GEOMETOR • nicomachus

Introductio Arithmetica (Ἀριθμητικὴ Εἰσαγωγή) — Nicomachus of Gerasa on the Quadrivium, Ratio Unfolding, Figurate Gnomons & Harmonic Proportion

Critical four-track Digital Scriptorium Book Codex and exact symbolic geometry & number-theory suite for Nicomachus of Gerasa's Introduction to Arithmetic (c. 100 CE)—the foundational Neo-Pythagorean treatise that organized the Four Mathematical Sciences (mathemata, rendered quadruvium by Boethius), unfolded all rational inequalities from primordial Equality (\(1 : 1 : 1\)), constructed polygonal and solid numbers by arithmetic gnomons, proved the Sum-of-Cubes Theorem, and crowned \(6 : 8 :: 9 : 12\) as the Most Perfect Three-Dimensional Proportion uniting the Cube and the Pythagorean musical scale.

Every Codex unit is presented across four synchronized tracks powered by photon-platform/publish:

1. English — Public-domain critical translation (1926) of Martin Luther D'Ooge (dooge:1926), segmented to exact chapter and page folio markers.

2. Greek (Hoche 1866) — Verbatim polytonic Greek from Richard Hoche's Teubner critical edition (hoche:1866).

3. Summary — Deductive architecture, structural tables, and interactive diagram walkthroughs.

4. Critical Notes — Exact SymPy / Rational Trigonometry bridges, interactive .euclid-graphic SVGs (:g: / :eq:), Boethius De Institutione Arithmetica (boethius:friedlein:1867) parallels, and philological corrections (including Frank Egleston Robbins's notes on Means 8–9 in II.28).

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Codex (Introductio Arithmetica, Books I–II)

Enter the 4-Track Book Codex

• Unit I — Book I, Chs. 1–7, 13, 16: Philosophy, Magnitude vs. Multitude, the Four Mathematical Sciences (Quadrivium), the Odd Sieve of Eratosthenes & Perfect Numbers

• Unit II — Book I, Chs. 17–23: The Five Species of Relative Inequality & Nicomachus’s Rule of Three Terms Unfolding Every Ratio from Equality (1 : 1 : 1)

• Unit III — Book II, Chs. 1–2, 6–20: Inverse Reduction to Equality, Polygonal Alpha-Gnomons, Plato’s Same & Other (Squares vs. Oblongs) & Nicomachus’s Sum-of-Cubes Theorem

• Unit IV — Book II, Chs. 21–29: The Ten Neo-Pythagorean Means, Semicircle Geometry & the Cube’s Most Perfect Proportion (6 : 8 :: 9 : 12)

• Critical Apparatus: Master Chapter & Canon Concordance · Bibliography & Critical Editions · Mathematical & Philosophical Authorities · Glossary of Greek & Latin Arithmetical Terms

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Symbolic Constructions, Editorial Context & API

• Exact Symbolic Demonstrations (SymPy & Rational Trigonometry)

• Mission — Nicomachus as Architect of the Quadrivium

• Hoche’s Teubner Edition (1866), D’Ooge (1926) & Boethius’s Latin Transmission

• Python Package & CLI Reference

• Project Log

• Changelog