The article is a history of the “rise and fall” of descriptive geometry in Denmark interwoven with the development of the teaching of mathematics at higher level and the creation and change of the appurtenant institutions. At the University of Copenhagen, mathematics was only taught in the first year in the early 19th century, more however at the Naval and Land Cadet Academies, and in the late 1820s, basic perspective theory and descriptive geometry were introduced at the Royal Academy of Arts by Georg Frederik Ursin, who also suggested the creation of a Gewerbeschule after the German model. Hans Christian Ørsted managed to transform this into a proposal for a higher-level school (the Polytechnic College, modelled after the École Polytechnique), which opened in 1829, while a new Royal Military College with similar inspiration was founded in 1830. The first year, descriptive geometry was taught at the former school with little success, but from 1830 until 1861 Lieutenant Ludvig Stephan Kellner taught at both schools with decent results. His courses were based on his own material, which drew on Monge and G. Schreiber’s German version of Monge’s book as well as on Poncelet and Dupin; it claimed no mathematical originality but differed from Monge in style and pedagogy.
In 1850, the university was given a faculty for mathematics and natural sciences, but until well into the 20th century mathematics teaching was shared with the Polytechnic College. As Kellner retired, descriptive geometry was taught at the two colleges by different teachers, most important of whom is Carl Julius Ludwig Seidelin, who remained at the Polytechnic College until 1903, moving the contents toward general projective geometry. He was replaced by Johannes Hjelmslev, who was the first Danish teacher of the topic who could claim theoretical originality, not least because his “geometry of reality”, which is explained in the article in some detail. From the 1920s onward, the course, renamed “geometry”, moved toward analytic and differential geometry. Those taught after 1960 will find it hard to imagine how to attack the sample exam problems from the 1860s presented in the article.
For the entire collection see [Zbl 1426.01003].