DE DIVINA PROPORTIONE

Fra Luca Pacioli (Venice, 1509) — Critical Multi-Language Digital Edition

A unified digital edition of Fra Luca Pacioli's De Divina Proportione (Venice: Paganino de' Paganini, June 1, 1509), integrating the 318 high-resolution folio scans and 482 recalibrated woodcuts (214 illuminated initials, 180 marginal geometric diagrams, 23 Roman geometric alphabet plates, 5 architectural and Arbor Proportionis plates, and Leonardo da Vinci's 60 polyhedra plates) with four synchronized companion tracks:

• English (GEOMETOR Edition): Unabridged scholarly English translation with Euclidean dependency markup (:just:, :g:, .. enunciation::, .. assertion::, .. qed::, .. folio::) across all chapters and plates.

• Italiano (1509 / 1889): Diplomatic Italian text from the 1509 Venice Paganini edition and Constantin Winterberg’s 1889 Vienna edition.

• Deutsch (1889): Constantin Winterberg’s German critical translation (Quellenschriften für Kunstgeschichte, Vienna, 1889).

• Notes & Commentary: Historical, prosopographical, architectural, and mathematical apparatus for every chapter, incorporating Constantin Winterberg’s 1889 Vorwort & Einleitung and all seventeen Sachliche Anmerkungen.

Conspectus Totius Operis

• Winterberg’s Critical Introduction (Vienna, 1889, pp. III–V, 1–15) ([English · Deutsch])

• Part I: Compendio de Divina Proportione (Chapters I–LXXI, Folios 0017–0061) - Section 1 (Cap. I–VI): Dedicatory Epistle, Eulogy of Mathematics, Definition of the Divine Proportion, and Its Five Divine Attributes - Section 2 (Cap. VII–XXIII): The Thirteen Marvelous Effects of the Divine Proportion in Lines and Regular Polygons ([XIII.1]–[XIII.12], [X.73], [X.76]) - Section 3 (Cap. XXIV–LV): The Five Regular Platonic Solids, Proof of Their Uniqueness ([XI.21]), Constructions ([XIII.13]–[XIII.18]), Proportions (Book XIV), Twelve Mutual Inscriptions (Book XV), and Truncated/Elevated Dependent Bodies (Plates I–XL) - Section 4 (Cap. LVI–LXXI): The Sphere, Oblong Bodies (Columns and Pyramids), Mensuration, Panegyric to Ludovico Sforza, Concordance of Leonardo's Plates, and Mathematical Glossary (Plates XLI–LIX)

• Part II: Tractato de l’Architectura (Prohemio & Chapters I–XX, Folios 0061–0082) - Prohemio: Dedication to the Stonemasons of Borgo Sansepolcro, Promise of Piero della Francesca's Perspective, and Roll of Honor of the Captains of Sansepolcro - Chapters I–III: Vitruvian Human Proportions, the Head in the Equilateral Triangle ([I.1]), the Painter’s Net (Rete), and the Perfect Numbers 6, 10, and 16 ([IX.36]) - Chapters IV–XX: The Classical Orders (Ionic, Doric, Corinthian), Bases, Stylobates, Stereobates, Survey of Columns Across Italy, Epistyles, Friezes, Cornices, the Porta Speciosa, Polyhedra in Architecture, and Superimposed Columns

• Appendices: Roman Alphabet, Architectural Plates, Leonardo Polyhedra Plates & Winterberg’s Mathematical Commentary - Appendix I: The Roman Geometric Alphabet (Folios 0139–0183) - Appendix II: Architectural Plates & Arbor Proportionis (Folios 0137, 0185, 0213, 0215, 0311) - Appendix III: Polyhedra Plates by Leonardo da Vinci (Plates I–LIX, Folios 0187–0309) - Appendix IV: Winterberg’s Substantive Mathematical Notes (Sachliche Anmerkungen 1–17, 1889, pp. 338–352)

• Scholarly Apparatus: Bibliography & Cited Works · Index of Persons · Technical Glossary

Contents

• Winterberg’s Critical Introduction (1889)
  • 1. Pacioli, Piero della Francesca, and Leonardo da Vinci
  • 2. The Golden Section, Vitruvian Harmonic Ratios, and Aesthetic Rhythm
  • 3. Mathematical Structure of the Treatise & Critique of the Mutual Inscriptions
  • 4. Editorial Principles and Sources (1509 Venice Print & Vatican Manuscript)
• Part I: Compendio de Divina Proportione (Chapters I–LXXI)
  • Conspectus Capitum (Part I)
• Part II: Tractato de l’Architectura (Prohemio & Chapters I–XX)
  • Conspectus Capitum (Part II)
• Appendices: Woodcut Plates (1509) & Mathematical Commentary (1889)
  • Appendix I: The Roman Geometric Alphabet
  • Appendix II: Architectural Plates & Arbor Proportionis
  • Appendix III: Polyhedra Plates by Leonardo da Vinci
  • Appendix IV: Winterberg’s Mathematical Commentary (1889)

Scholarly Apparatus

• Bibliography & Cited Works
• Index of Persons
• Glossary of Geometric, Architectural & Latin Terms