In Euclidem

ΠΡΟΚΛΟΥ ΔΙΑΔΟΧΟΥ

ΕΙΣ ΤΟ ΠΡΩΤΟΝ ΤΩΝ ΕΥΚΛΕΙΔΟΥ ΣΤΟΙΧΕΙΩΝ

IN PRIMUM EUCLIDIS ELEMENTORUM LIBRUM COMMENTARII

Commentary on the First Book of Euclid’s Elements (c. 470 AD)

Greek Text: Gottfried Friedlein (Leipzig: B. G. Teubner, 1873)

English Translation: Thomas Taylor (London, 1788–1789 / 1792) & GEOMETOR Apparatus

Conspectus Totius Operis

Composed at the Neoplatonic Academy of Athens around 470 AD, Proclus Diadochus's Commentary on the First Book of Euclid’s Elements is the supreme surviving monument of ancient mathematical philosophy, axiomatic methodology, and the pre-Euclidean history of Greek geometry. Each unit of this Multi-Track Book Codex provides four synchronized reading tracks: English, Greek (1873), Summary, and Notes.

• Prologue I (Friedlein pp. 3–47): Prologue Part I: Mathematical Being & Common Science — Intermediate Being (Metaxy), Limit & Unlimited, Common Mathematical Principles, Critique of Abstraction, and the Ascent to Dialectic. (EN · EL · Summary · Notes)

• Prologue II (Friedlein pp. 48–84): 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. (EN · EL · Summary · Notes)

• Definitions (Friedlein pp. 85–177): Commentary on the Definitions (I.Def.1–23) — Point, Line & Flux, Straight Line, Surface, Plane & Horn Angles, Figure, Circle, Triangles, Quadrilaterals, and Parallel Lines. (EN · EL · Summary · Notes)

• Postulates & Axioms (Friedlein pp. 178–207): 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. (EN · EL · Summary · Notes)

• Propositions I.1–I.15 (Friedlein pp. 208–305): 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. (EN · EL · Summary · Notes)

• Propositions I.16–I.32 (Friedlein pp. 305–384): 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). (EN · EL · Summary · Notes)

• Propositions I.33–I.48 (Friedlein pp. 384–436): 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. (EN · EL · Summary · Notes)

Critical Apparatus & Concordances

• Friedlein Citation Concordance — Bidirectional mapping of all 164 canonical Friedlein loci cited across geometor/euclid (156 keys, 159 occurrences) and geometor/hoenen.

• Bibliography & Primary Sources — Editions, ancient mathematical sources, and companion GEOMETOR treatises.

• Index Nominum (Persons) — Prosopographical register of 54 geometers, philosophers, and commentators (including the complete Eudemian Summary).

• Greek & Neoplatonic Mathematical Glossary — Lexicon of 44 technical Greek, Latin, and English terms.