common Mathematical Principles, Critique of Abstraction, and the Ascent to Dialectic — Friedlein (1873) pp. 3–47 · Book I (Chaps. I–XV)

Prologue Part II: Philosophy & History of Geometry

Mathematical Imagination (Phantasia & Probole), Intelligible Matter, The Eudemian Summary of Greek Geometry, and the Purpose of the Elements — Friedlein (1873) pp. 48–84 · Book II (Chaps. I–IX)

Commentary on the Definitions (I.Def.1–23)

Point, Line & Flux, Straight Line, Surface, Plane & Horn Angles, Figure, Circle, Triangles, Quadrilaterals, and Parallel Lines — Friedlein (1873) pp. 85–177 · Book II (Definitions I–XXXV)

Hypotheses, Postulates, Axioms & Propositional Form

Epistemology of First Principles, Compass & Straightedge Postulates, Critique of Postulate 5, Common Notions, and the Six Parts of a Proposition — Friedlein (1873) pp. 178–207 · Book III (Petitions, Axioms & Prop. I Prefatory Sections)

Commentary on Propositions I.1–I.15: Triangles, Congruence & Perpendiculars

Equilateral Construction & Zeno’s Critique, Superposition (I.4), Pappus’s Proof of I.5, Converses & Reductio, Oenopides’ Gnomon (I.12), Vertical Angles & Porisms — Friedlein (1873) pp. 208–305 · Book III (Propositions I–XV & Porisms)

Commentary on Propositions I.16–I.32: Inequalities, Parallels & Angle-Sum

Exterior Angle, Epicurean Critique of I.20, Thales’ Ship-Distance Theorem (I.26), Ptolemy & Proclus on Postulate 5 (I.29), and the Pythagorean Angle-Sum Proof (I.32) — Friedlein (1873) pp. 305–384 · Book III (Props. XVI–XXVI) & Book IV (Props. XXVII–XXXII)

Commentary on Propositions I.33–I.48: Areas, Application & Pythagoras

Parallelograms & Locus Theorems (I.35), Pythagorean Application of Areas (Parabole, Hyperbole, Elleipsis, I.44), and Euclid’s Proof of I.47–I.48 — Friedlein (1873) pp. 384–436 · Book IV (Propositions XXXIII–XLVIII)