ABSTRACT
At the beginning of the 19th century, German scholars discussed the teaching of geometry. The debate between philosophers, educators and mathematicians centered on Euclid’s Elements. While some considered the book to be unsurpassed in terms of rigor and clarity, others called for a new presentation based on a systematic introduction of geometric figures. Meanwhile, a large number of textbooks were published as an alternative and supplement to the Elements. Although the authors had different point of views, the concepts of their books were similar in many aspects.
The talk presents an analysis of various German textbooks from the years 1800–1830, taking reviews into account. It works out how the conceptual departure from Euclid’s presentation of geometry was influenced by Naturphilosophie. We argue that the reformers’ efforts not only changed teaching of mathematics at schools and universities, but also the view of German geometers on the subject of their science. In the second part, citations of different examples from the first half of the 19th century will be underlined. It is shown that the early attempts to reform the teaching of geometry are crucial for understanding some peculiarities of the development of mathematics in Germany.
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