Four Books on Measurement 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, evidently became familiar costruzione legittima in written description of these principles found only, @ time, in unpublished treatise of piero della francesca.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.