Summary — Book IV: Polyhedral Nets, Cube Duplication & Perspective¶
Structural Overview (SLUB N1525 pp. 142–182, Figs. 29–63 + Errata)¶
First Printed Planar Fold-Out Nets (pp. 142–157, Figs. 29–43):
Publishes scored double-paper (zwifach gepabt papier) 2D fold-out nets paired with two-view ground plans and elevations for all 5 Platonic solids (Tetrahedron, Octahedron, Icosahedron, Cube, and double-rosette Dodecahedron, Figs. 29–33) plus the meridian-gore globe comb (Fig. 34).
Publishes the first planar nets for 7 Archimedean semi-regular solids (Truncated Tetrahedron, Truncated Cube, Cuboctahedron, Truncated Octahedron, Rhombicuboctahedron, Snub Cube, and Truncated Cuboctahedron, Figs. 35–41) and two non-uniform polyhedra (Figs. 42–43).
Delian Cube Duplication & Ballistic Weight Scaling (pp. 157–166, Figs. 44–51):
Translates the Delian altar problem into German for the first time via two mean proportionals ($g : c = c : d = d : e \implies c^3 = g^2 e$) using Sporus’s movable graduated ruler (Figs. 44–46), proportional scaling gauges (Figs. 47–49), Plato’s sliding carpenter’s square (Fig. 50, Euclid VI.8), and Hero’s rectangular neusis (Fig. 51, Euclid VI.2, 4, 15), applied to casting bells and $1\text{–}100\text{ lb}$ cannonballs.
Cube Sciagraphy, Central Perspective & Optical Machines (pp. 166–182, Figs. 52–63):
Couples plan and elevation light sources (
o, p) to project the exact cast shadow of a cube (Figs. 52–53), defines perspective via the transparent planar section (durchsichtige Abschneydung, Figs. 54–55), gives both the two-compass plan/elevation transfer method (Figs. 56–58) and the direct distance-point / $45^\circ$-diagonal method (Figs. 59–62), and illustrates the hinged glass frame and three-thread lute sighting apparatuses (pp. 178–181).