In the ‘sketchbook’ of Villard de Honnecourt from the first third of the thirteenth century we come across a head upon which a chequered grid with inscribed tilted squares has been drawn. The length of the nose determines the unit, the bridge of the nose between the eyebrows lies in the centre.
Villard’s planar-schematic system of the Gothic period neglects the natural human organism in favour of a linear image capable of being constructed.  As a former goldsmith’s apprentice in the workshop of his father, Dürer would have become acquainted with these kinds of late medieval cutting principles by stonemasons. 
A grid like this also lies across the Head of a Man, from which lines run into the corners of the painting. But this construction remains unique in the heads by Dürer studied thus far.
This kind of schematising also recalls the Booklet Concerning Pinnacle Correctitude by the master builder of the Regensburg Cathedral Matthäus Roritzer (c. 1440– between 1492 and 1495). In this first architectural treatise printed in the German language, of 1486, Roritzer gave instructions on how a Gothic pinnacle (Fiale) could be derived geometrically (“aus der rechten geometerey”) from the dimensions of its ground plan (“ain virvng”).
One would halve the sides of a square and erect a diagonal interior square. The same operation would be performed again and a third interior square constructed. Whenever one was placed diagonally within the other, a proportional figure would develop, like the one inscribed on Villard’s head. 
 With reference to Erwin Panofsky: Jean WIRTH, Villard de Honnecourt. Architecte du XIIIe siècle (Geneva, 2015), 102–08,
here 103. The author refers to the medieval understanding of the connection between anatomy and geometry: “(...) la conviction (...) que la géometrie est une loi de la nature, qu'on peut
expliciter par la géometrie la structure de la Création.”
 Hans RUPPRICH, Dürer. Schriftlicher Nachlass, vol. 2, Berlin 1966, 35; cf. cfr. Albrecht DÜRER, Vier Bücher von
menschlicher Proportion (1528). Mit einem Katalog der Holzschnitte, hrsg., kommentiert und in heutiges Deutsch übertragen von Berthold Hinz (Berlin 2011), 333.
 Matthäus RORITZER, Das Büchlein von der Fialen Gerechtigkeit und die Geometria Deutsch, facsimilie of the original edition (Regensburg, 1486 and 1487/88; reprinted, Wiesbaden, 1965, ed. by F. Geldner; Wiesbaden 1999); cf. Walter UEBERWASSER, ‘Nach rechtem Maß. Aussagen über den Begriff des Maßes in der Kunst des XIII-XVI. Jahrhunderts’, Jahrbuch der Preußischen Kunstsammlungen 56 (1935), 250–72.