LEONARDI PISANI PRACTICA GEOMETRIAE (1220)

With Foundational Bridges from Liber Abaci (1202/1228) and Flos (1225)

LEONARDI PISANI DE FILIIS BONACCII
(c. 1170 – c. 1245 · Citizen & Mathematician of Pisa)

PRACTICA GEOMETRIAE (ANNO M.CC.XX)
5 Synchronized Units · All 8 Distinctiones · Liber Abaci Cap. XII · Flos (1225)
Diplomatic Public-Domain Latin Text from Baldassarre Boncompagni (Romae, 1857 & 1862)
With Original GEOMETOR English Translation, Interactive .euclid-graphic Figures & Exact SymPy Verification

Conspectus Totius Operis

(Analytical Table of Contents)

UNIT I — PROLOGUE TO MASTER DOMINICUS, PISAN METROLOGY & DISTINCTIO I–II

(Epistola ad Magistrum Dominicum, Introductoria, Distinctio I–II · Boncompagni Vol. II, pp. 1–30, fol. 1r–18v)

Euclidean definitions and common conceptions, the Pisan pertica agrarian system ($6$ pedes, $36$ denarii, $66$-pertica stariorum), rectangular field mensuration, Euclid Book II geometric algebra, and iterative square-root extraction.

English · Latin (1220 / Boncompagni 1862) · Summary · Notes

UNIT II — DISTINCTIO III: MENSURATION OF FIELDS, HERON’S PROOF & CIRCLE BOUNDS

(Distinctio III: In mensuratione omnium camporum · Boncompagni Vol. II, pp. 30–110, fol. 18v–67v)

Scalene altitudes (cathetus and casus) on $(13, 14, 15)$, Fibonacci’s complete Euclidean incenter proof of Heron’s triangle formula $\Delta = \sqrt{s(s-a)(s-b)(s-c)}$, quadrilaterals and polygons, and the small-number 96-gon reformulation of Archimedes’ circle measurement ($\pi \approx \frac{1440}{458\frac{1}{3}} = \frac{864}{275}$).

English · Latin (1220 / Boncompagni 1862) · Summary · Notes

UNIT III — DISTINCTIO IV: DIVISION OF PLANAR FIGURES AMONG CONSORTS

(Distinctio IV: De divisione camporum inter consortes · Boncompagni Vol. II, pp. 110–148, fol. 67v–92v)

Leonardo Pisano’s celebrated Latin transmission and expansion of Euclid’s lost treatise On Divisions of Figures: dividing triangles through a vertex, from an arbitrary point on a side, through interior and exterior points, parallel to the base via semicircle mean proportional, into three equal shares at the centroid $X(2)$, and across trapezoids and circles.

English · Latin (1220 / Boncompagni 1862) · Summary · Notes

UNIT IV — DISTINCTIO V–VI: CUBE ROOTS, SOLIDS & THE FIVE REGULAR POLYHEDRA

(Distinctio V–VI: De radicibus cubicis et dimensione corporum · Boncompagni Vol. II, pp. 148–202, fol. 92v–130v)

Positional cube-root extraction from $(a+b)^3$, mensuration of prisms, pyramids, cones, frustums, and spheres, and the inscription of all five Platonic solids inside a sphere of diameter $6$ via extreme and mean ratio ($\phi$) and Hypsicles’ Book XIV—the direct source of Piero della Francesca and Luca Pacioli.

English · Latin (1220 / Boncompagni 1862) · Summary · Notes

UNIT V — DISTINCTIO VII–VIII, FLOS (1225) & LIBER ABACI CONVERGENCE TO $\phi$

(Distinctio VII–VIII, Flos & Liber Abaci Cap. XII · Boncompagni Vol. II, pp. 202–247 & Vol. I, pp. 283–284)

Optical surveying of heights and depths with the quadrans shadow square, Subtilitates Geometricae inscribing the pentagon and decagon in diameter $10$ by al-Khwārizmī’s and Abū Kāmil’s census census quartic ($x^4 + 3125 = 125x^2$), the Flos sexagesimal cubic ($x^3 + 2x^2 + 10x = 20$), and the Liber Abaci rabbit recurrence $F_{n+1} = F_n + F_{n-1}$ converging to $\phi$.

English · Latin (1220 / Boncompagni 1862) · Summary · Notes

Apparatus Criticus et Concordantia