Bilingual Technical Glossary (1525 German • 1532 Latin)

Abstelen (Transfer by Orthogonal Projection)

Dürer’s workshop verb in Books I, III, and IV (“to steal off”) for transferring coordinates and chord widths between elevation (aufgezogner Grund) and ground plan (nidergedruckter Grund) via perpendicular projectors.

Aufgezogner Grund (Orthographia / Elevation)

The upright vertical elevation view coupled to the horizontal ground plan (nidergedruckter Grund) in Dürer’s two-view descriptive geometry.

Aug / Gesichtspunct (Oculus / Eye & Principal Vanishing Point)

In Book IV perspective, both the 3D station point of the beholder’s eye and its orthogonal foot on the transparent picture plane toward which lines perpendicular to the frame converge.

Ausschweiffung (Circular Serif Fillet)

Compass-drawn serif bracket tangent to both a Roman capital’s stem and the framing square’s edge (Book III, pp. 115–130; e.g., radius $\frac{1}{7}$ of the square side on the outer feet of A).

Barlini / Parrlini (Linea parallela / Parallel Line)

Dürer’s vernacular coinage (Book I, Fig. 2) for straight or curved equidistant parallel lines.

Brennspiegellini / Brennlini (Parabola / Burning-Mirror Line)

Dürer’s German term (Book I, Figs. 35–36) for Apollonius’s parabola, sliced parallel to a cone generator and used immediately to focus parallel solar rays in a burning mirror.

Corpora regularia (Regular & Semi-Regular Polyhedra)

The five Platonic and seven Archimedean solid bodies unfolded into planar nets in Book IV (Figs. 29–41).

Demonstrative vs. Mechanice

Dürer’s explicit epistemological distinction in Book II between exact deductive Euclidean constructions (demonstrative) and practical craftsman approximations (mechanice).

Durchsichtige Abschneydung (Planar Section of the Visual Pyramid)

The transparent glass picture plane slicing the rectilinear visual rays (Streimlinien) between the 3D object and the eye (Book IV, pp. 173–181).

Eierlini (Ellipsis / Egg-Line)

Dürer’s German coinage (Book I, Fig. 34) for the conic ellipse. While Dürer’s woodcut narrows slightly toward the cone apex like a hen’s egg, his own 12-station orthographic transfer formula $w_k = \frac{\sqrt{2k(12-k)}}{3}$ proves exact bilateral symmetry ($w_{12-k} = w_k$).

Rechte Fierung & Ort-Fierung (Square & 45° Diamond Module)

The upright square framing Roman Antiqua capitals ($10 \times 10$ or $9 \times 9$) and the stacked unit squares + $45^\circ$ diamond caps generating Gothic Textura minuscules (Book III).

Fischblosen (Vesica Piscis / Fish-Bladder Lens)

Symmetric lens of two intersecting congruent circles used in Book II, Fig. 18 to construct the workshop nonagon ($9$-gon).

Gabellini (Hyperbola / Fork-Line)

Dürer’s German coinage (Book I, Fig. 37) for the conic hyperbola cut parallel to the cone’s axis.

Muschellini (Linea conchois / Conchoid of Nicomedes)

The “mussel-shell line” $r = b + a\sec\theta$ constructed pointwise and mechanically in Book I, Figs. 31–33.

Nidergedruckter Grund (Ichnographia / Ground Plan)

The top-down horizontal ground plan paired below the upright elevation (aufgezogner Grund).

Ortstrich / Diameter (Diagonal or 45° Mitre Line)

Corner-to-corner square diagonal governing Book II circle quadrature, Book III shifted-circle bowls (O, Q, C, D), and Textura mitre cuts.

Punct (Punctum / Point)

Book I’s opening Euclidean definition: that which has neither magnitude, length, breadth, nor thickness, yet is the beginning and end of all bodily things.

Richtscheyt (Regula / Straightedge)

Unmarked straightedge paired with the compass (Zirckel).

Schlangenlini (Linea serpentina / Serpentine S-Curve)

Inflected doubly-curved line introduced alongside straight and circular lines at the opening of Book I (Fig. 1).

Schneckenlini (Cochlis / Planar Spiral & Volute)

Archimedean and projective planar spirals constructed across 12 angular sectors in Book I (Figs. 7–11, 17–24).

Schrauffenlini (Helix / Screw-Thread Spatial Helix)

Cylindrical and conical spatial helices projected in plan and elevation (Book I, Figs. 12–15).

Winckelmeß (Norma / Carpenter’s Right-Angle Square)

Right-angle square used both for perpendiculars and, with a sliding bar, in Plato’s mechanical cube-duplicating instrument (Book IV, Fig. 50).

Zirckel & Unverruckter Zirckel (Compass & Fixed-Aperture Compass)

Divider compass, including single-aperture (“rusty compass”) constructions mit unverrucktem Zirckel (Book II, Fig. 16).