Cross-Corpus Concordance (Underweysung ↔ GEOMETOR)

The table below links the thirteen canonical mathematical loci across Books I–IV of Albrecht Dürer’s Underweysung der Messung (1525) to their algebraic fields in geometor.durer and sister editions across the GEOMETOR Digital Scriptorium.

ID	1525 Locus	Vernacular / 1532 Latin	Topic & Epistemic Mode	Algebraic Field	Sister Repos
UDM-I-01	Book I, pp. 007–009, Figs. 1–4	Punct, Schlangenlini, Barlini / Linea serpentina, Parallela	Elementary Lines & Parallels (axiomatic)	$\mathbb{Q}$	euclid, elements, hilbert, proclus
UDM-I-02	Book I, pp. 011–024, Figs. 7–24	Schneckenlini, Schrauffenlini / Cochlis, Helix	12-Sector Spirals, Ionic Volutes & Spatial Helices (kinematic)	$\mathbb{Q}(\sqrt{3})$ at $30^\circ$ stations	thompson, phyllotaxis, divine
UDM-I-03	Book I, pp. 031–033, Figs. 31–33	Muschellini / Linea conchois	Conchoid of Nicomedes & Slotted Trammel (neusis)	Quartic locus $r = b + a\sec\theta$	pappus, klein
UDM-I-04	Book I, pp. 034–039, Figs. 34–37	Eierlini, Brennspiegellini, Gabellini / Ellipsis, Parabola, Hyperbola	Two-View Descriptive Geometry of Conics (demonstrative)	$\mathbb{Q}(\sqrt{2}, \sqrt{5}, \sqrt{13})$	pappus, model
UDM-II-01	Book II, pp. 054–056, Figs. 3–8, 22–28	Ebne Pflasterung / Planorum coaptatio	Regular, Star & Pentagonal Parquetries (combinatorial)	$\mathbb{Q}, \mathbb{Q}(\sqrt{2}), \mathbb{Q}(\sqrt{3}), \mathbb{Q}(\phi)$	divine, pacioli
UDM-II-02	Book II, pp. 058–059, Figs. 15–16	Fünffeck demonstrative vs. unverruckt / Pentagonum	Euclid $\mathbb{Q}(\phi)$ Pentagon vs. Rusty-Compass Pentagon	$\mathbb{Q}(\phi)$ vs. $\mathbb{Q}(\sqrt{3}, \sqrt{6\sqrt{3}-4})$	euclid, elements, pacioli, lemoine, divine
UDM-II-03	Book II, pp. 057–061, Figs. 11, 15, 18, 19	Sibeneck, Neuneck, Eylffeck, Dreytzeheneck	Workshop 7-, 9-, 11-, 13-gons (mechanice)	$\mathbb{Q}(\sqrt{3})$ vs. Eisenstein $P_7(q)$	klein, lemoine, elements
UDM-II-04	Book II, pp. 069–075, Figs. 29–36	Vergleichung der Ebnen & Quadratura Circuli	Area Transformations & $\frac{8}{10}$-Diagonal Circle Quadrature	$\mathbb{Q}(\sqrt{2})$ vs. $\pi_{\text{Dürer}} = \frac{25}{8}$	euclid, elements, klein
UDM-III-01	Book III, pp. 077–114, Figs. 1–27	Seulen, Horalogia & Thurnschrift	Columns, Nuremberg $49^\circ$ Sundials & Optical Scaling	Projective & Gnomonic Pencils	pappus, thompson
UDM-III-02	Book III, pp. 115–141	Lateinisch ABC & Textur	Roman Antiqua ($10 \times 10$ Square) & Modular Textura	$\mathbb{Q}(\sqrt{2}, \sqrt{449})$	pacioli, thompson
UDM-IV-01	Book IV, pp. 142–158, Figs. 29–43	Aufgeschnittene Corpora	First Printed Planar Nets (5 Platonic + 7 Archimedean)	$\mathbb{Q}, \mathbb{Q}(\sqrt{3}), \mathbb{Q}(\sqrt{5}, \sin 36^\circ)$	pacioli, euclid, elements, plato, divine
UDM-IV-02	Book IV, pp. 159–164, Figs. 44–51	Duplicatio Cubi & Büchsenkugeln	Delian Cube Doubling (Sporus, Plato, Hero) & Ballistics	$\mathbb{Q}(\sqrt[3]{2})$	plato, pappus, klein, euclid
UDM-IV-03	Book IV, pp. 165–181, Figs. 52–63	Perspectiva (Durchsehung)	Cube Sciagraphy & Homogeneous Glass-Frame Projection	$\mathbb{P}^3(\mathbb{Q}) \to \mathbb{P}^2(\mathbb{Q})$, $\operatorname{CR} = -1$	pappus, model