Dürer’s Underweysung der Messung and the Geometric Construction of Alphabets RANGSOOK YOON
Albrecht Dürer’s theoretical writings have been claimed as the “birthplace of German scientifi c prose,” to borrow Erwin Panofsky’s term, and they have been extensively studied by art historians and historians of science alike, whether to explicate their sources of inspiration or to account for his scientifi c contributions and infl uences. 1 Dürer’s published treatises, such as the Course in the Art of Measurement with a Compass and Ruler ( Underweysung der Messung mit dem Zirckel un[d] Richtscheyt ) and the Four Books on Human Proportion ( Vier Bücher von menschlicher Proportion )— which were issued respectively in 1525 and 1528-as well as unpublished fragmentary notes related to them are indeed inexhaustible sources of information, not only about his own thoughts and ideas but also about his milieu and the Renaissance era, in which mathematical and geometric knowledge played an increasingly signifi cant role. As the historian Paul Lawrence Rose writes, it is almost impossible to separate the classical basis of the mathematical renaissance from the general classical revival undertaken by the Italian humanists. 2
It is abundantly clear that Dürer was well acquainted with writings of Euclid and Vitruvius, not to mention Italian mathematicians and theoreticians of his time. In 1507, during his second stay in Venice, he acquired the Latin edition of Euclid’s Opera , published by Johannes Tacuinus in La Serenissima in 1505. 3 With the help of his best friend and patron, Willibald Pirckheimer (1470-1530), Dürer translated portions of Euclid’s propositions, specifi cally those that pertained to perspective. 4 Dürer also wrote, “I took the matter to heart and studied Vitruvius who has written a little about the proportions of man,” testifying to his familiarity with Vitruvius’s Ten Books on Architecture ( De architectura ). 5 Furthermore, in 1523, he obtained ten books of unknown titles, which formerly belonged to Bernhard Walther, the Nuremberg mathematician and astronomer. 6 Thus it can be inferred that these books also had something to do with his scientifi c interest. It is documented that Walther possessed books in his library that Dürer would have been eager to obtain, notably a manuscript copy of Leon Battista Alberti’s De pictura (1435-36). 7
Extensive studies have been conducted on a range of Dürer’s theorems and his use of the empirical applications of mathematical and geometrical problems, although not all aspects of his investigations have received an equal degree of
scholarly attention. One noteworthy instance of relative neglect is a segment in the third chapter in Dürer’s Underweysung der Messung , which deals with how to confi gure proper ( recht ) alphabet letters based upon geometric principles-or the art of measurement ( Kunst der Messung ). When examined by others, this was done largely to account for the sources that Dürer might have consulted, as well as his contributions to the development of typographic and calligraphic matters. 8 As can be seen in a 1976 article by Horst Heiderhoff, scholars have often emphasized the signifi cance of this section of the Underweysung der Messung within the process of paving a way for mechanical “reproducibility” (to borrow a phrase by Walter Benjamin) and the standardization of alphabet letters as established according to Dürer’s geometric rules. 9
This chapter contextualizes Dürer’s concern with the geometric construction of alphabets within the larger humanist culture of Renaissance Europe, where ancient and “modern,” Northern European and Italian, science and art all seem to have converged relatively seamlessly. By examining how his methodical explanations about lettering processes are closely related to some of the better-known parts of the Underweysung der Messung regarding perspective, this chapter sheds light on some of the theoretical undercurrents. Specifi cally, I focus on his instructions to others regarding how to place lettering on high walls using perspectival techniques, which brings out the centrality of the privileged status of geometric knowledge regarding perspective in Dürer’s time.