Latin & Mathematical Glossary

Lexicon of the 16 foundational Neo-Latin, typographic, projective, and symbolic-geometry terms across De lineis rectis se invicem secantibus statica constructio (1678) and geometor.ceva.

Static & Algebraic Terminology (Liber Primus)

  • statica constructio (Static Construction) — Ceva’s methodological principle (Prooemium): proving theorems on mutually intersecting straight lines purely by placing hypothetical Archimedean weights at vertices without drawing auxiliary Euclidean circles or construction lines.

  • centrum gravitatis (Center of Gravity / Barycenter) — The unique equilibrium point $P = \frac{u A + v B + w C}{u + v + w}$ of a system of point masses (Axiomata I–II & Petitio), invariant under associative grouping of partial fulcrums.

  • momentum ponderis (Static Moment / Lever Law) — Archimedes’ inverse-proportion rule (Lemmata I–II): weights $u$ at $A$ and $v$ at $B$ balance around fulcrum $F$ on $AB$ iff $u \cdot \overline{AF} = v \cdot \overline{FB}$ ($A : B = BF : FA$).

  • pondus subtractivum / F - A (Algebraic Negative Weight) — Ceva’s analytic innovation (Liber Primus, Elementum III & p. 5 Scholium: “pondus verò L more analytico, seu algebrico ita scribemus $F - A$, hoc est $F$ minus $A$”), assigning a subtractive/upward weight to capture exterior concurrency 149 years before Möbius (1827).

  • nota crucis † pro additione (A † F) — Milanese printer Ludovico Monza's typographic obelus/dagger † denoting algebraic addition (A † F $= A + F$) throughout the 1678 quarto.

  • ratio composita (Compound Ratio) — Sequential product of ratios $\frac{AF}{FB} \cdot \frac{BD}{DC} \cdot \frac{CE}{EA} = 1$, translated from static weight cancellation via Commandino and Clavius (Props. VII–VIII).

  • linea ceviana (Cevian) — Any straight line joining a vertex of a triangle, polygon, or tetrahedron to the opposite sideline or face plane.

  • sectio harmonica (Projective Harmonic Range) — Collinear quadruple $(B, C; D, D') = -1$ where $D$ is a cevian foot ($BD/DC = w/v$) and $D' = EF \cap BC$ is the dual Menelaus transversal intersection ($BD'/D'C = -w/v$).

Polygons, Conics, Spatial Statics & Indivisibles (Liber I–II & Appendix)

  • coniugatum isotomicum (Isotomic Conjugate) — Reciprocal-weight concurrency $P^* = (u^{-1} : v^{-1} : w^{-1})$ obtained by reflecting cevian feet across side midpoints (Liber Secundus, Prop. I Corollarium), pairing Gergonne $X(7)$ with Nagel $X(8)$.

  • punctum contactus / Gergonne X(7) — Concurrency center of cevians to the contact points of an inscribed circle or ellipse, proved in Ceva’s Liber Secundus, Proposition I (1678).

  • quadrilaterum non in eodem plano (3D Skew Quadrilateral) — Non-planar 3D cycle $ABCD$ (Liber Primus, Elementum V Corollarium) whose four weighted edge fulcrums are coplanar and have intersecting opposite joins at $O$.

  • mira concordia septem linearum (7-Line Tetrahedral Equilibrium) — Simultaneous concurrency (Liber Primus, Prop. XXIII) of the 4 vertex-to-opposite-face-barycenter cevians and 3 opposite-edge fulcrum joins of a weighted tetrahedron at a single 3D center $O$.

  • sectio cylindrica / projectio affinis (Cylindrical Projection) — Oblique plane section of a circular cylinder (Liber Secundus, Lemma I, citing Serenus and Borelli) mapping circles to ellipses while preserving all collinear segment ratios.

  • ungula cylindrica (Cylindrical Hoof) — Solid wedge cut from a right circular cylinder by a plane through a base diameter, proved in Appendix Geometrica, Prop. VII to equal $\frac{2}{3} R^2 H = \frac{2}{3}$ of its circumscribed triangular prism.

  • indivisibilia Cavallerii & cautio superficierum — Ceva’s closing demonstration (Appendix Geometrica) that summing parallel chords or circles on curved surfaces without slant frustum elements ($ds = dz / \cos\alpha$) produces false surface areas.

  • Spread Ceva & Quadrance — Radical-free Rational Trigonometry formulation $\frac{s(\angle BAD)}{s(\angle DAC)} \cdot \frac{s(\angle CBE)}{s(\angle EBA)} \cdot \frac{s(\angle ACF)}{s(\angle FCB)} = 1$ verified over $\mathbb{Q}$ in geometor.ceva.