Underweysung der Messung (Nuremberg, 1525 / Camerarius, 1532)¶
Dem meinen insonders lieben Herren vnd freünd / Herren Wilibalden Pirckheymer entbeüt ich Albrecht Dürer mein willig dienst. … Dann aus der messung mag man allerley gestalt vnnd ding für sich nemen zu machen.
—Albrecht Dürer, Dedication to Willibald Pirckheimer, Nuremberg, 1525
Four-track bilingual Digital Scriptorium edition of Albrecht Dürer’s Underweysung der Messung, mit dem Zirckel un[d] Richtscheyt, in Linien Ebnen unnd gantzen Corporen (durer:1525), pairing a fresh GEOMETOR English translation (English) directly from the 1525 Nuremberg Early New High German editio princeps (SLUB Dresden PPN 27778509X) with the diplomatic 1525 German copy-text (German (1525)), structural digests (Summary), and exact algebraic and historical commentary (Notes) collated against Joachim Camerarius's 1532 Paris Latin edition (durer:1532:camerarius) and Dürer’s posthumous 1538 Nuremberg second edition (durer:1538).
Four Books (Vier Bücher)
- Book I — Dedication, Lines, Spirals & Orthographic Conic Sections
- Title & Dedication to Willibald Pirckheimer (1525)
- Point, Elementary Lines & Parallel Curves (Figs. 1–5)
- Planar Spirals (Schneckenlinien), Volutes & Spatial Helices (Figs. 6–27)
- Two-View Orthographic Conic Sections & Kinematic Curves (Figs. 34–42)
- Book II — Plane Figures, Regular Polygons, Parquetries & Quadrature
- Plane Enclosure, Exterior Corners vs. Interior Angles & Quadrilaterals (Figs. 1–8)
- Demonstrative vs. Mechanice Regular Polygons & the Rusty Compass (Figs. 9–20)
- Gothic Tracery, Planar Tilings & Pentagonal Parquetries (Figs. 21–27)
- Euclidean Area Transformations & Circle Quadrature (Figs. 28–36)
- Book III — Architecture, Nuremberg Sundials, Optical Scaling & Typography
- Columns, Entasis, Enveloped-Sphere Helices & Monumental Towers (Figs. 1–19)
- Nuremberg Sundials (PHOTONMATHPLACEHOLDER000217END Pole) & Optical Tower Scaling (Figs. 20–27)
- Roman Antiqua Capitals (A–Z) & Modular Gothic Textura
- Book IV — Regular & Archimedean Nets, Cube Duplication & Perspective
- First Printed Planar Fold-Out Nets for Platonic & Archimedean Solids (Figs. 29–43)
- The Delian Altar: Doubling the Cube & Cannonball Scaling (Figs. 44–51)
- Cube Sciagraphy & Central Projection Perspective Apparatuses (Figs. 52–63)
Critical Apparatus
- Cross-Corpus Concordance (Underweysung ↔ GEOMETOR)
- Bibliography & Archival Witnesses
- Primary Editions of Dürer
- Classical, Medieval & Renaissance Sources
- Modern Mathematical & Historical Studies
- Dramatis Personae
- Abū al-Wafāʾ al-Būzjānī (940–998)
- Leon Battista Alberti (1404–1472)
- Hieronymus Andreae / Formschneider (d. 1556)
- Apollonius of Perga (c. 240 – c. 190 BC)
- Archimedes of Syracuse (c. 287 – c. 212 BC)
- Joachim Camerarius (1500–1574)
- Gerolamo Cardano (1501–1576)
- Albrecht Dürer (1471–1528)
- Euclid of Alexandria (fl. c. 300 BC)
- Lodovico Ferrari (1522–1565)
- Carl Friedrich Gauss (1777–1855)
- Hero of Alexandria (fl. c. 60 AD)
- Johannes Kepler (1571–1630)
- Felix Klein (1849–1925)
- Émile Lemoine (1840–1912)
- Leonardo da Vinci (1452–1519)
- Gaspard Monge (1746–1818)
- Johann Neudörfer the Elder (1497–1563)
- Nicomedes (c. 280 – c. 210 BC)
- Luca Pacioli (c. 1447–1517)
- Pappus of Alexandria (c. 290 – c. 350 AD)
- Piero della Francesca (c. 1415–1492)
- Willibald Pirckheimer (1470–1530)
- Plato (c. 428 – c. 348 BC)
- Claudius Ptolemy (c. 100 – c. 170 AD)
- Matthäus Roriczer (c. 1435–1495)
- Sporus of Nicaea (c. 240 – c. 300 AD)
- D’Arcy Wentworth Thompson (1860–1948)
- Marcus Vitruvius Pollio (c. 80 – c. 15 BC)
- Pierre Laurent Wantzel (1814–1848)
- Bilingual Technical Glossary (1525 German • 1532 Latin)
- Abstelen (Transfer by Orthogonal Projection)
- Aufgezogner Grund (Orthographia / Elevation)
- Aug / Gesichtspunct (Oculus / Eye & Principal Vanishing Point)
- Ausschweiffung (Circular Serif Fillet)
- Barlini / Parrlini (Linea parallela / Parallel Line)
- Brennspiegellini / Brennlini (Parabola / Burning-Mirror Line)
- Corpora regularia (Regular & Semi-Regular Polyhedra)
- Demonstrative vs. Mechanice
- Durchsichtige Abschneydung (Planar Section of the Visual Pyramid)
- Eierlini (Ellipsis / Egg-Line)
- Rechte Fierung & Ort-Fierung (Square & 45° Diamond Module)
- Fischblosen (Vesica Piscis / Fish-Bladder Lens)
- Gabellini (Hyperbola / Fork-Line)
- Muschellini (Linea conchois / Conchoid of Nicomedes)
- Nidergedruckter Grund (Ichnographia / Ground Plan)
- Ortstrich / Diameter (Diagonal or 45° Mitre Line)
- Punct (Punctum / Point)
- Richtscheyt (Regula / Straightedge)
- Schlangenlini (Linea serpentina / Serpentine S-Curve)
- Schneckenlini (Cochlis / Planar Spiral & Volute)
- Schrauffenlini (Helix / Screw-Thread Spatial Helix)
- Winckelmeß (Norma / Carpenter’s Right-Angle Square)
- Zirckel & Unverruckter Zirckel (Compass & Fixed-Aperture Compass)