## The factor

The regularity in the Head of a Man is carried out with a ruler and compass. But the schema is based on mathematical magnitudes. Partial distances of the head and face can be represented in aliquote fractions (divisible into a whole number) of the face length. (One face length forms – following Vitruvius – a tenth of an entire imagined body length.)

The dimensions result in simple fractions of 1/2 to 1/12. Even the widening of the hair on both sides of the throat was not an accidental inspiration of the painter’s but was coordinated. It amounts to one facial length plus a ninth. Clear numerical relations, in fractions of the respective facial lengths, also exist in Dürer’s Munich Self-Portrait with Fur-Lined Robe as well as the Sudarium of St. Veronica in Vienna.

The manner of – verifiably – implementing proportionality as fractions of a given magnitude is familiar from Dürer’s major work of art theory, Four Books on Human Proportions (1528). In this treatise he offered two mathematical methods for endowing human bodies (in differing types: male, female, and for a child) with good measurements: the factor method and the measuring-stick method.

Current research separates Dürer’s proportion studies of many years into an early geometric phase and an arithmetic phase that began at the latest in 1512–13. [1] But even in his search for geometric regularities for the human body, Dürer proceeds from defined numerical relations.

Sketches exist with (body) constructions by Dürer in which the measurement are both given as numerical values as well as constructed with compass and ruler. One is held by the Albertina in Vienna: the recto-verso drawing of an Adam from 1504. While on the side with the figure construction, Dürer created the upper body geometrically, the standing leg displays proportion numerals in accordance with the factor method (for example, the width of the calf = 1/16 the body length).

[1] Albrecht DÜRER, Vier Bücher von menschlicher Proportion (1528). With a catalogue of the woodcuts, ed., commented and translated into modern German by Berthold Hinz (Berlin 2011), 333-335; cf. Hans RUPPRICH, Dürer. Schriftlicher Nachlass, Bd. 2 (Berlin 1966), 24-54; Markus RATH, Die Gliederpuppe. Kult - Kunst - Konzept, (Actus et Imago. Berliner Schriften für Bildaktforschung und Verkörperungsphilosophie, ed. by Horst Bredekamp / Jürgen Trabant) (Berlin / Boston 2016), 330-331.