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E. G. Ziegenbalg’s Danish Translation of Euclid’s Elements: Conclusion

Toke Lindegaard Knudsen (State University of New York at Oneonta)


Vernacular editions of Euclid's Elements began to appear in the mid-sixteenth century [Wardhaugh 2021, 76]. In 1744, E. G. Ziegenbalg’s Danish translation of the Elements gave Denmark and Norway their first vernacular edition. The edition covers Books 1–6 and 11–12; that an edition of Euclid covered only these eight books was not unusual [Wardhaugh 2021, 76].

The effort to bring out a Danish translation of the Elements was not only due to Ziegenbalg's interest in the text and efforts to translate it. The emphasis on the value of vernacular editions in Ramus' introduction reveals that the mathematical community in Copenhagen at the time felt a need to have such an edition available in Denmark–Norway. Ramus himself had previously translated a work by Christian Wolff from German to Danish, which demonstrates his interest in making texts on mathematics available in Danish. The book production of Ziegenbalg's translation, with its distinct typography based on the organization of the text in Ramus' 1740 Latin edition of the Elements, shows that funding was available for such a project. The funding possibly came from the royal court, which had supported Ziegenbalg's studies for some time (note in particular Ziegenbalg's enthusiastic praise of King Christian VI).

The preface and introductions in Ziegenbalg's Danish edition shed light on the material available to the mathematicians in Copenhagen studying and translating Euclid's Elements into Danish. Besides the Latin editions of Ramus, the editions of Gregory [1703] and Tacquet [1722] were available, as were works by Christian Wolff. The presence of these works in Copenhagen offers clues to the connections the mathematicians at the University of Copenhagen had with mathematicians elsewhere.

Ziegenbalg's translation is—and was used as—a textbook. The carefully considered organization of the text makes the book a noteworthy teaching tool. It shows us how Ramus and his mentee Ziegenbalg envisioned how the material in Euclid should be taught to students. Both Ramus and Ziegenbalg saw Euclid's Elements as the foundation and source of all mathematics, and, given the importance of mathematics in other pursuits, they saw value in having a segment of the population understand Euclid. Such an understanding among a broader group of people would be better facilitated by a Danish edition with a pedagogical approach.

The physical book of Ziegenbalg's edition of Euclid’s Elements thus provides us with a window into an episode in the history of the Elements. It belongs with our Mathematical Treasures. Perhaps even today its contents can inspire us to contemplate how to best teach mathematics.

Toke Lindegaard Knudsen (State University of New York at Oneonta), "E. G. Ziegenbalg’s Danish Translation of Euclid’s Elements: Conclusion," Convergence (October 2021)