Theoretical works Albrecht Dürer

dürer s work on geometry called 4 books on measurement (underweysung der messung mit dem zirckel und richtscheyt or instructions measuring compass , ruler). first book focuses on linear geometry. dürer s geometric constructions include helices, conchoids , epicycloids. draws on apollonius, , johannes werner s libellus super viginti duobus elementis conicis of 1522.

the second book moves onto 2 dimensional geometry, i.e. construction of regular polygons. here dürer favours methods of ptolemy on euclid. third book applies these principles of geometry architecture, engineering , typography.

in architecture dürer cites vitruvius elaborates own classical designs , columns. in typography, dürer depicts geometric construction of latin alphabet, relying on italian precedent. however, construction of gothic alphabet based upon entirely different modular system. fourth book completes progression of first , second moving three-dimensional forms , construction of polyhedra. here dürer discusses 5 platonic solids, 7 archimedean semi-regular solids, several of own invention.

in these, dürer shows objects nets. finally, dürer discusses delian problem , moves on construzione legittima , method of depicting cube in 2 dimensions through linear perspective. in bologna dürer taught (possibly luca pacioli or bramante) principles of linear perspective, , evidently became familiar costruzione legittima in written description of these principles found only, @ time, in unpublished treatise of piero della francesca. familiar abbreviated construction described alberti , geometrical construction of shadows, technique of leonardo da vinci. although dürer made no innovations in these areas, notable first northern european treat matters of visual representation in scientific way, , understanding of euclidean principles. in addition these geometrical constructions, dürer discusses in last book of underweysung der messung assortment of mechanisms drawing in perspective models , provides woodcut illustrations of these methods reproduced in discussions of perspective.

four books on human proportion

dürer s work on human proportions called 4 books on human proportion (vier bücher von menschlicher proportion) of 1528. first book composed 1512/13 , completed 1523, showing 5 differently constructed types of both male , female figures, parts of body expressed in fractions of total height. dürer based these constructions on both vitruvius , empirical observations of, 2 3 hundred living persons , in own words. second book includes 8 further types, broken down not fractions albertian system, dürer learned francesco di giorgio s de harmonica mundi totius of 1525. in third book, dürer gives principles proportions of figures can modified, including mathematical simulation of convex , concave mirrors; here dürer deals human physiognomy. fourth book devoted theory of movement.

appended last book, however, self-contained essay on aesthetics, dürer worked on between 1512 , 1528, , here learn of theories concerning ideal beauty . dürer rejected alberti s concept of objective beauty, proposing relativist notion of beauty based on variety. nonetheless, dürer still believed truth hidden within nature, , there rules ordered beauty, though found difficult define criteria such code. in 1512/13 3 criteria function ( nutz ), naïve approval ( wohlgefallen ) , happy medium ( mittelmass ). however, unlike alberti , leonardo, dürer troubled understanding not abstract notions of beauty how artist can create beautiful images. between 1512 , final draft in 1528, dürer s belief developed understanding of human creativity spontaneous or inspired concept of selective inward synthesis . in other words, artist builds on wealth of visual experiences in order imagine beautiful things. dürer s belief in abilities of single artist on inspiration prompted him assert 1 man may sketch pen on half sheet of paper in 1 day, or may cut tiny piece of wood little iron, , turns out better , more artistic s work @ author labours utmost diligence whole year .