GEOMETOR • cusa

Nicholas of Cusa (*Nicolaus Cusanus*, 1401–1464): *De Docta Ignorantia* (1440) & *Scripta Mathematica* (1445–1459) — Synchronized 4-Track Latin/English Digital Scriptorium Book Codex and 100% Exact Symbolic SymPy Demonstrations.

geometor/cusa (geometor-cusa) unites into a single critical edition and symbolic geometry package:

1. Four-Track Synchronized Book Codex (docsrc/de_docta_ignorantia/, :layout: book): Every unit is presented across English (100% original GEOMETOR translation rendered directly from the Latin), Latin (1440 / 1514–1913) (collated from Rotta 1913 with Raymond Klibansky's McGill archival restorations and the 1514 Paris / 1565 Basel Opera), Summary, and Critical Notes:
   • Unit I (`unit-1-maximum-ignorantia`): Dedicatio, De Docta Ignorantia Book I, Chapters 1–4 (Comparative Proportion, Polygon-in-Circle Exhaustion & Coincidence of Maximum and Minimum), and Epistola auctoris (Kues, February 12, 1440).
   • Unit II (`unit-2-mathematica-transsumptio`): Book I, Chapters 11–12 (Incorruptible Certitude of Mathematicalia & the Three-Step Method of Transsumptio).
   • Unit III (`unit-3-coincidentia-figurarum`): Book I, Chapters 13–15 (Coincidence of Infinite Circle, Straight Line, Triangle & Sphere).
   • Unit IV (`unit-4-linea-sphaera-infinita`): Book I, Chapters 16–23 (The Infinite Line as Universal Measure, Triunity vs. Quaternity & the Infinite Sphere).
   • Unit V (`unit-5-cosmologia-complementa`): Book II, Chapters 11–12 (Centerless Cosmic Relativity & the Noble Moving Earth) + De Geometricis Transmutationibus (1445), De Mathematicis Complementis (1453), De Mathematica Perfectione (1458), and the complete Aurea Propositio in Mathematicis (August 8, 1459).
2. 100% Exact Symbolic Geometry Engine (`src/geometor/cusa/`): Built on geometor.model with Model(..., auto_intersect=False) and zero floating-point coordinates:
   • Circle–Line Coincidence & Möbius Inversion (`coincidentia_circle_line.py`): Exact quadratic-radical sagittae (1, 2-\sqrt{3}, 4-\sqrt{15}, 8-3\sqrt{7}), scaling law \lim_{R\to\infty} R\,h(x,R) = x^2/2, and conformal unit-circle inversion mapping C_R to finite rational circles M_R = (0, -\frac{R}{2R+1}) converging to C'_\infty = (0, -\frac{1}{2}).
   • Triangle–Line Coincidence in Rational Trigonometry (`coincidentia_triangle_line.py`): Pure rational spreads s_{A_n} = \frac{4n^2}{(n^2+1)^2} \to 0, s_B = \frac{1}{n^2+1} \to 0, Triple Spread Formula identity, and Triple Quad collinearity residual \frac{16}{n^2} \to 0.
   • Polygon Exhaustion & *Scripta Mathematica* (`polygon_exhaustion_and_complementa.py`): Radical polygon tower (n = 3, 4, 6, 8, 12), 1445 sesquiquartal rectification (\pi_{\text{Cusa}} = \frac{24\sqrt{21}}{35} \approx 3.14233762), and 1458–1459 three-ray law \theta \approx \frac{3\sin\theta}{2+\cos\theta} with fifth-order Maclaurin residual \frac{\theta^5}{180}.
   • Nine Dark/Light `.euclid-graphic` SVGs (`render.py`): Exported to docsrc/_static/figures/ with interactive data-ref and data-latex-* attributes.

# Compile all 4-track Codex units, SVGs, witness manifests & apparatus
python -m geometor.cusa compile

# Run standalone symbolic demonstrations
python demos/coincidentia_circle_line.py
python demos/coincidentia_triangle_line.py
python demos/polygon_exhaustion_and_complementa.py

# Lint, test & build Sphinx Book Codex
ruff check src demos tests
pytest -v
publish build

MIT License. Primary Latin witnesses are in the public domain; all English translations in geometor/cusa are 100% original GEOMETOR scholarly translations released under MIT.