principles by which the proportions of the figures can be modified, including the mathematical simulation of convex and concave mirrors; here Dürer also deals with human physiognomy. The fourth book is devoted to the theory of movement. Appended to the last book, however, is a self-contained essay on aesthetics, which Dürer worked on between 1512 and 1528, and it is here that we learn of his theories concerning 'ideal beauty'. Dürer rejected Alberti's concept of an objective beauty, proposing a relativist notion of beauty based on variety. Nonetheless, Dürer still believed that truth was hidden within nature, and that there were rules which ordered beauty, even though he found it difficult to define the criteria for such a code. In 1512/13 his three criteria were function ('Nutz'), naïve approval ('Wohlgefallen') and the happy medium ('Mittelmass'). However, unlike Alberti and Leonardo, Dürer was most troubled by understanding not just the abstract notions of beauty but also as to how an artist can create beautiful images. Between 1512 and the final draft in 1528, Dürer's belief developed from an understanding of human creativity as spontaneous or inspired to a concept of 'selective inward synthesis'. In other words, that an artist builds on a wealth of visual experiences in order to imagine beautiful things. Dürer's belief in the abilities of a single artist over inspiration prompted him to assert that "one man may sketch something with his pen on half a sheet of paper in one day, or may cut it into a tiny piece of wood with his little iron, and it turns out to be better and more artistic than another's work at which its author labours with the utmost diligence for a whole year". Book on Fortification In 1527, Dürer also published Various Lessons on the Fortification of Cities, Castles, and Localities (Etliche Underricht zu Befestigung der Stett, Schloss und Flecken). It was printed in Nuremberg, probably by Hieronymus Andreae and reprinted in 1603 by Johan Janssenn in Arnhem. In 1535 it was also translated into Latin as On Cities, Forts, and Castles, Designed and Strengthened by Several Manners: Presented for the Most Necessary Accommodation of War (De vrbibus, arcibus, castellisque condendis, ac muniendis rationes aliquot : praesenti bellorum necessitati accommodatissimae), published by Christian Wechel (Wecheli/Wechelus) in Paris. The work is less proscriptively theoretical than his other works, and was soon overshadowed by the Italian theory of polygonal fortification (the