Dürer Renaissance of about 1570 to 1630, in the early nineteenth century, and in German nationalism from 1870 to 1945. The Lutheran Church commemorates Dürer annually on 6 April, along with Michelangelo, Lucas Cranach the Elder and Hans Burgkmair. Theoretical works In all his theoretical works, in order to communicate his theories in the German language rather than in Latin, Dürer used graphic expressions based on a vernacular, craftsmen's language. For example, "Schneckenlinie" ("snail-line") was his term for a spiral form. Thus, Dürer contributed to the expansion in German prose which Luther had begun with his translation of the Bible. Four Books on Measurement Dürer's work on geometry is called the Four Books on Measurement (Underweysung der Messung mit dem Zirckel und Richtscheyt or Instructions for Measuring with Compass and Ruler). The first book focuses on linear geometry. Dürer's geometric constructions include helices, conchoids and epicycloids. He also draws on Apollonius, and Johannes Werner's 'Libellus super viginti duobus elementis conicis' of 1522. The second book moves onto two-dimensional geometry, i.e. the construction of regular polygons. Here Dürer favours the methods of Ptolemy over Euclid. The third book applies these principles of geometry to architecture, engineering and typography. In architecture Dürer cites Vitruvius but elaborates his own classical designs and columns. In typography, Dürer depicts the geometric construction of the Latin alphabet, relying on Italian precedent. However, his construction of the Gothic alphabet is based upon an entirely different modular system. The fourth book completes the progression of the first and second by moving to three-dimensional forms and the construction of polyhedra. Here Dürer discusses the five Platonic solids, as well as seven Archimedean semi-regular solids, as well as several of his own invention. Four Books on Human Proportion Dürer's work on human proportions is called the Four Books on Human Proportion (Vier Bücher von Menschlicher Proportion) of 1528. The first book was mainly composed by 1512/13 and completed by 1523, showing five differently constructed types of both male and female figures, all parts of the body expressed in fractions of the total height. Dürer based these constructions on both Vitruvius and empirical observations of "two to three hundred living persons", in his own words. The second book includes eight further types, broken down not into fractions but an Albertian system, which Dürer probably learned from Francesco di Giorgio's 'De harmonica mundi totius' of 1525. In the third book, Dürer gives