Initial Release: Menelai Sphaericorum Libri III Codex & Exact Symbolic Transversals

Established geometor/menelaus (v0.1.0) as a dual Digital Scriptorium Book Codex and exact symbolic geometry package:

• Multimodal Scan-Verified 4-Track Book Codex: Inspected the high-resolution archival page scans of Edmond Halley’s Menelai Sphaericorum Libri III (Oxford, 1758, with George Costard’s Praefatio), Claudius Ptolemy’s Syntaxis Mathematica I.13 (ed. Heiberg, 1898), and Axel Anthon Björnbo’s Studien über Menelaos’ Sphärik (Teubner, 1902), authoring a 100% original English translation paired with Latin/Greek diplomatic witnesses, analytical summaries, and mathematical notes across Units I–IV.

• Exact Planar, Spherical & Projective Demonstrations:

  • Verified Planar Menelaus via Euclidean parallel auxiliary CH || DF (signed ratio product -1, unsigned +1), universal polynomial converse, External Angle-Bisector Axis, Desargues’s Axis, Pascal’s Hexagrammum Mysticum, Monge’s 3-Circle Similicenters, and Wildberger Rational Trigonometry quadrance/spread laws.

  • Built an exact 3D unit-sphere (\(x^2 + y^2 + z^2 = 1\)) solver verifying positive spherical excess (\(\tan(E/2) = 1/17 > 0\), Prop. I.11), polar triangle duality and AAA spherical congruence (Prop. I.17), Spherical Menelaus’s Theorem (Prop. III.1) in both Ptolemaic double-arc chords and sines, spherical cross-ratio pencil invariance (Prop. III.8), and spherical orthocenter concurrency (Prop. III.10).

  • Formalized projective \(\mathbb{P}^2\) polarity and complete-quadrangle harmonic conjugation pairing Ceva triples (+1) with Menelaus trilinear polars (-1) across X(1), X(2), X(4), and X(7).