Summary — Book III: Architecture, Sundials, Scaling & Typography

Structural Overview (SLUB N1525 pp. 077–141, Figs. 1–27 + Alphabets)

1. Architectural Solids, Moldings, Entasis & Twisted Columns (pp. 077–107, Figs. 1–19):

   • Generates cylindrical, polygonal, and twisted shafts (Seülen), upright and oblique cones / pyramids (Piramides), and Late Gothic rib-vault pier sections (Pfeyler) by coupling ground plans to elevations.

   • Praises Vitruvius, codifies six elementary lathe/plane molding curves (blatte Fasen, Holkelen, Wellen, Eck, Winckel, Schlangenlini), gives two geometric rules for column entasis, and envelopes spheres along a 60-station spatial helix to draw serpentine columns, memorial monuments, and spiral market-tower ramps.

2. Nuremberg Gnomonics ($49^\circ$ Latitude) & Optical Scaling (pp. 108–114, Figs. 20–27):

   • Divides the quadrant into $90^\circ = 3 \times 3 \times 2 \times 5$ and sets Nuremberg’s polar elevation $\varphi = 49^\circ$ (equinoctial complement $41^\circ$) to construct equatorial, vertical South-wall, horizontal, and truncated-cube polyhedral sundials.

   • Projects equal visual angles from eye point c across a circular arc onto high walls so monumental inscriptions and statues read uniformly from ground level.

3. Constructive Typography: Roman *Antiqua* & Modular *Textura* (pp. 115–141):

   • Constructs A–Z in the $10 \times 10$ (and $9 \times 9$) rechte Fierung with $1 : frac{1}{3}$ stroke contrast, tangent circular serif fillets (Ausschweiffung), and two-circle shifted-diagonal bowls (O, Q, C, D, G).

   • Builds Gothic Textura minuscules combinatorially from the foundational i-stem (3 unit squares + 2 $45^\circ$ Ort-Fierungen), proving the $\sqrt{2}$ stem pitch of n and m.