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GEOMETOR • proclus establishes the complete, open-access digital critical edition and bidirectional citation concordance of Proclus Lycius Diadochus’s In Primum Euclidis Elementorum Librum Commentarii (Commentary on the First Book of Euclid’s Elements, c. 470 AD).

Why Proclus Anchors the GEOMETOR Canon

Across the classical canon of GEOMETOR, Proclus’s Commentary serves as the indispensable historical, axiomatic, and epistemological bridge:

  1. Historical Foundation for Euclid (`geometor/euclid` & `geometor/elements`): Sir Thomas Little Heath’s Thirteen Books of Euclid’s Elements cites Gottfried Friedlein’s 1873 Teubner edition of Proclus across 156 distinct page-and-line loci (159 citing occurrences). Without Proclus, we would lack Eudemus of Rhodes’s History of Geometry (Friedlein 64–70), Pappus’s zero-construction proof of I.5 (Friedlein 249–250), Oenopides’s astronomical gnomon (Friedlein 283), Thales’s ship-distance theorem (Friedlein 352), Claudius Ptolemy’s treatise on the Parallel Postulate (Friedlein 365–368), the Pythagorean angle-sum proof (Friedlein 379), and the Pythagorean origin of application of areas (parabole, hyperbole, elleipsis, Friedlein 419–420).

  2. Epistemological Dialogue with Hoenen (`geometor/hoenen`): In De Noetica Geometriae (1954), Petrus Hoenen S.J. engages Proclus directly (Friedlein 12, 49, 97, 139–140, 185, 191, 365–373) on the inexactitude of sensible figures, the role of mathematical imagination (φαντασία) and intelligible matter (ὕλη νοητή), Geminus’s definition of the straight line as uniform undeviating flux, and the epistemological crisis of the Fifth Postulate.

  3. Formal Logic of Constructive Geometry: Proclus’s codification of The Six Canonical Parts of a Geometric Proposition (Protasis, Ekthesis, Diorismos, Kataskeue, Apodeixis, Symperasma, Friedlein 203–207) articulates the exact logical grammar uniting synthetic Greek geometry with modern constructive verification.

Editorial Principles

  • 100% Authentic Public-Domain Sources: Pairs Gottfried Friedlein’s 1873 Teubner polytonic Greek edition (urn:cts:greekLit:tlg4036.tlg011.opp-grc1) with Thomas Taylor’s 1788–1789/1792 English translation and fresh GEOMETOR scholarly commentary.

  • Strict Historical Separation: Preserves the historical treatise cleanly without embedding modern Python construction scripts, linking outward via :just: to geometor/euclid and geometor/elements.