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De Lineis Rectis Codex (1678)¶

DE LINEIS RECTIS

SE INVICEM SECANTIBVS

STATICA CONSTRVCTIO.

AD SERENISSIMVM FERDINANDVM CAROLVM Ducem Mantuæ, Montisferrati, Guastallæ, &c.

AVCTORE IOANNE CEVA Mediolanensi.

MEDIOLANI, Ex Typographia Ludouici Montiæ. MDCLXXVIII. SVPERIORVM PERMISSV.

Latin Text: 1678 Milan Editio Princeps (BNCF Florence ita-bnc-mag-00001346-001)

Original English Translation, Interactive SVG Plates & Symbolic Apparatus: GEOMETOR Scriptorium

Conspectus Operis¶

Published in Milan in 1678 by Ludovico Monza when Giovanni Ceva was thirty years old, De lineis rectis se invicem secantibus statica constructio (1678) transformed Archimedes' Law of the Lever into a universal calculus of geometric incidence and proportion. Each unit of this Four-Track Bilingual Book Codex provides synchronized reading tabs (English, Latin, Summary, and Notes) wired to interactive .euclid-graphic SVG figures:

Unit I (Dedication, Prooemium, Printer’s Note & Liber Primus Opening · pp. 1–7, Tab. 1, Figs. 1–8): Static Foundations, Negative Weights & Skew Quadrilaterals — Dedication to Ferdinando Carlo Gonzaga, Prooemium honoring Donato Rossetti and defining statica constructio, Monza's typographic obelus † for addition (A † F), Axiomata I–II, Lemmata I–II ($A : B = BF : FA$), Elementum I (Menelaus sector), Elementum II (interior concurrency), Elementum III & p. 5 Scholium (algebraic negative weights F - A), and Elementa IV–V Corollarium (3D non-planar skew quadrilateral). (EN · LA · Summary · Notes)
Unit II (Liber Primus Props. VI–XXII · pp. 7–35, Tab. 1–3, Figs. 9–27): Liber Primus: Caravaggio’s Euclidean Proof, Ceva & Menelaus Concurrencies & Spread Ceva — Prop. VI pure Euclidean parallel-line proof credited to Pietro Paolo Caravaggio Jr. (tab. 1. fig. 10), Props. VII–VIII & Lemma IV (compound-ratio Ceva theorem $\frac{AF}{FB}\cdot\frac{BD}{DC}\cdot\frac{CE}{EA} = 1$ citing Commandino & Clavius, static proof of Menelaus's theorem, and projective harmonic division $(B, C; D, D') = -1$), canonical centers $X(1), X(2), X(4), X(6), X(7), X(8), J_A$ over $\mathbb{Q}$, and radical-free Spread Ceva's Theorem. (EN · LA · Summary · Notes)
Unit III (Liber Primus Props. XXIII–XXVI & Liber Secundus · pp. 36–72, Tab. 3–7, Figs. 28–61): 3D Tetrahedron Seven-Line Equilibrium, Circumscribed Conics, Isotomic Conjugates & Odd Polygons — Liber Primus Props. XXIII–XXVI (3D Tetrahedron 7-Line Static Equilibrium “mira quadam concordia” at spatial center $O$), Liber Secundus Lemma I (Borelli–Serenus cylindrical projection from circle to ellipse), Prop. I & Corollarium (Gergonne contact point $X(7)$ and isotomic conjugate Nagel point $X(8)$), and Odd $(2m+1)$-gon Multilateral Ceva Concurrency. (EN · LA · Summary · Notes)
Unit IV (Appendix Geometrica · pp. 73–104, Tab. 8–10, Figs. 62–85): Appendix Geometrica: Synthetic Area Proofs, Ungula Cubature, Centroids & Indivisibles Caution — Pure synthetic area-ratio demonstrations ($[\triangle PAB]/[\triangle PAC] = BD/DC$) independent of mechanics, Hippocrates' lune quadrature (Prop. II), cylindrical ungula cubature $= \frac{2}{3}$ prism (Prop. VII), hemisphere $5 : 3$ centroid (Prop. XIII, hailing Luca Valerio as “subtilissimus nostri æui Archimedes”), paraboloid $2 : 1$ centroid (Prop. XIV, citing Torricelli), and Ceva’s famous Closing Caution on Cavalieri’s Indivisibles on curved surfaces (indivisibilia & slant frustum). (EN · LA · Summary · Notes)

Editorial & Translation Note¶

All primary Latin texts in this codex are transcribed directly from the 1678 Milan editio princeps (BNCF Magl. ita-bnc-mag-00001346-001, Printed page N = PDF page N + 17). Every English translation (-en), executive geometric summary (-summary), and historical-mathematical commentary (-notes) is 100% originally authored for GEOMETOR directly from Ceva’s Neo-Latin.

Critical Apparatus & Concordances¶

Cross-Corpus Geometric Concordance — Bidirectional mapping linking Ceva’s 1678 propositions to archimedes, euclid, elements, menelaus, ptolemy, pappus, apollonius, etc, altshiller-court, wildberger, and model.
Bibliography & Primary Editions — 1678 Milan imprint, classical authorities, Renaissance staticians, and modern barycentric/projective works.
Index Nominum (Persons) — Prosopographical register of 26 geometers, staticians, printers, patrons, and commentators.
Latin & Mathematical Glossary — Lexicon of 16 technical Neo-Latin, typographic, and symbolic-geometry terms.