Mission

Recovering the Academy’s Architectural Blueprint of Geometry, Proportion & Noetic Ascent

geometor/plato (Loci Mathematici et Geometrici) anchors the fourth-century Athenian fountainhead of the GEOMETOR historical and constructive canon. Over the portal of the Academy (c. 387 BC) stood the celebrated maxim Ἀγεωμέτρητος μηδεὶς εἰσίτω (“Let no one ignorant of geometry enter”). Within its precincts, Plato of Athens united Pythagorean harmonic ratio theory with Theodorus's and Theaetetus's investigations of quadratic irrationals and Eudoxus's general theory of proportion—creating the intellectual crucible out of which Euclid's thirteen books of Elements emerged.

Why GEOMETOR Needs Plato

Across six existing editions and symbolic engines in GEOMETOR, 58 distinct ``plato:*`` citation declarations converge upon seven dialogues:

  1. The Genesis & Telos of Euclid’s *Elements* (geometor/euclid & geometor/elements — 21 citations): In The Thirteen Books of Euclid's Elements, Sir Thomas Heath continually turns to Plato to establish pre-Euclidean mathematical terminology and method: figure as limit of solid (Meno 76a \(\rightarrow\) Elements I, Defs. 13–14 & XI, Def. 2), doubling the square by the diagonal (Meno 82b–85b \(\rightarrow\) I.47 & X.9), elliptic application of areas from hypothesis (Meno 86e–87b \(\rightarrow\) VI.27–28), Theodorus's and Theaetetus's powers (Theaetetus 147d–148b \(\rightarrow\) X, Defs. 1–4 & X.9), optical straightness (Parmenides 137e \(\rightarrow\) I, Def. 4), solid geometry’s program (Republic VII 528a–d \(\rightarrow\) XI–XII), and the five cosmic solids (Timaeus 53c–56c \(\rightarrow\) XIII.13–18).

  2. Proclus’s Neoplatonic Philosophy of Geometry (geometor/proclus — 15 citations): In In Primum Euclidis Elementorum Librum Commentarii, Proclus Diadochus constructs his entire ontology of mathematical objects from four Platonic pillars: Limit and Unlimited (Philebus 16c–26d), the middle ontological station of discursive understanding on the Divided Line (Republic VI 509d–511e), recollection awakened through diagrams (Meno 82b–85d), and the cosmic polyhedra as the telos of the Elements (Timaeus 53c–56c).

  3. Aristotle’s Logic of Hypotheses & Mathematical Intermediates (geometor/aristotle — 8 citations): Aristotle's Posterior Analytics opens by resolving Meno’s paradox (71a29), contrasts demonstrative axioms with unexamined mathematical hypotheses, preserves Plato’s doctrine of immutable mathematical intermediates (Metaphysics A.6 987b14–18), and debates the planar-triangle physics of Timaeus 53c–56c (De Caelo III.7–8).

  4. Renaissance Divine Proportion & Scholastic Noetics (geometor/pacioli — 9 citations; geometor/hoenen — 5 citations): Fra Luca Pacioli builds De Divina Proportione (1509) directly around Timaeus’s geometric bond and five regular bodies, while Fr. Peter Hoenen, S.J. (De Noetica Geometriae, 1954) invokes Meno’s diagonal inquiry and Republic’s Divided Line as perennial proof that geometric necessity is grasped by intellectual insight into concrete configurations rather than blind formalist manipulation.

Editorial & Symbolic Principles

  • 100% Verbatim Public-Domain Sources: Every Greek passage is parsed directly from John Burnet's Oxford Classical Text (Platonis Opera, 1900–1907), synchronized by Stephanus page and section (a–e) with Benjamin Jowett's 3rd revised English edition (1892) and audited via SHA-256 digests in resources/loci_mathematici/sources_manifest.json.

  • Corrective Mathematical Philology: Where Jowett’s literary Victorian prose paraphrases technical Greek mathematical expressions—such as rendering τρίγωνον as “figure” at Meno 87a or compressing δυνάμει τριπλάσιον (“triple in square power”, i.e. \(Q = 3\)) at Timaeus 54b—the Critical Notes track supplies verbatim Greek mathematical translations and exact algebraic proofs.

  • Strict Content / Code Separation: The 4-track Book Codex (Loci Mathematici et Geometrici — Plato on Geometry, Proportion & Noetic Ascent) contains zero embedded Python scripts, preserving pure philological and philosophical integrity while linking to 100% exact SymPy & Rational Trigonometry models in src/geometor/plato/ and Demonstrations.