Cross-Corpus Geometric Concordance

Bidirectional concordance mapping propositions and static constructions in Giovanni Ceva's De lineis rectis se invicem secantibus statica constructio (Milan, 1678) to sister repositories across the GEOMETOR canon and exact symbolic verifiers in geometor.ceva.

Ceva 1678 Cross-Corpus Concordance

Ceva 1678 Locus

Geometric / Static Proposition

Sister GEOMETOR Canon

Symbolic Verifier (geometor.ceva)

Lib. I, Axiomata I–II & Lemmata I–II (pp. 1–2; Tab. 1, Figs. 1–3)

Uniqueness of centrum gravitatis & Archimedes’ Lever Law ($u \cdot \overline{AF} = v \cdot \overline{FB}$)

archimedes Equipond. I.4–7; euclid V–VI

static_barycentrics.solve_static_barycentrics

Lib. I, Elementum I & Prop. VIII (pp. 2–3, 10–12; Tab. 1, Figs. 4, 12)

Static proof of Menelaus's Transversal Theorem & harmonic range $(B, C; D, D') = -1$

menelaus III.1; ptolemy I.13; pappus VII

static_barycentrics.construct_cevian_menelaus_harmonic

Lib. I, Elementum II & Prop. VII (pp. 3–4, 8–10; Tab. 1, Figs. 5, 11)

Interior cevian concurrency $\frac{AF}{FB}\cdot\frac{BD}{DC}\cdot\frac{CE}{EA} = 1$ at $P = \frac{uA+vB+wC}{u+v+w}$

etc $X(1), X(2), X(4), X(6)$; altshiller-court

static_barycentrics.construct_ceva_concurrency

Lib. I, Elementum III & p. 5 Scholium (Tab. 1, Fig. 6)

Analytic negative weight F - A for exterior concurrency (excenter $J_A$)

etc excenters; Möbius (1827)

static_barycentrics.evaluate_canonical_centers

Lib. I, Elementa IV–V Coroll. (pp. 5–7; Tab. 1, Figs. 7–8)

Planar & 3D skew quadrilateral (“non in eodem plano”) fulcrum coplanarity & concurrency

elements XI; pappus

polygon_tetrahedron.verify_skew_quadrilateral_ceva

Lib. I, Prop. VI (pp. 7–8; Tab. 1, Fig. 10)

Pure Euclidean parallel-line proof credited to Pietro Paolo Caravaggio Jr.

euclid / elements I.29, VI.2, VI.4

static_barycentrics.prove_ceva_barycentric_identity

Lib. I, Props. IX–XXII (pp. 12–35) & Rational Trigonometry

Medians $X(2)$, altitudes $X(4)$, bisectors $X(1)$, symmedians $X(6)$, & radical-free Spread Ceva

etc; wildberger Divine Proportions

static_barycentrics.verify_spread_ceva

Lib. I, Props. XXIII–XXVI (pp. 36–43; Tab. 3, Figs. 28–31)

3D Tetrahedron 7-Line Equilibrium (“mira quadam concordia” at $O$)

archimedes; elements XII

polygon_tetrahedron.solve_tetrahedron_static_equilibrium

Lib. II, Lemma I & Prop. I + Coroll. (pp. 45–50; Tab. 4, Figs. 32–37)

Cylindrical ellipse projection, Gergonne X(7) & Isotomic Nagel X(8)

apollonius; etc $X(7), X(8)$; casey

static_barycentrics.construct_isotomic_conjugate

Lib. II, Props. II–XIV (pp. 50–72; Tab. 4–7, Figs. 38–61)

Odd $(2m + 1)$-gon multilateral Ceva concurrency ($\prod_{i=0}^{2m} r_i = 1$)

pappus; altshiller-court

polygon_tetrahedron.construct_pentagon_ceva

Appendix Geometrica, Props. I–XVI & Closing Scholium (pp. 73–104; Tab. 8–10)

Synthetic area ratios ($[\triangle PAB]/[\triangle PAC] = BD/DC$), Lune, Ungula $= \frac{2}{3}$ prism, $5:3$ & $2:1$ centroids, & Indivisibles Caution

euclid VI.1, XII.2; archimedes; hoenen

polygon_tetrahedron.verify_appendix_invariants