Dramatis Personae

Abū al-Wafāʾ al-Būzjānī (940–998)

Persian mathematician in Baghdad whose Book on Those Parts of Geometry Needed by Craftsmen systematized single-aperture (“rusty compass”) polygon constructions—including the direct structural antecedent of Dürer’s Book II Fig. 16 pentagon and the half-equilateral heptagon.

Leon Battista Alberti (1404–1472)

Italian humanist and architect whose De pictura (1435) formulated linear perspective as the planar intersection (intersegazione) of the visual pyramid, realized physically in Dürer’s Book IV glass-frame and sighting-thread instruments.

Hieronymus Andreae / Formschneider (d. 1556)

Nuremberg master blockcutter and typographer who cut types and woodblocks for Dürer and printed the enlarged posthumous second edition of Underweysung der Messung (1538).

Apollonius of Perga (c. 240 – c. 190 BC)

Author of the Conics, whose Greek classification (ellipsis, parabola, hyperbola) Dürer introduced into German mathematics in Book I (pp. 034–039) as Eierlini, Brennspiegellini, and Gabellini.

Archimedes of Syracuse (c. 287 – c. 212 BC)

Greek geometer whose On Spirals, Measurement of a Circle, and thirteen semi-regular solids underpin Dürer’s Book I spirals, Book II circle quadrature discussion, and Book IV Archimedean polyhedral nets.

Joachim Camerarius (1500–1574)

Nuremberg humanist scholar and rector whose 1532 Paris Latin translation Institutionum Geometricarum Libri Quatuor carried Dürer’s geometric discoveries across learned Europe.

Gerolamo Cardano (1501–1576)

Italian algebraist who, together with Lodovico Ferrari, proved in De subtilitate (1550) that every Euclidean construction can be carried out with straightedge and a fixed compass opening.

Albrecht Dürer (1471–1528)

Nuremberg painter, engraver, woodcut master, and mathematician. Combining goldsmith precision, Italian perspective theory, and Pirckheimer’s Greek mathematical library, he created in Underweysung der Messung (1525) the first printed German mathematical treatise, two-view descriptive geometry, Renaissance geometric typography, and planar polyhedral fold-out nets.

Euclid of Alexandria (fl. c. 300 BC)

Honored by Dürer as der scharpfsinnig Euclides (“the acute-minded Euclid”). Dürer purchased Zamberti’s 1505 Venice Latin Elements in 1507 and built his demonstrative proofs on Books I, II, IV, VI, XI, XII, and XIII.

Lodovico Ferrari (1522–1565)

Italian mathematician who solved the quartic equation and established universal constructibility with a fixed (“rusty”) compass opening in response to the Renaissance single-aperture tradition.

Carl Friedrich Gauss (1777–1855)

Proved in Disquisitiones Arithmeticae (1801) that a regular $n$-gon is constructible by ruler and compass only when odd prime factors of $n$ are distinct Fermat primes ($3, 5, 17, 257, 65537$).

Hero of Alexandria (fl. c. 60 AD)

Greek engineer and geometer whose rectangular neusis for two mean proportionals is presented explicitly by Dürer in Book IV, Fig. 51 (durch Heronem den Krichen).

Johannes Kepler (1571–1630)

Imperial mathematician who proved the exact symmetry of Dürer’s conic ellipse in 1604 and expanded Dürer’s Book II pentagonal tilings and Book IV Archimedean solids in Harmonices Mundi Book II (1619).

Felix Klein (1849–1925)

Expositor of algebraic impossibility proofs (Famous Problems of Elementary Geometry, 1895) governing cube duplication, heptagon inscription, angle trisection, and circle quadrature.

Émile Lemoine (1840–1912)

Founder of Géométrographie (1902), quantifying operational ruler-and-compass complexity.

Leonardo da Vinci (1452–1519)

Illustrator of the spatial perspective polyhedra in Luca Pacioli’s Divina Proportione (1509), which Dürer re-conceived in Book IV as planar cut-and-fold nets.

Gaspard Monge (1746–1818)

Codifier of Géométrie descriptive (1799), systematizing the coupled orthographic plan-and-elevation method invented by Dürer in 1525.

Johann Neudörfer the Elder (1497–1563)

Nuremberg master calligrapher and Rechenmeister closely associated with Dürer’s typographic work.

Nicomedes (c. 280 – c. 210 BC)

Discoverer of the conchoid curve and mechanical trammel reconstructed by Dürer as the Muschellini in Book I, Figs. 31–33.

Luca Pacioli (c. 1447–1517)

Author of Divina Proportione (1509), uniting golden-section polyhedra and $1:9$ Roman capital letterforms; key Italian foil to Dürer’s 1506 Bologna journey and 1525 Underweysung.

Pappus of Alexandria (c. 290 – c. 350 AD)

Author of the Synagoge, preserving Archimedes’s 13 semi-regular solids, cube-duplication neuseis, and projective cross-ratio invariance.

Piero della Francesca (c. 1415–1492)

Author of De prospectiva pingendi and Libellus de quinque corporibus regularibus, foundational precursor to Renaissance descriptive foreshortening and polyhedral geometry.

Willibald Pirckheimer (1470–1530)

Nuremberg patrician humanist, translator of Greek classics, Dürer’s closest friend, and dedicatee of Underweysung der Messung (1525).

Plato (c. 428 – c. 348 BC)

Author of the Timaeus on the five cosmic solids; credited in Book IV (pp. 159–162, Fig. 50) with both the Delian oracle narrative and the sliding carpenter’s-square instrument for doubling the cube.

Claudius Ptolemy (c. 100 – c. 170 AD)

Author of Almagest I.10, source of the compact single-circle demonstrative pentagon in Dürer’s Book II, Fig. 15.

Matthäus Roriczer (c. 1435–1495)

Regensburg master mason and printer of Geometria Deutsch (c. 1487), transmitting medieval stonemason rules for the single-aperture pentagon, heptagon, and nonagon.

Sporus of Nicaea (c. 240 – c. 300 AD)

Greek mathematician cited explicitly by Dürer in Book IV (durch Sporum, Figs. 44–46) for the two-mean-proportionals neusis.

D’Arcy Wentworth Thompson (1860–1948)

Author of On Growth and Form (1917/1942), whose Chapter XVII coordinate grids build directly upon Albrecht Dürer’s proportional coordinate transformations.

Marcus Vitruvius Pollio (c. 80 – c. 15 BC)

Roman architect praised by Dürer as der alt Römer Vitruuius for column orders, Ionic volutes, sundials, and the Delian altar account.

Pierre Laurent Wantzel (1814–1848)

Proved in 1837 the algebraic impossibility of ruler-and-compass cube duplication, general angle trisection, and regular $7$-, $9$-, $11$-, and $13$-gons.