About GEOMETOR Ceva

Historical, philological, and symbolic-modeling provenance for geometor-ceva in the GEOMETOR Digital Scriptorium.

Public-Domain Textual Provenance & Copyright Audit

All primary Latin texts in this repository are transcribed directly from the 100% Public Domain 1678 Milan quarto editio princeps:

• Giovanni Ceva (1678): De lineis rectis se invicem secantibus statica constructio. Ad Serenissimum Ferdinandum Carolum Ducem Mantuae, Montisferrati, Guastallae, &c. Auctore Ioanne Ceva Mediolanensi. Mediolani: Ex Typographia Ludovici Montiae, MDCLXXVIII. Superiorum Permissu. (Biblioteca Nazionale Centrale di Firenze exemplar ita-bnc-mag-00001346-001; [16] + 104 printed pages and 10 folding copperplates containing Figs. 1–85, with Printed page N = PDF scan page N + 17).

Every English translation (-en), executive summary (-summary), interactive SVG diagram, and historical-mathematical commentary (-notes) in this codex is 100% originally translated and authored for GEOMETOR directly from Ceva’s 1678 Latin. No modern copyrighted translations or sourcebook excerpts were consulted or reproduced.

Typographic Conventions of the 1678 Milan Imprint

In his prefatory Typographus Lectori note, Milanese printer Ludovico Monza informs the reader that his shop lacked sufficient cast sorts of the Greek cross + and therefore employed the typographic dagger/obelus † to denote algebraic addition of weights (e.g., A † F for $A + F$ concentrated at an interior fulcrum), paired with the analytic minus sign - (F - A for $F - A$, Liber Primus p. 5 Scholium) when balancing an exterior fulcrum. Our Latin track preserves Ceva’s authentic notation alongside clear editorial explanation.

Position in the GEOMETOR Canon

geometor-ceva bridges classical Greek synthetic geometry and modern projective, barycentric, and rational-trigonometric architecture across the GEOMETOR workspace:

• Archimedean Statics to Barycentric Coordinates: Connects geometor/archimedes (Equiponderants I.6–7) directly to homogeneous barycentric coordinates in geometor/etc ($X(1), X(2), X(4), X(6), X(7), X(8)$) and Möbius's Der barycentrische Calcul (1827).

• Projective Dualism & Harmonic Ranges: Unites Ceva’s concurrency theorem with geometor/menelaus and geometor/pappus through the harmonic cross-ratio $(B, C; D, D') = -1$ verified via geometor.model.is_harmonic.

• Radical-Free Rational Trigonometry: Extends Ceva’s theorem to geometor/wildberger via Spread Ceva’s Theorem, verified over $\mathbb{Q}$ on the Heronian $(13, 14, 15)$ triangle without a single square root.