Concordantia Geometrica (Cross-Corpus Concordance)

Linking Leonardo Pisano’s Loci to Euclid, Heron, Archimedes, Pacioli, and the GEOMETOR Canon

This concordance maps the principal propositions and algebraic constructions of Leonardo Pisano’s Practica Geometriae (1220), Flos (1225), and Liber Abaci (1202/1228) across ten sister repositories in the GEOMETOR Digital Scriptorium and symbolic engine.

Master Concordance of Fibonacci Loci

Codex Unit	Boncompagni (1857–1862) Locus	Mathematical & Constructive Core	GEOMETOR Sister Canon Links
Unit I	Prologus, Introductoria & Dist. I (Vol. II, pp. 1–18, fol. 1r–11v)	Euclidean definitions; Pisan pertica ($6$ pedes, $36$ denarii, $66$-pertica stariorum); Book II identities & III.35 chords	euclid (I.def.1–23, II.1–10, III.35) · elements (G.1–G.58) · pacioli (Summa Dist. IX) · wildberger (lattice quadrance)
Unit I	Distinctio II (Vol. II, pp. 18–30, fol. 11v–18v)	Positional, sexagesimal, and Pisan uncia square-root extraction via Euclid II.4 gnomon completion	euclid (II.4) · heron (Metrica I.8 root iteration) · archimedes (rational bounds for $\sqrt{3}$)
Unit II	Distinctio III, Pars I (Vol. II, pp. 39–41, fol. 23v–25r)	Scalene cathetus & casus on $(13, 14, 15)$; complete Euclidean incenter proof of Heron’s formula $\Delta = \sqrt{s(s-a)(s-b)(s-c)}$	heron (Metrica I.8) · euclid (I.9, I.12, II.12–13, IV.4) · etc ($X(1)$ Incenter) · wildberger (Archimedes’ quadrea)
Unit II	Distinctio III, Pars IV (Vol. II, pp. 88–91, fol. 53v–55v)	Small-number 96-gon bisection ($1440 : 458\frac{1}{5}$ and $1440 : 458\frac{4}{9}$), yielding $\pi_{\text{Fib}} = \frac{864}{275}$ and $\frac{864}{275 - 1/11} = \frac{22}{7}$	archimedes (Dimensio Circuli Props. 1 & 3) · euclid (I.9, III.18, VI.3, XII.2)
Unit III	Distinctio IV, Pars I (Vol. II, pp. 110–121, fol. 67v–74v)	Preservation of Euclid’s On Divisions of Figures: cuts from vertex, side point $D$, interior/exterior point, parallel to base (VI.13), & centroid $X(2)$	euclid (On Divisions, I.31, I.37–38, VI.2, VI.13, VI.19, VI.28–29) · etc ($X(2)$ Centroid) · pappus (Synagoge VII)
Unit III	Distinctio IV, Pars II–IV (Vol. II, pp. 121–148, fol. 74v–92v)	Trapezoid parallel cut $c = \sqrt{(q a^2 + p b^2)/(p+q)}$ ($(7^2, 13^2, 17^2)$ progression), quadrilaterals, polygons & circular arcs	euclid (On Divisions Props. 19–29) · heron (Metrica III) · wildberger (congruum quadrance triples)
Unit IV	Distinctio V–VI (Vol. II, pp. 148–202, fol. 92v–130v)	Cube roots $(a+b)^3$; sphere/cone volumes; all five regular polyhedra in sphere $d = 6$ via $\phi$ ($e_{12} = \sqrt{15} - \sqrt{3}$) & Hypsicles Book XIV	euclid (II.11, VI.30, XII.7–18, XIII.8–18, XIV) · archimedes (Sphere & Cylinder) · pacioli (De Divina Proportione) · divine ($\phi$ sections)
Unit V	Distinctio VII (Vol. II, pp. 202–206, fol. 131r–133v)	Optical sighting of heights, valley depths & plains via rods and the 12-part quadrans shadow square	euclid (Optics Props. 18–21, VI.4) · pappus (projective sighting rays)
Unit V	Distinctio VIII (pp. 207–224), Flos (pp. 227–247), & Liber Abaci Cap. XII (Vol. I, pp. 283–284)	Pentagon & decagon in $d = 10$ via census census ($x^4 + 3125 = 125x^2$) & XIII.9–10; Flos cubic $1;22,7,42,33,4,40$; rabbit ratios $F_{n+1}/F_n \to \phi$	euclid (IV.10–11, X.36–73, XIII.9–10) · divine (convergents to $\phi$) · phyllotaxis (parastichy numbers $1..377$) · pacioli