mission¶
geometor.menelaus recovers, translates, models, and proves the foundational geometric architecture of Menelaus of Alexandria (c. 70–140 CE), author of the three-book Sphaerica (Sphaericorum Libri III) and discoverer of the Menelaus Transversal Theorem—the bridge linking Greek spherical astronomy to modern synthetic projective geometry.
Our mission unites three pillars of the GEOMETOR Digital Scriptorium:
Public-Domain Philological Fidelity: Present scan-verified diplomatic Latin texts from Edmond Halley’s posthumous Oxford edition (Menelai Sphaericorum Libri III, 1758, with preface by George Costard) alongside the oldest extant polytonic Greek witness in Claudius Ptolemy’s Syntaxis Mathematica I.13 (ed. Heiberg 1898) and the stemmatic apparatus of Axel Anthon Björnbo (Studien, 1902), paired with a 100% original English scholarly translation.
Intrinsic Spherical Geometry Without Stereometric Detours: Highlight Menelaus’s decisive conceptual revolution over Theodosius: isolating the triangulum sphaericum bounded by minor great-circle arcs, demonstrating positive spherical excess (\(A + B + C > \pi\), Prop. I.11) and AAA spherical congruence (Prop. I.17) without appealing to Euclid’s Parallel Postulate, and discovering spherical cross-ratio invariance (Prop. III.8) two centuries before Pappus.
100% Exact Symbolic Verification (`SymPy` & `geometor.model`): Formalize every planar, rational-trigonometric, unit-sphere (\(x^2 + y^2 + z^2 = 1\)), and projective \(\mathbb{P}^2\) Ceva–Menelaus duality theorem over \(\mathbb{Q}\) and closed-form radical extensions with zero floating-point approximations, keeping historical prose and executable Python strictly separated.